1) The document presents models for predicting soil implement forces, including equations to calculate draught and vertical forces for a wide range of implements like tines, discs, and mouldboard ploughs. 2) The models were developed based on extensive laboratory and field studies investigating the effects of variables like tine width, depth, rake angle, and speed on implement forces. 3) When compared to measured force values, the general soil mechanics equation accurately predicted horizontal forces within an average error of -3% and vertical forces within an average error of 33%, providing a good basis for agricultural equipment design.

1. Integrated Soil TillageIntegrated Soil Tillage
Force PredictionForce Prediction
ModelsModels
Richard GodwinRichard Godwin
andand
MichaelMichael O’DoghertyO’Dogherty
Engineering GroupEngineering Group
National Soil Resources InstituteNational Soil Resources Institute

2. Soil implement forcesSoil implement forces
Sugar cane fields – Iran Land preparation – South Australia
Autumn cultivations - Cambridge

3. Soil failure patternsSoil failure patterns
After: Godwin and Spoor, 1977

4. MohrMohr –– Coulomb RelationshipsCoulomb Relationships
Coulomb Equation
τ
σ
φ
c
τ = c + σ tan φ
σ3
σ1
σ1
σ3
C = cohesion
Ø = internal friction
σ3 σ1

5. General Soil Mechanics EquationGeneral Soil Mechanics Equation
2 dimensional passive soil failure2 dimensional passive soil failure
Direction of travel
( )( )[ ] )sin(2
δαγ γ +++= wqdNcdNNdH qcat
Ht
Vt
α
P
Normal
δ
Blade or tine face
Soil
surface
( )( )[ ] )cos(2
δαγ γ +++−= wqdNcdNNdV qcat
+ vertical forces act
After: Hettiaratchi , Witney and Reece,1966

6. Dimensionless N Factor’sDimensionless N Factor’s
Nγ
α
φ
δ = 0
δ = φ
δ = 0
δ = 0
δ = φ
δ = φ
Nγ
Nc
Nc
Nq
Nq
20
10
1
0
Nγδ = Nγδ = 0 Nγδ = φ Nγδ = 0
δ /φ
After: Hettiaratchi, Witney and Reece, 1966

7. Narrow Tine EquationsNarrow Tine Equations
3 dimensional soil failure3 dimensional soil failure
After: Godwin and Spoor, 1977
Tine width (w) + crescent
effects
( ){ }13
1
−− mmdw +

8. Inertia termsInertia terms
wdN
g
v
a
2
γ
Inertia term =
where
( )
( ) ( ) ( )( )( )αβφβδαβα
φββ
cottan1cotsincos
cottan
+++++
++
=aN
After :McKyes, 1985

9. General Soil Mechanics EquationGeneral Soil Mechanics Equation
for blades and narrow tinesfor blades and narrow tines
Including velocity effectsIncluding velocity effects
Horizontal
( ) ( )( ) ( ) )sin(6.0)1(3
1
δαγγ γ +++−−+++= dwdNvmmdwqdNcdNNdH aqcat [ ]22
Force = [( Soil factors )(Implement size) + Inertia term ]Direction
Vertical
( ) ( )( ) ( )[ ] )(cos6.0)1( 2
3
12
δαγγ γ +++−−+++−= dwdNvmmdwqdNcdNNdV aqcat
After: Hettiaratchi et al.,1966; Godwin and Spoor, 1977; Godwin et al.,1984; McKyes,1985 and
Wheeler and Godwin, 1996

10. Deep or Very Narrow TinesDeep or Very Narrow Tines
–– Lateral failureLateral failure

11. Deep tine failureDeep tine failure
After: Godwin and Spoor, 1977
Critical depth, dc
Lateral Force (Q) is based
on Meyerhof (1951)
Bearing Capacity Equation
and N factors

12. Additional component for very narrow tinesAdditional component for very narrow tines
( ) ( ) ( )22
sin15.0 cqcc ddwNddwcNQ −
′
−+−
′
= γφ
( )
( )( ) ⎥
⎦
⎤
⎢
⎣
⎡
−
+−
+
=
′
1
2sinsin1
sin1
cot
tan2
φηφ
φ
φ
φθ
e
Nc
( )
( )( )φηφ
φ φθ
+−
+
=
′
2sinsin1
sin1 tan2
e
Nq
Hence the total horizontal force is
HT
Q
dc
d
D = HT + Q
Lateral failure under plate glass After: Godwin and Spoor ,1977

13. Laboratory studiesLaboratory studies
Controlled conditions for soil
disturbance and implement
force measurement

14. Effect of tine widthEffect of tine width
-0.5
0
0.5
1
1.5
2
3
0 10 20 30 40 50 60
Tine width, mm
Force,kN
After: Godwin and Spoor, 1977
Vertical force
Predicted
2.5
Horizontal forceMeasured▀

15. Effect of tine depthEffect of tine depth
0
0.5
1
1.5
2
2.5
100 120 140 160 180 200 220 240
Tine depth, mm
Force,kN
After: Godwin and Spoor, 1977
Vertical force
3
3.5
Horizontal force
▀
Predicted
Measured

16. Effect of rake angleEffect of rake angle
-1
-0.5
0
0.5
1
1.5
2
2.5
3
3.5
30 40 50 60 70 80 90 100
Tine rake angle, degrees
Force,kN
After: Godwin and Spoor, 1977
Horizontal force
Vertical force
▀
Predicted
Measured

17. Effect of speedEffect of speed
0
1
2
3
4
5
0 2.5 5 7.5 10 12.5 15 17.5 20
Speed, km/h
Force,kN
After: Wheeler and Godwin, 1996
√ 5gw* √ 5g(w+0.6d)
*After: Schuring and Emori, 1964
Horizontal force
Vertical force
Measured
Predicted

18. Multiple tinesMultiple tines
After: Godwin, Spoor and Soomro, 1984

19. MultipleMultiple --interacting tine modelinteracting tine model
Imaginary tines Real tine
di
d
d
D =ns HTs + nd HTd – ni HiT
( ) ( )}{[ ] ( )δαγ γ +−−++−+= sin13
12
mmdNqdNcdNdnHnHnD iqicaiiiTddTss
After: Godwin, Spoor and Soomoro, 1984

20. Effects of tine spacingEffects of tine spacing
Spacing
Too close
Optimum
Too wide
After: Godwin, Spoor and Soomro, 1984

21. Effect of tine spacingEffect of tine spacing
▲ Predicted
● Measured
After: Godwin, Spoor and Soomro, 1984

22. Anchor performanceAnchor performance
Mg
Ht
Vt
Vt+ Mg
Pa
( ) ( )( )[ ] )sin()1(3
12
δαγ γ +−−+++= mmdwqdNcdNNdH qcat
( ) tta HMgVP ++= δtan
( ) ( )( )[ ] )(cos)1(3
12
δαγ γ +−−+++−= mmdwqdNcdNNdV qcat
where
After: Godwin and Wheeler, 1996

23. Anchor forcesAnchor forces
0
10
20
30
40
50
60
0 0.2 0.4 0.6 0.8 1
Anchor depth, m
Anchorforce,kN
After: Godwin and Wheeler, 1996
Compact sandy loam: field
Loose sandy loam: laboratory
Compact sandy loam: laboratory
Predicted ■ Measured

24. Disc forcesDisc forces

25. Disc harrow modelDisc harrow model
( )( ) θθγγ γ sin22sin 22
dRddNdRcdNNdP qfcai −−++=
Passive reaction
Passive soil crescent
reaction
Direction of travel Bearing capacity/
scrubbing reaction
Plan of disc
λ = clearance angle
θ
θ = sweep angle
λ
Surcharge effects Effective width
Vs =cNc’A
Nc’ Bearing Capacity Number
Scrubbing reaction
A Area
After. Godwin, Sieg and Allott, 1987

26. Disc forcesDisc forces
( ) θδα sinsin += PDp
( )δα +−= cosPVp
( ) θδα cossin += PSp
( ) ( )θλδα −−= sintanss VD
( )
λ
θλπ
2
sin
−
′= AqVs
( ) ( )θλδα −−= costanss VS
sp DDD +=
sp VVV +=
sp SSS −=
PassivePassive
TotalTotal
DraughtDraught
VerticalVertical
Lateral
ScrubbingScrubbing
Lateral
After. Godwin, Sieg and Allott, 1987

27. Effect of sweep angle on draught forceEffect of sweep angle on draught force
0
0.5
1
1.5
2
2.5
3
3.5
0 20 40 60 80 100
Disc sweep angle, deg
Draughtforce,kN
Measured
Predicted
▀
After. Godwin, Sieg and Allott, 1987

28. Effect of sweep angle on lateral forceEffect of sweep angle on lateral force
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
0 20 40 60 80 100
Disc sweep angle, deg
Lateralforce,kN
After. Godwin, Sieg and Allott, 1987
Measured
Predicted
▀

29. Effect of sweep angle on disc forcesEffect of sweep angle on disc forces
Sweep angle (θ), degrees
Force,kN
Horizontal
Vertical
Lateral
Predicted
Measured
After: Godwin et al, 1987 and Gill et al, 1979

30. Mouldboard plough forcesMouldboard plough forces

31. Mouldboard plough forcesMouldboard plough forces
Landside
Mouldboard
Point
Share
Ht
Hp
Hs
Hmc
He
HcsHms Hfs
βθ
Direction of travelDirection of travel
Landside frictional drag force
Lifting energy force
Momentum change force
Passive share force
Passive point force
After: Saunders, Godwin and O’Dogherty , 2000

32. Mouldboard plough draught forceMouldboard plough draught force
Ht = Hp + Hs + Hmc + He + Hcs + Hms + Hfs
( ) ( ) βδαγγ γ sinsin/22
+++= sssacasss wgdNvNcdNdH
Total forceTotal force
WhereWhere
( ) ( ){( )θδθγ costansin11)/ 2
−−+= vdwdwgH ssppmc
( ) sssppe ddwdwH += γ2
( ) ( ) δβδαγγ γ tancossin/22
+++= sssasscs wgdNvNcdNdH ca
( )( ) ( ) δδθθγ tantansin1sin/ 2
−+= vdwdwgH ssppms
( ) δδγ tantan95.0 sssppfs dwdwH +=
After: Saunders, Godwin and O’Dogherty , 2000

33. Effect of velocity on plough draught forceEffect of velocity on plough draught force
0
0.5
1
1.5
2
2.5
3
3.5
0 1 2 3 4 5
Speed (m/s)
DraughtForce(kN)
225mm deep, measured, predicted
125mm deep, measured, predicted
After : Balafoutis,2003
Laboratory studies : Sandy loam soilLaboratory studies : Sandy loam soil

34. 0
1
2
3
4
5
6
7
0 0.5 1 1.5 2 2.5
Speed (m/s)
DraughtForce(kN)
Effect of velocity on plough draught forceEffect of velocity on plough draught force
225mm deep, measured, predicted
180 mm deep, measured, predicted
After : Balafoutis,2003
Field studies : Sandy clay soilField studies : Sandy clay soil

35. ShallowShallow -- high speed mouldboard ploughhigh speed mouldboard plough
Because depth has a greater effect on draught
force than forward speed, shallow high speed
ploughs are becoming a popular alternative

36. Soil parameters Tine parameters
Force prediction spreadsheet modelsForce prediction spreadsheet models

37. Predicted v measured tinePredicted v measured tine and disc forcesand disc forces
HorizontalHorizontal
0
1
2
3
4
0 1 2 3 4
Measured draught force, kN
Predictedforce,kN
1:1
-20%
After: Godwin and O’Dogherty, 2003
Average error -3%
5 +20%

38. -1
-0.5
0
0.5
1
1.5
2
2.5
-0.5 0 0.5 1 1.5 2
Measured vertical force, kN
Predictedverticalforce,kN
1:1
+50%
-50%
After: Godwin and O’Dogherty, 2003
Average error + 33%
VerticalVertical
Predicted v measured tinePredicted v measured tine and disc forcesand disc forces

39. 0
1
2
3
4
5
6
0 1 2 3 4 5
Total Measured Force (kN)
TotalPredictedForce(kN)
-20%
+20%
1:1
125 mm
225 mm
Laboratory studies : Sandy loam soilLaboratory studies : Sandy loam soil
Predicted v measured plough draught forcesPredicted v measured plough draught forces
After : Balafoutis,2003

40. 0
2
4
6
8
10
12
0 1 2 3 4 5 6 7 8
Total Measured Force (kN)
TotalPredictedForce(kN)
1:1
+20%
+20%
180 mm
225 mm
Predicted v measured plough draught forcesPredicted v measured plough draught forces
Field studies : Sandy clay soilField studies : Sandy clay soil
After : Balafoutis,2003

41. ConclusionsConclusions
The general soil mechanics equation has been
developed to enable the draught and vertical forces
to be calculated for a wide range of implements.
The use of the equations has:
1. predicted the magnitude of the horizontal soil
force with an average error of -3%, with the
majority of comparisons within ±20%,
2. predicted the magnitude of the vertical soil force
with an average error of +33%, with the majority
of comparisons within ±50%, and
3. provided a good basis for designers of
cultivation equipment for optimal design of
cultivating tools.
The spreadsheet model will be freely available.

42. AcknowledgementsAcknowledgements
Gordon Spoor,Gordon Spoor,
Tony Reynolds,Tony Reynolds,
DanDan HettiaratchiHettiaratchi
andand
The DouglasThe Douglas BomfordBomford TrustTrust