 [page 25↓] 
The developed biomass sensor “PendulumMeter” works mechanically through a pendulum that is moved by forces created from cereal stems touching the pendulums cylindrical body. The combined forces of the stems push against the cylindrical body, moving it out of place in an angular motion with the aid of a support tube that is connected to a pivot point. The pivot is the focus point of the relationship between the unmoved pendulum and the deflected pendulum which is described by the angle of deviation α.
Taking measurements using a pivoted cylindrical body, moving horizontally through a standing cereal population (figure 8), the angle of deviation α is caused by the resultant force F_{R} which deviates the cylindrical body from the undeviated position B into the deviated position B’. The resultant force is itself determined by a combination of the following parameters: height of the pivot point h_{P}, length of the pendulum l_{P}, height of the undeviated cylindrical body h_{A0}, mass of the pendulum m _{P}, driving velocity v_{D}, mass of the stems m _{S} – including moments of inertia, bending moments of resistance of the stems R_{Mb}, friction force between pendulum and stems F_{F}, number of stems n_{S}, and plant height h_{Pl}.
Figure 8: Advanced measurement principle of the pendulummeter.  

Through keeping the technical parameters, height of pivot point, length of pendulum, mass of pendulum, and driving velocity within the field almost constant, therefore, the angle of deviation [page 26↓]varies only according to the plant parameters mass of the stems, bending moment of resistance of the stems, number of stems, height of plants and friction. This measurement principle works only during movement due to the dynamic motion of the pendulum.
It follows from this dynamic motion that the cylindrical body moves against the stems, thus forcing the pendulum to deviate from the original position with the angle zero into a position of angle α. In this position, the force the pendulum applied onto the stems is equal to the force the stems develop against the pendulum, while they are themselves moved out of place.
The resultant force F_{R} of the pendulum depends on the weight of the cylindrical body, and the length of the pendulum, and is measured initially at 90 degrees deviation, and then calculated for the measured angle according to the following mechanical background (figure 9):
Figure 9: Force diagram of the pendulummeter.  

The resultant force F_{R} in Newtons can be divided into its vertical F_{V} and horizontal F_{H} force components, calculated from the weight at 90° deviation F _{A}, using equation 12:
F A (N) = m (kg) · g (m s ^{2} ) 
[12] 
 [page 27↓] 
where F A is the force of the pendulum at 90° deviation of the pendulum, m is the mass of the pendulum at 90° deviation of the pendulum, and g is the gravity. The resultant force F _{R} for a specific angle α is calculated by equation 13:
F R _{} (N) = F A (N) · sin α 
[13] 
where F R is the resultant force of the pendulum at a specific angle of deviation, and F A is the force of the pendulum at 90° deviation of the pendulum. The vertical force F _{V} for a specific angle α is calculated by equation 14:
F V (N) = F A (N) · sin ^{2} α 
[14] 
where F V is the vertical force of the pendulum at a specific angle of deviation, and F A is the force of the pendulum at 90° deviation of the pendulum. The horizontal force F _{H} for a specific angle α is calculated by equation 15:
F H _{} (N) = F A (N) · sin α · cos α 
[15] 
where F H is the horizontal force of the pendulum at a specific angle of deviation, and F A is the force of the pendulum at 90° deviation of the pendulum.
According to standard engineering theory the resultant force F_{R} of the pendulum, working in the opposite direction, equals the force that the stems are applying against the cylindrical body. Thus equation 13 aids calculating the force of the sum of the stems that are working to deviate the pendulum.
The resultant force of the stems can be divided into three causes:
In mechanical theory a still standing cereal stem is considered a onefixed end cylindrical hollow beam, a cantilever. Due to this closedform solution, bending moment of resistance, mass moment of inertia and friction force can be calculated by standard mechanical equations.
While some of these factors can be calculated, such as the second moment of the area I, others can only be determined by material tests such as the elasticity of the material E. All calculations [page 28↓]are based on a single stem, while the pendulummeter touches numerous stems to various degrees of bending at every single moment.
Although in this work it is not possible to calculate bending moment of resistance and mass moment of inertia or friction due to a lack of data, such as the inner and outer diameter of the stems, the modulus of elasticity E, or the height of the gravity point of the stem, it is nevertheless good for explaining some of the results of the pendulummeter measurements.
During measurements the most commonly seen bending type, the curved bending, is the one shown in figure 10 as type 2. This type was encountered at all growthstages in paddy rice and winter wheat, and in winter rye at the growthstages BBCH 32 to 59. After heading the bending types encountered in winter rye changed from type 2 to type 3, the uformed bending. The rigid type 1, linear bending, was seen only on single standing plants after flowering with a low contact height of the cylindrical body.
Figure 10: Bending types of cereals during measurements.  

 [page 29↓] 
A sensory device to bend cereal stems requires mechanical parts which make contact with the stems or plants. The pendulummeter consists of three major parts thus forming a pendulum: a housing at the pivot point, a rigid tube, and a contact bar (figure 11). The contact bar is a rigid, hollow plastic tube with 5 cm outer diameter forming a cylindrical body of one meter length to engage the plant stems, which is arranged transverse to the measurement direction. The cylindrical body is the part of the pendulum receiving the forces created by the plant stems. A tube connects it with the pivot point, and its rigidity transfers the forces straight to the other end of the rigid tube where the deviation of the pendulum is measured by the potentiometer.
Figure 11: Construction of the pendulummeter and its operating in rice.  

The pivot point arrangement consists of a metal housing (figure 12), containing two ball bearings and seal rings, and supports a stub shaft which forms a pivot axis. This pivot axis transmits the swinging motion from the rigid tube to the potentiometer. This potentiometer, an incremental encoder type RB from IFM Electronics, measures the angular motion as electrical variation between +5 and 5 Volts. The friction of the seal rings causes a slight dampening of the swinging movement of the pendulum, that can swing over an operating range of 200° between +110° and 90°. A pendulum length of 0.1 m was not possible due to the friction of the pivot point with the seal rings disturbing the swinging of the pendulum. Caused by different construction materials, the pendulummeter used in rice had different weights, and hence a different vibration time, than [page 30↓]the pendulummeter used in the German winter wheat and winter rye crops.
Figure 12: Length cut of the potentiometer.  

For the optimisation of measurements the following parameters of the pendulummeter can be varied: the height of the pivot point h_{P}, the height of the cylindrical body h_{A0}, the mass of the pendulum m _{P} and the length of the pendulum l_{P}. Since the height of the pivot point and the height of the cylindrical body determine together the length of the pendulum, and the measurement takes place through physical contact with the plants, the focus of the optimisation trials is on the height of the pivot point, the height of the cylindrical body, and the mass of the pendulum. These three parameters can be related to plant parameters.
Firstly, the height of the pivot point is usually tested instead of the length of the pendulum, starting with heights of the pivot point considerably higher than the plant height, reducing the height in steps of 0.1 meters, with the exception of one parameter trial in winter rye 1998. Each step is a single parameter until the plants show marks of destruction.
The setting for the height of the cylindrical body h_{A0} takes place similarly. The lowest average plant height limits the maximum height of the cylindrical body, which changes mostly in steps of 0.1 meter, and the lowest setting height is 0.1 meter. The cylindrical body in all cases operates over a width of one meter.
 [page 31↓] 
To determine the mass of the pendulum, the cylindrical body is weighted at a deviation of 90 degrees, and depends on the length of the pendulum (table 4). Resulting from the varying lengths of the pendulum, the self weight of the pendulum differs between 0.5 kg and 0.75 kg. To change the pendulum mass from its own weight to one kilogram or more, additional weights are added that fit closely inside the cylindrical body.
In the optimisation tests the mass of the pendulum starts with the self weight, then added up to one kilogram, and increases in steps of 0.5 kg until the plants show marks of destructiveness. With regard to rice most parameter settings are tested with the self weight of the pendulum, since the rice plants show sometimes marks of destructiveness at even the 1 kg weight of the pendulum.
Length of the Pendulum (m) 
0.200 
0.300 
0.400 
0.500 
0.600 
0.700 
Rice Pendulum (kg) 
0.450 
0.497 
0.519 
0.533 
0.556 
0.576 
Wheat / Rye Pendulum (kg) 
0.522 
0.549 
0.574 
0.595 
0.615 
0.635 
Length of the Pendulum (m) 
0.800 
0.900 
1.000 
1.100 
1.200 
1.300 
Rice Pendulum (kg) 
0.604 
0.618 
0.644 
0.693 
0.734 
 
Wheat / Rye Pendulum (kg) 
0.657 
0.676 
0.696 
0.716 
0.735 
0.752 
With the determined mass of the pendulum at a specific length, it is possible to calculate the resultant force at various angles that is necessary to deviate the pendulum. Using equation 12 and 13, the resultant force is calculated for a specific angle of the rice pendulum with a length of one meter and a self weight of 0.644 kg. Thus, it is possible to calculate the resultant forces for a wide range of angles (figure 13).
Figure 13 provides a good illustration of the relation between resultant force and angle, which is not linear but second degree polynomial. Nevertheless, the difference between goodness of fit for the linear and square formulas is small. The necessary amount of resultant force required to deviate the pendulum for one unit of angle increases the greater the deviation becomes.
 [page 32↓] 
Figure 13: Angle versus resultant force relationship.  

Based on the measurement principle, there are several factors which are in standard mechanical theory considered either dependent on the mass or highly influenced by the mass of a body.
The mass moment of inertia is dependent on the mass of a body, as can be seen in equations 1 and 2, and also the acceleration is dependent on the mass of a body as shown in equation 3.
The bending moment of resistance is highly influenced by the second moment of the area I of the body as described by equation 4 and 5. The factor bending distance x depends upon the curvature of the stem, and is considered equal within a field. The second moment of the area I is a geometrical factor giving a cross section of the material of the stem and HITAKA 1968 reported a correlation coefficient between I and the fresh weight per unit length of 0.75. Young’s modulus of elasticity E was stated (NISHIYAMA 1986) to have a close correlation with the specific weight of the material. Several works (HITAKA 1968, GOWIN 1989, TOMASZ 1989) described a negative correlation between E and I, meaning an increase in I decreases the elasticity and vice versa. Several studies (HITAKA 1968, NISHIYAMA 1986) provided evidence that the bending rigidity E I has a correlation with I, when culm length and E are the same, and that the bending rigidity E I increases with E, when culm length and I are the same. MÜLLER 1988 suggested that bending rigidity E I is in direct proportion to the fourth power of the external diameter of the stem ,when E doesn’t change much. HITAKA 1968 found a good correlation between E and fresh weight per unit length. The bending rigidity E I, as the product of the modulus of elasticity E and the second moment of area I, showed according to HITAKA [page 33↓]1968 and NIKLAS 1990 a decrease along the stem from the bottom to the top. Leaf sheaths increase E I of the stems by 15% according to MÜLLER 1988, while HITAKA 1968 found a contribution of 52 % of the leaf sheath for the first internode, and 12.5 % for the fourth internode, to the bending resistance of the stems in rice.
HITAKA 1968 also found high correlation coefficients between E I and:
The sliding friction between the biomass sensor and the plants is not dependent on the mass of the plant, but on the friction coefficient between both surfaces. Additionally, dependencies of the gliding friction were associated with pressure (USREY et al. 1992) and moisture content of the crop (KUTZBACH 1989, HUISMAN 1978).
Due to the lack of data for the various factors in the equations, the changes of these factors within the test strip, and the summarised measurement of various different stems at once, a calculation of bending moment of resistance and of the mass moment of inertia is not possible. But a weighing of the participation of the factors on the measurement is possible. USREY et al. 1992 reported a friction coefficient of 0.306 between rice and polyethylene. For a vertical force of 1 Newton this gives a friction force of 0.3 Newton, or 30 % of the vertical force in general. Kinetic friction coefficients of 0.19, 0.23, and 0.31, were reported between winter wheat straw and steel (HUISMAN 1978), as well as friction coefficients of 0.2 to 0.4 between polyvinylchloride and Italian ryegrass (KUTZBACH 1989). An eventual change of the friction coefficient during crop growth is unexplored. Due to the square power of the height of the centre of gravity in equation 1 at the most growthstages and the low masses above the centre of gravity at the early growthstages, the mass moment of inertia is also considered of lower influence on the angle of deviation for the tested velocities.
As the main factor for the deviation of the pendulum is seen to be the bending moment of resistance of the stems, and most of the variables in the equations 17 are correlated or influenced by the mass of the stems. Not taken into account are the rotary induced forces onto [page 34↓]the plants since the pendulum can only move in one dimension.
O’DOGHERTY et.al. 1989 used a rotary potentiometer for measuring E, and GROBLER & POTGIETER 1989 used a pendulum to measure fibre toughness in asparagus, while HITAKA 1968 used a top load at the panicle base to bend the rice stems. All three devices are in important parts similar to the pendulummeter, as is the snaptest (MURPHY et al. 1958) which was found highly correlated with lodging resistance. Similarly tested GROBLER & POTGIETER 1989 fibre toughness of asparagus with a pendulum device. The widely used diskmeters and platemeters utilise the bending moment of resistance of the stems as does the pendulummeter, but they are lacking the mass moment of inertia effect of the stems, and instead of sliding friction they encounter adhesive friction. Since the bending moments were in both measurement devices the most important factors, the diskmeters and platemeters can be considered highly similar.
The equations are also based on the ideal form of a cantilever, but the stems vary to different extents from this form, most notably are the nodes and the leaf sheaths, and E and I can only be used according to standard material science, when an elastic and isotropic material is provided. The stem can be considered elastic as long as it moves fully back into its former form, but only small layers of the stem can be judged as isotropic. Nevertheless, the use of these equations are common standard in determining the values of the stem, as long as it belongs to the type 2 in figure 6. Type 1 is a maximum rigid stem which also provides tensile forces onto the root. The equations are also not suitable for bending type 3 with maximum elasticity and low second moment of area, where the stressstrain relation is not linear.
The stiff cylindrical body, the rigid tube and a compact connection from tube to potentiometer are fundamental for a good transmittance of the forces of the stems against the cylindrical body into a corresponding angle of deviation. Every movement within the hardware produces noise in terms of biomass sensing. Also necessary is a robust construction of the hardware for a longterm field use.
The mentioned pendulum parameters have to be optimised with regard to plant parameters such as plant height, since the biomass sensor is a contact sensor, and hence, dependent on the contact with the plant. Despite the reported importance of the length of the pendulum l_{P} (EHLERT & SCHMIDT 1996), the height of the cylindrical body is the most critical pendulum parameter to be optimised, since this is the parameter in direct contact with the plants. The relationship between the angle of deviation and the resultant force is strictly curvilinear, but the linear regression would be sufficient for sensing the resultant force, or the biomass respectively.
 [page 35↓] 
Due to the measurement principle of recording angles, it is as well necessary to record the slope of the field, since the slope is already deviating the pendulum without having anything to measure. The slope sensor is screwed inside the cabinet (figure 14) containing the electronics. It is calibrated on a platform without inclination and measures the slope as a voltage reading. It is a AccuStar ^{®} ^{}Electronic Clinometer from Lucas Control Systems Products, with an accuracy of 0.1 degrees for slopes of less than 10 degrees. The slope measurements are taken into account for the angle of deviation versus biomass relationship with 0.1 degree increments to correct the pendulum measurements.
Figure 14: Slope sensor inside the electronic cabinet (red arrow).  

An incremental visual encoder senses the velocity of the carrier (figure 15) during pendulum measurements. It senses the velocity through counting the holes in the disc that is mounted on the sprocket of a back wheel.
Since it was constructed at the Institute of Agricultural Engineering ATB, its accuracy is compared to the timer of the laptop, and a standard deviation of less than 0.08 m s^{1 }was [page 36↓]calculated out of 25 replicated measurements. These values are sufficient to control the velocity during measurements. The measurements for the optimisation trials were done with a velocity of 2.5 m s^{1} which is the lower speed range of field sprayers during application spraying.
Figure 15: Velocity sensor of the carrier for the optimisation trials.  

A mechanical trigger (figure 16) is used to indicate the separation of the plots in the field. Sticks separate the plots in the field, instead of using a Global Positioning System GPS. The metal finger of the trigger is pushed backwards by the stick separating the plots, thus is the other end of the finger pivoted away from the inductive sensor. Once the other end of the metal finger is out of the range of the inductive sensor, the trigger switches either from 0 to 5 volts or vice versa. A rubber band is pulling the finger back into place for the next switch.
A buffer of one second in the electronic device prevents a second switch when the finger is pulled back in its place. All measurements belonging to one switch of the trigger belong to the same field plot in the recorded files. This trigger, together with the rails, is used instead of a GPS system to locate the position of the pendulummeter in driving direction. At a measurement frequency of 75 Hz and a velocity of 2.5 m s^{1}, the accuracy of the trigger is about 3 cm.
 [page 37↓] 
Figure 16: Trigger used to separate the plots in the field.  

While all four sensors measure and transmit data all the time, recording of the measurements starts with the first change of the trigger. The sensors – biomass sensor, slope sensor, speed sensor, and trigger – transmit the measurements as Volt signals to the electronic cabinet (figure 17). Every sensor has a different entry into the electronic cabinet.
Figure 17: Research carrier and signal transmission.  

 [page 38↓] 
In the cabinet, standard electronic devises process the signals and transmit them to the lap top. The two analogue devices inside the electronic cabinet need 24 Volts energy, supplied by two batteries. One analogue device converts the frequency signals of the speed sensor into Volt signals, while the other amplifies the signals of the biomass sensor. Slope and trigger signals are transmitted unchanged. During the recording, the measurement of each sensor is visible on the laptop screen.
In this way it is possible to observe the correctness of the measurements and to repeat them in case of errors. Figure 18 shows the view of the screen, as it is seen during the measurements. While the window of the other sensors is showing the correctness of the measurements, the window of the speed sensor is all important for control and needs immediate correction of the velocity of the carrier, because all the measurements should have the same constant speed to avoid biasing the measurements.
Figure 18: Screen shot of the laptop during biomass measurement.  

After finishing the measurement, the values for each sensor are saved in an ASCII file containing five columns – one column for each sensor and one for the timer of the laptop – and rows of measurements. Each row is a measurement at a specific time. The number of rows per unit time depend on the measurement frequency, with a frequency of 75 Hz there are 75 rows in one second. 75 Hz is the usual measurement frequency for all the tests. Each run in the parameter [page 39↓]optimisation trials and the trials for reduced plant protection is saved as a different file. With a velocity of 2.5 m s^{1}, it takes 2 seconds for one plot, hence 150 measurements belong to the same plot. A Visual Basic Macro reduces the data to an average per plot for further investigation. Due to the vibration of the pendulum, the plot average of the angle of deviation shows considerable difference to the original data (figure 19). Preliminary tests in one plot with ten repeats of the same parameter setting show a standard deviation of these reduced ten averages of 0.3 degrees. The number of replications that will be required in a particular experiment depends on the magnitude of the differences the experimenter wishes to detect and the variability of the data to be collected. The aforementioned standard deviation together with the assumption, that a deviation of less than one degree is not of importance for determining biomass, were calculated with equation 8 to five repeats as the necessary number of replications for determining the statistics of the parameter optimisation trials.
Figure 19: Original angle of deviation versus average angle per plot.  

The above mentioned calculation of the reduction of 150 measurements per plot to one value –the average of the plot – is based on the assumption that the average of a plot is a sufficient description of all measurements taken in one plot. A reduction of the measurements is necessary for the correlation with the single value of the plot biomass. Nevertheless, other statistical methods such as the median of the angle of deviation or the average of the vector, may as well be worth to use as a reduction method. Table 5 gives the value per plot for the three reduction methods average of the angle of deviation, average of the vector (equation 9), and the median of [page 40↓]the angle of deviation, measured in preliminary tests in rice, winter wheat, and winter rye, all at growthstage BBCH 39. For all crops the height of the pivot point h_{P} was 0.5 m, the height of the cylindrical body h_{A0} was 0.2 m, and the mass of the pendulum m _{P} was 1 kg for winter wheat and winter rye, and 0.497 kg for rice. The plot values for the average of the angle of deviation and the average of the vector were almost identical in all three crops, with differences of less than 0.007° in rice, less than 0.019° in winter wheat, and less than 0.176° in winter rye. The differences between the average of the angle of deviation and the median of the angle of deviation was considerably larger, with differences of 0.8° in rice, 1.4° in winter wheat, and 2.2° in winter rye. Although the difference between the average of the angle of deviation and the average of the vector was not decisive, in all further tests the measurements were reduced to the plot average of the angle of deviation.
Irrigated Rice 
Winter Wheat 
Winter Rye 

Plot 
Average angle of deviation 
Angle of mean vector 
Median 
Average angle of deviation 
Angle of mean vector 
Median 
Average angle of deviation 
Angle of mean vector 
Median 

(°) 
(°) 
(°) 
(°) 
(°) 
(°) 
(°) 
(°) 
(°) 
1 
13.413 
13.419 
14.000 
35.307 
35.303 
35.892 
53.467 
53.472 
53.964 
2 
16.664 
16.657 
15.824 
54.281 
54.262 
54.135 
51.039 
51.036 
51.090 
3 
12.437 
12.431 
11.872 
67.377 
67.377 
68.121 
53.169 
53.171 
53.702 
4 
12.389 
12.389 
12.176 
60.665 
60.667 
60.824 
59.789 
59.790 
59.972 
5 
9.780 
9.780 
10.351 
69.848 
69.849 
69.338 
51.443 
51.444 
51.874 
6 
10.714 
10.715 
10.351 
65.202 
65.202 
65.689 
8.294 
8.118 
5.898 
7 
9.640 
9.640 
9.439 
66.985 
66.985 
66.905 
4.007 
4.008 
4.330 
8 
9.034 
9.034 
9.135 
68.107 
68.104 
67.513 
28.511 
28.500 
26.273 
9 
8.282 
8.282 
7.919 
59.955 
59.957 
61.432 
41.665 
41.659 
40.250 
10 
6.052 
6.052 
6.094 
52.937 
52.948 
54.135 
37.894 
37.902 
38.812 
11 
5.085 
5.085 
4.878 
49.742 
49.741 
49.878 
36.428 
36.437 
37.767 
12 
2.273 
2.273 
1.838 
52.306 
52.309 
51.703 
31.765 
31.768 
31.759 
When using statistics the question of normal distribution of the measurement values is of basic meaning. Since all further statistics will be based on the 12 plot averages, and a test for normal distribution needs a large sample size, it was not possible to test those 12 plot values for normal distribution. Instead, the least square residuals of the linear and square regressions were plotted [page 41↓]against the fitted values to study if the errors were normally distributed, have a constant variance, and were independent of each other. In general, when the model is correct, the standardised residuals tend to fall between 2 and +2 and are randomly distributed about zero. The process of checking for model violations by analysing residuals is useful for uncovering hidden structures in the data and provide a visual indication of the model adequacy.
Winter Wheat and Rice
Figure 20 shows the standardised least square residuals plotted against predicted values of the linear and square regressions in irrigated rice at the growthstage BBCH 39. For both regressions the residuals fell between +0.06 and 0.06 which is a very narrow distribution about zero. In winter wheat the residuals fell between +0.3 and 0.3 for a parameter of 0.5 m h_{P}, 0.2 m h_{A0}, and 0.497 kg m _{P} The residuals of both regression models are randomly distributed and a trend is not detectable, even at that small scale, thus indicating that the variance is constant and homogeneous. The residuals show normality, as well as independence of the errors. The small scale indicates a high fit of both regression models. The residuals of the linear regression show sometimes an outlier for the value of the plot with the lowest biomass. The closeness of the median and the average of the angle of deviation in table 5 also points to a normal distribution of the measurements.
Figure 20: Typical residual plot of the linear and square regressions in wheat and rice.  

 [page 42↓] 
Winter Rye
Figure 21 shows the standardised least square residuals plotted against the predicted values of the linear and square regressions in winter rye at the growthstage BBCH 39, calculated for a pendulum setting of 0.5 m h_{P}, 0.2 m h_{A0}, and 1 kg m _{P}. For both regressions the residuals fell between +1 and 1 which is a wider distribution about zero than encountered in rice and winter wheat but still in the limits between +2 and 2. The residuals of the square regression model were randomly distributed. A trend is not visible for this model, thus indicating that the variance is constant and homogeneous. The residuals of the square regression show normality, as well as independence of the errors. The scale indicates a lower fit of the regression model in winter rye. The residuals of the linear regression didn’t show normality, though they are still between the limits of +2 and 2. The variance of the residuals of the linear regression show a strong relation between the least square and the predicted values, but it is not linear. The values need a weighing or a preliminary transformation, to recalculate this error. Without transformation the model is inadequate. But for reasons of comparison with winter wheat and rice, the linear regression for winter rye is not excluded.
Figure 21: Residual plot of the linear and square regressions in rye.  

 [page 43↓] 
The slope sensor is necessary to correct the bias of the slope within the field. Without slope sensor the slope of the field is deviating the biomass sensor pendulummeter without having touched a single stem. The error would be the slope of the terrain in degrees, hence in a plain field with almost no slopes the biasing effect would be very small, and a slope sensor wouldn’t be needed. Nevertheless, for the vast number of fields with slopes in some parts, the slope sensor has to be an integrated part of the biomass sensing of the pendulummeter. The slope sensor used here is of sufficient accuracy to correct the biomass sensor, and the unevenness of the soil surface, such as holes and furrows, can be diminished using the average of the slope sensor.
The speed sensor is also an integrated part of the measurement system due to the dynamic measurement principle. The sensor is important to keep the speed of the carrier constant while measuring a crop. The accuracy of the speed sensor is sufficient to control the speed during measurement, and to clarify the speed versus angle of deviation relationship. In some cases the visual encoder can be blocked by leaves sliding in between the small gap and thus stopping the counting of the discholes for that time.
The trigger is with 3 cm highly accurate to record position in moving direction, and together with the rails that prevent a sideways movement of more than 1 cm, they minimise a biasing of the location to a negligible factor. The exact positioning is the crucial point to pair the measurement data with the corresponding stems. The use of a GPS system was not possible because the vibration of the carrier prevented the necessary contact with the satellites.
To reduce the original measurements, which were usually recorded with a frequency of 75 Hz, to a number of values that can be handled, all three tested methods of data reduction were suitable. Though the reduction to an average of the angle of deviation or an average of the vector for one plot resulted in almost the same values, the median was not differing much.
The plotted residuals show no biasing influence of whatever possible cause for both the linear regression and the square regression in rice and winter wheat. In winter rye the plotted residual show a difference between the square regression and the linear regression. While the residuals of the square regression don’t show a bias or a foreign influence, the residuals of the linear regression show a square influence. For that reason in winter rye only the square regression can be used. This may not be true for other measurements in winter rye since at the tested winter rye sites the biomass per square meter is itself not linearly distributed but declines strongly with higher biomass. For reasons of comparison with rice and winter wheat, the linear regression will be presented as well.
 [page 44↓] 
The accuracy of repeat or replicate of a sensor is usually described by the standard deviation and the coefficient of variation of the repeats.
For the parameter optimisation trials each setting is tested with five repeats. For each plot of the test strip the average of the angle, their respective standard deviation SD, and coefficient of variation CV is calculated. The averages of the angle show large differences in these 12 plots (Table 6), which is important to correlate the measurement data with fresh mass, or dry mass respectively. The measurements were obtained in winter rye at BBCH 39 with a setting of 0.5 m h_{P}, 0.2 m h_{A0}, 1.0 kg m _{P}, 75 Hz frequency, and 2.5 m s^{1} carrier velocity.

Number 
Average 
Standard 
Coefficient 
Fresh Mass 
Dry Mass 


1 
2 
3 
4 
5 
(°) 
(°) 
(%) 
(kg m ^{} ²) 
(kg m ^{} ²) 
Plot 1 
53.0 
53.3 
52.5 
52.8 
53.5 
53.0 
0.49 
0.73 
1.412 
0.208 
Plot 2 
50.8 
51.0 
51.0 
51.5 
51.0 
51.1 
0.25 
0.49 
1.304 
0.189 
Plot 3 
52.9 
53.3 
52.9 
53.3 
53.2 
53.1 
0.20 
0.38 
1.596 
0.228 
Plot 4 
59.7 
59.5 
59.5 
59.7 
59.8 
59.7 
0.12 
0.21 
1.792 
0.261 
Plot 5 
51.4 
51.3 
51.1 
52.1 
51.4 
51.5 
0.36 
0.69 
1.320 
0.193 
Plot 6 
9.7 
9.2 
8.6 
9.6 
8.3 
9.1 
0.60 
6.65 
0.232 
0.038 
Plot 7 
3.5 
4.2 
3.1 
4.1 
4.0 
3.8 
0.45 
11.83 
0.192 
0.031 
Plot 8 
29.3 
28.8 
28.8 
29.2 
28.5 
28.9 
0.31 
1.06 
0.740 
0.119 
Plot 9 
42.1 
42.0 
42.0 
42.3 
41.7 
42.0 
0.24 
0.56 
1.092 
0.164 
Plot 10 
38.1 
38.2 
37.9 
37.9 
37.9 
38.0 
0.14 
0.38 
0.920 
0.136 
Plot 11 
36.9 
36.2 
36.2 
36.6 
36.4 
36.5 
0.29 
0.80 
0.816 
0.126 
Plot 12 
31.8 
32.4 
31.8 
31.5 
31.8 
31.9 
0.32 
1.01 
0.732 
0.110 
Average 





38.2 
0.31 
0.80 
1.012 
0.150 
 [page 45↓] 
Standard deviation and especially the coefficient of variation show differences between the plots. In general, the standard deviation is very low with values ranging between 0.1 and 0.6 degrees, and most of the plots show low coefficients of variation of less than 1.1 %. The exception are plot six and seven, where the average angle is low, the standard deviation higher than average, thus causing a much higher coefficient of variation in these two plots. These two plots have the lowest fresh and dry mass, and also a much lower plant height than the other plots, thus indicating that the measurement is already influenced by the biomass itself.
To reduce this influence of the biomass itself and optimising the different parameter settings in terms of repeatability, the relevant standard deviation and coefficient of variation for the parameter optimisation trials is calculated as the average over all 12 plots.
Due to the fact that the results of all parameter optimisation trials are similar, regarding standard deviation and coefficient of variation, one trial for each crop is vicariously described for all trials. Full records for all trials are in the appendix.
In winter rye at BBCH 39, the standard deviations of all the various parameter settings show only little differences (table 7). The standard deviations are generally very low, the mean of 12 plots is always less than 1.1 degree, for the most settings even lower than 0.5 degree. The minimum standard deviation of the 12 plots is similar, though still slightly lower than the mean. Nevertheless the maximum standard deviation, encountered in the 12 plots, show considerable differences between the settings, although still low with values of less than 2.2 degrees.
The coefficients of variation of the tested parameter settings show larger differences between the settings than the standard deviation. The values of the coefficients of variation for all settings except one are better than 5 %, for many even better than 2.5 %. An effect of the parameter mass of the pendulum m _{P} tends to increase the coefficient of variation, although it is obviously caused by the decrease in angle. In general, a low angle means a high coefficient of variation.
Some settings show zero or negative values for the minimum plot angle. Although a negative biomass is not possible, a negative measurement can occur at certain conditions. A high mass of pendulum provided, a plot with a low biomass can be measured as negative, if there is a high biomass with a high deviation in the preceding plot.

Pendulum 
Standard 
Coefficient 
Angle of 

h _{P } (m) 
h _{A0 } (m) 
m _{P } (kg) 
mean 
min. 
max. 
mean 
mean 
min. 
max. 
1.100 
0.200 
0.676 
0.35 
0.18 
0.66 
1.20 
29 
6 
43 
1.100 
0.200 
1.000 
0.30 
0.13 
0.49 
1.16 
26 
3 
40 
1.100 
0.200 
2.000 
1.11 
0.43 
2.13 
5.12 
22 
2 
35 
1.100 
0.200 
3.000 
0.43 
0.17 
1.10 
2.42 
18 
1 
31 
1.100 
0.300 
0.657 
0.56 
0.33 
1.09 
2.70 
21 
1 
37 
1.100 
0.300 
1.000 
0.32 
0.14 
0.47 
1.83 
17 
0 
33 
1.100 
0.300 
2.000 
0.37 
0.21 
0.70 
3.05 
12 
2 
27 
1.100 
0.300 
3.000 
0.39 
0.19 
0.80 
4.22 
9 
1 
23 
0.800 
0.200 
0.615 
0.38 
0.23 
0.76 
1.10 
34 
6 
51 
0.800 
0.200 
1.000 
0.35 
0.15 
0.66 
1.20 
29 
2 
46 
0.800 
0.200 
2.000 
0.40 
0.12 
0.69 
1.84 
22 
1 
37 
0.800 
0.200 
3.000 
0.36 
0.14 
0.79 
2.09 
17 
2 
32 
0.800 
0.300 
0.595 
0.37 
0.16 
0.70 
1.83 
20 
2 
40 
0.800 
0.300 
1.000 
0.37 
0.09 
0.59 
1.47 
25 
1 
45 
0.800 
0.300 
2.000 
0.47 
0.28 
0.75 
3.56 
13 
2 
30 
0.800 
0.300 
3.000 
0.42 
0.23 
0.60 
4.41 
9 
2 
24 
0.500 
0.200 
0.549 
0.27 
0.14 
0.40 
0.58 
46 
8 
68 
0.500 
0.200 
1.000 
0.31 
0.12 
0.60 
0.80 
38 
4 
60 
0.500 
0.200 
2.000 
0.44 
0.27 
0.64 
1.62 
27 
1 
48 
0.500 
0.200 
3.000 
0.51 
0.19 
0.88 
2.48 
21 
0 
39 
0.500 
0.300 
0.522 
0.48 
0.20 
1.04 
1.36 
35 
1 
62 
0.500 
0.300 
1.000 
0.55 
0.26 
1.09 
2.13 
26 
0 
50 
0.500 
0.300 
2.000 
0.41 
0.19 
0.66 
2.58 
16 
1 
36 
0.500 
0.300 
3.000 
0.44 
0.25 
0.61 
3.86 
11 
1 
28 
0.400 
0.200 
0.522 
0.44 
0.19 
0.73 
0.81 
54 
11 
76 
0.400 
0.200 
1.000 
0.57 
0.24 
0.82 
1.31 
43 
5 
66 
0.400 
0.200 
2.000 
0.71 
0.40 
1.11 
2.32 
31 
2 
53 
0.400 
0.200 
3.000 
0.74 
0.17 
1.37 
3.14 
23 
1 
43 
With regard to winter wheat at BBCH 39, the standard deviations of all the various parameter settings show only little differences (table 8). The standard deviations are generally very low, the mean of 12 plots is always less than 0.52°, and in the most cases, even lower than 0.3°.

Pendulum 
Standard 
Coefficient 
Angle of 

h _{P } (m) 
h _{A0 } (m) 
m _{P } (kg) 
mean 
min. 
max. 
mean 
mean 
min. 
max. 
0.400 
0.200 
1.000 
8.42 
7.44 
9.31 
13.33 
63 
36 
76 
0.500 
0.200 
1.000 
0.19 
0.07 
0.53 
0.32 
58 
35 
69 
0.500 
0.300 
1.000 
0.28 
0.13 
0.69 
0.58 
48 
19 
63 
0.600 
0.200 
1.000 
0.24 
0.06 
0.61 
0.45 
53 
32 
62 
0.600 
0.300 
1.000 
0.25 
0.07 
0.49 
0.58 
42 
17 
55 
0.700 
0.200 
1.000 
0.13 
0.06 
0.21 
0.28 
47 
28 
55 
0.700 
0.300 
1.000 
0.23 
0.06 
0.76 
0.62 
37 
14 
48 
0.800 
0.100 
1.000 
0.16 
0.10 
0.25 
0.32 
51 
37 
57 
0.800 
0.150 
1.000 
0.14 
0.05 
0.26 
0.28 
49 
33 
55 
0.800 
0.200 
0.615 
0.21 
0.09 
0.36 
0.42 
49 
33 
56 
0.800 
0.200 
1.000 
0.14 
0.10 
0.20 
0.31 
45 
28 
52 
0.800 
0.200 
1.500 
0.26 
0.07 
0.68 
0.63 
41 
23 
49 
0.800 
0.200 
2.000 
0.22 
0.06 
0.45 
0.58 
39 
20 
47 
0.800 
0.250 
1.000 
0.16 
0.04 
0.22 
0.40 
41 
21 
49 
0.800 
0.300 
1.000 
0.34 
0.09 
1.08 
0.96 
36 
15 
45 
0.800 
0.350 
1.000 
0.25 
0.05 
0.80 
0.84 
30 
8 
41 
0.800 
0.400 
1.000 
0.43 
0.13 
1.46 
1.94 
22 
2 
34 
0.800 
0.450 
1.000 
0.48 
0.20 
1.58 
3.36 
14 
3 
27 
0.800 
0.500 
1.000 
0.52 
0.12 
1.01 
7.62 
7 
1 
16 
0.900 
0.200 
1.000 
0.13 
0.04 
0.28 
0.31 
41 
24 
47 
1.000 
0.200 
1.000 
0.14 
0.06 
0.27 
0.35 
39 
24 
45 
1.100 
0.100 
0.696 
0.12 
0.05 
0.21 
0.25 
47 
36 
51 
1.100 
0.200 
1.000 
0.16 
0.08 
0.37 
0.43 
37 
24 
43 
1.100 
0.300 
1.000 
0.28 
0.07 
1.00 
0.97 
29 
11 
36 
1.200 
0.200 
1.000 
0.19 
0.12 
0.35 
0.49 
38 
25 
43 
The minimum standard deviation of the 12 plots is similar, though still slightly lower than the mean. The maximum standard deviation, encountered in the 12 plots, show differences between the settings, with values of less than 1.6 degrees. Trends in the standard deviation, caused by the pendulum parameters are not recognisable. One extreme outlying value is the setting of h_{P} 0.4 m, h_{A0} 0.2 m, m _{P} 1.0 kg, which shows a standard deviation of 8 degrees. The standard deviation is slightly lower for all settings in winter wheat than in winter rye.
The coefficients of variation of the tested parameter settings show similar results for the settings as the standard deviation. The values of the coefficients of variation for a wide range of settings [page 48↓]are better than 1 %, with one outlier and one trend. The outlier is the same as the before mentioned. The trend is visible for a rise of the height of the cylindrical body h_{A0} to 0.4 m, 0.45 m and 0.5 m, decreasing the range of angles, thus increasing the coefficient of variation to 2 %, 3.4 %, and 7.7 % respectively. This is caused by the plant height of 0.4 to 0.6 meter, with no stems and only leaves above a height of 0.4 to 0.45 meters. In general, a low angle means a high coefficient of variation. The coefficient of variation is considerably lower for all settings in winter wheat than in winter rye.
None of the settings show zero or negative values for the minimum plot angle. The angles most often range between 30°and 70°, and the plant height is not differing as much as in winter rye.
In irrigated rice at BBCH 39 – 42 DAT–, the standard deviations of all the various parameter settings show little differences (table 9). The standard deviations are, in general, very low, the mean of 12 plots is always less than 1.1 degree, and for a wide range of settings even less than 0.4 degree. The minimum standard deviation of the 12 plots is similar, though slightly lower than the mean standard deviation.
Pendulum

Standard

Coefficient

Angle of


h
_{P}

h
_{A0}

m
_{P}

mean

min.

max.

mean

mean

min.

max.

0.300 
0.100 
0.450 
0.21 
0.08 
0.34 
0.60 
35 
9 
47 
0.400 
0.100 
0.497 
0.36 
0.13 
0.62 
1.22 
29 
8 
40 
0.400 
0.200 
0.450 
0.63 
0.32 
1.07 
5.84 
11 
3 
19 
0.500 
0.100 
0.519 
0.29 
0.15 
0.41 
1.12 
26 
9 
36 
0.500 
0.100 
1.000 
0.40 
0.27 
0.85 
2.17 
18 
3 
29 
0.500 
0.100 
1.500 
0.30 
0.11 
0.68 
2.12 
14 
1 
23 
0.500 
0.100 
2.000 
0.29 
0.13 
0.48 
2.58 
11 
0 
19 
0.500 
0.200 
0.497 
0.55 
0.23 
0.96 
5.90 
9 
2 
16 
0.500 
0.300 
0.450 
1.10 
0.43 
1.77 
34.67 
3 
2 
4 
0.600 
0.100 
0.533 
0.31 
0.10 
0.88 
1.34 
23 
9 
31 
0.700 
0.100 
0.556 
0.32 
0.15 
0.79 
1.50 
21 
8 
28 
0.800 
0.100 
0.576 
0.21 
0.09 
0.38 
1.02 
20 
7 
26 
0.800 
0.200 
0.556 
0.58 
0.36 
1.08 
7.77 
7 
1 
12 
0.800 
0.300 
0.533 
0.90 
0.16 
2.47 
34.49 
3 
1 
5 
0.900 
0.100 
0.604 
0.28 
0.15 
0.60 
1.46 
19 
7 
25 
1.000 
0.100 
0.618 
0.27 
0.12 
0.45 
1.51 
18 
6 
23 
 [page 49↓] 
In addition, the maximum standard deviation of the 12 plots is low as well for all settings, with values of less than 2.5 degrees. The higher standard deviation tends to belong to the rising height of the cylindrical body h_{A0}. A height of 0.2 meters increases slightly the standard deviation, and a height of 0.3 meters doubles the standard deviation, compared to those settings with a height of the cylindrical body of 0.1 meter. Here it is important to take the plant height of 0.35 to 0.45 meters into account, meaning, a cylindrical body of a height of 0.30 meters is only touching the uppermost parts of a plant with a height of 0.45 meters.
The coefficients of variation of the tested parameter settings show the same trend between the settings as the standard deviation. The values of the coefficients of variation for all settings with a height of the cylindrical body of 0.1 meters are better than 2.6 %. The values of the coefficients of variation triple to 8 % for a height of the cylindrical body of 0.2 m, and jump to 35 % for a height of the cylindrical body of 0.3 m. As in winter rye and winter wheat, a low angle means a high coefficient of variation in irrigated rice as well.
Of the three crops winter wheat, winter rye and irrigated rice, the maximum standard deviation is the lowest in rice, followed by winter wheat, while winter rye has the highest maximum standard deviation. Regarding the variation in plant height, the order is the same: in irrigated rice plant height is the factor of the least variation of 5 % in this work, followed by winter wheat of around 100 %, while winter rye has the largest variation of these three crops in the factor plant height of 300 % encountered in this work.
The standard deviation and the coefficient of variation are different for the twelve plots with the highest values compared to the plots with the lowest biomass. But the differences in the standard deviation between the plots are small due to the, in general, very low standard deviation. The coefficient of variation CV shows a higher influence of the biomass, because the average angle of deviation of the biomass sensor is much lower in plots with a low amount of crop biomass, hence the coefficient of variation increases. In the plots with the low angles of deviation the high CV is not weighing too much, because in these plots there was almost no biomass to be harvested.
The parameter optimisation trials resulted in general in standard deviations that are very low for agricultural or biological materials. In most tested parameter settings SD was lower than 0.5°, and they were more or less the same in winter rye, winter wheat, and irrigated rice, and for all growthstages and pendulum parameters. These values are lower than the ones reported by EHLERT 1998 due to the exact replication of the measurement through trigger and rails. The [page 50↓]pendulum’s parameter show sometimes a slight influence on the standard deviation, but the magnitude is small, and they don’t give reasons to choose a specific setting to measure crop biomass. The standard error of the diskmeters and platemeters was only once reported and was found to be low (MOULD 1990). Standard deviations were not given in literature for the diskmeters and platemeters.
The coefficient of variation shows values of mostly less than 3 % for all crops and growthstages and pendulum parameters which are very low CVs for biological materials. Due to the dependence of CV on the average angle is the coefficient of variation low with high biomass and vice versa, which is supported by the results of VIRKAJÄRVI & MATILAINEN 1995 for a diskmeter biomass relationship. In winter rye some parameters show small negative values at the plots with a very low biomass, but the importance is negligible because in theses sites there is in this case no sufficient harvestable amount of biomass. The extreme outlier for one parameter in winter wheat can be considered a measurement error because the SD is about 10 times as high as all other standard deviations.
Only the height of the cylindrical body is of importance which has to properly touch the stems also in areas with low plant height. But the height of the cylindrical body is in this case not an absolute factor but a relative to the plant height acting factor. The other pendulum parameters show little influence on CV. With regard to standard deviation and coefficient of variation, the height of the cylindrical body is the only parameter that can be optimised in relation to the plant height in such a way that it is in proper touch with the stems and not just with the leaves.
For the diskmeters and platemeters, which are the devices principally closest to the pendulummeter, most research has shown a wide range of values for standard deviation and coefficient of variation. The CV of them was mostly higher than 20 % (BRYAN et al. 1989, MOULD 1990, GONZALEZ et al. 1990, GABRIELS & VAN DEN BERG 1993), only MOULD 1990 found a CV of 3–10 % for ryegrass, and STOCKDALE 1984 reported a CV of 10–22 %. HITAKA 1968 reported in rice coefficients of variation of 0.21 % for the area of cross section, 0.25 % for the modulus of elasticity, and 0.30 % for the bending rigidity of stems, hence low values for the central factors in the measurement principle of the pendulummeter.
 [page 51↓] 
Of the two approaches, that are describing the quality of a sensor, one is the accuracy of repeat, and the other one is the degree, by which a desired factor can be described through a measured factor. Therefore, the goodness of fit is the second approach to describe the quality of the biomass sensor.
For the parameter optimisation trials, the twelve plot averages of the angle of deviation are correlated with their corresponding fresh and dry plant mass values. Due to the curvilinear relationship between the angle of deviation and the force needed to deviate the pendulum, for every setting a linear and a square (second degree polynomial) goodness of fit is determined. In addition, the standard error of estimate is calculated for every linear goodness of fit, and also for the square goodness of fit, if the latter differs considerably from the first. Due to the fact that the results of all parameter optimisation trials are similar, regarding the goodness of fit, one exemplified growthstage of each crop is vicariously described for all trials. Full records for all parameter optimisation trials are in the appendix.
Winter Rye
In winter rye at growthstage BBCH 59, the linear goodness’ of fit R^{2}s between angle of deviation and fresh plant mass, show only small differences between the tested parameter settings (table 10). The linear goodness’ of fit between angle and fresh plant mass range between 0.84 and 0.94, all of them with a significance higher than 0.99. The linear goodness’ of fit increase slightly with an increase in the height of the cylindrical body h_{A0} from 0.3 m to 0.5 m, though an optimum is not reached in this trial. The height of the pivot point doesn’t show tendencies, and increasing the mass of the pendulum increases linear goodness’ of fit in most cases. Because of the unknown limits at which destruction of the plants occur, only a small range of the parameter settings were tested in the first parameter trials, and the range of the tested parameters was expanded, the better the limits of nondestructiveness of the measurements were known. The actual height of cylindrical body, at which the decrease in the linear goodness’ of fit R^{2}s starts, as in rice and winter wheat, is not visible. Also other trials don’t show this optimum, because the uppermost height of the cylindrical body is the lowest plant height in the plots. Thus, with one or two plots of very low plant height in the test strip, the optimum height of the cylindrical body is not reached as in the other plots with double or triple plant heights. The linear R^{2} for the angledry plant mass relationship is the same as for the fresh plant mass.

Parameters 
Fresh Mass 
Dry Mass 
Angle 

h _{P} (m) 
h _{A0} (m) 
m _{P} (kg) 
linear R ^{2} 
linear SE 
square R ^{2} 
square SE 
linear R ^{2} 
linear SE 
square R ^{2} 
square SE 
mean (°) 
min. (°) 
max. (°) 
0.500 
0.200 
0.549 
0.85** 
9.8 
0.98** 
3.6 
0.80** 
11.0 
0.98** 
3.7 
58 
5 
80 
0.500 
0.200 
3.000 
0.94** 
4.3 
0.99** 
1.9 
0.91** 
5.3 
0.99** 
1.7 
30 
0 
50 
0.500 
0.300 
0.522 
0.89** 
9.0 
0.98** 
3.9 
0.85** 
10.5 
0.98** 
3.8 
51 
2 
78 
0.600 
0.200 
0.574 
0.84** 
9.2 
0.98** 
3.4 
0.80** 
10.3 
0.98** 
3.5 
54 
5 
74 
0.600 
0.200 
3.000 
0.92** 
4.6 
0.99** 
1.8 
0.89** 
5.5 
0.99** 
1.8 
30 
1 
49 
0.600 
0.300 
0.549 
0.87** 
9.0 
0.98** 
4.0 
0.83** 
10.2 
0.98** 
3.8 
48 
0 
72 
0.700 
0.200 
0.595 
0.85** 
8.2 
0.98** 
3.1 
0.81** 
9.3 
0.98** 
3.2 
50 
6 
69 
0.700 
0.200 
3.000 
0.91** 
4.8 
0.99** 
1.9 
0.88** 
5.6 
0.99** 
1.9 
30 
1 
47 
0.700 
0.300 
0.574 
0.89** 
7.7 
0.98** 
3.7 
0.85** 
8.9 
0.98** 
3.4 
42 
1 
65 
0.800 
0.200 
0.615 
0.84** 
7.9 
0.98** 
3.2 
0.80** 
8.8 
0.98** 
3.2 
48 
6 
66 
0.800 
0.200 
3.000 
0.92** 
4.6 
0.98** 
2.3 
0.88** 
5.4 
0.98** 
2.2 
29 
1 
46 
0.800 
0.300 
0.595 
0.88** 
7.2 
0.97** 
3.7 
0.85** 
8.3 
0.98** 
3.3 
41 
2 
62 
0.900 
0.200 
0.635 
0.86** 
7.1 
0.98** 
2.8 
0.82** 
8.0 
0.98** 
2.8 
44 
5 
61 
0.900 
0.200 
3.000 
0.92** 
4.1 
0.98** 
2.4 
0.89** 
4.9 
0.98** 
2.3 
27 
2 
43 
0.900 
0.300 
0.615 
0.88** 
6.7 
0.97** 
3.6 
0.85** 
7.7 
0.97** 
3.3 
38 
3 
57 
1.000 
0.200 
0.657 
0.86** 
6.5 
0.98** 
2.6 
0.82** 
7.3 
0.98** 
2.5 
42 
6 
57 
1.000 
0.200 
3.000 
0.92** 
3.9 
0.98** 
2.3 
0.89** 
4.6 
0.98** 
2.2 
26 
2 
41 
1.000 
0.300 
0.635 
0.89** 
6.1 
0.96** 
3.6 
0.85** 
7.0 
0.97** 
3.4 
36 
4 
54 
1.100 
0.200 
0.676 
0.87** 
6.0 
0.98** 
2.6 
0.83** 
6.9 
0.98** 
2.5 
38 
4 
53 
1.100 
0.200 
3.000 
0.92** 
3.7 
0.97** 
2.3 
0.89** 
4.4 
0.98** 
2.1 
23 
1 
38 
1.100 
0.300 
0.657 
0.89** 
5.5 
0.96** 
3.4 
0.86** 
6.4 
0.97** 
3.2 
32 
4 
49 
1.400 
0.200 
0.735 
0.86** 
5.4 
0.98** 
2.3 
0.82** 
6.1 
0.98** 
2.3 
34 
4 
47 
1.400 
0.200 
3.000 
0.91** 
3.5 
0.98** 
1.8 
0.87** 
4.2 
0.98** 
1.7 
23 
3 
35 
1.400 
0.300 
0.716 
0.89** 
4.7 
0.97** 
2.5 
0.85** 
5.5 
0.97** 
2.5 
29 
3 
43 
** Significance > 0.99 * Significance > 0.95 † not significant 
 [page 53↓] 
The square goodness’ of fit between angle of deviation and fresh plant mass show only small differences, regarding the pendulum’s parameter settings. The square goodness’ of fit range between 0.96 and 0.99, all of them with a significance higher than 0.99. The square goodness’ of fit compared to the pendulum’s settings show a nil tendency for the height of the cylindrical body h_{A0, }and neither for the other two parameters_{, }due to the small range. The square goodness’ of fit for the angle dry plant mass relationship is performing equally well for the fresh plant mass. The determination of plant mass by the square goodness’ of fit is much better than by the linear goodness’ of fit.
Due to the considerable differences between the linear and square goodness’ of fit, the standard error of estimate is calculated for both of them. The standard error of estimate, calculated for linear goodness of fit, is rather high for winter rye at BBCH 59, with values ranging between 3.5 and 9.8 for fresh plant mass, and similarly for dry plant mass. The standard error of estimate is much higher in winter rye than in irrigated rice and winter wheat, without having larger angles of deviation. There is a tendency of increasing standard errors of estimate when the angle of deviation increases. For average angles of 30° the standard error of estimate is around 5, while for average angles of 50° there is a standard error of estimate of 9. There is as well a strong incidence that the mass of the pendulum lowers the standard error of estimate: with a pendulum mass of 0.6 or 0.7 kg the standard error of estimate is about twice as high as for a mass of 3 kg. A similar tendency is visible for the height of the pivot point. If the pivot point rises from 0.5 m to 1.4 m, the standard error of estimate decreases from 9.8 to 5.4. The standard error of estimate for the square goodness of fit is much smaller with values ranging between 1.8 and 4.0 for fresh plant mass, and similar values for dry plant mass. The standard error of estimate for the square goodness of fit is in the range of the values encountered in irrigated rice and winter wheat for the linear goodness of fit. Thus showing, that the square formula for the relationship between biomass and angle has not only the higher R^{2}, but also a much lower standard error of estimate.
Winter Wheat
In winter wheat at the growthstage BBCH 39, the linear goodness’ of fit R^{2}s between the angle of deviation and fresh plant mass, calculated for the tested parameter settings, show only little differences (table 11). The linear R^{2}s between angle and fresh plant mass range between 0.80 and 0.92, all of them with a significance higher than 0.99. The linear goodness’ of fit decrease slightly with an increase in the height of cylindrical body h_{A0} to 0.5 m, though by far not as sharply as in irrigated rice. The linear goodness’ of fit compared to the pendulum’s parameter settings show a slight tendency for the height of cylindrical body h_{A0. }By increasing the height of the cylindrical body from 0.1 m to 0.3 m, the linear values of R^{2} increase as well.

Parameters 
Fresh Mass 
Dry Mass 
Angle 

h
_{P}

h
_{A0}

m
_{P}

linear

linear

square

linear

linear

square

mean

min.

max.

0.400 
0.200 
1.000 
0.90** 
3.9 
0.95** 
0.91** 
3.8 
0.94** 
63 
36 
76 
0.500 
0.200 
1.000 
0.88** 
3.6 
0.93** 
0.89** 
3.6 
0.92** 
58 
35 
69 
0.500 
0.300 
1.000 
0.91** 
4.2 
0.94** 
0.91** 
4.1 
0.93** 
48 
19 
63 
0.600 
0.200 
1.000 
0.89** 
3.1 
0.93** 
0.89** 
3.1 
0.92** 
53 
32 
62 
0.600 
0.300 
1.000 
0.90** 
3.7 
0.93** 
0.90** 
3.7 
0.92** 
42 
17 
55 
0.700 
0.200 
1.000 
0.87** 
2.9 
0.92** 
0.87** 
2.9 
0.91** 
47 
28 
55 
0.700 
0.300 
1.000 
0.89** 
3.4 
0.92** 
0.89** 
3.4 
0.91** 
37 
14 
48 
0.800 
0.100 
1.000 
0.86** 
2.2 
0.92** 
0.86** 
2.2 
0.91** 
51 
37 
57 
0.800 
0.150 
1.000 
0.86** 
2.4 
0.92** 
0.86** 
2.4 
0.91** 
49 
33 
55 
0.800 
0.200 
0.615 
0.86** 
2.6 
0.91** 
0.85** 
2.6 
0.90** 
49 
33 
56 
0.800 
0.200 
1.000 
0.87** 
2.7 
0.92** 
0.86** 
2.7 
0.91** 
45 
28 
52 
0.800 
0.200 
1.500 
0.86** 
2.8 
0.93** 
0.86** 
2.8 
0.91** 
41 
23 
49 
0.800 
0.200 
2.000 
0.86** 
2.9 
0.93** 
0.86** 
2.9 
0.92** 
39 
20 
47 
0.800 
0.250 
1.000 
0.86** 
3.0 
0.92** 
0.86** 
3.0 
0.91** 
41 
21 
49 
0.800 
0.300 
1.000 
0.87** 
3.2 
0.92** 
0.87** 
3.2 
0.91** 
36 
15 
45 
0.800 
0.350 
1.000 
0.89** 
3.3 
0.92** 
0.89** 
3.3 
0.91** 
30 
8 
41 
0.800 
0.400 
1.000 
0.92** 
2.9 
0.92** 
0.91** 
3.0 
0.91** 
22 
2 
34 
0.800 
0.450 
1.000 
0.88** 
3.0 
0.90** 
0.86** 
3.2 
0.90** 
14 
3 
27 
0.800 
0.500 
1.000 
0.81** 
2.2 
0.88** 
0.78** 
2.3 
0.86** 
7 
1 
16 
0.900 
0.200 
1.000 
0.85** 
2.6 
0.91** 
0.85** 
2.6 
0.90** 
41 
24 
47 
1.000 
0.200 
1.000 
0.83** 
2.5 
0.91** 
0.84** 
2.5 
0.90** 
39 
24 
45 
1.100 
0.100 
0.696 
0.81** 
1.9 
0.89** 
0.81** 
1.9 
0.88** 
47 
36 
51 
1.100 
0.200 
1.000 
0.83** 
2.3 
0.91** 
0.83** 
2.3 
0.89** 
37 
24 
43 
1.100 
0.300 
1.000 
0.84** 
2.9 
0.90** 
0.83** 
2.9 
0.89** 
29 
11 
36 
1.200 
0.200 
1.000 
0.80** 
2.3 
0.89** 
0.80** 
2.3 
0.88** 
38 
25 
43 
** Significance > 0.99 * Significance > 0.95 † not significant 
 [page 55↓] 
The linear R^{2} reaches an optimum at 0.4 m height of cylindrical body, and decreases slightly with a further rise of the height of the cylindrical body. The actual height of cylindrical body, at which the decrease in the linear goodness’ of fit starts, is dependent on the plant height during measurement. Considering the plant height of 0.55 m to 0.65 m, this optimum is about 60 % of the total plant height. The linear R^{2} for the angledry plant mass relationship is the same as for the fresh plant mass.
The square goodness’ of fit between angle of deviation and fresh plant mass show only little differences, regarding the parameter settings. The square goodness’ of fit range between 0.88 and 0.95, all of them with a significance higher than 0.99. The square R^{2}s compared to the pendulum’s settings show no tendency relative to the height of the cylindrical body h_{A0}, and neither for the other two parameters_{}The square goodness’ of fit for the angledry plant mass relationship perform equally well for the fresh plant mass. There is a slight tendency towards a better determination of plant mass through the square R^{2}s than through the linear R^{2}s.
Due to the similarity of linear and square goodness of fit, the standard error of estimate is calculated only for the linear goodness of fit. The standard error of estimate, calculated for the tested parameter settings, is rather low for winter wheat at BBCH 39, with values ranging between 1.9 and 4.2 for fresh plant mass, and similarly for dry plant mass. The standard error of estimate is higher in winter wheat than in irrigated rice, but the range is smaller in winter wheat, thus preventing to show tendencies influenced by the parameter settings or the angle of deviation.
Rice
In irrigated rice at the growthstage BBCH 39, the linear goodness’ of fit between angle of deviation and fresh plant mass, calculated for a wide range of parameter settings, show only little differences (table 12). The linear R^{2}s^{}between angle and fresh plant mass range between 0.88 and 0.97, all of them with a significance higher than 0.99. The linear R^{2}s drop sharply for the two settings with a height of cylindrical body h_{A0} of 0.3 m, showing a linear R^{2} of 0.62 and 0.24 respectively. The linear R^{2}s compared to the pendulum’s settings show a strong trend for the height of cylindrical body h_{A0. }By increasing the height of the cylindrical body, the linear R^{2}s decrease. The actual height of the cylindrical body, at which the decrease in the linear goodness’ of fit starts, is dependent on the plant height. Once the cylindrical body is not touching the stem of the plant, but just the leaves, the linear goodness of fit is decreasing. The significance decreases together with the linear R^{2}. The linear goodness’ of fit for the angledry plant mass relationship is the same as for the fresh plant mass.

Parameters 
Fresh Mass 
Dry Mass 
Angle 

h _{P} 
h _{A0} 
m _{P} 
linear 
linear 
square 
linear 
linear 
square 
mean 
min 
max 
(m) 
(m) 
(kg) 
R ^{2} 
SE 
R ^{2} 
R ^{2} 
SE 
R ^{2} 
(°) 
(°) 
(°) 
0.300 
0.100 
0.450 
0.93** 
2.9 
0.97** 
0.94** 
2.7 
0.97** 
35 
9 
47 
0.400 
0.100 
0.497 
0.88** 
3.1 
0.93** 
0.90** 
2.9 
0.94** 
29 
8 
40 
0.400 
0.200 
0.450 
0.91** 
1.4 
0.92** 
0.88** 
1.6 
0.90** 
11 
3 
19 
0.500 
0.100 
0.519 
0.94** 
1.9 
0.96** 
0.95** 
1.8 
0.96** 
26 
9 
36 
0.500 
0.100 
1.000 
0.94** 
1.9 
0.95** 
0.94** 
1.9 
0.94** 
18 
3 
29 
0.500 
0.100 
1.500 
0.96** 
1.3 
0.96** 
0.96** 
1.3 
0.96** 
14 
1 
23 
0.500 
0.100 
2.000 
0.97** 
1.1 
0.97** 
0.96** 
1.2 
0.96** 
11 
0 
19 
0.500 
0.200 
0.497 
0.94** 
1.0 
0.95** 
0.91** 
1.2 
0.93** 
9 
2 
16 
0.500 
0.300 
0.450 
0.62** 
0.4 
0.62 * 
0.59** 
0.4 
0.59 * 
3 
2 
4 
0.600 
0.100 
0.533 
0.95** 
1.6 
0.97** 
0.95** 
1.5 
0.96** 
23 
9 
31 
0.700 
0.100 
0.556 
0.95** 
1.3 
0.97** 
0.95** 
1.3 
0.97** 
21 
8 
28 
0.800 
0.100 
0.576 
0.93** 
1.4 
0.97** 
0.94** 
1.4 
0.96** 
20 
7 
26 
0.800 
0.200 
0.556 
0.93** 
0.8 
0.93** 
0.90** 
1.0 
0.90** 
7 
1 
12 
0.800 
0.300 
0.533 
0.24 † 
0.8 
0.33 † 
0.21 † 
0.8 
0.35 † 
3 
1 
5 
0.900 
0.100 
0.604 
0.93** 
1.3 
0.96** 
0.94** 
1.3 
0.96** 
19 
7 
25 
1.000 
0.100 
0.618 
0.88** 
1.7 
0.94** 
0.89** 
1.6 
0.94** 
18 
6 
23 
** Significance > 0.99 * Significance > 0.95 † not significant 
 [page 57↓] 
The square goodness’ of fit between angle of deviation and fresh plant mass show only little differences. The square goodness’ of fit between angle and fresh plant mass range between 0.92 and 0.97, all of them with a significance higher than 0.99. The square goodness’ of fit drop sharply for the two settings with a height of cylindrical body h_{A0} of 0.3 m, showing a square goodness of fit of 0.62 and 0.33 respectively. The square goodness’ of fit compared to the pendulum’s settings show a strong trend for the height of the cylindrical body h_{A0. }By increasing the height of the cylindrical body, the square goodness’ of fit decreases, similar to the linear goodness of fit. The significance decreases together with the square goodness of fit. The square goodness of fit is performing equally well for the fresh plant mass. There is a slight tendency towards a better determination of plant mass through the square goodness of fit than through the linear goodness of fit.
Due to the similarity of linear and square goodness of fit, the standard error of estimate is calculated only for the linear goodness of fit. The standard error of estimate, calculated for the tested parameter settings, is rather low for irrigated rice at BBCH 39, with values ranging between 0.4 and 3 for fresh plant mass, and similarly for dry plant mass. There is a slight tendency towards a rise in the standard error of estimate with higher angles of deviation. Trends caused by the parameter settings are not visible.
Although the results of the exemplary growthstages prove true for most parameters in the optimisation trials, differences can be seen over a wider range of growthstages. This is especially true for the exemplary growthstage in winter rye, where the standard error of estimate is considerably lower for the square R^{2} than for the linear. If the linear and square standard errors of estimate with their respective upper and lower limits are plotted against the measured growthstages, then the influence of the crop growth becomes distinctive. The standard error of estimate of the square regression shows generally a better performance at the growthstages BBCH 59 and 69, than in the linear regression (figure 22). For the earlier growthstages only the standard error of estimate for the linear regression is calculated, due to the closeness of the linear and square R^{2}. It is obvious that something in the stem of winter rye is either changing or becoming more pronounced with heading and stem elongation.
The standard errors of estimate for the linear and square regressions in winter wheat and rice don’t show a difference between the different growthstages, and the standard errors of estimate are only slightly increasing with later growthstages. Thus the standard errors of estimate support the results of the plotted residuals.
 [page 58↓] 
Figure 22: Range of the standard error of estimate for the linear and square goodness of fit at different growthstages of winter rye.  

Likewise show the upper and lower limits of the goodness of fit changes with the growthstages. Of the three crops winter rye, winter wheat and irrigated rice, only winter rye shows a large difference between the linear and the square goodness’ of fit. This difference increases with increasing growthstage of the crop (figure 23).
Figure 23: Range of the linear and square goodness’ of fit R^{2} in various growthstages in winter rye.  

 [page 59↓] 
For the growthstages BBCH 32 and 39, the upper and lower limits of the linear and square R^{2}s are congruent. For the later growthstages, the square R^{2}s have higher values, and a narrower range between the upper and the lower limit, than the linear R^{2}s. In addition, the upper limit of the linear R^{2}s^{}reach only up to the lower limits of the square R^{2}s. Thus it can be seen in winter rye that the square R^{2 }is more suitable to determine biomass at the growthstages BBCH 59 and 69, while in winter rye for the growthstages BBCH 32 to 39, and in winter wheat and irrigated rice for all growthstages, both, the linear and the square R^{2}, are suitable to determine biomass.
According to the R^{2}s (figure 23), the biomass sensor pendulummeter shows a very good determination of winter rye crop biomass at the growthstages BBCH 39 to 69. At the preceding growthstage BBCH 32, the biomass sensor shows a decreased ability to determine crop biomass, and at the growthstage 25, a measurement is not possible, because the lowest height of the cylindrical body is 0.1 m and the plant height is merely reaching that height. Winter wheat does not show this large difference between linear and square goodness of fit. According to the goodness of fit (figure 24), the pendulummeter shows a very good determination of winter wheat crop biomass at the growthstages BBCH 34 to 75, while at the preceding growthstage BBCH 32, no winter wheat crop could be measured, and at BBCH 25 no measurement is possible. Due to the rapid growth at BBCH 32 and BBCH 34, it was not possible to test both for one crop, and the results for winter rye at BBCH 32 and winter wheat at BBCH 34 have to be seen jointly, thus indicating for both cereals that BBCH 32 is the first measurable growthstage. But at BBCH 32 the ability to determine biomass is suboptimal compared to the later growthstages.
Figure 24: Range of the linear and square goodness’ of fit R^{2} in various growthstages in winter wheat.  

 [page 60↓] 
Irrigated rice IR 64, similar to winter wheat, does not show large difference between linear and square goodness’ of fit. According to the goodness’ of fit (figure 25), the sensor shows a very good determination of rice crop biomass at all tested growthstages from BBCH 25 to 65. As figures 23 to 25 show, the earliest growthstage, at which the biomass sensor pendulummeter can be used, is BBCH 25 in irrigated rice, and BBCH 32 in winter wheat and winter rye. Since the plants are rather small in these growthstages, there are fewer pendulum parameter settings suitable for measuring biomass. Though the results are similar to the other parameter trials, they show the limits of the sensor, thus forcing a specific presentation of the results.
Figure 25: Range of the linear and square goodness’ of fit R^{2} in various growthstages in irrigated rice.  

As figures 23 to 25 show, the earliest growthstage, at which the biomass sensor pendulummeter can be used, is BBCH 25 in irrigated rice, and BBCH 32 in winter wheat and winter rye. Due to the small plant size are there only a few potential pendulum parameters suitable for testing and measuring.
Winter Rye
The earliest growthstage in winter rye that has a sufficient plant height to use the pendulummeter is BBCH 32. The plant height is 37 cm to 54 cm. Table 13 shows the linear and square goodness’ of fit for dry and fresh plant mass, the standard error of estimate for the linear goodness of fit, and the average angle for the entire measurement strip.

Parameters 
Fresh Mass 
Dry Mass 
Angle 

h
_{P}

h
_{A0}

m
_{P}

linear

linear

square

linear

linear

square

mean

0.300 
0.100 
1.000 
0.65** 
3.7 
0.66** 
0.59** 
4.0 
0.64** 
45 
0.400 
0.100 
1.000 
0.58** 
3.9 
0.63 * 
0.52** 
4.1 
0.61 * 
37 
0.500 
0.100 
0.574 
0.51** 
3.2 
0.55 * 
0.46 * 
3.4 
0.54 * 
39 
0.500 
0.100 
1.000 
0.49 * 
3.5 
0.54 * 
0.43 * 
3.8 
0.52 * 
34 
0.500 
0.100 
1.500 
0.52** 
3.2 
0.54 * 
0.46 * 
3.4 
0.52 * 
29 
0.500 
0.100 
2.000 
0.49 * 
3.3 
0.52 * 
0.43 * 
3.5 
0.48 † 
26 
0.500 
0.200 
1.000 
0.55** 
3.8 
0.55 * 
0.50 * 
4.0 
0.51 * 
15 
0.600 
0.100 
1.000 
0.45 * 
3.2 
0.50 * 
0.38 * 
3.3 
0.47 † 
32 
0.700 
0.100 
1.000 
0.53** 
3.0 
0.53 * 
0.48 * 
3.2 
0.49 * 
12 
0.800 
0.100 
1.000 
0.51** 
2.9 
0.51 * 
0.45 * 
3.0 
0.46 † 
13 
0.900 
0.100 
1.000 
0.50** 
2.6 
0.50 * 
0.44 * 
2.8 
0.46 † 
12 
1.100 
0.100 
1.000 
0.49 * 
2.4 
0.51 * 
0.43 * 
2.5 
0.48 † 
12 
1.100 
0.200 
0.676 
0.01 † 
2.6 
0.01 † 
0.00 † 
2.6 
0.03 † 
4 
** Significance > 0.99 * Significance > 0.95 † not significant 
Like in the parameter optimisation trials for winter wheat BBCH 34 and rice BBCH 25, both, the linear and the square R^{2}s are very similar for all pendulum parameter settings. Nevertheless, the values for both goodness’ of fit are much lower for this growthstage than for the later ones. For the most settings, the linear R^{2}s range between 0.4 and 0.65, the square R^{2}s perform a little bit better, both with a significance mostly between 0.95 and 0.99. In addition, there is a slight difference between the goodness’ of fit for fresh mass and dry mass. The standard error of estimate is with values less than 3.9 higher than for winter wheat and rice at their respective growthstage. The biomass sensor is equally suitable for determining fresh and dry mass.
Tendencies are not clearly expressed for the height of the cylindrical body, because in this trial the tested heights of the cylindrical body touch only the lower half of the plant. The influence of the mass of pendulum on the R^{2}s is also not pronounced. The height of the pivot point tends to influence the measurements. In this trial it shows, the lower the height of the pivot point, the better is the R^{2}, which goes hand in hand with an increase in average angle of the test strip.
Winter Wheat
BBCH 34 is the earliest growthstage in winter wheat, tested for a parameter optimisation trial (table 14), although measurements at BBCH 32 were possible.

Parameters 
Fresh Mass 
Dry Mass 
Angle 

h
_{P}

h
_{A0}

m
_{P}

linear

linear

square

linear

linear

square

mean

0.300 
0.100 
1.000 
0.81** 
3.0 
0.83** 
0.78** 
3.2 
0.79** 
49 
0.400 
0.100 
1.000 
0.81** 
2.6 
0.82** 
0.78** 
2.8 
0.79** 
43 
0.500 
0.100 
1.000 
0.88** 
1.6 
0.88** 
0.84** 
1.9 
0.84** 
38 
0.500 
0.100 
2.000 
0.86** 
1.9 
0.90** 
0.81** 
2.3 
0.84** 
30 
0.500 
0.200 
1.000 
0.82** 
2.4 
0.83** 
0.77** 
2.6 
0.78** 
20 
0.600 
0.100 
1.000 
0.83** 
1.9 
0.86** 
0.77** 
2.2 
0.79** 
35 
0.700 
0.100 
1.000 
0.82** 
1.7 
0.86** 
0.74** 
2.0 
0.78** 
34 
0.700 
0.140 
1.000 
0.80** 
1.9 
0.86** 
0.73** 
2.3 
0.78** 
29 
0.700 
0.170 
1.000 
0.80** 
2.2 
0.86** 
0.74** 
2.5 
0.79** 
24 
0.800 
0.100 
0.635 
0.82** 
1.3 
0.84** 
0.75** 
1.6 
0.77** 
34 
0.800 
0.100 
1.000 
0.80** 
1.5 
0.84** 
0.72** 
1.8 
0.75** 
32 
0.800 
0.100 
1.500 
0.84** 
1.5 
0.87** 
0.77** 
1.8 
0.80** 
28 
0.800 
0.100 
2.000 
0.83** 
1.6 
0.86** 
0.76** 
2.0 
0.78** 
25 
0.800 
0.140 
1.000 
0.81** 
1.7 
0.86** 
0.74** 
2.0 
0.78** 
27 
0.800 
0.170 
1.000 
0.77** 
2.1 
0.80** 
0.70** 
2.4 
0.72** 
23 
0.800 
0.200 
1.000 
0.71** 
2.2 
0.71** 
0.63** 
2.5 
0.63 * 
20 
0.800 
0.240 
1.000 
0.51** 
2.6 
0.56 * 
0.43 * 
2.8 
0.49 * 
13 
0.800 
0.270 
1.000 
0.32 † 
2.7 
0.42 † 
0.24 † 
2.8 
0.35 † 
9 
0.800 
0.300 
1.000 
0.38 * 
1.6 
0.41 † 
0.27 † 
1.7 
0.30 † 
5 
0.900 
0.100 
1.000 
0.81** 
1.4 
0.84** 
0.73** 
1.6 
0.75** 
30 
1.100 
0.100 
1.000 
0.81** 
1.2 
0.84** 
0.72** 
1.5 
0.74** 
28 
1.100 
0.200 
1.000 
0.66** 
1.9 
0.67** 
0.60** 
2.1 
0.61 * 
17 
** Significance > 0.99 * Significance > 0.95 † not significant 
By testing growthstage BBCH 34 instead of BBCH 32 it was possible to elaborate more clearly the importance of plant height and stem elongation for the measurements with the pendulummeter. The importance of these earliest measurable growthstages is not only highlighted by the fact, that there are fewer for biomass sensing suitable pendulum parameters, but they are at the same time crucial growthstages for the application of plant growthregulators and fungicides. The plant height at this growthstage was 44 cm to 50 cm.
Table 14 shows the linear and square goodness’ of fit for dry and fresh plant mass, the standard error of estimate for the linear goodness of fit, and the average angle for the entire measurement strip. Similar to the other parameter optimisation trials, both goodness’ of fit are very similar for all pendulum settings. Nevertheless, the values for both goodness’ of fit are considerably lower [page 63↓]for this growthstage than for the later ones. For the most settings, the linear R^{2}s range between 0.80 and 0.88, and the square R^{2}s perform a little bit better, mostly with a significance higher than 0.99. In addition, there is a slight difference between the R^{2}s for fresh mass and dry mass. The standard error of estimate is rather low with values less than 3.0, though higher than for rice at BBCH 25. The biomass sensor is equally suitable for determining fresh mass and dry mass.
Strong tendencies are visible for the height of the cylindrical body. While all settings with a height of the cylindrical body of 0.1 m perform well, an increase from 0.1 m to 0.3 m in the height of the cylindrical body has a strong effect on the goodness’ of fit, decreasing their values from 0.8 to 0.3. A considerable decrease show settings with higher heights of the cylindrical body than 0.2 m. More or less, a height of the cylindrical body touching the upper half of the plant doesn’t perform well, while the settings touching the lower half of the plant show a good performance. There is also a slight trend to an increased R^{2} with an increase in the mass of pendulum.
Rice
The earliest growthstage in rice having sufficient plant heights to use the pendulummeter is BBCH 25, respectively 28 DAT. The plant height at this growthstage was 33 cm to 36 cm. Table 15 shows the linear and square R^{2}s for dry and fresh plant mass, the standard error of estimate for the linear goodness of fit, and the average angle for the entire measurement strip.
Similar to the other parameter optimisation trials, both goodness’ of fit are very high for a height of cylindrical body of 0.1 m, with values between 0.91 and 0.96. The standard error of estimate is at the same time rather low with values less than 2.2. The square goodness’ of fit perform slightly better than the linear goodness’ of fit, all with a significance above 0.99. The biomass sensor is equally suitable for determining fresh mass and dry mass.
Strong tendencies are visible for the height of the cylindrical body. While all settings with a height of the cylindrical body of 0.1 m perform well, an increase from 0.1 m to 0.2 m in the height of the cylindrical body has a strong effect on the R^{2}s, decreasing the values to 0.6  0.8. A setting with 0.3 m height of the cylindrical body decreases the R^{2} to less than 0.3, with an average angle for all measurements of 2°, which is almost no deviation. There is also a slight trend to decrease the goodness of fit with an increase in the mass of pendulum.

Parameters 
Fresh Mass 
Dry Mass 
Angle 

h
_{P}

h
_{A0}

m
_{P}

linear

linear

square

linear

linear

square

mean

0.300 
0.100 
0.450 
0.90** 
2.1 
0.93** 
0.89** 
2.2 
0.91** 
25 
0.400 
0.100 
0.497 
0.91** 
1.7 
0.96** 
0.91** 
1.7 
0.94** 
23 
0.400 
0.200 
0.450 
0.80** 
0.8 
0.80** 
0.77** 
0.8 
0.78** 
6 
0.500 
0.100 
0.519 
0.95** 
1.0 
0.97** 
0.94** 
1.1 
0.96** 
19 
0.500 
0.100 
1.000 
0.96** 
0.7 
0.96** 
0.95** 
0.8 
0.95** 
13 
0.500 
0.100 
1.500 
0.94** 
0.7 
0.94** 
0.92** 
0.8 
0.93** 
9 
0.500 
0.200 
0.497 
0.63** 
0.9 
0.64* 
0.59** 
0.9 
0.60 * 
5 
0.600 
0.100 
0.533 
0.95** 
0.9 
0.97** 
0.94** 
1.0 
0.95** 
18 
0.600 
0.200 
0.519 
0.69** 
0.7 
0.75** 
0.66** 
0.7 
0.73** 
5 
0.600 
0.300 
0.497 
0.06 † 
0.5 
0.23 † 
0.06 † 
0.5 
0.25 † 
2 
0.700 
0.100 
0.556 
0.93** 
0.9 
0.97** 
0.93** 
0.9 
0.95** 
17 
0.800 
0.100 
0.576 
0.92** 
0.9 
0.96** 
0.91** 
0.9 
0.95** 
15 
0.800 
0.200 
0.556 
0.69** 
0.6 
0.70** 
0.68** 
0.6 
0.69** 
4 
0.900 
0.100 
0.604 
0.91** 
0.9 
0.96** 
0.90** 
1.0 
0.95** 
14 
1.000 
0.100 
0.618 
0.85** 
1.2 
0.94** 
0.85** 
1.2 
0.93** 
14 
1.000 
0.200 
0.604 
0.73** 
0.6 
0.75** 
0.73** 
0.6 
0.75** 
4 
** Significance > 0.99 * Significance > 0.95 † not significant 
The accuracy of biomass determination, presented as fresh mass or dry mass, is in the exemplified growthstages, as it is for the most growthstages, sufficient to very good. The pendulum parameters mostly don’t show an influence on the quality of the regressions in all three crops and for most of the growthstages. The pendulum parameter that is usually differing in terms of goodness of fit is the height of the cylindrical body h_{A0}, which is also most important for the measurement due to the measurement principle, since it decides where the plants are touched. Therefore, there are large differences between the goodness of fit when the plant stems are touched, and those few parameter settings when due to a high h_{A0} only the tops of the plants and the leaves were touched. As long as the plant stems are in contact with the cylindrical body, the goodness of fit is high, resulting in the advice, that the cylindrical body always has to be in contact with the stems for a proper measurement. These results support the correlation between bending rigidity and fresh weight found by HITAKA 1968. For the height of the pivot point and the mass of the pendulum, no optimisation can be considered via the goodness of fit. Similarly, PALAZZO & LEE 1986 couldn’t find an influence of the size of a diskmeter on R^{2}. The [page 65↓]determined goodness of fit is mostly higher than those reported for the preceding pendulum device (EHLERT & SCHMIDT 1996, EHLERT 1998), due to the accurate correspondence of plants and measurements through trigger and rails. The biomass sensor pendulummeter is also equally able to determine fresh mass as it is to determine dry mass. The dry mass and the fresh mass are usually very good correlated on the scale of 5 m^{2}.
In rice, all growthstages show only slight differences between the linear and square regressions with low standard errors of the regression equation. For the diskmeters and platemeters a low standard error of the regression was also reported (HARMONEY et al. 1997). The slight difference between linear and square regression is explained by the nonlinearity of the forceangle relationship of the pendulum. The earliest tested growthstage BBCH 25 also shows good results, as do the later growthstages, for those parameters fully in contact with the plant stems. Earlier measurements are not possible due to the small plant heights. The standard error of most regressions can be considered low to medium, and it increases with plant growth.
The results for winter wheat are very similar to the ones obtained for rice, except that at the growthstage 25 no measurement is possible due to the low plant height. A very similar device was used by (ELSAYED YOUSSEF GHONIEM et al. 1980) to test for grain loss of the wheat ears before harvest. A physical effect on the ear or panicle was not observed despite the findings of ELSAYED YOUSSEF GHONIEM et al. 1980. A potential effect of the measurements on the flowering cereals is not evident, but has to be observed.
The results in winter rye are differing in several parts. The measurements at BBCH 32 result in low accuracy of determination of biomass due to the low plant height. A sensing of biomass at BBCH 69 may be impossible due to the randomly distributed appearance of BRAZIER stem buckling (NIKLAS 1998). This stem buckling in winter rye can start as early as heading and is caused by the decrease of stem bending rigidity (SPIEWOK 1970, SPIEWOK 1974, SKUBISZ 1984, NIKLAS 1990, CROOK & ENNOS 1994), senescence of leaf sheaths (HITAKA 1968), and the increase of dry matter content of the stems (SPIEWOK 1970, SPIEWOK et al. 1970, SPIEWOK 1974). These causes for stem buckling at later growthstages might as well be associated with the different performances of the linear and square regressions. In winter rye there is a large difference between the linear regression equations and the square regression equations in the accuracy of determining biomass throughout the most growthstages. The square regression fits much better, and with a lower standard error of the regression, than the linear, supporting the results of the plotted residuals. This is further pronounced by the curvilinear angleforce relationship of the pendulummeter. Additionally showed the tested winter rye strips also a square relationship for the height of the plants and the biomass itself. Square relationships [page 66↓]are not an unusual phenomenon in agricultural science and were reported for biomass at various times (MILLER et al. 1984, JORGENSEN et al. 1997) for various measurement methods.
It can be considered that the measurements in winter rye and winter wheat at BBCH 25 are not possible with the pendulummeter, that at BBCH 32 the accuracy is low, but suitable as long as there are no other sensors for that growthstage and purpose, and that at BBCH 34 the accuracy of determining biomass is high till the stems lodge or loose their elasticity.
The goodness of fit of the pendulummeter fits in with the best results of the diskmeters and platemeters, which reach in pure grass stands an R^{2} of 0.7 or higher (POWELL 1974, CASTLE 1976, EARLE & MC GOWAN 1979, BAKER et al. 1981, MICHELL & LARGE 1983, SHARROW 1984, STOCKDALE 1984, PALAZZO & LEE 1986, SCRIVNER et al. 1986, KARL & NICHOLSON 1987, PETERSON & HUSSEY 1987, LACA et al. 1989, GONZALEZ et al. 1990, MOULD 1990, MOULD 1992, VIRKAJÄRVI & MATILAINEN 1995, REEVES et al. 1996, HARMONEY et al. 1997, MOSIMANN et al. 1999). For most of the reported relationships between the height of the resting disk or plate and the grass yield, a linear regression was sufficient, but several researchers used a square regression (POWELL 1974, EARLE & MC GOWAN 1979, BAKER et al. 1981, STOCKDALE 1984, GONZALEZ et al. 1990, VIRKAJÄRVI & MATILAINEN 1995), and MOULD 1990 even used a cubic regression.
After knowing the accuracy of the repeat and the accuracy of biomass determination, it follows to proper understand the influence of the independent parameters on the dependent parameter. In the case of the biomass sensor pendulummeter the question arises about the relationship between the angle of deviation as the dependent parameter on the one side and the three pendulum parameters as the independent variables on the other side. At best it is possible to recalculate the angle of deviation if one or more pendulum parameters are changed.
Multiple regression was used to detect, which pendulum setting has the strongest influence on the angle of deviation. The option of forward stepwise regression allows to evaluate the increment at each step of the goodness of fit R^{2} of the multiple regression caused by entering several independent variables. It also evaluates, if it is worthwhile to keep a variable as a predictor in the model or to exclude it. The three independent variables used in this multiple linear regression were the height of pivot point h_{P}, the height of the cylindrical body h_{A0}, and the [page 67↓]mass of the pendulum m _{P}. The first step of the forward stepwise regression gives the weighing of the influence of the entered independent variables, upon which the including or excluding and the ranging of the variables is based. Table 16 shows the range of R^{2} increments and the number of entry into the regression of the independent variables height of pivot point h_{P}, height of the cylindrical body h_{A0}, and mass of the pendulum m _{P}. R^{2} increment and number of entry was first calculated individually for each of the 12 plots, based on the measurements obtained in the optimisation trials in rice, winter rye, and winter wheat, all at BBCH 39. They were later summarised for all plots.
Winter Rye BBCH 39 



Range of R ^{2} increment 
Step in 
h _{A0} 
0.10 – 0.42 
1/2/3/ 
m _{P } 
0.31 – 0.41 
1/2/ 
h _{P} 
excluded – 0. 45 
1/2/3/excluded/ 
Winter Wheat BBCH 39 


Range of R ^{2} increment 
Step in 
h _{A0} 
0.47 – 0.85 
1 
m _{P} 
0.01 – 0.04 
3 
h _{P} 
0.05 – 0.43 
2 
Rice BBCH 39 


Range of R ^{2} increment 
Step in 
h _{A0} 
0.36 – 0.66 
1 
m _{P} 
0.13 – 0.49 
2 
h _{P} 
excluded – 0. 13 
3/excluded/ 
While the number of the stepin of the multiple stepwise forward regression never change in the 12 plots of rice and winter wheat, it changes from plot to plot in winter rye. With regard to rice, the height of the cylindrical body enters as first variable, and the mass of the pendulum as the second, while the height of pivot point is the third variable, if not excluded. In winter wheat, as in rice, the height of the cylindrical body enters as first variable. But unlike rice, the height of pivot point h_{P} enters as second, and the mass of the pendulum as third variable, with no exclusion. In winter rye, all dependent variables enter as first or second into the regression in one or the other plot. And only the h_{P} is excluded in some plots.
Regarding the increment of R^{2}, the height of the cylindrical body has the highest influence on the angle of deviation in rice and winter wheat. The mass of the pendulum shows the second highest increment of R^{2} in rice, while it is negligible in winter wheat. When adding the height of the pivot point into the model, the increment in R^{2} is low in rice, while it enters as the second [page 68↓]variable in winter wheat. In winter rye, the influence of all three variables on the increment of R^{2} is low to medium, depending on the plot. The height of the pivot point is the only variable, that is sometimes excluded.
The regression equations are the final result of the stepwise forward multiple regression. The regression equations were calculated separately for each of the 12 plots of a optimisation trial. Table 17 shows the equations for the multiple regression between the three independent variables height of pivot point h_{P}, height of cylindrical body h_{A0}, and mass of pendulum m _{P}, and the measured angle of deviation, measured in winter rye at growthstage BBCH 39 and calculated for all 12 plots. In the first plot, the regression equation for the change of the angle y can be formulated as equation 12:
y = 89.9 106.4 h_{A0 }(m) 8.3 m _{P }(kg) 18.1 h_{P }(m). 
[12] 
The regression equation is highly significant with a goodness of fit of 0.90. That means that the measured angle of the deviated pendulum decreased 106° with an increase of 1 m of h_{P}, decreased 8° with 1 kg increase of m _{P}, and decreased 18° with an increase of 1 m of h_{A0}. This does not necessarily mean, that an increase of 1 m of h_{A0} is possible. In the case of winter rye at BBCH 39, an increase of 1 m height of cylindrical body would rise the sensor above the crop, and a measurement would be impossible. The change of the measured angle caused by a change in h_{A0} is much larger than the change caused by h_{P} or m _{P}.
Plot 
1 
2 
3 
4 
5 
6 
Intercept 
89.9 
88.2 
91.4 
95.8 
88.1 
22.8 
h _{A0 } (m) 
106.4 
104.2 
101.9 
88.2 
100.9 
52.7 
m _{P} _{} (kg) 
8.3 
8.6 
8.3 
8.5 
8.7 
3.1 
h _{P} (m) 
18.1 
17.3 
20.7 
22.6 
17.9 
excluded 
R ^{2} 
0.90** 
0.88** 
0.89** 
0.89** 
0.89** 
0.73** 
FM (kg m ^{2} ) 
1.412 
1.304 
1.596 
1.792 
1.320 
0.232 
Plot 
7 
8 
9 
10 
11 
12 
Intercept 
13.2 
63.0 
79.4 
75.7 
73.5 
68.9 
h _{A0} (m) 
36.7 
124.1 
120.3 
129.3 
126.7 
133.8 
m _{P} (kg) 
1.8 
6.4 
8.0 
7.7 
7.7 
7.3 
h _{P} (m) 
excluded 
7.5 
13.8 
11.3 
10.1 
8.1 
R ^{2} 
0.68** 
0.85** 
0.88** 
0.86** 
0.88** 
0.87** 
FM (kg m ^{2} ) 
0.192 
0.740 
1.092 
0.920 
0.816 
0.732 
** Significance > 0.99 * Significance > 0.95 † not significant 
 [page 69↓] 
The regression equations show considerable differences between the plots. The intercepts, for example, range between 13 and 90. The coefficients of the variable height of cylindrical body h_{A0} range between 134 and 37, while the coefficients of the variable mass of the pendulum m _{P} range between 2 and 9. The coefficients of the variable height of pivot point h_{P} range between 7 and 23, if not excluded as in plot six and seven. If the very extreme plots six and seven are not taken into consideration, the range of the coefficients is much narrower, but still differing.
By comparing the regression equations with the fresh mass of the plots, it becomes visible that several variables are influenced by the biomass itself. The intercept of the regression equation and the coefficient of the variable height of pivot point h_{P} indicate a strong influence of the fresh mass, while there is only a low similarity between the fresh mass and the coefficients of the variables mass of pendulum m _{P} and height of cylindrical body h_{A0}. The goodness of fit of the regression equations also change between the plots. They range between 0.85 and 0.90, except for the 6^{th} and 7^{th} plot, where they drop to 0.73 and 0.68 respectively. All R^{2}s were highly significant. The multiple regression for the 12 plots in winter wheat BBCH 39 and rice BBCH 39 presented similar results caused by the influence of the biomass and are given in the appendix.
Through keeping two pendulum settings constant, while only changing the third, it is possible to calculate the influence of one such setting on the measured angle of deviation of the pendulummeter. Simple linear regression was used to calculate the change of the measured angle of a plot, thus being able to see the change of the measured angle through the 12 plots of a test strip. Assuming, that some of the pendulum’s settings will show the influence of the biomass, as it was seen in the multiple regression equations. Calculation of the simple linear regression, as for the multiple regression, is based on the measurements obtained by the parameter optimisation trials.
The Effect of the Height of Pivot Point
Table 18 shows the results of the simple linear regression, their goodness’ of fit, and their corresponding fresh mass FM as a measure for the biomass, for a change of the independent variable h_{P} in all 12 plots for the crop winter rye measured at the growthstage BBCH 39. Constant was h_{A0} at 0.2 m, and m _{P} at 1 kg. The linear regression equations for the crops winter wheat and rice are given in the appendix. All regression equations in winter rye show highly significant R^{2}s, with values between 0.67 and 0.93, and an outlier for the plot with the lowest fresh mass. The intercepts of the regression equations for 12 plots range between 5 and 74, but most of them are in a smaller range between 36 and 74.

Winter Rye BBCH 39 

Plot 
1 
2 
3 
4 
5 
6 
Intercept 
65.1 
63.3 
67.0 
74.4 
63.8 
12.0 
Slope 
24.9 
23.8 
27.0 
29.3 
24.5 
4.1 
R ^{2} 
0.93** 
0.91** 
0.91** 
0.92** 
0.90** 
0.67** 
FM (kg m ^{2} ) 
1.412 
1.304 
1.596 
1.792 
1.320 
0.232 
Plot 
7 
8 
9 
10 
11 
12 
Intercept 
4.6 
35.7 
53.0 
48.0 
45.4 
39.5 
Slope 
1.0 
12.8 
21.2 
18.9 
16.8 
14.2 
R ^{2} 
0.11** 
0.76** 
0.88** 
0.84** 
0.81** 
0.82** 
FM (kg m ^{2} ) 
0.192 
0.740 
1.092 
0.920 
0.816 
0.732 
** Significance > 0.99 * Significance > 0.95 † not significant 
As in the multiple regression equations, the intercepts of the linear regression equation are all positive. Opposite to the intercepts, all the slopes of the linear regression equations are negative. That means that an increase of the variable height of the pivot point will always decrease the angle of deviation. The slopes in winter rye range between 1 and 29.
Both the intercepts and the slopes are strongly related to the amount of fresh mass of the corresponding plots. But while the intercept is positively influenced by the biomass, the slope is negatively related to it. This result supports the results obtained for the multiple regression.
Regarding the necessity to recalculate the measured angle when using different settings, the influence of the biomass itself and the large differences between each regression equation will cause difficulties. Since calibration curves exist for a change of the height of pivot point every 0.1 m, it was of interest to calculate the difference in the angle of deviation caused by a change of the height of the pivot point of 0.05 m. 0.05 m is the most likely setting that was not covered by the optimisation trials. Therefore, the slopes of the two most extreme equations, observed in the plots 4 and 7 in winter rye, were used to calculate the largest possible difference. In plot 4, a recalculated angle would be changed by 1.47°, while in plot 7 the angle would change by 0.05°. Thus giving a difference between the two most extreme equations of 1.4° as an error term for using one or the other equation for recalculating existing calibration curves for a change of the height of pivot point of 0.05 m.
 [page 71↓] 
The Effect of the Height of Cylindrical Body
Simple linear regression was used to calculate the change of the measured angle of a plot for a change of the variable height of the cylindrical body h_{A0}, while keeping the other two variables constant. Table 19 shows the results of the simple linear regression, their goodness’ of fit, and their corresponding fresh mass FM, for a change of the independent variable height of the cylindrical body h_{A0} in all 12 plots for the crop winter rye at the growthstage BBCH 59. The height of the pivot point was kept constant at 1.1 m, as was the mass of the pendulum at 1 kg.
All regression equations show highly significant goodness’ of fit, with values in winter rye between 0.74 and 0.93. The intercepts of the regression equations for 12 plots in winter rye range between 35 and 84, but most of them are lying in a smaller range between 63 and 84. As in the multiple regression equations, the intercepts of the linear regression equations are all positive. Opposite to the intercepts, all the slopes of the linear regression equations are negative. That means that an increase of the variable height of the cylindrical body will always decrease the angle of deviation. The slopes in winter rye range between 27 and 46. The intercepts and the slopes are both similar to the amount of fresh mass of the corresponding plots, but not as much as in the regression equations for the change of the pivot point. While the intercept is positively related to the biomass, the slope is negatively related to it. This result supports the results of the multiple regression for winter rye at BBCH 39.
Winter Rye BBCH 59


Plot 
1 
2 
3 
4 
5 
6 
Intercept 
76.7 
83.5 
83.6 
83.6 
81.2 
39.3 
Slope 
36.8 
32.7 
29.0 
26.5 
45.5 
43.6 
R ^{2} 
0.92** 
0.91** 
0.91** 
0.92** 
0.90** 
0.74** 
FM (kg m ^{2} ) 
1.640 
1.847 
2.003 
2.070 
1.295 
0.429 
Plot 
7 
8 
9 
10 
11 
12 
Intercept 
34.9 
63.0 
76.8 
77.9 
72.7 
65.4 
Slope 
37.8 
39.9 
38.4 
41.0 
40.4 
39.7 
R ^{2} 
0.77** 
0.91** 
0.93** 
0.92** 
0.90** 
0.94** 
FM (kg m ^{2} ) 
0.436 
1.051 
1.244 
1.271 
1.154 
1.089 
** Significance > 0.99 * Significance > 0.95 † not significant 
 [page 72↓] 
Regarding the necessity to recalculate the measured angle when using different settings, the influence of the biomass itself and the large differences between each regression equation will cause problems. Since measurements exist for a change of h_{A0} of 0.1 m, it was of interest to calculate the difference in the angle of deviation caused by a change of the height of the cylindrical body of 0.05 m. This is the most likely setting that is not covered by most of the optimisation trials. Therefore, the slopes of the two most extreme equations, in winter rye observed in the plots 4 and 5, were used to calculate the largest possible difference. In plot 4, a recalculated angle would be changed by 2.28°, while in plot 5 the angle would change by 1.33°. Thus giving a difference between the two most extreme equations of 0.9° as an error term for using one or the other equation for recalculating existing calibration curves for a change of h_{A0} of 0.05 m. These differences were much higher than the differences calculated for a change of h_{P}.
The Effect of the Mass of the Pendulum
Simple linear regression was used to calculate the change of the measured angle of a plot for a change of the variable mass of the pendulum m _{P}, while keeping the other two variables constant. Table 20 shows the results of the simple linear regression, their goodness’ of fit and their corresponding fresh mass FM, for a change of the independent variable m _{P} in all 12 plots.
Winter rye was calculated for the growthstage BBCH 39. The height of the pivot point is kept constant at 1.1 m, while h_{A0} is a constant at 0.2 m. All regression equations show highly significant goodness’ of fit, with values in winter rye between 0.86 and 0.98.
Winter Rye BBCH 39


Plot 
1 
2 
3 
4 
5 
6 
Intercept 
41.3 
41.0 
40.9 
45.7 
41.2 
11.1 
Slope 
4.8 
5.0 
4.9 
5.0 
5.4 
3.5 
R ^{2} 
0.98** 
0.98** 
0.98** 
0.98** 
0.98** 
0.92** 
FM (kg m ^{2} ) 
1.412 
1.304 
1.596 
1.792 
1.320 
0.232 
Plot 
7 
8 
9 
10 
11 
12 
Intercept 
6.1 
25.1 
33.8 
31.3 
31.5 
28.3 
Slope 
1.9 
4.4 
5.1 
5.1 
5.3 
5.2 
R ^{2} 
0.86** 
0.95** 
0.98** 
0.98** 
0.98** 
0.98** 
FM (kg m ^{2} ) 
0.192 
0.740 
1.092 
0.920 
0.816 
0.732 
** Significance > 0.99 * Significance > 0.95 † not significant 
 [page 73↓] 
The intercepts of the regression equations for 12 plots in winter rye range between 6 and 46, but most of them are lying in a smaller range between 25 and 46. As in the multiple regression equations, the intercepts of the linear regression equation are all positive. Opposite to the intercepts, all the slopes of the linear regression equations are negative. That means that an increase of the variable mass of the pendulum will always decrease the angle of deviation. The slopes range at low values between 1.9 and 5.4.
Regarding the necessity to recalculate the measured angle when using different settings, the influence of the biomass itself and the large differences between each regression equation will cause difficulties. But due to the smaller range of the slopes and the low values of the slopes, the differences between the lowest and the highest slopes is not as big a problem as with h_{A0} and h_{P}. Since measurements exist in the optimisation trials for a change of m _{P} in increments of 0.5 kg, it was of interest to calculate the difference in the angle of deviation caused by a change of the mass of the pendulum of 0.1 kg, a change that can be encountered by constructing a pendulum of different materials. Therefore, the slopes of the two most extreme regression equations, here observed in the plots 5 and 7, are used to calculate the largest possible difference. In plot 5, a recalculated angle will change by 0.54°, while in plot 7 by 0.19°. Thus giving a difference between the two most extreme equations of 0.4° as an error term for using one or the other equation for recalculating existing measurements for a change of m _{P} by 0.1 kg.
The Effect of the Length of the Pendulum
The influence of the length of the pendulum on the change of the angle of deviation was not determined since the length of the pendulum is the distance between the height of the pivot point and the height of the cylindrical body. In a contact measurement as it is with the pendulummeter, the height of the cylindrical body is of importance. If the height of the cylindrical body is a constant, the length of the pendulum can be expressed as the height of the pivot point, as it is done in this context.
The strongest influence on the angle of deviation has the height of the cylindrical body h_{A0}, followed mostly by the mass of the pendulum, and the height of the pivot point is often the parameter with the lowest influence if not excluded. The coefficient of h_{A0} is the highest, followed by h_{P}, and the lowest coefficient is m _{P}. The fresh mass is influencing the multiple regression between the three pendulum parameters versus the angle of deviation to various degrees. Due to this large influence of the biomass on the coefficients and the intercepts, a recalculation of the angle of deviation into an untested parameter setting leads to a large error, and [page 74↓]a calibration is advisable if not necessary. So far, it is not possible to identify the factors of the biomass that influence the differences in the regressions.
The linear regressions between the single parameters h_{A0}, h_{P} and m _{P} versus the angle of deviation show changes of the equation with a change in biomass for the slopes of the regression or the intercepts or both. Therefore, a recalculation of an angle of deviation by the regression equation results always in a bias due to the biomass, and a recalibration seems advisable.
The slopes of the parameter h_{P} are negative in the linear regression with the angle of deviation because the angle in the potentiometer becomes more acuteangled, provided h_{A0} is the same during the measurement. The slopes of the parameter h_{A0} are negative due to the contact with higher parts of the stems. Several researchers (SPIEWOK 1970, GOWIN 1980, SKUBISZ 1984, NIKLAS 1990, CROOK & ENNOS 1994) reported an increase in bending rigidity E I from the ear to the root. The slopes of the parameter m _{P} are negative due to a deeper bending of the stems, thus narrowing the angle at the potentiometer. HITAKA 1968 used higher masses at ear base to deviate the stem more deeply.
A change of these relationships during crop growth is most likely, since several researchers found a change of the modulus of elasticity E during crop growth (GOWIN 1980, GAWDA & HAMAN 1983, SKUBISZ 1984, O’DOGHERTY et al. 1989, USREY et al. 1992, MOLDENHAUER & MOLDENHAUER 1994, O’DOGHERTY et al. 1995), although the second moment of the area I is not changing during crop growth (O’DOGHERTY et al. 1995).
Since determining the actual plant mass in the field is a timeconsuming and destructive method without using the pendulummeter as a sensor, most research was done relating crop density in terms of tiller density and stem density to yield, diseases, and crop models. Therefore, it is of high interest to know the relationship between the measurements of the pendulummeter and other, here called secondary, plant parameters such as plant height, stem or tiller density, and with regard to rice the number of plant hills.
The relationship between the above mentioned plant parameters and the measured angle of deviation of the pendulummeter was calculated using simple linear regression. Measurements were done with 2.5 m s^{1} velocity and 75 Hz. The results for winter rye are shown in table 21, where the first row shows the BBCH growthstage, and the next rows the used pendulum [page 75↓]settings. The first column gives the related plant parameter, and the second column gives the regression parameters of those plant parameters, and all plant heights are calculated in meters.
The results show a highly significant goodness of fit of 0.59 between the measured angle and the number of tillers for the growthstage BBCH 59, decreasing to a significant goodness of fit of 0.55 at the next growthstage. The standard error of estimate of the regression equation is high with values between 13 and 15. No values were obtained for the earlier growthstages due to a lack of time.
The regression results for the plant parameter average plant height are similar, with highly significant goodness of fit of 0.90 to 0.95 for the average plant height. The exception is the first measured growthstage BBCH 32, where the average plant height has a slightly lower goodness of fit with 0.81. The standard error of estimate is in general medium to high. The average plant height shows a goodness of fit with the model in terms of goodness of fit and standard error. The goodness of fit for the average plant height is increasing with the growthstages. The slopes for the average plant height are all positive, while the intercepts are all negative. The slopes for the number of tillers or stems are all zero, with mostly negative intercepts. Except for the last growthstage, where it is slightly positive.
As a matter of fact, the plant height is the parameter that differentiated much more than the number of tillers or stems.
GrowthStage 
BBCH 32 
BBCH 39 
BBCH 59 
BBCH 69 

h _{P} (m) 
0.3 
0.4 
0.8 
1.1 

h _{A0} (m) 
0.1 
0.2 
0.6 
0.8 

m _{P} (kg) 
1 
3 
0.5 
1 

Number of tillers or stems 
Intercept 
– 
– 
27.7 
33.6 
Slope 
– 
– 
0.3 
0.2 

R² 
– 
– 
0.59** 
0.55 * 

SE 
– 
– 
15.00 
13.85 

Average plant height 
Intercept 
10.3 
39.5 
34.8 
24.0 
Slope 
142.1 
129.7 
80.2 
45.4 

R² 
0.81** 
0.90** 
0.94** 
0.95** 

SE 
2.76 
4.45 
5.74 
4.49 

** Significance > 0.99 * Significance > 0.95 † not significant – no measurements 
 [page 76↓] 
The results of the linear regression between the two plant parameters and the measured angle of deviation for winter wheat are shown in table 22, where the first row shows the BBCH growthstage, and the next row the used pendulum settings. The first column gives the related plant parameter, and the second column gives the regression parameters. All plant heights are calculated in meters. Measurements were done with 2.5 m s^{1} velocity, and 75 Hz frequency. The results show highly significant goodness of fit of 0.92 between the measured angle and the number of tillers at the growthstage BBCH 39, with a very low standard error of estimate. The growthstage BBCH 39 is the only one where the tiller number was counted.
The regression results for the average plant height are similar, with highly significant goodness of fit of 0.72 to 0.85 for the average plant height versus angle of deviation. The exception was the first measured growthstage BBCH 34, where the average plant height shows no relation to the measured angle. The standard error of estimate is low to medium for the average plant height.. The goodness of fit for the average plant height is indifferent for the growthstages. The slope for the number of tillers or stems is zero.
As a matter of fact in the winter wheat field, used here for this regression calculations, the plant height and the tiller or stem density are differentiating similarly in the same plots.
GrowthStage 
BBCH 34 
BBCH 39 
BBCH 59 
BBCH 69 

h _{P} (m) 
0.5 
0.5 
0.8 
0.7 

h _{A0} (m) 
0.1 
0.3 
0.4 
0.3 

m _{P} (kg) 
1 
1 
1 
1 

Number of tillers or stems 
Intercept 
– 
2.6 
– 
– 
Slope 
– 
0.2 
– 
– 

R ^{2} 
– 
0.92** 
– 
– 

SE 
– 
3.85 
– 
– 

Average plant height 
Intercept 
12.6 
155.1 
60.3 
37.9 
Slope 
53.7 
343.4 
155.3 
111.4 

R ^{2} 
0.05 † 
0.84** 
0.85** 
0.72** 

SE 
4.57 
5.34 
5.97 
5.37 

** Significance > 0.99 * Significance > 0.95 † not significant – no measurements 
 [page 77↓] 
The results of the linear regression between the plant parameters, average plant height and tiller density, and the measured angle of deviation for rice are shown in table 23. The procedure was the same as in winter rye and winter wheat. The results show a highly significant goodness of fit of 0.91 between the measured angle and the number of hills for the growthstage BBCH 39, decreasing to a significant goodness of fit of 0.33 at the next growthstage, and reaches a highly significant goodness of fit of 0.72 for the growthstage BBCH 65.
There is also a highly significant goodness of fit of 0.93 between the measured angle and the number of tillers for the growthstage BBCH 39, and an R^{2} of 0.85 at the growthstage BBCH 65. The number of hills and the number of tillers show low to medium standard errors. The regression results for the average plant height show lower values, with significant low R^{2} between 0.40 and 0.34. The standard error of estimate is in general medium to high. The slopes for the number of tillers and for the number of hills regression equations are all zero, with mostly negative intercepts.
As a matter of fact, and opposite to winter rye, the plant height is the parameter that differentiated the least, much less than the number of tillers or stems.
GrowthStage 
BBCH 39 
BBCH 49 
BBCH 65 

h _{P} (m) 
0.5 
0.5 
0.4 

h _{A0} (m) 
0.1 
0.1 
0.2 

m _{P} (kg) 
1 
2 
0.5 

Number of hills 
Intercept 
1.3 
12.4 
20.8 
Slope 
0.8 
0.5 
2.3 

R ^{2} 
0.91** 
0.33 * 
0.72** 

SE 
2.30 
5.39 
6.76 

Number of tillers or stems 
Intercept 
1.6 
– 
3.8 
Slope 
0.1 
– 
0.1 

R ^{2} 
0.93** 
– 
0.85** 

SE 
2.01 
– 
4.89 

Average plant height 
Intercept 
68.9 
41.4 
96.1 
Slope 
209.5 
139.1 
194.2 

R ^{2} 
0.40 * 
0.34 * 
0.36 * 

SE 
5.84 
5.38 
10.21 

** Significance > 0.99 * Significance > 0.95 † not significant – no measurements 
 [page 78↓] 
From the view of a biomass sensor is the possibility of sensing additional plant parameters, such as plant height and tiller density, most interesting, since biomass is not a common basis for decision making in agriculture. Instead of biomass, other plant parameters, such as tiller density and plant height, are widely used. The ability of the pendulummeter to sense these plant parameters depends mainly on the factor that is more heterogen. That means if the plant height is the least heterogen parameter as in rice, the biomass sensor determines with a high goodness of fit the number of tillers, but the angle of the pendulummeter has no or just a low relationship with the plant height. If the plant height is much more heterogen than the tiller density as in winter rye, the biomass sensor has a high goodness of fit with the height of the plants, but the angle of the pendulummeter has no or only a low relationship with the tiller density. If both factors, the tiller density and the plant height are equally heterogen, the biomass sensor can determine both factors with similar and high goodness’ of fit, mostly with an R^{2} higher than 0.7.
In standard agricultural literature concerning rice, the number of hills is well correlated with biomass, but in these tests it shows a good performance only once, but in the other test there is a low R^{2}, which might be caused by uneven damage by rats.
When using a sensor with a dynamic measurement principle, it can be assumed that the velocity of the carrier has a major influence on the measurements. To clarify the influence of the velocity on the angle of deviation, tests were conducted with an identical parameter setting but different velocities. The velocities ranged between 0.5 m s^{1} and 3.5 m s^{1}, arranged in 0.5 m s^{1} steps, but the five repeats were not exactly in the wanted 0.5 m s^{1} order, due to the handpushed acceleration. The tests were done for all crops at different growthstages, usually on a 5 m^{2} plot. Due to the high similarity of the results are the majority of the tests given in the appendix, and an exemplary result is presented here. As shown in figure 26 is the speed of elementary influence on the measured angle of deviation, tested with the pendulum setting 0.8 m of h_{P}, 0.3 m of h_{A0}, and 1 kg of m _{P}, and a frequency of 75 Hz.. Also given in figure 26 are the linear and square regressions, their formula and goodness of fit for the relationship between carrier speed and angle of deviation in one plot in winter rye at BBCH 39.
The carrier speed changes the measured angle of deviation from 31° at a velocity of 0.5 m s^{1} to 44° at a speed of 3.5 m s^{1}. The relationship is slightly better described by the square regression equation than by the linear equation, though the difference in the goodness of fit is small, 0.99 [page 79↓]and 0.97 respectively, for velocities less than 4 m s^{1}. The linear regression equation shows an increase of 4.4° with a rise of the velocity of 1 m s^{1}. Although it is not possible to test the pendulummeter without speed, the linear regression equation calculates an intercept of 27° for a zero speed.
Figure 26: The influence of carrier velocity on the measured angle of deviation.  

Since in the aforementioned optimisation trials the biomass was showing a considerable influence on the angle of deviation, one velocity test was done in winter wheat 1999 over 60 meters, or 12 plots respectively. Of the twelve plots, only the plots 4  12 were used, since the high speeds of 3.5 m s^{1} were not reached in the first three plots.
The influence of the carrier speed on the angle of deviation in plots with different biomass, or initial angle of deviation at a speed of 0.5 m s^{1} respectively, are shown in figure 27 for a visual impression, and in table 24 for the linear regression equations and goodness’ of fit. The crop was measured in growthstage BBCH 49, with the pendulum setting 1.0 m h_{P}, 0.3 m h_{A0}, 1 kg m _{P}, and 75 Hz measurement frequency.
As shown in table 24, the goodness of fit R^{2} is for the most plots higher than 0.9, except for the plots 6 and 7, where the goodness of fit is 0.8, and plot 5, where the goodness of fit is only 0.03. As an explanation has to be considered, that the highest biomass, or in that case, the highest initial angle of deviation, is in plot 4. In plot 5, and to a much lesser degree also in the plots 6 and 7, the angles are biased at high carrier speeds by the high deviation in plot 4. Nevertheless, in all plots except plot 5 is a close relationship between the speed and the angle of deviation.
 [page 80↓] 
Figure 27: Linear regressions in 9 plots for the change of the measured angle of deviation at different carrier velocities.  

Visible in figure 27 is the influence of the initial angle, hence the biomass: the higher the initial angle at a speed of 0.5 m s^{1}, the higher the slopes becomes, as well as the intercepts, for the regression between the carrier speed and the angle of deviation. Plot 5 shows here no change of the angle of deviation with the change in velocity (black dotted line in figure 27).

Linear Regression Equation 
Goodness of Fit 
Angle of Deviation (°) 

Plot 
Slope 
Intercept 
R ^{2} 
at 0.5 m s ^{1} 
at 3.3–3.8 m s ^{1} 
4 
5.11 
15.7 
0.99** 
19.09 
34.38 
5 
0.19 
4.9 
0.03 † 
3.83 
2.45 
6 
2.94 
0.8 
0.81** 
2.38 
12.70 
7 
2.49 
1.2 
0.88** 
3.36 
12.09 
8 
2.60 
2.1 
0.92** 
4.62 
11.61 
9 
3.02 
6.1 
0.98** 
7.92 
16.74 
10 
3.69 
14.1 
0.99** 
16.42 
27.33 
11 
4.67 
14.1 
0.99** 
17.81 
31.09 
12 
2.47 
7.9 
0.97** 
9.96 
16.55 
** Significance > 0.99 * Significance > 0.95 † not significant 
 [page 81↓] 
There also good evidence that there are similar tendencies between the intercept, a zero speed assumed, and the angle of deviation at a speed of 0.5 m s^{1}, or at a speed of 3.3 to 3.8 m s^{1}. The slopes are varying between 2.47° and 5.11° for a change of velocity of 1 m s^{1}, not taking plot 5 into account.
To correct the angle of deviation in case of 1 m s^{1} velocity changes of the tractor in the field would result in a difference of more than 2.5°, depending on which slope would be used to recalculate the angle. Considering the highest possible change of the angle of deviation of 5° in plot 4 when the speed was changed by 1 m s^{1}, that difference is high. Due to the fact, that the angle versus speed relationship is always close for different cultures and growthstages, and the biasing effect of the biomass itself, the other speed results are given in the appendix.
Discussion
The angle of deviation is in the range of less than 4 m s^{1} closely related to the speed. The goodness of fit is always very high, except when plots with a low biomass follow right behind a plot with a high biomass. The square goodness of fit is almost perfect in the tested speed range, but the linear regression is almost as good as the square regression. The difference is very similar to the forceangle relation of the pendulummeter in figure 9, but according to equation 2, the mass moment of inertia is dependent on the square power of the carrier speed. Regarding the small differences between the square and linear regressions, a linear regression is sufficient to describe the angle versus speed relationship. According to equation 2, the mass moment of inertia is changed by a factor 6.25 when the speed increases from 1 m s^{1} to 2.5 m s^{1}. The bending moment, according to equation 3, is not depending on the carrier speed, hence it is considered a constant in the speed measurement. The friction is also not changing with speed as several works stated (RICHTER 1954, SHINNERS et al. 1991, USREY et al. 1992). Hence, the mass moment of inertia, together with the higher number of stem tested per unit time, is the cause of the changes in the angle of deviation with an increased speed.
The speedangle regressions clearly show an influence of the biomass, meaning a high angle at low speeds will be increased much more by an increasing speed than a lower angle. A recalculation during field measurements by using the slopes of the regression results in a large error. Therefore, it is advisable to keep the speed constant within the field, or within the measurements that are compared.
The speed might have biased the goodness of fit in the parameter optimisation trials, because while pushing the carrier, little changes in speed of 0.5 m s^{1} were always possible and included in the goodness of fit of the parameter optimisation trials.
 [page 82↓] 
The force which is applied by the wind upon the plants results in movements and vibrations of the stems, forcing the stems to bent. Mechanically the force of the wind is similar to the force the biomass sensor is putting on the plants.
The effect of the headwind in the range of 0 to 4 m s^{1} wind speed in rice at BBCH 65 is illustrated in figure 28. The plant height of the 5 m^{2} plot was on average 65 to 70 cm, the pendulummeter was adjusted to 0.6 m h_{P}, 0.3 m h_{A0}, 0.497 kg m _{P}, and the carrier speed was 1 m s^{1}. The blue dots are the plot averages and the differences between the five replicates are almost as high as the effect of the constant headwind. The linear regression is not significant with an R^{2} of 0.13, and the square regression is significant with an R^{2} of 0.27. The intercepts of the regression equations are, in these cases, the average measurements without wind. Nevertheless, there is to some degree a tendency to increase the angle of deviation with an increase of headwind higher than 2 m s^{1}.
Figure 28: Effect of wind speed of head wind on the measurements.  

The effect of the water height of standing water in irrigated rice at BBCH 39 on the measurements of the pendulummeter is shown in figure 29. The rice crop was measured with various water heights, ranging of 0.5 cm to 11.5 cm. The plant height in the 5 m^{2} plot was on [page 83↓]average 0.4 m, the pendulummeter was adjusted to 0.5 m h_{P}, 0.1 m h_{A0}, 0.519 kg m _{P}, 75 Hz frequency, and the carrier speed was 1 m s^{1}. The dots symbolise the replicates for the same water height. The linear regression is highly significant with an R^{2} of 0.27. The intercept of the regression equation is in this case, the average measurements with low water heights, nevertheless, the slope of the linear regression is very small, and the effect of the recommended water height of 3 cm is rather indifferent.
Figure 29: Effect of water height in irrigated rice on the biomass measurements.  

Weeds are a major problem in plant production and their occurrence in patches with high population densities of one or several weed species give reason to determine the possible effect of two common weed species, creeping thistles and loose silkybent, on the measurements.
The Effect of Creeping Thistles
With their strong woody stems, creeping thistles (Cirsium arvense (L.) Scop.) are different from the slender cereal stems. The influence of this weed species on the measurements was tested in a 5 m^{2} winter wheat plot at growthstage BBCH 39. In this plot was a single thistle 10 cm higher than the surrounding crop. Figure 30 shows the online measurements of the plot with the thistle and the same online plot measurements when the thistle was cut out. The pendulummeter was adjusted to 0.8 m h_{P}, 0.1 m h_{A0}, 0.635 kg m _{P}, 75 Hz measurement frequency, and 2.5 m s^{1} carrier speed. The calculated plot average of the angle of deviation is 16.2° with the thistle, and 12.6° [page 84↓]without the thistle, resulting in a difference of 3.6°, or 25 % of the plot average respectively, due to the biasing strength of one single thistle. But the single measurements recorded in the plot show a much larger difference than the plot averages. The black arrow indicates the position of the thistle, up to where the measurements are running similarly, and behind that point the blue dotted line shows the large bias of the thistle by splitting up with the other measurement line.
Figure 30: Nonreduced measurement data of the pendulummeter in winter wheat including and excluding a single thistle in the crop.  

The Effect of Loose SilkyBent
Loose silkybent (Apera spicaventi (L.) Pal. Beauv.) often appears in numbers after heading of the cereal crops. The effect of this weed species was tested in a 5 m^{2} plot of winter wheat at growthstage BBCH 69. In the plot were 171 silkybents with an on average 20 cm higher plant height than the surrounding crop. The silkybents were distributed all over the plot. The pendulummeter was set to 1.1 m h_{P}, 0.3 m h_{A0}, 0.657 kg m _{P}, 75 Hz frequency, and 2.5 m s^{1} carrier speed. The calculated plot average is 55.1° including all of the silkybents, and 53.7° without the silkybents, resulting in a difference of 1.4°, or less than 5 % of the plot average.
The Effect of Day and Daytime
Since the use of the pendulummeter for sensing online crop biomass for sitespecific applications is not limited to a few hours, the time of the measurements during the day and on [page 85↓]several days may have an influence on the biomass measurements. It follows from this concern that a winter rye crop at BBCH 39 was measured with the same parameter setting on various daytimes and on two consecutive days in May 1998. The morning dew and the slight rain of 0.6 mm as the two most important weather conditions on that day are shown in the figure as well. Figure 31 gives the results of the measurements as a day profile for two plots of different growth pattern. The pendulummeter was adjusted to 0.8 m of h_{P}, 0.3 m of h_{A0}, 0.595 kg of m _{P}, 75 Hz measurement frequency, and 2.5 m s^{1} carrier speed.
Figure 31: Measurements of the pendulummeter during various times of two consecutive days in two plots with different growth pattern.  

On the 3^{rd} of May 1998, plot 1 has an average of 36.3° of all measurements during that day, while in plot 2 the average is only 4.5°. The standard deviation of all measurements of that day is 0.35° in plot 1, and 0.34° in plot 2. The measurements are stabile for the two plots during the day. The average of the measurements of the 4^{th} of May is 39.6° for plot 1, and 4.3° for plot 2. The difference of the average measurements from the 3^{rd} of May to the 4^{th} of May is +3.3° for plot 1, and 0.2° for plot 2. Plot 1 has a high biomass as indicated by the large angle of deviation and has a large increment during night time, while plot 2 has a low average angle, or a low biomass respectively, and no change during night time.
The Effect of GrowthStage
Crop growth is determined by a large increase in crop biomass, and between growthstages BBCH 30 to 69 in a large increase in plant height. Because of the high accuracy of determining biomass of the pendulummeter, a biasing effect of rapid growth might be possible. Therefore, [page 86↓]the square regressions of the 1998 fresh mass versus angle relationship are pooled in winter rye to test for the possibility of joint regression equations for different growthstages. Measurements were done with the pendulum setting of 0.8 m h_{P}, 0.3 m h_{A0}, 0.595 kg m _{P}, 75 Hz measurement frequency, and 2.5 m s^{1} speed. Regressions were then pooled, and goodness of fit as well as standard error of estimate of the square regression was determined and compared to the number of days between the growthstages. Figure 32 illustrates the fresh mass versus angle relationships for the growthstages BBCH 39 and 59, and their respective regression equations.
Figure 32: Square regressions for two growthstages in winter rye 1998.  

Remarkable is the closeness of the lower regression slopes of the growthstages BBCH 39 and 59, while the upper slopes differ almost 30°. This result is supporting the growth pattern evident in figure 31 for the measurements during two consecutive days, where the plot with a low biomass didn’t show a change in the measurements, whereas the plot with a high biomass showed crop growth within two days. Since in the year 1998 there were only 11 days between those growthstages, the difference of 30° between the two regression lines at BBCH 39 and 59 in 11 days resulted in a crop growth of almost 3° per day on average. Hence, rapid crop growth can bias measurements taken over several days in one field, or taken on one day in a field with differences in crop development. The pooled square regression between the growthstage BBCH 39 and 59 has following equation 13:
y = 8.58 x^{2} +48.19 x 7.23 
[13] 
The pooled square regression results in an R^{2} of 0.64 with a standard error of the regression equation of 12.40, and runs between the two regression lines given in figure 32.
 [page 87↓] 
The Effect of Variety, Year, and Season
With regard to irrigated rice, two different varieties from two different seasons and two different seeding methods were pooled together by a square regression. Figure 33 shows the resulting square regression of the angle versus dry mass with confidential limits for IR 64 and IR 72. While IR 64 is a machinetransplanted irrigated rice grown in the dry season, IR 72 is a directseeded irrigated rice grown in the wet season. Both varieties were tested with a setting of 0.5 m h_{P}, 0.2 m of h_{A0}, m _{P} of 1 kg, 75 Hz frequency, and 2.5 ms^{1} carrier speed. Though they were tested at different dates, they were both in the growthstage BBCH 65. The pooled square regression for them has an R^{2} of 0.94, and a standard error of the regression of 3.53. The estimated 95 % confidential limits are narrow, but more than 5 % of the dots are out of the limits.
Figure 33: Pooled square regression in rice for dry season, transplanted IR 64, and wet season, directseeded IR 72.  

The yearly influence on the biomass versus angle relationship in winter rye was detected at the growthstage BBCH 39. The pendulum was set to 1.1 m h_{P}, 0.3 m of h_{A0}, m _{P} of 0.657 kg in the years 1998 and 1999. A pooled square regression is obtained with an R² of 0.88, and a standard error of the regression of 7.59, for the dry mass versus angle relationship with the following regression equation 14:
y = 8.8678x^{2} + 53.529x 5.873. 
[14] 
A pooled square regression of two different winter wheat varieties, ZENTOS and BATIS, in two [page 88↓]different years 1998 and 1999, tested at BBCH 69 with a pendulum setting of 1.1 m h_{P}, 0.3 m h_{A0}, and 0.657 kg m _{P}, results in an R^{2} of 0.75 with a standard error of the regression of 3.12 and following equation 15:
y = 1.5496x^{2} + 13.336x +34.475. 
[15] 
The Influence of BiomassHeightRatio
Regarding the influence of bending moment and bending distance on the angle of deviation, it is so far not clear, whether the crop height or the crop density, hence the biomassheight ratio can bias the measurements. Figure 34 shows the result of: first, the 12 plots with large changes in crop height, and second, the change in biomass versus angle relationship without the influence of the crop height. Therefore, a winter wheat crop at BBCH 69 was tested with the parameter setting of 0.8 m h_{P}, 0.3 m of h_{A0}, m _{P} of 0.595 kg, 75 Hz measurement frequency, and 2.5 m s^{1}. A test strip of 12 plots with natural differences in crop height was measured, and then one plot with a high crop height was systematically thinned by cutting randomly 25 stems out of the plot between the measurements.
Figure 34: Angle versus biomass relation for 12 plots of natural biomass and of one plot randomly thinned out in increments of 25 stems.  

The two regression lines start at the same point, but spread wider the lower the amount of biomass gets in the plot. The lower parts of the regression lines have differences of more than 10°, with the systematically thinned plot being higher than the natural plot with a low plant height. That indicates that the biomassheightratio can bias the measurements, since the crop height has a larger influence than the crop density regarding the same amount of biomass.
 [page 89↓] 
The Effect of Stem Inclination
Stem inclination is usually the first step of lodging in cereals. Due to the measurement principle, a permanent lean of the stem from the vertical position may effect the measurements. Therefore, one winter wheat plot and one winter rye plot were tested in both directions of the stem inclination at different growthstages to clarify the biasing effect of inclination. Table 25 shows the results of the measurements for the one way with a slight inclination of less than 5°, and the return way against the same slight inclination. In the case of winter wheat, there is only a minor difference of 0.5° between the two measurement directions at BBCH 32 and 39, which increases to almost 1° at later growthstages, where the slight inclinations of the stems become visible as a 5° difference. The difference between the measurement directions is much higher in winter rye, with 0.2° at BBCH 39, and increasing to 1.5° – 45° at later growthstages, when the stem is slightly inclining and the ear is turning downwards.
BBCH GrowthStage 
3234 
39 
59 
69 
Winter rye; 0.8 m h _{P} , 0.3 m h _{A0} , 1.000 kg m _{P} , 75Hz, 1 m s ^{1} 

one way (°) 
– 
26.69 
45.09 
64.27 
return way (°) 
– 
26.55 
43.68 
59.79 
difference (°) 
– 
0.14 
1.41 
4.48 
Winter wheat; 1.1 m h _{P} , 0.1 m h _{A0} , 0.696 kg m _{P} , 75 Hz, 1 m s ^{1} 

one way (°) 
26.69 
41.52 
61.10 
– 
return way (°) 
27.17 
41.97 
61.98 
– 
difference (°) 
0.47 
0.45 
0.88 
– 
For an inclination of 30° of winter wheat stems at BBCH 69, the results are shown in table 26. That test was done with two different masses of the pendulum, 2 kg and 0.657 kg. The results show a difference of less than 1° for both masses, with a higher difference for 2 kg mass of the pendulum.
Winter wheat; 30° Inclination of the stem, 1.1 m h _{P} , 0.3 m h _{A0} , 75 Hz, 1 m s ^{1} , BBCH 69 

m _{P} (kg) 
2.000 
0.657 
Measurement in one way (°) 
27.73 
45.24 
Measurement in return way (°) 
28.72 
46.01 
Difference (°) 
0.99 
0.77 
 [page 90↓] 
The Effect of the Depth of the Tramline
The effect of the depth of the tramline on the angle of deviation was determined indirectly by changing the two pendulum parameters h_{P} and h_{A0} simultaneously in 12 plots with 75 Hz and 2.5 m s^{1}. Though that was not usually a part of the optimisation trials, one of the optimisation trials in rice gave sufficient data to calculate this effect. Based on an original measurement with the pendulum parameter setting of 0.6 m h_{P}, 0.3 m h_{A0}, and 1 kg m _{P}, the measured angles of deviation ranged between 16.6° and 55.4°. A tramline depth of 10 cm would result in the parameter setting of 0.5 m h_{P}, 0.2 m h_{A0}, and 1 kg m _{P}, which had a range in angles of deviation from 34.6° to 69.4°. The bias due to the depth of the tramline of 10 cm is here the difference between the two settings, hence the bias would range from 14.0° to 18.4°, approximately 30 % to 100 % of the original value.
Headwind in the range of 0 m s^{1} to 4 m s^{1} has a low influence on the angle of deviation of the pendulummeter. The reduction of the angles from 0 m s^{1} to 2 m s^{1} might be caused by slight nonvisible changes in the position of the stems, while reclining back into the upright position, which was reported by HITAKA 1968 who used this difference to determine lodging susceptibility. The increase in angles between the wind speeds 2 m s^{1} and 4 m s^{1}, and the much better fit of the square regression, supports the results of HITAKA 1968 who found a similar relation between the wind force on one tiller and the wind speed. Nevertheless, the reported bending angle of 10° at a wind speed of 3 m s^{1} is much larger than the change in the angle of deviation of the pendulummeter. The pendulummeter measurements are much less influenced by the wind than the stems themselves, probably because the cylindrical body touches the stems at much lower heights than the wind is penetrating into the crop. But even higher wind speeds will have a larger influence on the angle of the pendulummeter regarding the results of HITAKA 1968.
The effect of water height on the pendulummeter is low and the influence is only visible at 8 cm and 12 cm water height, which is not the usual water height in irrigated rice. Recommended are 3 cm. Although water height might change the angle through different growth pattern of the elongated basal internodes (WU 1965), it is itself negligible as a biasing factor.
The effects of weeds can range from not pronounced to a strong influence on the angle of deviation, depending on the strength of the stem of the weed species, their growthstage, plant height, and their number. Loose silkybent has a very thin stem, and is biasing the pendulummeter only slightly when in large numbers. Creeping thistles can bias the biomass measurements [page 91↓]even in small numbers, due to the thick stem, high rigidity of the stem, and the large plant height. Due to the weed distribution in patches (WARTENBERG 1996, DAMMER et al. 1998, DAMMER 1999), the measurements are further biased. Similar problems were reported for the diskmeters and platemeters, where the goodness of fit dropped to zero because of weeds and other species in grass stands (POWELL 1974, STOCKDALE 1984, KARL & NICHOLSON 1987, LACA et al. 1989). VIRKAJÄRVI & MATILAINEN 1995 reported a relation between R^{2} and uniformity of botanical composition.
The measurements are stabile during one day, but rapid growth can change the angle of deviation from one day to the other, thus also biasing the goodness of fit calculated in the parameter optimisation trials, which took usually 2 days for the measurements. The 0.6 mm of rain in the second day didn’t influence the measurements, although HITAKA 1968 reported an increase in breaking strength due to wetness. Daily growth will also bias the measurements within large fields where there are sites with plants in different stages of development, like BBCH 32 and BBCH 34. The growthstages in European cereals with rapid growth are BBCH 32 to BBCH 59 depending on the weather conditions. Rapid plant growth needs high temperatures, in cool temperatures there is much more time between the growthstages, hence the bias is much smaller within a field. Irrigated rice shows a very regular growth and there the bias is much smaller.
The growthstages usually need different regression equations, although a pooling in several cases is possible but results in a large standard error of the regression and a decline of R^{2}. Consequently are the parameter settings well suited in one growthstage different from the favourable settings in another growthstage, thus calling for different favourable settings for most growthstages. It follows, that using a single parameter setting for all growthstages and crops doesn’t seem advisable, because for choosing a favourable pendulum setting this setting has to be related to plant size which is varying with seasons and years. The differences in the regression equations for different growthstages was often stated for the diskmeters and platemeters (POWELL 1974, CASTLE 1976, EARLE & MC GOWAN 1979, BAKER et al. 1981, MICHELL & LARGE 1983, STOCKDALE 1984, PALAZZO & LEE 1986, SCRIVNER et al. 1986, KARL & NICHOLSON 1987, PETERSON & HUSSEY 1987, BRYAN et al. 1989, GONZALEZ et al. 1990, MOULD 1992, VIRKAJÄRVI & MATILAINEN 1995, HARMONEY et al. 1997). Changes in bending rigidity (LACA et al. 1989) and dry matter content (POWELL 1974, STOCKDALE 1984) were suggested as reasons for the differences in the regressions at different growthstages, but (BAKER et al. 1981) found no change due to maturity. The dry matter content of a plant is easier to determine than bending parameters, but the dry matter content differs for the growthstages (SPIEWOK 1974) and influences strongly the bending [page 92↓]rigidity of the stems (HITAKA 1968, SPIEWOK 1970, SPIEWOK et al. 1970, SINGH & BURKHARDT 1974, SPIEWOK 1974, SKUBISZ 1984, CROOK & ENNOS 1994, O’DOGHERTY et al. 1995). Additionally increases leaf senescence in later growthstages (HITAKA 1968), thus contributing less to the bending moment of the stems.
The pooled regression for two rice varieties, with two planting methods, and grown in two different seasons, shows a high R^{2} and a medium standard error of the regression. This is interesting from several viewpoints. The two planting methods usually result in a different lodging susceptibility (NISHIYAMA 1986, CROOK & ENNOS 1994), but the sensor is not sensitive to these differences, such as the reported differences in bending angle due to planting depth (HITAKA 1968). The two different seasons result in different growth habits (WU 1965), such as in the wet season there are heavier main tillers, poorer leaf sheath protection, lower breaking strength, longer basal internodes, and longer stems. The angle versus biomass relation is not sensitive to these factors in rice. The two varieties are not only almost identical in phenotype, they also have the same biomassangle relationship for that growthstage. The pooled regression of the two wheat varieties is not performing as well as the two rice varieties, but still with a sufficient R^{2 }and an medium standard error of the regression. For the diskmeters and platemeters was the influence of season reported by several researchers (POWELL 1974, CASTLE 1976, STOCKDALE 1984, PALAZZO & LEE 1986, KARL & NICHOLSON 1987, BRYAN et al. 1989, REEVES et al. 1996), but VIRKAJÄRVI & MATILAINEN 1995 found no influence. The influence of varieties was reported as well for the diskmeters and platemeters (SCRIVNER et al. 1986, PETERSON & HUSSEY 1987, BRYAN et al. 1989), but mostly neglected. Despite these results are the data not sufficient to determine the influence of different varieties or cultivation methods, but they are suitable to show the possible bias of the anglebiomass relationship due to these factors. The pooled yeartoyear regression in winter rye shows a good degree of determination, but high standard errors of the regression. If possible, it is advisable to recalibrate the sensor. KARL & NICHOLSON 1987 suggested pooled regressions for several years for the diskmeters and platemeters, but most were calibrated, when measuring new fields, dates, varieties, and cultivation methods were encountered.
The influence of the biomassheightratio shows that the plant height with less tillers increases the angle of the pendulum more than a higher tiller density at a low plant height for an equal biomass value. This indicates that the bending distance is of high importance for the pendulummeter.
The effect of stem inclination can be considered minor till BBCH 59 in rye and in wheat. The increase in difference between the measurements in the two opposite directions show the biasing [page 93↓]of the biomass sensor due to the stem leaning. The test in wheat with a stem inclination of 30° also shows a minor bias, even lower than the bias in rye with less inclination, thus indicating that stem inclination, which is common in winter rye after BBCH 65, has a low biasing influence on the pendulummeter, as long as the crop is sufficiently elastic.
The effect of the depth of tramline results in a large error. With the here presented data, it is not possible to exclude the influence of the biomass on the change of angle by a change of the two pendulum parameters h_{A0} and h_{P}. The problem is not mathematical, but the deeper the tramline the lower is the cylindrical body, hence the cylindrical body touches lower parts of the stems, which have a different bending resistance (HITAKA 1968, SPIEWOK et al. 1970, SINGH & BURKHARDT 1974, SPIEWOK 1974, GOWIN 1980, SKUBISZ 1984, MÜLLER 1988, NIKLAS 1990, O’DOGHERTY et al. 1995).
Using a nondestructive sensor which is in contact with the measured item, it is important to know the limits for which the measurements are nondestructive. The pendulum parameter which was damaging the crop sooner or later is the mass of the pendulum m _{P}. Of the other two parameters, the height of the cylindrical body is, in the range of the tested parameters, not encountering a limit at which it proves destructive to the crop. The height of the pivot point is sometimes causing destruction, but at other times not. Table 27 shows the experienced limits at which destruction occurred for the parameters h_{P} and h_{A0}. For all three crops the destruction limit of the pendulum mass increases till BBCH 69.
Winter Rye 

BBCH 
32 
39 
59 
69 
m _{P} (kg) 
2.5* 
>3.0* 
>3.0* 
5* 
h _{P} (m) 
– 
– 
0.4 
0.8a 
Winter Wheat 

BBCH 
34 
39 
59 
69 
m _{P} (kg) 
2.0 
2.0 
5.0 
4.0 
h _{P} (m) 
– 
– 
0.4 
0.5 
Irrigated Rice 

BBCH 
25 
39 
49 
65 
m _{P} (kg) 
1.5* 
2.5* 
2.5* 
3* 
h _{P} (m) 
– 
– 
– 
0.3 
a = only in second year 1999 
 [page 94↓] 
The limits are always higher in winter rye and winter wheat than in rice. The values in rice are only true under good weather conditions. Strong rains and windy conditions are limiting the mass of the pendulum to less than 1 kg for the entire crop. Whereas the values in winter rye are only true for stems without a medium to severe infestation of eye spot. Eye spot of the disease class 5 already buckles at a mass of the pendulum of 0.5 kg at the first measurement in later growthstages. Then all infected stems buckle, but not the entire crop. In all three crops there is no destruction limit encountered for the early growthstages. The first damages were seen at BBCH 59, and the limits are increasing with succeeding growthstages. Remarkably is the limit for winter rye at BBCH 69, which had a lower destruction limit in 1999 than in 1998. The limits are mostly around 50 % of the plant height.
Discussion
The limits of destructiveness show a difference between rice, wheat and rye. At no time is h_{A0} a parameter which can damage the plants, since it deviates out of the way. The parameter h_{P} is only at later growthstages a destructive factor, usually if it is lower than about half the plant height. The destructive height of the pivot point can change with the years, but the ratio plant height to height of the pivot point is roughly the same in rye. Consequently is a parameter setting in one year well suited for biomass sensing while it is destructive in another year. The parameter m _{P} is at almost all growthstages the factor having a destruction limit. The stems can carry only a specific amount before they buckle, usually named breaking force of the stem (HITAKA 1968, NIKLAS 1998), which is in some cases related to the weight of the stem (GARBER & OLSON 1919, DAVIS & STANTON 1932, ATKINS 1938a, ATKINS 1938b). The maximum breaking strength found by BARTEL 1937 supports the destructive limits of the parameter m _{P}. The limits at which m _{P} becomes destructive can be considerably lower, when bad weather conditions with rain and wind take place as in rice, and the limit drops to 0.5 kg for the entire crop, hence a sensing is impossible. The limits in rye can be as low as 0.5 kg for several stems, provided at least a medium infection with eye spot, but sensing of the crop is still possible.
Talking about a measurement system is so long incomplete as major sources of errors are not defined, and the defined errors have to be discussed by their distribution around the average. Everything influencing or changing the measurement and not being a part of the desired crop biomass is called error by definition. Random errors are distributed at random around an average, mostly in a Gaussian distribution, and have in their average no influence on the measurement.
 [page 95↓] 
For the presented measurement system, the following are seen as random errors:
The other class of errors is not normally distributed, but rather into one direction or one side, thus changing the measured average of the angle of deviation into one direction. They are called systemic errors, because they influence the measurement as long as the error itself is not measured to correct the biomass average. The following list gives important systemic errors:
The pendulummeter most likely will transmit the bacterial diseases caused by Xanthomonas Campestris, because some of the used inoculation techniques are similar to the contact measurement of the pendulummeter, such as rubbing leaves with fingers (OU 1972, HOSSAIN et al. 1997). Therefore is the use of the pendulummeter not advisable in regions with known incidences of bacterial diseases. Of the Southeast Asian rice production area is 8 % affected by bacterial leaf blight caused by Xanthomonas Campestris (KHUSH & TOENNIESSEN 1991). But Xanthomonas Campestris related diseases are also known in wheat systems (DUVEILLER [page 96↓]& MARAITE 1995). Rats, stem fungi diseases, stem borers, and the wheat stem sawfly infect parts of the stems, and thus prevent or bias the measurements. Rats cut off either partly or fully the upper stems of the plants, thus affecting 9 % of the rice production area in Southeast Asia (KHUSH & TOENNIESSEN 1991). The mentioned fungi diseases alter the material of some parts of the stems, thus lowering the carrying capacity of the stem which buckle at the altered parts. The larvae of stem borers and stem sawflies tunnel internally the stems, thus cutting off the stem or causing lodging. Of the Southeast Asian rice production area are 18 % affected by the yellow stem borer and 5 % by the striped stem borer (KHUSH & TOENNIESSEN 1991). Under bad weather conditions, the pendulummeter itself can produce lodging of the crop by toppling over plants which are already carrying additional weight in form of water soakedup by the plant material and droplets on the leaves. Then the additional weight of the pendulum is already too much. Severely lodged crops are not in reach for the cylindrical body.
Following incidents were seen as obstacles, thus hindering or preventing the use of the biomass sensor pendulummeter:
 [page 97↓] 
The so far presented results are focussing on the biomass sensor itself. Furthermore, the pendulummeter is intended as a sitespecific sensor, and for a sitespecific biomass sensor it’s inescapable to look for its use in sitespecific agriculture and sitespecific crop protection. Biomass itself has rarely been a decision base for determining application rates in agriculture due to the difficulties of its determination in the field. An online biomass sensor, nevertheless, opens up a wide range of opportunities for the use of biomass data in decision making processes, because it is a rapid and easy tool while the crop is still growing. The rare use of biomass data as a parameter in crop cultivation, hence in sitespecific plant protection, means that possibilities and potentials are mainly unexplored. Therefore are the here presented field trials only the first of many steps and trials to explore the use of biomass data as a decision base for a sitespecific application of plant growthregulators and fungicides. The present recommendations for fungicides and plant growthregulators are based, among others, on crop density as in the decision support system PRO_PLANT. As long as there are no sensors for determining crop density, biomass data can bypass this bottleneck in sitespecific plant protection. Unfortunately are BBCH 32 and 34 the earliest growthstages in which the pendulummeter can work in European cereals. Available growthregulators are usually applied between the growthstages BBCH 25  49, depending on the agent. Early applications of fungicides are sprayed at BBCH 25  29, intermediate between 31 and 49, while late applications are applied up to BBCH 69.
Lodging is a prime concern in cereal production. Though plant breeders have developed cultivars with stiff straw to reduce lodging potential, complete elimination of lodging, however, has not been achieved. Plant growthregulators, such as MODDUS^{®} with the agent trinexapacethyl, form an integral part in crop management to minimise lodging in cereals. Regarding the measurement principle of the pendulummeter, the biomass sensor is perfectly suited for directing different application rates of growthregulators, though still not all factors that influence lodging and their magnitudes is known to calculate application rates.
To help in determining the effects of a sitespecific differentiated application of the growthregulator, the trial layout was divided into three tramlines, of which one was the uniformily treated tramline, one was the sitespecific differentiated tramline, and the third was the control tramline without any treatment. The calculated averages of the angle of deviation of the biomass sensor are shown in figure 35, and the measurements in the two tramlines are similar though not identical. The green vertical flag lines in figure 35 indicate the change of the application rates [page 98↓]between zero and 0.6 l ha^{1} of MODDUS in the sitespecific tramline, 0.6 l ha ^{1} being the recommended rate. The changes of the application rate were marked in the field by flags, where the field sprayer was switched on and off. A change of the application rate in less than 50 m was not possible. The intermediate biomass on the first 100 m was determined for a zero application to accentuate the possible limits of lodging in that trial.
Figure 35: The pendulummeter measurements of the sitespecific and the uniform tramlines in the trial for a reduced application of plant growthregulators in winter rye, the respective change between sites in the sitespecific tramline, and additional results.  

 [page 99↓] 
As illustrated in figure 35, the sitespecific tramline had four different sites: the first site with a low to intermediate angle of deviation, hence biomass, and zero application of growthregulator, the second with high biomass and full application of growthregulator, the third site with a very low crop biomass and zero growth regulator, and the fourth site with high biomass and full application of the growthregulator. Also shown in figure 35 is the average plant height of the respective sites at the application time at BBCH 49, the average reduction of plant height compared to the control at BBCH 75, as well as the average of the angle of deviation in the application sites.
For determining the success of the application of plant growthregulators, two measures can be taken into account. The first is the prevention of lodging and the reduction in plant height, and the second is the grain yield. The grain yield, each strip being weighted on a truck balance, showed little differences between the two variants, with 2.625 t ha^{1} for the sitespecific strip and 2.724 t ha^{1} for the uniform test strip, both with 14 % grain moisture. Regarding the preventing of lodging and the reduction in plant height, it can be stated that the reduction in plant height was between 17 and 20 cm in the area of full application, compared to the control tramline, but without surprise there being no reduction for areas without application of growthregulators. In the sitespecific tramline, lodging was prevented, which was highlighted by the fact that lodging occurred in the neighbouring control strip as shown in figure 36.
Figure 36: Test tramlines for the sitespecific trial of plant growthregulator and lodging area in the control.  

 [page 100↓] 
Discussion
This first field trial, with the use of a biomass sensor for sitespecific differentiated application of growthregulators, shows the potential usefulness of this approach, how an online realtime biomass sensor can be used in this relatively new field of precision farming.
The trial layout is standard in precision farming, but treating some tramlines with the common application rate, and the other ones with a sitespecific reduced rate, faces always the problem of nonequally conditions between the tramlines. To my knowledge nothing is published about the relationship between biomass and the necessary application rate for growthregulators, and scarce are the reports about the relationship between biomass and lodging. SHEEHY (IRRI, unpublished) reported that elite rice cultivars lodge above a grain yield of 10.5 t ha^{1}. The artificial crop lodging caused by the pendulummeter always occurred in plots with the highest biomass, except the stem buckling experienced by single stems. GONZALEZ et al. 1990 reported a biomass limit in grass stands, above which lodging happened, indicating that there is a limit of the biomass despite the bending resistance, above which lodging occurs.
Therefore, at the sites with a low or a medium angle of deviation, no growthregulator was sprayed, while at the sites with medium to high biomass the full application was sprayed. Regarding the prevention of lodging, no plants lodged in the sitespecific tramline as well as in the uniform tramline. This indicates that in the low biomass sites the growthregulator was not necessary under the experienced weather conditions. In the neighbouring site of the control tramline, lodging occurred at the end of the tramline, where in the neighbouring sitespecific tramline the highest angles of deviation were measured. For this site it can be stated that the high biomass needed growthregulators though the result has to be repeated and the application rate for a specific angle of deviation has to be retested and clarified. The tested variety AMILO is listed in the German variety list BESCHREIBENDE SORTENLISTE 1998 as low to intermediate susceptible to lodging, further indicating the variability of lodging susceptibility due to the variety. This means different sitespecific application rates for the same biomass when the variety is more or less susceptible to lodging. The application rate will be dependent on the future weather conditions of the crop, because bad weather is the principle cause of lodging (KONO & TAKAHASHI 1964, HITAKA 1968). The grain yield was almost the same, giving no reason to change the approach for the sitespecific application of growthregulators. The decision basis used by several researchers (SCHULZKE 1982, SCHÄDLICH et al. 1985, SCHÄDLICH et al. 1986, SCHULZKE & THIERE 1986, SCHULZKE et al. 1986) can not be transformed into an angle of deviation, since they used soil types and crop density as decision basis.
 [page 101↓] 
The primary cause of lodging is a team work of heavy winds and rainfalls, at best worked out by HITAKA 1968. There are two sets of plant and environmental factors involved in the process of lodging: factors forcing the plant over and others resisting the motion induced by wind and rain (figure 37, source GRACE 1977).
Figure 37: Some of the processes determining lodging in cereals (source: GRACE 1977).  

Lodging will occur in plants when the wind force applied onto the plant either exceeds the shear strength in the soil surrounding the roots or exceeds the strength of the stem. In addition to the wind’s force, any extra weight on the plant through rainfall interception or neighbouring stems damaged by diseases like eye spot and stem borers will increase the moment of the displaced stem.
As the top of the plant is displaced from the vertical, a second bending moment results from the force of gravity acting on the mass of the plant which is no longer directly over its supporting base, which illustrates a high similarity to the measurement with the pendulummeter. The gravity term becomes important when the head of the plant accounts for a large part of the plants total weight, as is the ear or the panicle during ripening, highlighted by the fact that lodging occurs usually after heading and increases with grain filling.
 [page 102↓] 
The bending moment originated by the wind increases with plant height so shorter plants are more lodging resistant (PINTHUS 1973, SCHÄDLICH & HOFFMANN 1984, SCHÄDLICH 1986), because longer stems are stronger levers. The main goal of plant growthregulators is the reduction of plant height to reduce this bending moment, and thus lodging (TATNELL 1995).
Because the bending force is highest at the base of the cereal stem, the structural properties of these parts are most important in resisting the bending motion. Internal factors such as thickness of stem wall, stem diameter, and stem rigidity are therefore of high importance. External factors such as extra loading due to precipitation, reduced shear strength in wet soils, weakening of the stem due to the duration of bending, wind gust frequency, and the vibrations of the stem, as well as previous damaging due to fungi and insect diseases all enhance the probability of lodging. HITAKA 1968 stated a high correlation between bending moment of rice stems and their breaking strength. Fresh weight of the plant can increase 30 % during rainfall (HITAKA 1968), and changes in moisture content also affect bending resistance of the stem.
Reported agronomic factors associated with lodging and summarised by SCHÄDLICH & SCHULZKE 1986 are: amount of nitrogen, source of nitrogen, amount of seeds per area, soil types, soil moisture, temperature, crop density, growthstage at the beginning of spring, duration of growthstages, time of stem elongation.
The similarity between the measurement by the pendulummeter and the wind force onto the plant is a major advantage for using this sensor in sitespecific application of plant growthregulators. This approach is already followed up by UDOH et al. 2000.
The use of the sensor for sitespecific applications of plant growthregulators will be limited to the intermediate and late application timings due to the impossibility of earlier measurements with the sensor. Sitespecific application of plant growthregulators will be focussed on temperate cereals since they are not applied in tropical rice and rarely used in European and American rice production.
 [page 103↓] 
Powdery mildew, caused by Erysiphe graminis DC. F. sp. tritici E. Marchal, is the most dominant fungi disease encountered in German cereal production. Disease severity is dependent on many factors, including cultural practices, variation in weather conditions, the level of cultivar susceptibility, and regional and infield location. The disease may occur during all stages of growth.
To determine the effects of a sitespecific differentiated application of fungicides, the trial layout was divided into two tramlines, of which one was the uniformily treated tramline, and the other one was the sitespecific differentiated tramline according to the biomass sensor data.
The averages of the angle of deviation of the biomass sensor were calculated for every meter of the 320 meters long tramlines as given in figure 38. It was decided to either spray 33 %, or 66 % of the full application rate, or the full application of the recommended rate according to the measured angle of deviation. The green vertical flags in figure 38 indicate the change of the application rates between 0.33, 0.66 and 1.0 l ha^{1} of JUWEL, or 100, 200 and 300 l ha^{1} water respectively. These changes in application rate were determined according to the blue angle of deviation in figure 38 for the sitespecific tramline. Spraying was based on the angle of deviation and not on the actual crop biomass. A zero application site was not included into that first field trial due to the lack of weather forecast data and future disease expectations.
As seen in figure 38 had the sitespecific tramline three different sites: the first site with an angle of deviation of 35°  45°, hence a low crop biomass, and an application of 0.33 l ha^{1} of the fungicide in 100 l ha^{1} water. The second site with an intermediate crop biomass, an angle of deviation of 40°  50°, and an application of 0.66 l ha^{1} of the fungicide in 200 l ha^{1} water. And the third site with the highest crop biomass with an angle of deviation of 50°  60° and full application of the recommended 1.0 l ha^{1} of the fungicide. Also shown in figure 38 are the values of the average angle of deviation of those sites at the application time at BBCH 41, and the average percentage number of powdery mildew infected plants in the uniform tramline. The measured angle of the pendulummeter proves the similarity in wide areas of the tramlines, but the selected tramlines are not as similar as in the growthregulator trial.
For determining the success of sitespecific fungicide treatment, the grain yield and the fungi infestation are the measure of success here. The grain yield shows small differences between the two variants, with 7.684 t ha^{1} for the sitespecific strip and 6.825 t ha^{1} for the uniformily treated test strip, both for 14 % grain moisture.
 [page 104↓] 
Figure 38: The pendulummeter measurements of the sitespecific and the uniform tramlines in the trial for a reduced application of fungicides in winter wheat, the respective change between sites in the sitespecific tramline, and additional results.  

The influence of crop biomass on disease incidence of powdery mildew, visible by the angle of deviation of the pendulummeter, is illustrated in figure 39. In figure 39 is given the angle of deviation of the uniform tramline, measured at BBCH 41, together with the percentage of powdery mildew infected leaf area, measured at BBCH 75 in the same tramline. Here, the percentage of infected leaf area rises the higher the crop biomass is.
 [page 105↓] 
Figure 39: The angle of deviation in the uniformily sprayed tramline at BBCH 41 and the percentage of powdery mildew infected leaf area at BBCH 75.  

Discussion
Only a few reports exist regarding the potentials of sitespecific application of fungicides. Those works were usually based on field assessment maps, some of them using leaf area indices to control sitespecific differentiated application rates of fungicides. Due to a close relationship between leaf area and plant biomass, the biomass sensor pendulummeter has a high potential for a sitespecific online control of fungicide application rates. In this case, the presented field trial is a first step to introduce the biomass sensor pendulummeter to the potentials of sitespecific reduced application rates of the strobilurinfungicide JUWEL in winter wheat.
This first field trial, with the use of a biomass sensor for sitespecific differentiated application of fungicides, is not a sufficient base to determine the actual usefulness of this approach, but they show the way, how an online realtime biomass sensor can be used in this relatively new field of precision farming. As with the sitespecific application of growthregulators, the sitespecific fungicide trial layout is standard in precision farming. First of all, a sitespecific application of fungicides according to the pendulummeter is possible and it is working. The grain yield is not differing much indicating that a reduced amount of the fungicide is sufficient to protect the crop. The slight yield differences may be explainable by the differences between the two tramlines although the tested tramlines were selected visually for the highest possible similarity. The [page 106↓]smaller yield for the uniform treatment is probably caused by the slightly lower biomass in the uniform tramline compared to the sitespecific tramline. However, the test trial can be considered successful, but further research has to clarify the relationship between biomass and disease incidence. Nevertheless, this approach is always dependent on weather conditions, with possible unfavourable results in seasons with cool and rainy weather conditions.
The second result is a strong influence of the biomass on the powdery mildew infestation. Thus proving that this approach of using biomass data for the sitespecific application of fungicide against powdery mildew has a rational base.
To my knowledge nothing is known about the biomassapplication rate relationship for the fungicide application. Thus further research is necessary to find algorithms for this approach. The tested variety BATIS is listed in the German variety list BESCHREIBENDE SORTENLISTE 1998 as low to intermediate susceptible to powdery mildew. This means that sitespecific application rates will have to change with different varieties. The bonitation in the control strip shows a relationship between biomass and disease incidence of powdery mildew, although this is dependent on the weather conditions. For powdery mildew a dependency on air humidity was stated (FRIEDRICH 1995). A dependency of the air humidity on the biomass seems likely, but wasn’t found in the literature.
A LAImeter was successfully used (JORGENSEN et al. 1997, SECHER 1997) as a base for sitespecific application of fungicides. According to CALVERO & TENG 1997 is the simulation model BLASTSIM.2 partly based on the leaf area index of rice to simulate and manage a rice blast (Magnaporthe grisea Barr. and Pyricularia grisea (Cooke) Sacc.) epidemic, thus being potentially applicable in sitespecific matters. According to several reports (AASE 1978, WANJURA & HATFIELD 1985, DOBERMANN & PAMPOLINO 1995, RETTA & ARMBRUST 1995), the leaf area index or the leaf area is correlated with leaf mass, stem area related with stem mass, hence the plant surface with the crop biomass.
WARTENBERG & JÜRSCHICK 1995 found a high correlation between the plant surface and the culm length. By using the pendulummeter’s angle of deviation, the fungicide can be applied according to the amount of biomass, according to LAI, or according to the leaf area as the prime application area.
Mainly unexplored is also the relationship of the biomass on most of the leaf infecting fungi diseases.
Since the used fungicide JUWEL is a systemic fungicide, it is necessary to discuss the spraying object. Several researchers have used leaf area as the prime object of spraying. Without doubt [page 107↓]this can be stated as correct for fungicides working as protective agents. As it is formulated by BÖRNER 1990, these “fungicides have to be applied as uniformily onto the above ground plant surface as possible”, since they “protect the plant externally against fungi attacks”. Protective fungicides are not intruding into the plants as systemic fungicides do. Systemic fungicides, such as the here used JUWEL, intrude into the plants and attack fungi from inside the plant, thus being able to defeat even fungi already grown into the plants.
Although systemic fungicides are intruding plants via leaves and roots, the actual object is the entire plant and not only its surface. Bearing in mind the use of levels of antibodies in human medicine, such as the level of a vaccine to ensure a successful vaccination, this means that the fresh mass of the plant is the proper object of systemic fungicide spraying to ensure the necessary level of the fungicide agent in the plant. In terms of units this level can be expressed by one or more parts of the fungicide agent per million parts of the plant PPM. Unfortunately, to my knowledge no publications can be found about the PPM relationship between fresh mass and systemic fungicide agents.
The use of the sensor for sitespecific applications of fungicides will be limited to the intermediate and late application timings. Earlier measurements with the sensor between BBCH 25 and BBCH 31 are impossible in winter rye and winter wheat and will be left over for other sensors. Sitespecific application of fungicides will be focussed on European cereals because they are widely applied in European cereal production. Sitespecific fungicide application in tropical rice production and American cereal production systems will have a lower priority due to the lesser use of fungicides there.
 [page 108↓] 
The aforementioned results were all obtained with a pendulummeter mounted on a handpushed research carrier. Trigger and rails were sufficient to record positioning. Under practical farming conditions neither trigger nor a handpushed carrier is acceptable. Only a tractorbased pendulummeter with an automatic online recording of the angle of deviation together with the GPS positioning data is acceptable for farmers.
Therefore, the programming of the measurement software μ –meter Nextview was customised to a joint recording of the angle of deviation of the pendulummeter together with the positioning data of a Trimble^{®} 132GPS. A prototype of the tractorbased pendulummeter was mounted on the backward threepoint linkage. A realtime view of the prototype tractorbased pendulummeter measurement is visible in the attached video. The measurement frequency was 1 Hz, a higher frequency was not possible with the present system. Figure 40 shows the 1 Hz point measurements of the angle of deviation of the tractorbased pendulummeter, measured in the tramlines of the winter wheat field Baasdorf at growthstage BBCH 39. The shown measurement points are original data, not averaged or reduced values.
In figure 40 the tramlines are easily visible through the measurement points. The dots have dark blue to light blue colour for lower measurement values, and light red to dark red colours for higher angles of deviation. The black line indicates the edge of the field. No biomass data was collected at that site, therefore is this map rather a measurement map than a biomass map.
The majority of the field shows light red dots, indicating angles of deviation between 62° to 70°. Several patches show dark red dots with angles of 70° to 78°. In the southwest corner of the field is a site with a low biomass measurement with angles of deviation between 46° and 62°, illustrated by the light and medium blue dots, and also a few dots with even lower angles. Though the legend gives negative values of the angle of deviation as well, they were rarely measured in the sites with low biomass where the pendulum was swinging strongly and a measurement frequency of 1 Hz could record the negative values with the same probability as the other values. Nevertheless, the important range of the measurement values are the angles of deviation between 46° and 78°. Those angles show approximately 100 % difference between the areas of low biomass and the areas of high crop biomass.
This map is in an offline spraying mode the endproduct, but in the intended and not yet realised online realtime spraying mode, with a sensor in front controlling a field sprayer while passing across a field, it will be a byproduct for researchers and farmers to store and express the obtained information on biomass.
 [page 109↓] 
Figure 40: Online recorded measurements with the tractorbased pendulummeter.  

 [page 110↓] 
Based on these point data, a crop biomass map of the Baasdorf winter wheat field is interpolated in Arcview (figure 41). Clearly visible are sites of different crop biomass, though the most parts of the field are in a small range of angles between 62° to 70°. Nevertheless, there are large areas with higher and lower crop biomass. The sites with angles of deviation of 54° to 62°, and also the areas of 70° to 78°, clearly indicate zones with the need for a differentiated crop management.
In the area of sitespecific application of plant growthregulators it might be possible to arrange two or three management zones within the field. The full application rate may be advisable at the sites with a high biomass, and a zero application at those with low biomass measurements. The application rate at sites with intermediate biomass can potentially be lower than the full application, but to what degree and with which success is unknown, nevertheless, the risk will increase.
The application rate for fungicide spraying can be grouped to the same management zones within the field as for the plant growthregulator, but amount of fungicide agent will have to be determined at the field according to actual disease pressure within these management zones. These questions have to be investigated in future researches.
Discussion
The presented tractorbased pendulummeter for online mapping of crop biomass is the final result of this work. In difference to the before described results, there are some changes between the research carrier and the tractor as a carrier for the pendulummeter. The measurement frequency of 1 Hz is too low and will bias the measurements due to the vibration of the pendulum, causing at some points negative values. This will have to be technically changed to higher measurement frequencies and the before mentioned reduction methods to an average or median. Location of the pendulum and the antenna are different, but negligible in a field. Movements of the tractor are much more influencing on the pivot point than the movement of the research carrier, due to the lever arm and the high centre of gravity of the tractor.
The dotted lines of the measurements in the tramlines represent only the biomass within the tramline, and these measurement points are interpolated for the adjoining areas, although these areas might be different due to the sideways heterogeneity in the field. The areas with low or high biomass are clearly pronounced in the interpolated map, which will be the basis for an offline treatment.
 [page 111↓] 
Figure 41: Interpolated map of the measured angle of deviation.  

 [page 112↓] 
Determining the proper amount of application rate will be the crucial decision, and biomass data will be the base for arranging the field into management zones, either online or offline.
Provided the growthrate is identical within the field and there are no differences in the growthstage between the sites, then a 100 % difference in biomass will result in a 100 % difference of grain yield. Though the weather at later growthstages will be mostly unknown at the time of measurement, actual biomass can be seen as yield potential as it is an important part of crop growth models. Crop growth models were already used to derive sitespecific yield potentials and thus management information (BOONE et al. 1997, WERNER et al. 2000).
The integrated slope sensor can as well be used, in connection with the biomass maps and slopeclimate models or CERESmodels to test for future growth patterns due to north or south slopes (BERGOLD 1993) and water stress (MAIER 1993).
The stored information either as maps or as measurement files may be useful for the farmer to see for himself his management results, and politics might enforce these maps in environmentally critical sites. Additionally, these maps enable researchers to test on fieldscales the dependencies between crop biomass and various diseases. These relationships were neglected so far due to the high amount of time and labour for the destructive sampling methods.
Despite the dependency of the biomass maps on the availability of GPS signals are the actual sensorsprayer combinations not dependent on the GPS signals, because the sensorsprayer combination acts as a unit in an online realtime application and application rate is based on the biomass data and not on the location within the field.
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