ESTIMATING TRACTOR DRAWBAR PULL

FROM SOIL PROPERTIES

H. P. HarrisonMember CSAE

Department of Agricultural EngineeringUniversity of Alberta

Edmonton, Alberta

byR. G. Cessford

Junior Member CSAE

Department of Agricultural EngineeringUniversity of Alberta

Edmonton, Alberta

INTRODUCTION

The ability to predict the performance of a tractor in the field haslong been a goal of the agriculturalengineer. Extension personnel, andsome farmers, have been guided bytaking some percentage of the drawbar pull reported by the NebraskaTractor Tests. Friesen and Domier(2) more recently suggest the useof the coefficient of traction (static)as a guide. In general, farmers solvethis problem on a trial and errorbasis. Only.when a tractor of a different size is purchased is difficultyexperienced and then questions oftire size, amount of ballast, allowableslippage, etc., are raised. Reece (8)has stated, "The principal problem isto determine the maximum thrustthat the tractor can exert and the wayin which it grows with slip". He hasmodified Coulomb's equation forshear stress as follows:

P _ (aC + R tan <f>)X 1

where P = soil thrust (lbs.)

a = tire contact area(sq. in.)

C — cohesion (psi)

R — dynamic soil reaction, driving wheels(lbs.)

<f> — internal angle offriction (degrees)

X — slip function.

The derivation of the slip function(X) cannot be noted here but it isessentially a function of the slippageand the length of the tire contact, L.In addition, Reece has determinedvalues of the slip function at maximum drawbar horsepower as a function of L. This provides a logicalbasis for comparing tractive performance. Reece concludes that thetheory is oversimplified but feels itis probably adequate for evaluatingtwo wheel versus four wheel drive

62

tractors. In view of this it is alsoprobably adequate to evaluate different sizes of two wheel drive tractors and even different tire sizes andamounts of ballast. The latter arecommon queries of farmers becauseof the options provided by the tractormanufacturers.

Unfortunately equation 1 cannot beapplied for local soils as the soildynamic parameters C and <f> are unknown. Rutledge and MacHardy (9)in their study on the influence ofweather on field tractability circumvented this difficulty by using alinear relationship between the shearforce and the plastic parameters ofsoil developed by NichoFs (6). Fortheir purpose they chose the relationship for soils within the plastic range.Since tillage is not normally carriedout in this range NichoFs relationshipfor soils below the plastic range,

which is noted below, is appropriate.r — 0.Q6M (pn + 20) + a- +

PI 0.6 2

where r — shear stress (psi)o- = normal stress (psi)M — moisture con

tent (%)PI — lower plastic limitPn — plasticity number —

.6 (% clay) - 12

The distinct advantage for eitherrelationship is that the plastic parameters are known for most of the soilsin Alberta. Equation 1 then becomes:

P = (R +

8))X ..

+•06aM

PI(.6c +

3

where c is the clay content of the soilin percent. With the exception of R,values required are readily availableand appear in Tables 1 and 4.

TABLE I. MECHANICAL ANALYSIS OF ALBERTA SOILS (Ap horizon)*

Soil Zone Soil Series Soil Class Mechanical

Analysis%S %Si %C

PlasticityNumber**

Pn

LiquidLimit***

Pu

Brown Cavendish

Foremost

Seven Persons

SL

L

C

77

45

18

11

35

32

12

20

50

0

18.0

19

29

46

Dark

Brown

CarmangayGranum

Coaldale

LS

L

CL-C

81

42

28

10

37

30

9

21

42

0.6

13.2

19

26

43

Thin

Black

Irma

Elnora

Three Hills

LS-SL

L

C

77

37

16

12

38

36

11

25

58

3.0

22.8

23

39

59

Black Peace Hills

Angus RidgeMalmo

LS

L

SIC

82

42

15

10

33

35

8

25

50

3.0

18.0

20

42

60

GreyWooded

CulpBreton

Maywood

LS

L

CL-SICL

80

42

30

8

36

42

12

22

28

1.2

4.8

14

26

36

Based on data obtained from the Department of Soil Science,University of Alberta.Calculated by the formula Pn = 0.6C-12Although values are given for liquid limit for the soil classesLS-SL, it should be noted that the liquid limit for cohesionlesssoils is meaningless (5).

CANADIAN AGRICULTURAL ENGINEERING, VOL. 11, No. 2, NOVEMBER 1969

TABLE II. ANALYSIS OF VARIANCE OF THE DIRECT SHEAR RESULTS

Source of Variation Degrees of Sum of Mean

Freedom Squares Squares F

Replicates 2 0.22 0.11 0.06

Soils (S) 1 951.06 951.06 490.24*

Moisture (M) 2 255.12 127.56 65.75*

Pressure (P) 2 230.44 115.22 59*. 39*S x M 2 219.26 109.63 56.51*

S x P 2 59.89 29.94 15.43*

M x P 4 32.12 8.03 4.14*

S x M x P 4 7.14 1.78 0.92

Error 34 65.83 1.94

Total 53 1,821.08 1.94

* Significant at .01 probabi lity level (10)

The validity of using NichoFs equation for soil strength is questioned inthe light of recent investigations. Additional variables have been foundwhich effect the shear strength. Hanson, Johnson and Young (4), for example, found that soil densities andloading velocities are significant.Vomcil and Chancellor (11) concluded that soil strength may changewith water content in a manner notadequately described by the Atter-berg limits (plastic parameters).These and other findings raise seriousquestions with respect to the relationship suggested by Nichols. On theother hand because of their simplicityit would be highly desirable if theseequations could be applied to thepractical problems of traction andtillage. In view of this a study to determine the practical limits of applying equation 2 (and therefore equation 3) was initiated.

EXPERIMENTAL PROCEDURE

A completely randomized factorialdesign was used for the experiment.It was a 2 X 3 X 3 factorial with thefollowing levels:

Soil, S — 2: i = 1,2.

Moisture, M — 3: j — 1. . . 3.

Normal stress, a- — 3: k — 1. . . 3.

Replicates, R — 3: 1 — 1. . . 3.The complete mathematical description for any observation is

xijkl = f* + S, + M,+ <rk +(SM)„ + (So-).k + (cr)|k +(SMor).jk + el|kl 4

Since a fixed effects model was used(i.e. S, M and a- were fixed) theerror term, ejjkl, was used for testing

main effects and interactions. The results of the statistical analysis appearin Table 2.

study, a method of determining shearing stress in the soil while varying thesoil properties and normal loadingwas required. It was also desired toachieve normal stresses of the approximate magnitude found under thetraction wheel of a rubber tired tractor (3). The direct shear apparatuswas chosen because it met the aboverequirements and in addition provideddirect, easily computed results with aminimum of sample preparation.

The type of shear apparatus usedwas "box shear" (as distinct from ringshear) which consists basically of arectangular box the top half of whichcan slide over the bottom half. Theinside dimensions of the shear boxwere 2.37 X 2.37 inches giving aninitial shear area of 5.62 in2. The normal load on the failure plane was applied through a load capby means ofa crossbar and loading yoke. The baseand load cap both had projectingmetal gratings imbedded in the interior surfaces to ensure a uniformdistribution of stress along the failuresurface. Movements of the shear boxwere measured by means of dialgauges and the horizontal (shearing)force was measured by means of acalibrated proving ring.

Soil

Three Hills Clay and Elnora Loam,both cohesive soils, were chosen onthe basis of widely separated claycontents and ready availability. Bothwere from the Ap horizon and hadbeen ground to a maximum particlediameter of 2 mm. Particle sizeanalyses for these and other soils inAlberta may be found in Table 1.

Preparation of the samples for theshear tests involved dividing each of

Equipment

Soil strength parameters whichestimate the shear strength of a soilmay be obtained by using severaldifferent soil shear devices. These include the triaxial shear, shear box andannular shear ring devices. A majordisadvantage of these methods is thatthe strength for a given soil conditionis a function of the device used toobtain it (1).

To meet the objectives of this

the soil types into smaller lots andmoisturizing them to the desiredlevels. The three soil moisture contents were approximately 20, 25 and30 percent. TTiese levels were selectedto cover a range between the 1/3atmosphere and 15 atmosphere percentages for both soil types. Samplesof air-dry soil were placed in a container and sufficient water was addedto achieve the desired moisturelevels. Each moisturized sample wasthen mixed for 5 minutes beforebeing transferred to a sealed plasticbag. The sealed samples were left for7 days to allow the moisture to reachequilibrium within each sample.

Procedure

Soil samples were placed in theshear box removing the larger voidsin the process. All samples were allowed to consolidate for 5 minuteswhile subject to the normal stress inorder to achieve a uniform level ofdensity. In all cases the rate of deformation had become extremely slowby the end of the 5-minute interval.

Each sample was sheared at avelocity of approximately 1.5 inch perminute and total shearing force wasread from the calibrated proving ringdial. Shearing force was recorded at1/25 inch increments of deformationuntil failure was reached. The strainrate of 1/5 inch per minute waschosen for this experiment because itwas the fastest rate at which reliablereadings could be taken from theshear apparatus.

The soil was then removed fromthe test apparatus and part of it usedfor moisture content determination.The results are given in Table 3 andare plotted on a graph of maximum

CANADIAN AGRICULTURAL ENGINEERING, VOL. 11, No. 2, NOVEMBER 196963

TABLE HI. COMPARISON OF EXPERIMENTAL SHEAR STRENGTHSWITH CALCULATED VALUES

Soil Moisture Normal Stress Maximum Shear Strength Maximum Shear Strength-*Type Content(%) o(psi) Replicates x(psi) (calculated) t(psi)____ 12 3

Three

Hills

Clay

EInora

Loam

20.8

26.4

31.1

18.6

23.2

28.7

10.41

11.83

19.24

13.21

15.71

23.03

11.61

16.43

21.24

12.67

17.14

21.78

10.41 12.14 13.03 14.46

14.83 15.89 16.43 16.07

19.24 20.71 19.64 18.92

10.41 13.39 13.92 13.39

14.83 17.32 15.89 16.07

19.24 18.75 18.92 21.43

10.41 10.00 10.36 11.78

14.83 13.93 13.04 13.21

19.24 16.78 14.82 16.24

10.41

14.83

19.24

10.41

14.83

19.24

6.43 6.78 6.25

8.04 16.07** 7.32

8.39 8.04 8.21

3.21 2.32 2.50

2.80 3.04 3.21

3.32 3.39 4.11

12.48

16.90

21.31

12.88

17.30

21.70

13.21

17.63

22.04

11.45

16.14

20.55

11.90

16.32

20.73

12.12

16.54

20.95

* calculated from equation 2.** rejected as in error.

.a, 20

»-

toi/>

•" 15

*-to

XCO

5

x

<

10

THREE HIUS ClAY

EINORA LOAM

• <r, - 10.4 psi

• «r2 * 14.8 psia tr, • 19.24 psi

LOWER PLASTIC LIMIT

(ELNORA LOAM)VI

K (THREE HILLS CLAY)

15 20 25 30 35

PERCENT WATER

'LOWER PLASTIC LIMIT

40 45

1. Maximum shear strengths of Three Hills clay and EInora loam at differentmoisture contents and normoJ stresses.

shear stress versus soil moisture (Fig.1). The maximum shear stresses ascalculated from equation 2 appear inTable 3.

Mohr strength Envelopes (5) wereplotted using the experimental datafor each soil-moisture combination.Values of C and d> were obtainedfrom these curves and are shown inTable 5.

RESULTS AND DISCUSSION

The analysis of variance (Table 2)indicates that not only the maineffects but all the first order interactions were significant. The significance of the main effects indicatedthat the variations in shear strengthbetween soil types, among the threemoisture levels and among the threenormal pressures were statisticallysignificant. The first order interactions, soil X moisture, soil X pressure and moisture X pressure werealso statistically significant. The latterindicates a differential response ofthe maximum shear stress dependingon the interactions of the factorsshown.

It can be seen (Table 3), (Fig. 1)that shear strength was considerablydifferent for the two soils at approximately the same moisture content.The shear values increased directlywith normal stress as expected. Increasing the moisture content at agiven normal stress had much lesseffect on the shear strength of ThreeHills Clay than on the EInora Loam(Fig. 1). The relation of moisturecontent to maximum shear strengthshown in this figure does not agreewith the results obtained by Nichols.Nichols determined shear values fromthe Atterberg plasticity constants insuch a way that the maximum shearvalues for the soil at any normal stressalways occurred at the lower plasticlimit. Instead they appear to correspond more closely with those obtained by Vomocil and Chancellorwho concluded that the Atterberglimits do not adequately describe therole of water in its effects on soilstrength.

It can be seen (Table 3) that experimental and calculated valueswere in fairly good agreement (atleast for practical purposes) for theThree Hifis Clay which had a plasticity number, Pn, of 22.8. Some ofthe calculated shear strengths wereslightly higher than experimental

64CANADIAN AGRICULTURAL ENGINEERING, VOL, 11, No. 2, NOVEMBER 1969

values, particularly at higher normalstresses.

In the case of EInora Loam, whichhad a plasticity number of 3.0, thecalculated values for shear were considerably higher than the experimental values, especially at the highermoisture contents. Only at the lowestmoisture contents and the lowest normal stress was there reasonableagreement. This might indicate (although statistical evidence is lacking)that the prediction equation wouldprovide reasonably accurate strengthvalues for EInora Loam at moisturecontents below 20%.

In view of the results obtained itappears that the soils (Table 1) canbe divided into three arbitrary classeswith respect to the applicability ofequations 2 and 3.

1. Cohesionless soils (Pn « 0)— equation cannot be used.

2. Soils with an intermediateplastic range (10>Pn>3) -equation can be used for mois

ture contents up to approximately 20%.

3. Highly plastic soils (PN>10)— equation can be used forany moisture content up to thelower plastic limit.

It should be noted, however, that thisproposed grouping is based on plasticity number only, while equation 2includes both plasticity number andlower plastic limit. Therefore, the reliability of such a grouping may bequestionable. The soil types (Table1) were arranged according to thisclassification (Table 4).

Table 5 indicates that the angle ofinternal friction, <£>, decreases withincreasing moisture content for bothsoil types. The cohesion intercept,however, varies directly with moisture content for the Three Hills Clayand inversely with moisture contentfor EInora Loam. In the case of ThreeHills Clay, the behavior of <£ wouldindicate that at the lowest moisturecontent, the soil was behaving muchlike a dry granular material with

TABLE IV. PROPOSED GROUPING OF ALBERTA SOILS

Group* Soil Series Soil Class Lower Plastic

Limit PI

PlasticityNumber

II

Cavendish SL

Foremost L

Carmangay LS

Irma LS-SL

Peace Hills LS

Culp LS

Granum L

Breton L

EInora

Angus RidgeMaywood

L

L

CL-SiCL

36

39

31

0.6

1.2

3.0

3.0

4.8

III

Coaldale

Seven Persons

Malmo

Three Hills

CL-C

C

SIC

C

30

28

42

36

13.2

18.0

18.0

22.8

Group I: equation 2 not applicable.Group II: equation 2 applicable up to approximately 20% mc.Group III: equation 2 applicable up to lower plastic limit.

TABLE V. EXPERIMENTAL VALUES OF C AND <£

Soil

Three Hills Clay

EInora Loam

Moisture Content <%) C(psi) 4(degrees)

20.8

26.4

31.1

18.6

23.2

28.7

1.2 46

5.6 36

6.1 34

4.9 29

4.1 12.5

1.1 7

CANADIAN AGRICULTURAL ENGINEERING, VOL. 11, No. 2, NOVEMBER 1969

practically all of the resistance toshear resulting from internal friction.At higher moisture contents, the soilexhibited greater plasticity with a resulting increase in the contribution ofcohesion to shear strength. The EInora Loam, on the other hand, has amuch lower clay content and a lowerliquid limit. Therefore, increases inmoisture content within the moisturerange studied resulted in reduced cohesion due to the relatively thickeradsorbed layers of water.

Payne and Fountain (7) report thetypical values of C and (f> to be 1.5psi and 34%° for 50 widely differingsoils. On this basis the cohesion andtherefore the soil strength for the twosoils tested appears large. This wouldalso appear to be suggested by thework of Friesen and Domier (2). Fora specific tire, soil and soil moisture,equation 3 can be reduced and solvedfor the slip function where:

X = P/R + constant 5

This equation is now similar to thatfor determining the coefficient oftraction Ct. To be the same, the rolling resistance would have to be subtracted from the soil thrust P, theweight transfer from R, and the constant equal to zero. The slip functionfor an 18.4 X 34 tire at 16% slip isapproximately .72 whereas Friesenand Domier (2) report the maximumCf to be .55.

The discrepancy appears to be dueto the value of the soil strength asdetermined by the direct shear apparatus or predicted by equation 2.This may be partly explained by thefact that both the Atterberg limitsand the experimental shear valueswere obtained from re-moulded soilsamples while traction in the fielddepends on in place shear values.Consequently, soil may fail in a different manner under a traction tirethan in the direct shear apparatusused. In view of the above, equation3 should be limited for the present tocomparisons of tractor sizes, tires andballast and with certain soils andmoisture contents.

CONCLUSIONS

Difficulties in predicting tractorperformance in the field still remain.The results of this study show thatNichols* relationship for determining

continued on page 73

65

torily. Air temperatures of 50°F and80 percent relative humidity havebeen held for 3 days with ± 0.5°Fdry bulb and ± 1°F wet bulb variation. Temperatures of 100°F andrelative humidities from 35 to 90 percent with ± 1°F dry bulb and± 1.5°F wet bulb variation during a3 day test have been obtained. Testswith birds in the chamber and atintermediate temperature and humidity values have been maintained forup to 6 weeks of continuous operation within the variation mentionedpreviously.

Surface temperature variations onthe thermal radiation plates of ±-2.5°F were encountered. This wasfound to be the result of non uniformair velocities from the air inlets. Redesigning the air inlets for a morestreamlined flow will alleviate thisproblem.

The water spray in addition tomaintaining pre-selected humiditiesalso removes fine dust, ammonia andexcess carbon dioxide.

Temperatures of water enteringand leaving heating and chillingcoils, spray water, air entering andleaving the chamber, air leaving thefan and spray water zone weremonitored by iron-constantan thermocouples connected to a 24 point po-tentiometric recorder.

A computer programme was developed to monitor the operation ofthe equipment. Water volume recorders for the heat exchange coilsare required before the computerprogramme will be able to provideits full potential.

CONCLUSIONS

Equipment was developed to control the environment of a 16 squarefoot chamber for poultry by providing accurate control of thermal radiation, air temperature, wet bulb temperature, air velocity and Hght intensity. When all monitoring equipment for input and output factors isadded, a complete energy balancecan be determined. With accurateenvironment control, genotype byenvironment interactions can beevaluated.

ACKNOWLEDGEMENTS

The authors wish to thank Mr. F.Seipp of Broadway Refrigeration Co.,Vancouver, for the design and de

velopment of the refrigeration andchilled water storage. Thanks arealso due to Mr. W. Anderson andMr. D. Lunam (3rd year MechanicalEngineering students) who constructed the equipment. Appreciation is also expressed to the CanadaDepartment of Agriculture ResearchBranch for financial support of thisproject.

REFERENCES

1. Longhouse, A. D., H. Ota, R. E.Emerson, J. O. Heishman, 1967.Heat and Moisture Design Datafor Broiler Houses. A.S.A.E. PaperNo. 67-442.

2. Roberts, C. W. 1964. Estimationof Early Growth Rate in theChicken. Poultry Science 43: 238-252.

3. Skoglund, W. C. and D. H. Palmer,1962. Light Intensity Studies withBroilers. Poultry Science 41: 1839-1842.

4. {Staley, L. M., C. W. Roberts andD. C. Crober, 1967. The Effect ofThermal Radiation on EarlyGrowth of the New HampshireChicken. Can. Agr. Eng. 9: 39-42.

5. Suggs, C. W., 1967. Temperatureand Enthalpy Equivalence ofThermal Radiation. Trans. Amer.Soc. Agr. Eng. 10: 727-729.

ESTIMATING TRACTOR . . .

continued from page 65

soil strength is not in complete agreement with results obtained from direct shear tests on two Alberta soils.Predicted tractor drawbar performance based on soil strength as determined by equation 2 or by thedirect shear apparatus may not correspond to values obtained in actualfield tests. However, comparisons oftractor sizes, tire sizes and ballast maybe made provided the limitations oflaboratory or calculated shear valuesare taken into consideration.

Better relationships of in situ soilstrength to soil parameters are required to adequately describe tractorfield performance.

REFERENCES

1. Bailey, A. C. and Weber, J. A.

CANADIAN AGRICULTURAL ENGINEERING, VOL. 11, No. 2, NOVEMBER 1969

1965. Comparison of Methods ofMeasuring Soil Shear StrengthUsing Artificial Soils. Transactions of the A.S.A.E., 8: (2) 153-156, 160.

2. Friesen, O. H. and Domier, K. W.1967 and 1968. Traction Tests.Extension Service Branch, Manitoba Department of Agriculture.

3. Gill, W. R. and VandenBerg,G. E. 1967. Soil Dynamics inTillage and Traction. AgricultureHandbook No. 316. AgriculturalResearch Service. U.S. Dept. Agr.pp. 355-362.

4. Hanson, T. L., Johnson, H.P. andYoung, D. F. 1967. DynamicShearing Resistance of Soils.Transactions of the A.S.A.E., 10:(4) 439-443, 447.

5. Means, R. E. and Parcher, J. V.1964. Physical Properties of Soils.Charles E. Merrill Books Inc.,Columbus, Ohio.

6. Nichols, M. L. 1932. The Dynamic Properties of Soil III. ShearValues of Uncemented Soils. Agr.Eng., 13 (8), 201-204.

7. Payne, P. C. J. and Fountaine,E. R. 1954. The Mechanism ofScouring for Cultivation Implements. N.I.A.E. Tech. Memo 116.

8. Reece, A. R. 1967 Tractor Designand Tractive Performance. Proc.of Agricultural Engineering Symposium. Inst, of Agric. Engs.,Penn Place, Reckmansworth,Herts, U.K.

9. Rutledge, P. L. and MacHardy,F. V. 1968. The Influence of theWeather on Field Tractability inAlberta. Can. Agr. Eng., 10: (2),70-73.

10. Steele, R. G. D. and Torrie, J. H.1960. Principles and Proceduresof Statistics. McGraw Hill BookCompany, Inc., New York.

11. Vomocil, J. A. and Chancellor,W. J. 1967. Compression andTensile Failure Strengths ofThree Agricultural Soils. Transactions of the A.S.A.E., 10: (6),771-774.

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