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
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
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
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
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
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.