The design of feeler wheel toppers for sugar beet

J. agric. Engng Res. (1986) 34,3 19-33

1

The Design of Feeler Wheel Toppers for Sugar Beet 2.

Specification

of topper mass and spring and damper restraint M. J. O’DOGHERTY*

In this paper a design procedure is outlined by which the specification of topper mass and compression spring and/or viscous damper restraint can be determined for effective topper operation at speeds up to 8 km/h. Theoretical studies were made of the forces applied to a crown under the action of the topper feeler wheel. Field and laboratory studies were made of the failure of beet crowns under vertical load applied by feeler wheels. The forces required to top beet were measured together with the effect of horizontal force and impulse on the stability of growing roots. These studies enabled criteria to be deduced for the requisite spring rate, pre-load, and/or damping coefficient for a given topper equivalent mass and operating speed. The mass of the topper should be a minimum and a drum feeler employed. To operate at 8 km/h an equivalent mass of not more than 29 kg should be employed. The spring rates required for topper control range from 20.7 to 26.1 kN/m for topper equivalent masses from 20 to 29 kg. Field experiments with restrained lightweight designs have shown significant improvements in topping performance when compared with heavier conventional units. 1.

Introduction

In Part 1 it was shown that the motion of a topper could be described by a mathematical model which predicts the impulse applied to the feeler wheel on initial contact with a beet crown and then determines the subsequent topper behaviour from its equation of motion. The analysis was conducted for a topper with restraint by means of a compression spring, with or without pre-load, and/or a viscous damper. The degree of restraint required is principally determined by the speed of operation and the topper mass, which also affects the relationship between the spring rate and an associated pre-load or damping coefficient. In practice, however, the choice of spring rate is restricted by the ability of beet crowns to sustain forces either vertically or horizontally. A minimum force on the crowns is necessary to provide sufficient force to penetrate the foliage. In addition, both the initial spring compression and the pre-load force on the soil must be limited. These considerations result in a range of spring rates being available to the designer, between minimum and maximum allowable values for a given topper mass and maximum operating speed. In practice, however, as high a spring rate as possible should be chosen to produce a rapid acceleration to soil level between successive beet in the row. In this paper, a method is described for determining the degree of restraint required to control topper motion so as to follow beet crowns and top at the specified horizon.

2.

Control of topper motion

It is possible to calculate the loci of the edge of the topping knife from the solutions of the equation of motion of the topper for a particular impulse and a knowledge of topper geometry.’ Fig. I shows loci for an unrestrained topper over a range of speeds from 3.2 to 8 km/h together with the geometric locus which is followed by the knife edge if the feeler wheel remains in contact

*Field Machinery Received

25 January

Division,

National

1985; accepted

Institute

of Agricultural

in revised form 28 October

Engineering,

Wrest Park,

Silsoe, Bedfordshire

MK45 4HS

1985

319 0021-8634/86/080319+

13 103.00.‘0

0

1986 The Brutish Society

for Research

m Agrtcultural

Engmeering

320

FEELER

WHEEL

TOPPERS

FOR SUGAR

BEET,

2

Notation

maximum vertical displacement of feeler wheel centre with no restraint maximum vertical displacement of feeler wheel centre with spring and/or damper restraint maximum permissible vertical displacement of feeler wheel centre to control topper hi motion so as to cut crowns in the appropriate plane distance between knife edge and axis of supporting shaft in vertical plane along the 1, row x distance below soil level of centroid of area of cross-section of beet model geometry ( = 0.6290,) vertical setting of topping knife (distance of knife edge below feeler wheel periphery) maximum beet diameter xo (D,), critical diameter of beet at soil level for topper control criteria FN sum of forces acting normal to beet crown surface during contact of feeler wheel FP minimum force required to cause effective engagement of feeler wheel with beet crowns maximum force which can be supported by soil when acted upon by topper F, maximum load at crown apex of largest beet (Ds = 140 mm) which limits probability FV of crown failure to less than 5% M moment of horizontal component of normal force, FN, about the centroid of the area of cross-section of model beet geometry below soil level maximum initial compression of restraining spring 6 angle made by topper arm to horizontal when displaced from rest position at soil a, level angle to horizontal made by line from knife edge to centre of supporting shaft. with pk topper at ground level Other symbols used are defined in the Notation of Part 1 h,

h,

with the beet crown. The curves show clearly the adverse effect of increasing topper speed. At a speed of 3.2 km/h the effect of the impulse is small and the locus will quickly fall below the geometric locus so that subsequently the feeler wheel follows the beet crown. At 5.6 km/h the locus is close to the geometric locus, and the knife enters at the appropriate topping level although the feeler wheel has not retained contact with the crown, because the locus is slightly above the geometric locus over most of its length. At 6.4 km/h and above the loci are well above the geometric locus and at 8 km/h the knife passes over the crown. These results indicate, therefore, that for the conditions specified, the beet will be accurately topped up to a speed of just over 5.6 km/h but at greater speeds there is a need to apply restraint to modify the knife loci. The effect of restraint by a linear spring at a speed of 8 km/h is shown in Fig. I for values of o ranging up to 100 rad/s. This shows the marked effect that restraint has on the loci which is very similar to that of reducing speed. The results show that spring restraint enables the maximum vertical displacement of the knife to be limited to a value no greater than the height at which the topping knife enters the beet under quasi-static conditions. Whether this maximum occurs before or after the locus intersects the beet surface, it is possible for the blade to enter at the appropriate horizon. The forms of the loci for a spring and damper @=O to 1) were closer to that of the geometric locus than when a spring alone is used, so that a better control of topper motion can be achieved without the possibility of a secondary impulse which may occur if the loci are disparate. From an analysis of the loci it was concluded that the maximum vertical displacement is sufficient to assess the effect of restraint. Limiting this value to the height at which the knife

321

M. J. O’DOGHERTY

0

0

50

100

150

Horizontal

movement

of

knife,

mm

Horizontal

movement

of knife,

mm

200

Fig. 1. (Top) Effect of speed, V, on loci of knife edge over range 3.2 to 8 km/h; ---, geometric locus. (Bottom) Effect of natural circular frequency w on loci of knife edge at 8 km/h. Bold lines indicate beet crown profile. (D,=120mm;r~=229mm,a=34~5”,cp0=15~2”,e=0~1)

should enter the beet is an adequate criterion to ensure that the restraint results in topping at the appropriate horizon. 3.

Criterion for topper control

A critical criterion was developed’ which showed that the restraint required is defined at a beet diameter at soil level for which the vertical knife setting is correct, viz.

The basis of the criterion is that for beet equal to, or larger than, the critical diameter, the vertical displacement of the topping knife is limited to that appropriate to its setting with the feeler wheel maintaining contact with the crown. For beet smaller than the critical diameter, however, which would normally be overtopped, some loss of contact of the feeler wheel is allowable, provided that the knife does not enter the beet above the correct topping plane. The critical criterion for defining the maximum allowable displacement of the feeler wheel centre is given by

322

FEELER A,=

R

WHEEL

TOPPERS

FOR SUGAR

~~cosG% x 0.243 (D,),.

BEET,

2

. . (2)

l,cosp,,

The maximum vertical displacement in the absence of restraint is also required (see below) and is found by making the close approximation that . . (3)

J= m, V(1 + e) sin a cos (a - rpJ. By substitution in the expression for maximum restraint, the following relationship is obtained:

vertical displacement,

in the absence of

V2 h, = 2g’( 1 +e)’ sin’ a cos’ (a - pO).

. . (4)

The value of a required can be found from beet and topper geometry.’ 4.

Determination of restraint requirements

In order to specify the restraint required to control topper motion, the two principal cases were considered, i.e. a spring with a pre-load and a spring combined with a viscous damper. 4.1. Spring with a pre-load The maximum vertical displacement of the feeler wheel centre is given by

. . . (5)

where H = m&cosq, By rearranging this equation, a relationship can be obtained between equivalent spring rate, k,, and pre-load, FO. An appropriate design curve can be found by putting h,=hL from Eqn (2). The linear equation required is given by k@T[($-I;)

H-F,,]

...

(6)

This relationship is shown in Fig. 2 for the topper date given in Table 1. 4.2. Spring with a damper The maximum vertical displacement of the feeler wheel centre for j? < 1 is given by

The relationship between k, and damping coefficient, c,, was found by a numerical technique and is shown in Fig. 2 for the data of Table 1. 5.

Crown force constraints

The design curves of Fig. 2 relating spring rate and either pre-load or damping coefficient, show the range of combinations which is theoretically possible. In practice, the amount of restraining force which can be applied is limited by the ability of the beet crown to sustain forces vertically and horizontally, which imposes a maximum value on the value of k,. An expression was derived for the force acting normally to the crown when the feeler wheel was in contact with it,’ given by

323

M. J. ~‘D~~HERTY 40

Spr\ng

pre-load

(F,),

Eqwalent

N

damplng

coeff~clent

CC,), N m-’ 5

Fig. 2. Design curvesfbr topper restraint required at 8 km/h relating equivalent spring rate to spring pre-load (left) and damper coefficient (right). (Applicable to topper datagiven in Table I) Table 1 Typical data for a lightweight topper deisgn

/=914mm m, = 28.0 kg (m,), = 9.7 kg

1,=1043mm po= 15” ~,=27.5”

d= 126 mm

g’=

; 0

k, = 779 mm

g=1.095 0

It is assumed that feeler wheel and associated assemblies have their centre of mass at the feeler wheel axis and that the arm has uniform mass per unit length. The following values were used in the calculations of restraint: (Ds),=91~5mm z=42mm

e=O,l V= 8 km/h

ctrfG22

FN=- 4m G + k,D,G, e 1 The terms G,, G, and G, are complex topper geometry.’

+ F, set (a - 9) + m,g’ cos p set (a - q). dimensionless

parameters,

dependent

.

on beet crown and

5.1. Vertical force In order to obtain information on the forces which could be sustained by beet crowns a series of measurements was carried out for a range of beet sizes. 2 Forces were applied vertically to beet using both a proprietary multi-disc feeler wheel and a drum feeler. Twenty beet were used for size grades of 45 to 70, 70 to 95, 95 to 120 and > 120 mm, based on maximum diameter (DG). Beet were removed from the soil, complete with leaves, cut at approximately 25 mm below soil level and placed on a horizontal surface with their axes vertical and loaded through the feelers by a hydraulic jack. The force was progressively increased and the position of the wheel centre above the horizontal surface recorded, so that a load-penetration curve was established. The loading was increased until either there was failure of the crown, or the feeler discs or spikes made contact with the supporting surface. There was a much greater penetration of the multi-disc feeler into

324

FEELER

0

40

20

60

80

WHEEL

100

Maximum diameter

120

TOPPERS

I I40

FOR

SUGAR

BEET,

2

I 160

CD,), mm

Fig. 3. Variation of mean beet crown failure load with maximum beet diameter for drum feeler wheel (limits shown for the means represent the 95% range of observations)

the beet crown, at a given load, than for the drum feeler. This is because of the greater stress at the bearing areas of the teeth on the disc peripheries, which leads to crown failure at a much lower load, particularly for the smaller beet. The mean crown failure load is plotted in Fig. 3 for the drum feeler against maximum beet diameter, together with the 95% range of observations. Analysis of the forces predicted by Eqn (8) showed that the case of the feeler wheel at the crown apex (a =0) when V=O resulted in a conservative design criterion. In order to reduce the probability of crown failure to less than 5%, a limit of 1.78 kN was applied which can be substituted in the following criteria, developed from Eqn (8) (a) Pre-loaded spring:

Fv-md

1.

I!-<

‘we

-s

(H-z)

-

4 -secq7,,secy,

. . . (9)

2

(b) Spring and damper: k,<

F, - m&’ (H-z)

set q7oset p

. . . (10)

The criteria are applicable to the largest beet size considered (D, = 140 mm) and are conservative in that they ensure that smaller sizes are not subjected to excessive forces. 5.2. Horizontalforce Experiments were conducted in the field to measure the horizontal forces required to overturn roots.3,4 Force was applied to the beet crowns by a hydraulic ram mounted horizontally on a frame attached to the three-point linkage of a tractor (Fig. 4). A beet was isolated from its neighbours in the row and the ram positioned so as to apply force by means of a semi-circular collar as near to soil level as possible. The ram was operated by a manual pump until the beet was pushed over. The maximum force required was measured by a calibrated pressure gauge and the height of the line of application recorded.

325

M. J. O’DOGHERTY

Equlipme3rdfor the application of horizontalforce by a hydraulic ram to beet groMGng in the

20(

A

1 t

15( : ; E E 5 ; t : 0

IO 0

r

51

(3 i 0

Fig. 5. Variation of moment required to overturn beet with area of root vertical section below soil level

326

FEELER

WHEEL

TOPPERS

FOR

SUGAR

BEET,

2

The moment of the maximum force was calculated about the centroid of the area of crosssection of the root below soil level, in a vertical plane at right angles to the row. The roots were cut longitudinally and the area and position of the centroid of the underground section determined. Fig. 5 shows the overturning moments plotted against the area of the vertical root section for one series of measurements. The results resulted in correlations significant at the 0.1% level; the calculated regression line is drawn on the figure. There was considerable variability in the overturning moments and roots resisted greater overturning forces under dry soil conditions than for wet conditions. The resistance to overturning increased much more rapidly with beet size in dry than in wet soil conditions. From considerations of beet geometry, it can be shown that the maximum moment on the beet is given by M,,, = (FN sin a)maX(h +X>.

. .(ll)

The magnitude of the maximum horizontal force component is determined by evaluating FN sin a for a series of values of a [Eqn (S)] for a range of values of equivalent spring rate, over the appropriate range for the design curves (Fig. 2) with associated values of pre-load and damping coefficient. The maximum moments M,,, are then calculated from Eqn (11) using the value of (5 sin aLar and plotted against values of k,. An upper limit of 113 Nm was specified for the overturning moment, within which all the observed results lay. This limit applies to a beet of 140 mm soil diameter and it was shown that, if it is satisfied, the forces applied to smaller beet will also be within the requisite limits. From the calculated relationship between M,,,,, and k, it is possible to obtain the permissible upper limit of the equivalent spring rate, k,. The maximum horizontal force occurs at, or relatively close to, the point of initial contact with the beet, when the inclination of the normal force to the beet axis is significant. In general, the maximum horizontal force is smaller than the maximum vertical force. 6.

Lower limits of equivalent spring rate

In practice, there is a minimum spring rate which is appropriate. The use of pre-load means that the spring must have an initial compression and it is necessary to limit this to ensure that the free movement is not severely constrained. A maximum value of 6 = 25 mm was adopted in the criterion for minimum equivalent spring rate,’ i.e.

(-$-I ) w’cosyl, . . (12)

k,>

The pre-load is limited by the force which can be sustained by the soil. A maximum of designs, and substituted in the following criterion deduced’ by a consideration of topper geometry and Eqn (6): F, = 623 N was taken for this force, which is that applicable to current proprietary

ho

or; k, 2

4

T

w?- Fs sec2 q.

. . . (13)

327

M. J. O’DOGHERTY

When a damper is used there are no pre-load criteria but a minimum load at the top of the beet crown is required to ensure adequate sensing. The criterion adopted’ was based on Eqn (10) and limited the force on the crown to Fr= 667 N so as to cause penetration of the spikes on the drum feeler. This value was used in the following expression: k,a

7.

F, - megr (H-z)

. (14)

set fposet q ’

Procedure for specifying restraint

To calculate the restraint required at a particular operating speed it is necessary to know the principal geometrical parameters of the topper and the mass distribution of its components. Some typical values representative of the lightweight units used in the work are given in Table 1. It is necessary to define the operating speed at which it is required to achieve control, the coefficient of restitution between the topper feeler wheel and beet crowns and the vertical knife setting, which is directly dependent on the critical beet diameter. The values used for design calculations are those in Table 1; the value of e is considered to be a conservative one for practical considerations. The first step in the design procedure is to calculate the maximum vertical displacements of the feeler wheel centre with no restraint and the limit required when restrained [Eqns (2) and (4)]. These values can then be used to establish the relationships between equivalent spring rate and pre-load or damping coefficient [Eqns (6) and (7)]. For design purposes a linear approximation can be used for the relationship for a spring with a damper, which greatly simplifies the procedure (Fig. 2). The maximum and minimum equivalent spring rates which can be employed are then calculated from the appropriate criteria [Eqns (9) to (14)]. In practice the maximum spring rate is chosen because it minimises the length of the knife locus between successive beet; its value will depend on whether the vertical or the horizontal beet crown force criterion is the more severe. The use of a damper generally enables a higher spring rate to be employed. The restraint is calculated in terms of a dynamically equivalent system at the feeler wheel centre. The requisite characteristics can be calculated for any mounting position of springs or dampers from topper geometry.’ The effect of equivalent mass on the maximum values of k, for a spring and damper is shown in Fig. 6. The reduction in k, with increasing topper weight is much less than when using a pre-loaded spring. 40 -

cl

0

I IO

I 20

I 30

I 40

Equivalent mqss of topper

I 50

_

l/n,), kg

Fig. 6. Effect of equivalent mass of topper on maximum criteria for equivalent spring rate for a spring and damper. -, overturning moment < 113 Nm; ---, overturning moment <90 Nm; ---., vertical force < 1.78 kN. (Applicable to topper data given in Table 1)

FEELER

WHEEL

TOPPERS

FOR SUGAR

BEET,

2

Table 2 Suggested specification for lightweight topper for operation up to a speed of 8 km/h 1=380 to 510mm p0 = 10”to 20 rf= 150 to 190mm

Topper equivalent mass

Spring with pre-load

Spring and damper

Criterion

k

F

k

kg

kN:m

$

kN:m

25-29

23.3-20.8

116214

25424.7

128-264

25-29 20-23

20.7-16.6 24.0-22.4

147-262 44-93

24.2-22.1 26.1-25.4

156-292 3&91

m,,

General use Light soil conditions Very light soil conditions

c,.

Nm-‘s

An interesting finding is that the equivalent mass must be less than 32 kg for control to be achieved using a spring with a pre-load. This limitation does not apply when a damper is used. In general, the vertical force limitation criterion results in lower values of k, than the horizontal, but if a criterion of a maximum overturning moment of 90 Nm is used, which is representative of lighter soils,4 the overturning criterion results in the lowest values for k,. Table 2 gives some typical values for a topper of lightweight construction. The most important finding is the need to minimize the mass of the unit. This has the effect of minimizing the impulsive forces acting on the beet crown when the feeler wheel makes its initial contact and permits maximum acceleration of the unit towards the soil under the action of the restraining spring after a beet has been topped. This reduces the probability of knocking beet out of the ground (or a gross displacement which adversely affects topping) and enables the topper to accommodate a smaller inter-root spacing and accurately top a higher proportion of the crop. 8.

Field experiments

Measurements have been made of the magnitude of the forces which a topping knife imposes onf beet1*5*6 and of the effect of an impulse on the stability of roots.’ The knife forces were measured at speeds up to 8 km/h in different soil conditions6 and showed mean peak forces in a range 490 to 520 N. These values are generally much less than the forces required to uproot beet, except for organic soils for which they were comparable.3v4 In practice, however, knife forces are counteracted by the action of the feeler wheel, which is driven at a peripheral speed greater than the land speed. Some experiments were performed in which beet crowns were struck by a heavy pendulum and their displacements measured. ’ The impulse applied by the pendulum was related to that arising from the momentum of a topper and criteria for the impulse which can be sustained were derived from observations of root displacement. Two soil types were used and the conclusion was that the limit of impulsive moment which could be sustained by the beet was 2.8 Nms. The important conclusion from these measurements was that the speed of topping is limited to about 4.8 km/h, for an equivalent mass of 54 kg; if equivalent mass can be reduced to 29 kg then operating speed can be increased to 9 km/h without causing a high proportion of roots to be displaced. In organic soils it may be necessary to reduce speed to 5.5 to 7 km/h (m, = 29 kg) or reduce topper mass to 20 to 23 kg to operate at 8 km/h.

329

M. J. O’DOGHERTY

Fig. 7. Lightweight topper used injield experiments and trials

Percentage

undertopplng

Fig. 8. Characteristic curves of topper performance at 6.4 km/h relating percentage overtopping and percentage undertopping from jield trials. ( ? ? , ??: proprietary and lightweight units 1973; 0, ??: proprietary and lightweight units, 1974)

Field experiments with lightweight toppers (Fig. 7) have exhibited a considerable degree of variability and some inconsistencies.‘- l3 They show, however, that the use of a drum feeler wheel is successful in controlling the increase in overtopping with speed which has been observed with multi-disc feelers. The experiments generally used relatively low spring rates and indicated that the range of equivalent spring rates predicted by the theoretical work (17.5 to 25.3 kN/m) were necessary to obtain the requisite control of undertopping. In general, lightweight units with positive restraint gave a marked improvement in topping characteristics when compared with heavier conventional units’2,13 at operating speeds of 6.4 km/h or higher (Eg. 8). The differences in the topping characteristics of the two years are typical of such experiments and arise from differences in the geometry of the crowns and beet stand spacing.

330

FEELER

WHEEL

TOPPERS

FOR SUGAR

BEET,

2

The experiments have shown the importance of crop characteristics, and soil type and condition. In a crop of relatively small roots, where the crown has a low habit of growth, the effect of restraint is small. In light soils however, with large beet growing well out of the soil, the benefits of lightweight design at speeds in excess of 4.8 km/h become marked.13 9.

Conclusions

A design procedure has been developed to specify the degree of restraint required to achieve topping of beet at the required cutting horizon. Measurements were made of the maximum forces which beet can sustain vertically and horizontally under the action of feeler wheels. Knife forces during topping were measured and the effect of impulse assessed. Criteria were deduced for the maximum and minimum spring rates which can be employed for control. The magnitude of an appropriate spring pre-load or viscous damping coefficient can then be specified for any chosen spring rate. Minimum mass is the most important requirement of topper design which minimizes the impulse and force acting on the beet crown and provides maximum acceleration to soil level under the action of a spring after topping. In general, to operate at a speed of 8 km/h, an equivalent mass of not more than 29 kg is required. Toppers of this mass were constructed and used in field experiments. The feeler wheel should be of lightweight drum construction. Design studies were conducted on the basis of a maximum operating speed of 8 km/h and a coefficient of restitution of 0.1 between beet and feeler wheel. The restraint required is principally determined by operating speed and topper mass. For a range of equivalent masses of 25 to 29 kg, the maximum spring rates range from 23.2 to 20.8 kN/m, with associated pre-loads from 116 to 214 N. If a damper is used, higher spring rates in the range 25.4 to 24.7 kN/m can be employed, with damping coefficients from 128 to 264 Nm-is. Hence, not only can higher spring rates be used with a damper, but the variation with topper mass is less. In light soil conditions the maximum spring rates are reduced to 20.7 to 16.6 kN/m with a pre-loaded spring and to 14.1 to 22.1 kN/m for a spring with a damper. The associated pre-loads are in the range 15 to 27 N and the damping coefficients in the range 155 to 292 Nm- ‘s. Knife cutting forces during topping are too small to cause overturning of roots, except where beet are grown on organic soils. The impulse applied to beet crowns on initial contact by the feeler wheel may impose limitations on topper mass or speed in light soil conditions. Operating speeds greater than 8 km/h are generally possible for a topper equivalent mass of 29 kg. In very light soils, however, speed may have to be limited to 5.5 to 7 km/h to minimize the probability of root displacement. Field experiments showed that lightweight units, with positive restraint and a drum feeler, gave a significant improvement in topping performance compared with conventional units at speeds of 6.4 km/h or higher. In light soils, with large beet growing well out of the soil, the superior performance of lightweight toppers was marked at speeds in excess of 4.8 km/h. Acknowledgements Thanks are due to J. A. Wayman and F. W. Joyce who carried out the development designs and the subsequent field experiments and trials.

of lightweight

topper

References ‘I O’Dogherty, M. p Wayman, J. A. topping units. Silsoe, 1972 3 Wayman, J. A. DN/R/261/1600,

J. The mechanics of a sugar beet topper. Ph.D. thesis, University of Reading, 1976,664 The effect on sugar beet crowns of force applied vertically to the feeler wheels of two Departmental Note DN/R/259/1600, National Institute of Agricultural Engineering, The effect of force applied horizontally to sugar beet crowns. National Institute of Agricultural Engineering, Silsoe, 1973

Departmental

Note

331

M. 1. O’DOGHERTY

Wayman, J. A. Further studies of the effect of force applied horizontally

to beet crowns. Departmental Note DN/R/642/1600, National Institute of Agricultural Engineering, Silsoe, 1976 O’Dogherty, M. J. A dynamometer to measure the forces on a sugar beet topping knife. Journal of Agricultural Engineering Research 1975,20: 339-345. Wayman, J. A. Measurements of the forces acting on the knife of a sugar beet topping unit, 1971.

Departmental

Note DN/R/264/1600,

National Institute of Agricultural Engineering, Silsoe, 1973

Wayman, J. A. The effect of speed and restraint by springs and viscous damping on the performance

of a sugar beet topper. Departmental Note DN/R/265/1600, National Institute of Agricultural Engineering, Silsoe, 1973 Wayman, J. A. Field experiments to assess the performance of an experimental lightweight sugar beet topper. Departmental Note DN/R/366/1600, National Institute of Agricultural Engineering, Silsoe, 1975 Wayman, J. A. Field experiments to assess the performance of a vertically constrained lightweight sugar beet topper. Departmental Note DN/R/461/1600, National Institute of Agricultural Engineering, Silsoe, 1975 Wayman, J. A. Field experiments to assess the performance of an experimental lightweight sugar beet topper. Departmental Note DN/R/460/1600, National Institute of Agricultural Engineering. Silsoe, 1974 Wayman, J. A. Field trials of design variations of the prototype NIAE lightweight sugar beet topper, 1974. Departmental Note DN/R/632/1600, National Institute of Agricultural Engineering, Silsoe, 1976 Wayman, J. A.; O’Dogherty, M. J.; Joyce, F. W. Trials with lightweight sugar beet toppers. British Sugar Beet Review 1975,43(3): 123 O’Dogherty, M. J.; Wayman, J. A.; Joyce, F. W. Field trials with lightweight sugar beet toppers. Proceedings of 40th Winter Congress, IIRB, 1977, pp. 89-l 12