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Four-wheel drive or rear-wheel drive for high power farm tractors
Journal of Terramechanics, 1968, Vol. 5, No. 3, pp. 9 to 28. Pergamon Press Printed in Great Britain.
FOUR-WHEEL DRIVE OR REAR-WHEEL DRIVE FOR HIGH POWER F A R M TRACTORS* W. S6rINE COMPARED with rear-wheel driven tractors, farm tractors with four-wheel drive have not in the past had a large share of the market. Recently a larger number of tractor models with four-wheel drive have come onto the market in Germany, England and the U.S.A. The question of whether with farm tractors of higher capacity a larger proportion of models with four-wheel drive would be justified will be discussed in the present paper. DEVELOPMENT OF ENGINE POWER AND THE WEIGHT OF THE TRACTOR PER UNIT OF HORSEPOWER The increase in mean tractor engine horsepowers which has become apparent in the U.S,A. and the U.K. since 1947 and in the Federal Republic of Germany since 1954 is still continuing (Fig. 1). It is due to the demands of the agricultural industry for higher rates of work of farm machinery and equipment and, especially 100
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JSA /
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19,~7
1950
5,(,
50
62
66
70
74
78
FIG. 1. Development of mean engine horsepower of new models of tractors in the U.S.A. (top curve) and Federal Republic of Germany (lower curve) from 1947 to 1965 according to Seifert. in the U.S.A., it is promoted by the increase in the size of agricultural holdings and the desire to keep labour costs to a minimum. In that country the average power of new models of tractors was about 55 h.p. t in 1963 (64 h.p. in 1967) and in *Translated from Grundlagen der Landtechnik, 20, 1964, by E. Harris, National Institute of Agricultural Engineering, Silsoe, Bedford. 1"Metric horsepower throughout.
to
w. SiSHNE
Western Germany about 32 h.p. (40 h.p. in 1967). One third of all 1963 models of tractors in the U.S.A. was in the power range 65-100 h.p., whereas in Germany an increasing proportion was in the 45-60 h.p. class. In 1962 some tractor models of 100-120 h.p. appeared on the market (e.g. John Deere 5010). At the same time tractors with four-wheel drive in the 150-300 h.p. class have been developed (e.g. IHC 4300, Fig. 2). These are, however, no longer true farm tractors, but tractors with engines, transmissions and ground drives intended for the earthmoving industry which have been modified for agriculture. Since they are as yet likely to be produced only in small numbers, they will be neglected in the present considerations.
FIG. 2. IHC tractor 4300 on Nebraska University test track. The higher engine power of the tractor can be used to increase the working width, i.e. in the case of soil cultivation, to pull a plough with a larger number of bodies, to combine several implements (minimum tillage), or to travel at higher speed. In the first two cases the tractor and implement have to become heavier and hence correspondingly more expensive in proportion to the rate of work, so that the weight per unit of horsepower of the tractor remains constant at increasing engine power. In the third case only a small increase of tractor and implement weight is required, so that the weight per unit of horsepower can be reduced. This solution ought to be more economical. in fact all three methods are being followed at the same time and should also be developed further in the future. The working speeds are being raised only slowly because the tractor and implement must first be adapted to the higher speeds with respect to quality of work and ride comfort.
FOUR-WHEEL
DRIVE OR REAR-WHEEL
DRIVE
11
Figure 3a shows the weight of the tractor per unit of horsepower as a function of engine power. In the range above 70 h.p. the decrease in specific weight with n "c" G ®
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(3b) Specific w e i g h t ( k p / h . p . ) o f t r a c t o r s in r e l a t i o n t o e n g i n e p o w e r (h.p.) f r o m d a t a b y t h e I n s t i t u t fiJr S c h l e p p e r f o r s e h u n g o f the F A L . ( G ) I m p l e m e n t carrier; (A) 4 - w h e e l drive
increasing engine power does not appear to continue at first. However, it is improbable that this indicates a change in the erstwhile trend. With the new tractor models of 80-120 h.p. the specific weight is also likely to decrease when the power output is further developed. This will apply all the more, the greater the increase in forward speeds (Fig. 3b). FORMS
OF POWER
TRANSMISSION
BETWEEN
TRACTOR
AND SOIL
For tractors with a capacity of 60-140 h.p. the following means of transmitting tractive power are available : (1) through conventional rear-wheel drive
W. SOHNE
12
(2)
through four-wheel drive (a) with small front and large rear wheels (b) with wheels of equal size (c) in the form of a tandem tractor (3) through tracks. These means will now be compared critically.
What improvements are to be expected lrom ~our-wheel drive? The extent to which the drawbar pull of tractors can be increased by four-wheel drive compared with rear-wheel drive has been examined repeatedly [1-5]. The improvement in traction is due to two reasons : (1) In the case of four-wheel drive the entire weight of the tractor is utilized as a load on the driven axles, whereas w~h rear wheel drive the rolling resistance of •the front wheels, the axle load of which in operation is between 10 and 40 per cent of the total weight, has to be deducted from the tractive effort of the rear wheels. (2) In the case of a four-wheel drive tractor with wheels of equal size the front wheels compact the soil, reduce the total rolling resistance and lead to a better
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FIG. 4. Traction coefficient (top) and coefficient of rolling resistance (bottom) as a function of slip (%) under different soil conditions. (From top to bottom) Concrete, tarmac (dry); dry loam, stubble; loamy sand, stubble; loamy sand, wet; clay loam, wet; silt; soil slurry; silt, soil slurry; clay loam, wet; dry loam, stubble, loamy sand, stubble; concrete.
FOUR-WHEEL DRIVE OR REAR-WHEEL DRIVE
13
transmission of power by %he rear wheels. The extent of this improvement depends greatly on the soil condition. While in American measurements in a soil tank, i.e. on relatively loose soils, at 16 per cent slip the rear wheels had a 25-35 per cent better traction coefficient than the power-driven front wheels and at 40 per cent an improvement of 14-20 per cent was achieved in the second pass, the results of measurements obtained at the Institut fiir Schlepperforschung (/nstitute for tractor research) Braunschweig-ViSlkenrode on different soils show improvements of 6-18 per cent and 16 per cent slip and 6-11 per cent at 40 per cent slip [1], the greater improvements referring to soils with a low bearing capacity and the smaller ones to soils with good bearing characteristics. The tractive coefficient-slip curves of a tractor tyre on different types of soil and under a range of conditions can be combined in groups, as in Fig. 4. The calculations of examples made below are based on four different soil conditions, under which the tractor is likely to operate in the field and which, therefore, do not include extremes of unfavourable values, i.e. (a) dry loam, stubble field (b) sandy loam, stubble field (c) wet, sandy loam (d) wet clay loam. On the basis of the above measurements, traction coefficients have been assumed for four-wheel drive which are better than those for rear-wheel drive by the values given in Fig. 5. Using the tractor data given in Table 1, the power balances and
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14
W. S O H N E O0
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Drawbar pull 6-9. Comparison of power balances, efficiencies ~ and slip cr between four-wheel drive (dashed line) and rear-wheel drive (full line) in relation to drawbar pull (kp) under different soil conditions. Coefficients of traction and rolling resistance from Fig, 5. Tractor data used for the graphs are given in Table 1. N~=drawbar pull N~mioss due to slip N p = loss due to rolling resistance (a) Dry loam, stubble; (b) Dry, loamy sand, stubble; (c) Wet, loamy sand; (d) Wet clay loam. FIGS.
2800
kp
FOUR-WHEEL DRIVE OR REAR-WHEEL DRIVE
15
efficiencies were calculated for the above soil condition (Figs. 6-9). On the dry loam, stubble field (Fig. 6) the tractive effort at 20 per cent slip is 27 per cent and at 50 per cent slip 20 per cent higher than with rear-wheel drive, the optimum efficiency of power transmission being 77 instead of 70 per cent. On wet clay loam the drawbar pull at 30 per cent slip is as much as 57 per cent and at 50 per cent slip, 44 per cent higher, the optimum efficiency being 51 instead of 40 per cent. Thus, TABLE 1. ASSUMEDTRACTORDATAFOR THE CALCULATIONOF THE POWERBALANCE Rear-wheel drive
Four-wheel drive
Engine power, h.p. Tractor weight without ballast, kp static rear axle weight, kp static front axle weight, kp
85 3400 2300 1100
85 3400 1360 2040
Tractor weight with ballast and driver, kp static rear axle weight, kp static front axle weight, kp
4200 3100 1100
4200 1700 2500
Operational weight without ballast, kp/h.p. Operational weight with ballast, kp/h.p. Wheelbase, m Tyres, rear Tyres, front Height of drawbar, m Forward speed without slip for the sample calculation, m/sec
40 40 49"5 49'5 2'5 2'5 18'4/15-30 AS 12"4/11-36 AS 7"50-16 12-4/11-36 AS 0.45 0"45 2"0
2'0
even under relatively favourable soil conditions, the four-wheel drive shows considerable improvements in drawbar pull and performance. The advantages of fourwheel drive become all the more apparent the less the track is able to transmit power and the higher the rolling resistance. This is clearly shown in Figs. l0 and 11. Figure 10 shows how high the tractor weight G must be with rear- and 4-wheel drive to achieve a drawbar pull Z of 1 Mp under different soil conditions. These soil conditions are characterized by the ratio of drawbar pull to tractor weight which can be attained as a m a x i m u m with a rear-wheel driven tractor in each case. Figure 11 shows the m a x i m u m attainable drawbar pull of rear-wheel and four-wheel drive tractors as a percentage of tractor weight for different soil conditions. Figure 12 indicates the gross tractor weight per unit of horsepower required as a function of the (effective) forward speed at 20 per cent slip according to the drawbar pull-slip curves of Fig. 4 and the performance graphs of Figs. 6-8. However, a qualification was made that only 80 per cent of the engine power is to be transmitted. The full engine power can also be transmitted but of course only with correspondingly higher slip, The graph also shows the required gross tractor weigher under the assumption of a constant engine power of 85 h.p. It follows that at the same working speed a four-wheel drive tractor for soil a could be constructed 17 per cent, and for soils b and c 20 per cent lighter than a rear-wheel driven tractor to transmit the same engine power. If for all soil conditions the four-wheel drive tractor is 20
16
W. S()HNE <9
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Fl6. 10. Tractor weight G required with rear-wheel and four-wheel drive for a maximum attainable pull of Z of 1 Mp on different types of soil and soil conditions.
FIG. 11. Maximum attainable drawbar pull Z of tractors with rear-wheel and four-wheel drive on different types of soil and soil conditions in relation to tractor weight G. The optimum attainable ratio / £1n~x= Zmax/G = max. drawbar pull/tractor weight under given soil conditions for rear-wheel drive is chosen as a measure of soil condition. The scatter is due to different rolling resistances at given Xmax and to different load conditions of the front and rear axle and various load distributions between axles on the basis of the tractor specifications.
per cent lighter, then according to Figs. 6-9 the d r a w b a r pulls at 20 per cent slip will still b e : o n soil a 1-5 per cent
o n soil c 12 per cent
on soil b 7"5 per cent
o n soil d 40 per cent
and at 30 per cent slip o n soil d 25 per cent higher t h a n with rear-wheel drive. Figure 13 shows the engine power which c a n be transmitted a s s u m i n g a constant total weight of the tractor of 4.2 Mp. A c c o r d i n g to it a 21 a n d 24 per cent higher engine power c a n be t r a n s m i t t e d respectively. Moreover, Figs. 12 a n d 13 clearly show that the high performance of m o d e m traclors at low speed can no longer be t r a n s m i t t e d to the ground. A t a slipless speed
F O U R - W H E E L D R I V E OR R E A R - W H E E L D R I V E
17
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speed
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FIG. 12. Required gross specific weight (kp/h.p.) of tractors with four-wheel (dashed line) and rear-wheel drive (full line) as a function of the (effective) speed at 20% slip; the gross tractor weight indicated applies to an assumed constant engine output of 85 h.p. FIG. 13. Available engine power in relation to (effective) speed at 20% slip under the assumption of a constant total weight of the tractor of 4"2 Mp. (Vertical scales) Gross tractor weight (Mp) and gross specific weight (kp/h.p.), and (bottom) engine horsepower (horizontal scales) effective forward speed ( k m / h r ) and forward speed in the absence of slip (km/hr). These graphs are based on the drawbar pull-slip curves and performance curves of Figs. 6-8. It is assumed that the transmission efficiency is 90 per cent and the engine output is 80 per cent of the rated horsepower. Soil a : dry loam, stubble Soil b: sandy loam, stubble Soil c: wet sandy loam.
of 7'5 k m/h r or an effective speed of 6.0 km / hr the required gross weight per unit
of horsepower is given below.
With four-wheel drive, kp/h.p. With rear-wheel drive, kp/h.p.
Soil a
Soil b
Soil c
46"5 56"4
51"2 63"6
60"0 75-0
Is
W. S(JHNE
However, this gross weight per unit of horsepower is not the same as the net weight in Fig. 3. The latter can be increased up to 50 per cent by wheel weights and water ballasting of the tyres and by the weight of the driver. When ploughing with mounted ploughs the rear axle load can be increased by 65 per cent, according to Skalweit, by the weight of the plough and normal soil reaction, with the linkage in a floating position, and up to 85 per cent with a restrained linkage. Although with four-wheel drive the plough and the normal soil reaction also impose an additional load on the tractor, the weight transfer from the front to the rear wheels does not have the effect to increase drawbar pull because both axles are being driven. Assuming that the dead weight of the tractor is increased by 67 per cent in the case of rear-wheel drive and by only 55 per cent with four-wheel d r i v e the net weight per unit of horsepower required is :
With four-wheel drive, kp/h.p. With rear-wheel drive kp/h.p.
Soil a
Soil b
Soil c
30"0 33.7
33'0 38"1
38'7 44'9
Finally, if the slip-free speed can be increased to 10 k m / h r (corresponding to an effective forward speed of 8 km/hr), the net weight per unit of horsepower is reduced to :
With four-wheel drive, kp/h.p. With rear-wheel drive kp/h.p.
Soil a
Soil b
Soil c
22.5 25.3
24'7 28.5
29"0 33"6
It would thus be possible to develop a 100 h.p. four-wheel drive tractor with a ldead weight of 3 M p which is able to pull a 5-furrow plough at an effective speed of 9 k m / h r on light soil, a 4-furrow plough at 8 k m / h r on medium soil and a 3furrow plough at 7-8 k m / h r on heavy soil [13]. Despite the advantages of the four-wheel drive ~ractor on difficult soils the sales of this type of tractor in the power range up to 50 h.p. were considerably less than I0 per cent of the total number of this tractor size. This can be explained as follows: if a rear-wheel driven tractor of, for example, 35 h.p. on heavy soils is found to be inadequate, it is often regarded preferable to buy a 50 h.p. rear-wheel driven one than a 35 h.p., four-wheel driven tractor. The question is whether this idea is still valid at higher engine powers when, for example, a choice has to be made between an 80 h . p four-wheel drive tractor of 3200 kp weight or a 115 h.p. rearwheel driven model of 4600 kp which on difficult soils develop about the same drawbar pull. A model of similar tractors of different sizes (Fig. 14) may serve to answer this question. The weight of similar bodies increases by the third power but their plan area by the second power of their length. Accordingly, as the size of the tractor increases, the increase in weight is greater than that of its area of vertical projection, even if the tractors are not quite similar; i.e. at increasing tractor weight the ratio of weight over area of vertical projection* is increased, as shown in Fig. 15 for the *Since a comparative value only is sought, the projected area F has been taken to be the tractox width bs~h over the rear wheels times the tractor length lso~ from the front of the front wheel to the rear of the rear wheel.
F O U R - W H E E L D R I V E OR REAR-WHEEL D R I V E
,
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FIG. 14. Diagramatic plan view of rear-wheel driven farm tractors of different weights by two firms. The shaded areas indicate the contact areas between tyre and track, assuming a specific pressure of the rear wheels of 1 kp/crn ~ and of the front wheels of 2 kp/cmL
19
20
W. S{YHNE
tractors of Fig. 12. The specific pressure in the contact area between tyre and soil would increase accordingly, if the tyres were increased in size similarly. In view of the need to minimise soil compaction and increase the tractive effort, the pressure in the contact area should remain the same, indeed with larger tractors it ought to be even reduced. Therefore, the contact area should increase at least proportionately to weight and hence more than proportionately to the projected area or the tractor dimensions. According to Bekker [6] the bearing capacity of off-the-road tyres for I000
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FIG. 15. Ground pressure of farm tractors as in Fig. 14 in relation to weight G (kp). The product of bs~h × ls~h was taken as the ground area. earthmoving equipment and military vehicles of tyre diameter D and tyre width b does in fact increase as follows : G = 8550 (D.b) ~'~6 and that of farm tractor tyres, following the expression G = 2400 (D.b)V26; for approximately similar tyres, the equation is G =: 1850 D'a.b, 'where D and b are expressed in m and G in kp (Fig. 16). However, this means that the inflation pressure of the tyres and the specific pressure in the tyre-soil contact area are bound to increase at the same inflation pressure. The areas of contact between tyre and soil have been entered in Fig. 14 on the assumption that the ground pressure of the rear wheels is 1 k p / c m 2 and that of the front wheels 2 k p / c m ~. It will be seen in Figs. 14 and 16 that the tyres of the tractor weighing 7"6 M p are underdimensioned by comparison with the other tractors. These tyres should thus be given a higher inflation pressure. However, this reduces the range of applicability of this tractor compared with that of the other tractors. This consideration of similarity thus sets a physical limit to an increase in the size of conventional rearwheel drive tractors. Independently from this there are the following further limitations : (1) If the tractor is to be used for rowcrop work, the tyres should not exceed 9.5/9 in. in width at a row spacing of the potatoes of 6-25 cm, according to Thaer, and 12.4/11 in. at a row width of 75 cm. According to Schtinke, the corresponding limits for sugar beet are 11.2/ 10 in. at a row width of 450 m m and 12-4 in. at 500 mm. (2) As long as the tractor tyres are running in the furrow during ploughing, they should not be wider than 12.4/11 in. with 12 in. plough bodies and 14.9/13 in. for 14 in. bodies, if the furrows are not cleared to a greater width. This gives the maximum tractor weights and performances indicated in Table 2.
FOUR-WHEEL DRIVE OR REAR-WHEEL DRIVE
21
kp 5000
X Colculated from bearing capacity equation L--1850D2b o From dora in rnaker~
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eceserve of bearing copocity I 130% of static rear axle weight
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F]~. 16. Rear tyres used by the tractors of different weights in Fig. 14; comparison of static rear axle loads encountered with these tyres on the assumption of a 30 per cent increase in axle weight at the maximum bearing capacity of the tyres at an inflation pressure of 1"0 atm. Bearing capacity of tyres (kp) and tyre diameter of rear wheels (ram) vs total tractor weight (Mp). (Crosses) Calculated from bearing capacity equation L = 1850 D2b; (Circles) From data in maker's catalogues; (Area between curves) Reserve of bearing capacity; (Lower curve) 130 per cent of static rear axle weight. With a tractor weight of 7'6 Mp the 24"5-32 tyre has no reserve of bearing capacity. It would be adequate for a tractor of 5-6 Mp weight and still have the same reserve of bearing capacity, the 7"6 Mp tractor needed 28-32 tyres.
(3) Moreover, for considerations of soil compaction, soil-plastic flow and depth of the rut the axle weight in the field should not exceed a certain level. This acceptable axle weight depends in each case on the moisture content and type of soil and its resistance to compression. The weights of 3000 kp per axle and power transmissions of 80-100 h.p. per axle, mentioned previously as maxima, have already been exceeded by some recent tractor models. The axle weight could be increased further by use of large tyres with low inflation pressure. However, it will then be even more difficult to accommodate such tyres. (4) In accordance with road traffic regulations, the tractor width must not exceed 2.5 m. This sets a limit of 6 Mp (Fig. 17) if the width is not being restricted. For considerations of road loading the rear axle weight must not exceed 10 Mp. The weight limits imposed by road traffic regulations are well above the future size range of farm tractors and may be ignored in the present paper. The above considerations clearly show that there is an as yet unknown maximum of weight and horsepower for conventional rear-wheel drive tractors for physical
22
w. S/SaNE
TABLE 2. LIMITATION OF WEIGHT AND PERFORMANCE OF TRACTORS WITH REAR-WHEEL DRIVE THROUGH THE ROW SPACING OR FURROW WIDTH WHEN OPERATING ON LEVEL GROUND
Max. acceptable tyre size
Bearing capacity (kp)
Dead weight of tractor* (kp)
Weight per unit horsepower
Tractor performance (h.p.)
(kp/h.p.)
Row width of potatoes 62"5 cm 75 cm Row width of beet 45 cm 50 cm Working width o f plough
9-5/ 9-36 AS 12"4/11-38 AS
730 1100
1520 2280
49 40
31 57
11'2/10-28 AS 12'4/11-38 AS
800 1100
1660 2280
46 40
36 57
14"9/13-30 AS
1350
2800
39
72
body1"
14 in.
*At a rear axle weight of 65 per cent of tractor dead weight and 67"5 per cent utilization of bearing capacity at dead weight of the tractor. #The max. acceptable tyre width depends on the shape of the body, the clearance of the furrow depending on it, type and moisture content of soil and crop.
i
8010
m. Length of tractor /[m]=215+8,4,#S[Mpj
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5010
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P 7
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2
4 6' Weight o f t r a c t o r 6
8
Mp
10
Length (upper curve) and width of tractor (m) vs. tractor weight G (Mp).
FOUR-WHEEL DRIVE OR REAR-WHEEL DRIVE
23
reasons, which must not be exceeded. Bekker has shown that the "train" concept, i.e. splitting up o£ vehicles into several linked members is able to overcome these limits [5, 6]. In fact the four-wheel drive tractor with front and rear wheels of equal size represents the first step in this direction, because it enables the critical limits in the size of tractor wheels to be considerably extended. The same applies to a tandem tractor, in which a possible critical size of engine can also be avoided by splitting it up into two units. Starting from the specific weights indicated in Fig. 3 by a dotted line, the tractor dry weights shown in Fig. 18 as a function of engine power, will be obtained. From ,
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,
.
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;/
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!
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,20011,tb300
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FIG. 18. Dead weight of tractor (lower limit curve), weight of tractor with ballast and plough (upper limit curve), and weight on driving axle (Mp) when ploughing with rear-wheel drive (full bold line) and four-wheel drive (dashed bold line) vs. engine horsepower, as well as the required tyre dimensions in both cases. this were calculated the tractor weight with ballast and plough on the assumptions that at dry weights o£ up to 3 Mp they constitute 155 per cent of the dry weight, whereas for tractors between 3 and 10 Mp they are reduced from 155 to 135 per cent of the dry weights. When ploughing with mounted or semi-mounted ploughs the rear wheel axle weight of a standard tractor can be increased by the weight of the plough and the resultant soil forces on the plough to a level exceeding the dry weight of the tractor. On these assumptions, the bearing capacity of the 12.4/11-36 tyres is exceeded at an output of 53 h.p. and that of 14.0/13-30 tyres at 73 h.p.* By using four-wheel ~The h i g h e r m a x i m a given b y t h e a u t h o r in a n earlier p a p e r [7] h a v e b e e n calculated o n t h e basis o f a h i g h e r utilization o f t h e tyres at dry weight.
24
W. SOHNE
drive with wheels of equal size the total load when ploughing can be distributed evenly to both axles, such that in a static condition about 40 per cent of lhe tractor weight is supported on the rear axle and 60 per cent on the front axle. In order to keep weight transfer between the axles to a minimum, the wheelbase of four-wheel drive tractors should be relatively large. The limit for 14.9/13-30 tyres is then not reached until 120 h.p. Since in the future no tyres should run in the furrow at such a power output, tyres larger than 14-9/13-30 can be used. The four-wheel drive tractor thus offers a fair amount of scope for development. COMPARISON BETWEEN DIFFERENT GROUND DRIVE SYSTEMS Tractors with rear-wheel drive There is no doubt that the conventional rear-wheel drive is the simplest and fol all but very high horsepowers the cheapest form of power transmission. Moreover, as stated above, when ploughing with a mounted plough the rear axle can be additionally loaded by the weight of the plough and the soil forces acting on the plough, so that under certain conditions a rear axle weight equalling the total weight of the tractor may be obtained. Trailed implements and trailers also impose a considerable additional load on the rear axle. Under favourable soil conditions the differences in m a x i m u m drawbar pull, in the power balance and in efficiency ot power transmission compared with those of four-wheel drive are not very great. If under unfavourable soil conditions the drawbar pull of the standard rear-wheel driven tractor is not adequate, it can be increased by the following auxiliary means [8, 9] : the rear axle weight can be increased considerably by use of wheel weights or water ballasting; on frictional soils such as sand, sandy loam and light loam, the drawbar pull increases about linearly with rear axle weight. Tyre chains and strakes are not as effective on frictional soils. Dual tyres on their own also have little effect, but water ballasted dual tyres can more than double the rear axle weight and drawbar pull. A tyre girdle increases the traction coefficient on frictional soils by about 40 per cent [9]. On heavy wet loam and clay soil the traction coefficient m a y decrease with increasing rear axle weight. Only with water-ballasted dual tyres can the traction coefficient be increased slightly, and hence also the drawbar pull, in accordance with the higher load. Cage wheels can improve the traction coefficient by over 100 per cent, while about 50 per cent increases in the traction coefficient can be achieved with tyre girdles, though they tend to lead to smearing of the soil. A precondition for the use of traction aids in practice is that they do not have an adverse effect on road transport and can be easily removed. In view of this, on heavy, wet soil the use of tyres in conjunction with strakes which are easily retractable offers at present the best solution [9]. All these aids involve additional costs and extra work for fitting and removing ol retracting the strakes. It should therefore be examined whether in the 75 h.p. class a tractor of conventional design with power-driven small front wheels would not be more favourable. Four-wheel drive with small steered front wheels and large rear wheels This type of tractor can only be considered, as mentioned above, for those horsepower classes for which the rear wheels do not exceed certain sizes, as specified in
FOUR-WHEEL DRIVE OR REAR-WHEEL DRIVE
25
Table 2. The choice of whether such a tractor is to be preferred to a conventional rear-wheel driven tractor of the same or higher performance depends on the soil conditions under which the tractor is to be predominantly employed, possibly on the slope of the land and on the relationship between the extra cost of drive to the front wheels and that for a tractor of higher horsepower having the same drawbar pull under the relevant soil conditions, as well as on the respective running costs of these two tractors. If a tractor model is produced with or without front-wheel dlive, use of wide-rim tyres with low inflation pressure is recommended for front-wheel drive.
Four-wheel drive with wheels of equal size With tractors of high horsepower the rear wheels of which would become too large, four-wheel drive with wheels of equal size might be used. When at rest, 60-65 per cent of the weight should then be supported by the front wheels and 35-40 pet cent by the rear wheels, so that when a heavy load is being pulled an approximately equal weight distribution is obtained. The choice of steering is of decisive importance for the conception of these tractors. The conventional Ackermann steering of the front wheels is not likely to permit an adequate lock with the large tyres. In that case there are the following solutions : (1) (2)
articulated steering four-wheel steering.
With articulated steering the tractor frame is divided exactly in the centre between front and rear axle, the two parts being linked by a universal joint. Power steering is effected by means of hydraulic cylinders about this joint. The front and rear wheels always run in the same track, so that there is no straining of the front against the rear tyres when travelling through a bend and the rolling resistance in the bend is reduced. Articulate steering has disadvantages when tillage implements are mounted at the front. With four-wheel steering each wheel is driven and steered through a ball-andsocket joint. Apart from conventional steering in which only the front wheels are being deflected, the front and rear wheels can be turned in opposite directions, so that smaller turning radii can be achieved. Front and rear wheels can also be turned in the same direction. By this means it is possible to prevent pushing of the tractor on the slope. It also makes the tractor more manoeuvrable in narrow farmyards.
The tandem tractor Finally, the tandem tractor offers a special form of four-wheel drive and in the form of two 50 h.p. tractors it has gained some importance. With the tandem trac:tor two tractors without front axles are joined by a ball-and-socket joint and this articulated steering is operated hydraulically. The driver engages the transmissions at the front and rear simultaneously and operates the accelerator by remote control. In the case of a semi-tandem tractor the front axle remains on the front tractor and is used for steering. An advantage of this type is the use of two identical engines and the same conventional rear wheels of 50 h.p. tractors in mass production. In the long term it is unlikely that two engines will be used if the same performance can be achieved with a single engine. It may in fact be assumed that this is a transitionary
26
w. SOHNE
solution, because true tractors with an output of 100 h.p. were not available a few years ago when the tandem tractors first appeared. A further possible advantage considered was that by combining tractors of different horsepowers, e.g. 35 and 50 h.p., the following powers might be achieved : as individual tractor as tandem tractor
35 and 50 h.p. 35 + 3 5 - 70 h.p. 35 + 50--85 h.p. 50 + 50 = 100 h.p.
Although this possibility of combination appears at first very promising, it is doubtful whether the farmer will take the trouble to use two tractors either singly or joined together as tandem tractors as required. He is likely to prefer to use a more powerful tractor and an older used tractor of lower horsepower.
Track-laying tractors Although on heavy soils track-laying tractors were traditionally used as a highpowered tractor for normal field work, they are being replaced by four-wheel drive tractors in m a n y cases. Their disadvantages, such as low working speed, high primary cost, high maintenance costs due to wear of the tracks, great weight, difficult steering and inadequate ability to travel on the road, must be considered against the lower cost, higher forward speed and easier steering of the wheel tractor at the same high drawbar performance. The case is different in the earthmoving industry, where track-laying tractors are employed predominantly where high power for pushing or pulling is needed at low speed and over short distances. FURTHER ARGUMENTS FOR AND AGAINST FOUR-WHEEL DRIVE As already pointed out by Sonnen E13, four-wheel drive is particularly useful for tractors with front loaders because the axle below the loader supports a high additional load. Therefore four-wheel driven vehicles are used predominantly for tractor loaders in the building industry. Another advantage of four-wheel drive is an improved steerability on the slope. The steered and driven front wheels pull the tractor in the desired direction. An important disadvantage of four-wheel drive tractors are the high costs for an additional drive axle with differential gear and for the articulated or four-wheel steering, as well as for an overload protection or third differential between the axles. These costs can be more readily justified for tractors of high horsepower than for tractors up to 75 h.p. and partly absorbed. On a track with good adhesion characteristics the drive to the steered front wheels has to be disengaged in order to avoid twisting of the axles in relation to each other. Hydraulic power steering is essential for four-wheel drive tractors, both those with articulate and those with four-wheel steering, as well as for rear-wheel drive tractors of high horsepower and great weight. The development costs for tractors of high horsepower with four-wheel drive are relatively high and their sales are likely to be low as yet in view of the small number of large holdings in central Europe. It thus depends on such tractors being used
FOUR-WHEEL DRIVE OR REAR-WHEEL DRIVE
27
outside agriculture, particularly as special machines in the building industry, which is willing an able to bear higher costs of such machines than agriculture and forestry. As already stated by Franke [10], it therefore depends on whether the designer is able to create a basic type with many applications. An example of this is the Unimog which is being used extensively in other industries outside farming as a crosscountry vehicle with four-wheel drive and high speed. In Fig. 19 an attempt has been made to estimate the transfer of tractors with rear wheel drive to those with four-wheel drive in relation to tractor power. There is no
I
too
0
0
ao g .~.
{ oo k. ~3
i
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100
I
50
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Tractor engine h o r s e p o ~ r
FAG. 19. Estimated transition from the region of tractors with rear wheel drive to that of four-wheel drive tractors depending o n engine horsepower. The transition from rear-wheel drive (upper section of graph) to four-wheel drive (lower section) will have to take place earlier for tractors operating predomi nantly on heavy clay soils (upper curve) than for those employed predominantly on sandy soils.
doubt that up to 75 h.p. the rear wheel drive tractor will predominate also in future in view of its great simplicity. Only for unfavourable soil conditions will there be a relatively small, but perhaps increasing proportion of four-wheel drive tractors, predominantly with small, steered front wheels and large rear wheels, With farm tractors of high horsepower the four-wheel drive tractor with wheels of equal size and articulated or four-wheel steering will predominate. The transfer from rear wheel to four-wheel drive tractors will take place earlier for soft, wet loam or clay soils than for less sensitive frictional soils, as shown in Fig. 19. The relationship between four-wheel drive and rear-wheel drive tractor may change if hydrostatic transmissions should become more widely used, it can also change if greater demands are made with respect to ride comfort at increasing working speeds, which can be achieved only by providing suspension on all four wheels.
[1] [2] [3] [4]
REFERENCES F . J . SONt~EN. Zur Frage des Allradantriebes yon Ackerschleppern. (On the question of four-wheel drive tractors.) Land techn. Forsch., 12, 1 (1962). R. FRAre~E. Four-wheel drives. Paper presented at an Open Meeting on 15th Jan. 1963. C.B. RICHEY. Traction tests of a tandem-tractor. Trans AS,4E, 2~ 16 (1959). J. F. REED, A. W. COOPER and C. A. REAVES. Effects of two-wheel and tandem drives on traction and soil comFacting stresses. Trans ,4SAE, 2, 22 (1959).
2s [5] [6] [7] [8] [9] [10] [11] [12] [13]
w. SO'HNE M. G. BEKKER. Theory of land locomotion. The mechanics of vehicle mobility. The University of Michigan Press, Ann Arbor (1956). M . G . BEKKER.Off-the-road locomotion. Research and development in terramechanics. The University of Michigan Press, A n n Arbor (1960). W. S6HNE. Beitrag zur Mechanik des Systems Fahrzeug-Boden unter besonderer Beriicksichtigung des Ackerschleppers. (Contribution to the mechanics of the system vehicle-soil with special reference to farm tractors.) Grundl. Landtech., 17, 5 (1963). P . H . SOtrrHWELL. An investigation of traction and traction aids. ASAE Paper No. 62-622. Winter Meeting 1962, American Society of Agricultural Engineers. P . H . BAILEY.The comparative performance of some traction aids. J. agric. Engng Res., 1, 12 (1956). R. FRANKE. Der Allradantrieb f[ir Ackerschlepper. (Four-wheel drive for farm tractors.) Grundl. Landtech., 18, 580 (1963). F. BUCKINGHAM.Four-wheel drive. Implement and Tractor, 21, 46 (1963). W . F . BUCHELE. Design and operation of MSU tandem tractor. Trans ASAE, 2, 11 (1959). W. SOHNE and R. M()LLER. ~ b e r den Entwurf yon Streichblechen unter besonderer Beriicksichtigung yon Streichblechen fiir h6here Geschwindigkeit. (On the designing of mouldboards with special reference of mouldboards for higher speeds.) Grundl. Landtech., 15, 15 (1962).
FOUR-WHEEL DRIVE OR REAR-WHEEL DRIVE FOR HIGH POWER F A R M TRACTORS* W. S6rINE COMPARED with rear-wheel driven tractors, farm tractors with four-wheel drive have not in the past had a large share of the market. Recently a larger number of tractor models with four-wheel drive have come onto the market in Germany, England and the U.S.A. The question of whether with farm tractors of higher capacity a larger proportion of models with four-wheel drive would be justified will be discussed in the present paper. DEVELOPMENT OF ENGINE POWER AND THE WEIGHT OF THE TRACTOR PER UNIT OF HORSEPOWER The increase in mean tractor engine horsepowers which has become apparent in the U.S,A. and the U.K. since 1947 and in the Federal Republic of Germany since 1954 is still continuing (Fig. 1). It is due to the demands of the agricultural industry for higher rates of work of farm machinery and equipment and, especially 100
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0
19,~7
1950
5,(,
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70
74
78
FIG. 1. Development of mean engine horsepower of new models of tractors in the U.S.A. (top curve) and Federal Republic of Germany (lower curve) from 1947 to 1965 according to Seifert. in the U.S.A., it is promoted by the increase in the size of agricultural holdings and the desire to keep labour costs to a minimum. In that country the average power of new models of tractors was about 55 h.p. t in 1963 (64 h.p. in 1967) and in *Translated from Grundlagen der Landtechnik, 20, 1964, by E. Harris, National Institute of Agricultural Engineering, Silsoe, Bedford. 1"Metric horsepower throughout.
to
w. SiSHNE
Western Germany about 32 h.p. (40 h.p. in 1967). One third of all 1963 models of tractors in the U.S.A. was in the power range 65-100 h.p., whereas in Germany an increasing proportion was in the 45-60 h.p. class. In 1962 some tractor models of 100-120 h.p. appeared on the market (e.g. John Deere 5010). At the same time tractors with four-wheel drive in the 150-300 h.p. class have been developed (e.g. IHC 4300, Fig. 2). These are, however, no longer true farm tractors, but tractors with engines, transmissions and ground drives intended for the earthmoving industry which have been modified for agriculture. Since they are as yet likely to be produced only in small numbers, they will be neglected in the present considerations.
FIG. 2. IHC tractor 4300 on Nebraska University test track. The higher engine power of the tractor can be used to increase the working width, i.e. in the case of soil cultivation, to pull a plough with a larger number of bodies, to combine several implements (minimum tillage), or to travel at higher speed. In the first two cases the tractor and implement have to become heavier and hence correspondingly more expensive in proportion to the rate of work, so that the weight per unit of horsepower of the tractor remains constant at increasing engine power. In the third case only a small increase of tractor and implement weight is required, so that the weight per unit of horsepower can be reduced. This solution ought to be more economical. in fact all three methods are being followed at the same time and should also be developed further in the future. The working speeds are being raised only slowly because the tractor and implement must first be adapted to the higher speeds with respect to quality of work and ride comfort.
FOUR-WHEEL
DRIVE OR REAR-WHEEL
DRIVE
11
Figure 3a shows the weight of the tractor per unit of horsepower as a function of engine power. In the range above 70 h.p. the decrease in specific weight with n "c" G ®
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(3b) Specific w e i g h t ( k p / h . p . ) o f t r a c t o r s in r e l a t i o n t o e n g i n e p o w e r (h.p.) f r o m d a t a b y t h e I n s t i t u t fiJr S c h l e p p e r f o r s e h u n g o f the F A L . ( G ) I m p l e m e n t carrier; (A) 4 - w h e e l drive
increasing engine power does not appear to continue at first. However, it is improbable that this indicates a change in the erstwhile trend. With the new tractor models of 80-120 h.p. the specific weight is also likely to decrease when the power output is further developed. This will apply all the more, the greater the increase in forward speeds (Fig. 3b). FORMS
OF POWER
TRANSMISSION
BETWEEN
TRACTOR
AND SOIL
For tractors with a capacity of 60-140 h.p. the following means of transmitting tractive power are available : (1) through conventional rear-wheel drive
W. SOHNE
12
(2)
through four-wheel drive (a) with small front and large rear wheels (b) with wheels of equal size (c) in the form of a tandem tractor (3) through tracks. These means will now be compared critically.
What improvements are to be expected lrom ~our-wheel drive? The extent to which the drawbar pull of tractors can be increased by four-wheel drive compared with rear-wheel drive has been examined repeatedly [1-5]. The improvement in traction is due to two reasons : (1) In the case of four-wheel drive the entire weight of the tractor is utilized as a load on the driven axles, whereas w~h rear wheel drive the rolling resistance of •the front wheels, the axle load of which in operation is between 10 and 40 per cent of the total weight, has to be deducted from the tractive effort of the rear wheels. (2) In the case of a four-wheel drive tractor with wheels of equal size the front wheels compact the soil, reduce the total rolling resistance and lead to a better
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FIG. 4. Traction coefficient (top) and coefficient of rolling resistance (bottom) as a function of slip (%) under different soil conditions. (From top to bottom) Concrete, tarmac (dry); dry loam, stubble; loamy sand, stubble; loamy sand, wet; clay loam, wet; silt; soil slurry; silt, soil slurry; clay loam, wet; dry loam, stubble, loamy sand, stubble; concrete.
FOUR-WHEEL DRIVE OR REAR-WHEEL DRIVE
13
transmission of power by %he rear wheels. The extent of this improvement depends greatly on the soil condition. While in American measurements in a soil tank, i.e. on relatively loose soils, at 16 per cent slip the rear wheels had a 25-35 per cent better traction coefficient than the power-driven front wheels and at 40 per cent an improvement of 14-20 per cent was achieved in the second pass, the results of measurements obtained at the Institut fiir Schlepperforschung (/nstitute for tractor research) Braunschweig-ViSlkenrode on different soils show improvements of 6-18 per cent and 16 per cent slip and 6-11 per cent at 40 per cent slip [1], the greater improvements referring to soils with a low bearing capacity and the smaller ones to soils with good bearing characteristics. The tractive coefficient-slip curves of a tractor tyre on different types of soil and under a range of conditions can be combined in groups, as in Fig. 4. The calculations of examples made below are based on four different soil conditions, under which the tractor is likely to operate in the field and which, therefore, do not include extremes of unfavourable values, i.e. (a) dry loam, stubble field (b) sandy loam, stubble field (c) wet, sandy loam (d) wet clay loam. On the basis of the above measurements, traction coefficients have been assumed for four-wheel drive which are better than those for rear-wheel drive by the values given in Fig. 5. Using the tractor data given in Table 1, the power balances and
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14
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Drawbar pull 6-9. Comparison of power balances, efficiencies ~ and slip cr between four-wheel drive (dashed line) and rear-wheel drive (full line) in relation to drawbar pull (kp) under different soil conditions. Coefficients of traction and rolling resistance from Fig, 5. Tractor data used for the graphs are given in Table 1. N~=drawbar pull N~mioss due to slip N p = loss due to rolling resistance (a) Dry loam, stubble; (b) Dry, loamy sand, stubble; (c) Wet, loamy sand; (d) Wet clay loam. FIGS.
2800
kp
FOUR-WHEEL DRIVE OR REAR-WHEEL DRIVE
15
efficiencies were calculated for the above soil condition (Figs. 6-9). On the dry loam, stubble field (Fig. 6) the tractive effort at 20 per cent slip is 27 per cent and at 50 per cent slip 20 per cent higher than with rear-wheel drive, the optimum efficiency of power transmission being 77 instead of 70 per cent. On wet clay loam the drawbar pull at 30 per cent slip is as much as 57 per cent and at 50 per cent slip, 44 per cent higher, the optimum efficiency being 51 instead of 40 per cent. Thus, TABLE 1. ASSUMEDTRACTORDATAFOR THE CALCULATIONOF THE POWERBALANCE Rear-wheel drive
Four-wheel drive
Engine power, h.p. Tractor weight without ballast, kp static rear axle weight, kp static front axle weight, kp
85 3400 2300 1100
85 3400 1360 2040
Tractor weight with ballast and driver, kp static rear axle weight, kp static front axle weight, kp
4200 3100 1100
4200 1700 2500
Operational weight without ballast, kp/h.p. Operational weight with ballast, kp/h.p. Wheelbase, m Tyres, rear Tyres, front Height of drawbar, m Forward speed without slip for the sample calculation, m/sec
40 40 49"5 49'5 2'5 2'5 18'4/15-30 AS 12"4/11-36 AS 7"50-16 12-4/11-36 AS 0.45 0"45 2"0
2'0
even under relatively favourable soil conditions, the four-wheel drive shows considerable improvements in drawbar pull and performance. The advantages of fourwheel drive become all the more apparent the less the track is able to transmit power and the higher the rolling resistance. This is clearly shown in Figs. l0 and 11. Figure 10 shows how high the tractor weight G must be with rear- and 4-wheel drive to achieve a drawbar pull Z of 1 Mp under different soil conditions. These soil conditions are characterized by the ratio of drawbar pull to tractor weight which can be attained as a m a x i m u m with a rear-wheel driven tractor in each case. Figure 11 shows the m a x i m u m attainable drawbar pull of rear-wheel and four-wheel drive tractors as a percentage of tractor weight for different soil conditions. Figure 12 indicates the gross tractor weight per unit of horsepower required as a function of the (effective) forward speed at 20 per cent slip according to the drawbar pull-slip curves of Fig. 4 and the performance graphs of Figs. 6-8. However, a qualification was made that only 80 per cent of the engine power is to be transmitted. The full engine power can also be transmitted but of course only with correspondingly higher slip, The graph also shows the required gross tractor weigher under the assumption of a constant engine power of 85 h.p. It follows that at the same working speed a four-wheel drive tractor for soil a could be constructed 17 per cent, and for soils b and c 20 per cent lighter than a rear-wheel driven tractor to transmit the same engine power. If for all soil conditions the four-wheel drive tractor is 20
16
W. S()HNE <9
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Fl6. 10. Tractor weight G required with rear-wheel and four-wheel drive for a maximum attainable pull of Z of 1 Mp on different types of soil and soil conditions.
FIG. 11. Maximum attainable drawbar pull Z of tractors with rear-wheel and four-wheel drive on different types of soil and soil conditions in relation to tractor weight G. The optimum attainable ratio / £1n~x= Zmax/G = max. drawbar pull/tractor weight under given soil conditions for rear-wheel drive is chosen as a measure of soil condition. The scatter is due to different rolling resistances at given Xmax and to different load conditions of the front and rear axle and various load distributions between axles on the basis of the tractor specifications.
per cent lighter, then according to Figs. 6-9 the d r a w b a r pulls at 20 per cent slip will still b e : o n soil a 1-5 per cent
o n soil c 12 per cent
on soil b 7"5 per cent
o n soil d 40 per cent
and at 30 per cent slip o n soil d 25 per cent higher t h a n with rear-wheel drive. Figure 13 shows the engine power which c a n be transmitted a s s u m i n g a constant total weight of the tractor of 4.2 Mp. A c c o r d i n g to it a 21 a n d 24 per cent higher engine power c a n be t r a n s m i t t e d respectively. Moreover, Figs. 12 a n d 13 clearly show that the high performance of m o d e m traclors at low speed can no longer be t r a n s m i t t e d to the ground. A t a slipless speed
F O U R - W H E E L D R I V E OR R E A R - W H E E L D R I V E
17
Nx \N,
g F/g. /3 .
_~
/
/
/~
40
30
3
6
4
speed
Effective t
3
I
~
I
I
I
I
5 6 B Slipless speed
I
8 I
~
I0 km/h I
[
l
I I
~hm/~ ~
FIG. 12. Required gross specific weight (kp/h.p.) of tractors with four-wheel (dashed line) and rear-wheel drive (full line) as a function of the (effective) speed at 20% slip; the gross tractor weight indicated applies to an assumed constant engine output of 85 h.p. FIG. 13. Available engine power in relation to (effective) speed at 20% slip under the assumption of a constant total weight of the tractor of 4"2 Mp. (Vertical scales) Gross tractor weight (Mp) and gross specific weight (kp/h.p.), and (bottom) engine horsepower (horizontal scales) effective forward speed ( k m / h r ) and forward speed in the absence of slip (km/hr). These graphs are based on the drawbar pull-slip curves and performance curves of Figs. 6-8. It is assumed that the transmission efficiency is 90 per cent and the engine output is 80 per cent of the rated horsepower. Soil a : dry loam, stubble Soil b: sandy loam, stubble Soil c: wet sandy loam.
of 7'5 k m/h r or an effective speed of 6.0 km / hr the required gross weight per unit
of horsepower is given below.
With four-wheel drive, kp/h.p. With rear-wheel drive, kp/h.p.
Soil a
Soil b
Soil c
46"5 56"4
51"2 63"6
60"0 75-0
Is
W. S(JHNE
However, this gross weight per unit of horsepower is not the same as the net weight in Fig. 3. The latter can be increased up to 50 per cent by wheel weights and water ballasting of the tyres and by the weight of the driver. When ploughing with mounted ploughs the rear axle load can be increased by 65 per cent, according to Skalweit, by the weight of the plough and normal soil reaction, with the linkage in a floating position, and up to 85 per cent with a restrained linkage. Although with four-wheel drive the plough and the normal soil reaction also impose an additional load on the tractor, the weight transfer from the front to the rear wheels does not have the effect to increase drawbar pull because both axles are being driven. Assuming that the dead weight of the tractor is increased by 67 per cent in the case of rear-wheel drive and by only 55 per cent with four-wheel d r i v e the net weight per unit of horsepower required is :
With four-wheel drive, kp/h.p. With rear-wheel drive kp/h.p.
Soil a
Soil b
Soil c
30"0 33.7
33'0 38"1
38'7 44'9
Finally, if the slip-free speed can be increased to 10 k m / h r (corresponding to an effective forward speed of 8 km/hr), the net weight per unit of horsepower is reduced to :
With four-wheel drive, kp/h.p. With rear-wheel drive kp/h.p.
Soil a
Soil b
Soil c
22.5 25.3
24'7 28.5
29"0 33"6
It would thus be possible to develop a 100 h.p. four-wheel drive tractor with a ldead weight of 3 M p which is able to pull a 5-furrow plough at an effective speed of 9 k m / h r on light soil, a 4-furrow plough at 8 k m / h r on medium soil and a 3furrow plough at 7-8 k m / h r on heavy soil [13]. Despite the advantages of the four-wheel drive ~ractor on difficult soils the sales of this type of tractor in the power range up to 50 h.p. were considerably less than I0 per cent of the total number of this tractor size. This can be explained as follows: if a rear-wheel driven tractor of, for example, 35 h.p. on heavy soils is found to be inadequate, it is often regarded preferable to buy a 50 h.p. rear-wheel driven one than a 35 h.p., four-wheel driven tractor. The question is whether this idea is still valid at higher engine powers when, for example, a choice has to be made between an 80 h . p four-wheel drive tractor of 3200 kp weight or a 115 h.p. rearwheel driven model of 4600 kp which on difficult soils develop about the same drawbar pull. A model of similar tractors of different sizes (Fig. 14) may serve to answer this question. The weight of similar bodies increases by the third power but their plan area by the second power of their length. Accordingly, as the size of the tractor increases, the increase in weight is greater than that of its area of vertical projection, even if the tractors are not quite similar; i.e. at increasing tractor weight the ratio of weight over area of vertical projection* is increased, as shown in Fig. 15 for the *Since a comparative value only is sought, the projected area F has been taken to be the tractox width bs~h over the rear wheels times the tractor length lso~ from the front of the front wheel to the rear of the rear wheel.
F O U R - W H E E L D R I V E OR REAR-WHEEL D R I V E
,
~
FIG. 14. Diagramatic plan view of rear-wheel driven farm tractors of different weights by two firms. The shaded areas indicate the contact areas between tyre and track, assuming a specific pressure of the rear wheels of 1 kp/crn ~ and of the front wheels of 2 kp/cmL
19
20
W. S{YHNE
tractors of Fig. 12. The specific pressure in the contact area between tyre and soil would increase accordingly, if the tyres were increased in size similarly. In view of the need to minimise soil compaction and increase the tractive effort, the pressure in the contact area should remain the same, indeed with larger tractors it ought to be even reduced. Therefore, the contact area should increase at least proportionately to weight and hence more than proportionately to the projected area or the tractor dimensions. According to Bekker [6] the bearing capacity of off-the-road tyres for I000
I
,p/~2
!
"
]a=bs
r
2
, ~
306 c
, ~o
200
i 2000
i
=
I
4000 6000 Tractor weight 8
I
kp 8000
FIG. 15. Ground pressure of farm tractors as in Fig. 14 in relation to weight G (kp). The product of bs~h × ls~h was taken as the ground area. earthmoving equipment and military vehicles of tyre diameter D and tyre width b does in fact increase as follows : G = 8550 (D.b) ~'~6 and that of farm tractor tyres, following the expression G = 2400 (D.b)V26; for approximately similar tyres, the equation is G =: 1850 D'a.b, 'where D and b are expressed in m and G in kp (Fig. 16). However, this means that the inflation pressure of the tyres and the specific pressure in the tyre-soil contact area are bound to increase at the same inflation pressure. The areas of contact between tyre and soil have been entered in Fig. 14 on the assumption that the ground pressure of the rear wheels is 1 k p / c m 2 and that of the front wheels 2 k p / c m ~. It will be seen in Figs. 14 and 16 that the tyres of the tractor weighing 7"6 M p are underdimensioned by comparison with the other tractors. These tyres should thus be given a higher inflation pressure. However, this reduces the range of applicability of this tractor compared with that of the other tractors. This consideration of similarity thus sets a physical limit to an increase in the size of conventional rearwheel drive tractors. Independently from this there are the following further limitations : (1) If the tractor is to be used for rowcrop work, the tyres should not exceed 9.5/9 in. in width at a row spacing of the potatoes of 6-25 cm, according to Thaer, and 12.4/11 in. at a row width of 75 cm. According to Schtinke, the corresponding limits for sugar beet are 11.2/ 10 in. at a row width of 450 m m and 12-4 in. at 500 mm. (2) As long as the tractor tyres are running in the furrow during ploughing, they should not be wider than 12.4/11 in. with 12 in. plough bodies and 14.9/13 in. for 14 in. bodies, if the furrows are not cleared to a greater width. This gives the maximum tractor weights and performances indicated in Table 2.
FOUR-WHEEL DRIVE OR REAR-WHEEL DRIVE
21
kp 5000
X Colculated from bearing capacity equation L--1850D2b o From dora in rnaker~
4OOO "G 3000
[
i
i
,
0 o 2900
!< \ I
Om 1000
eceserve of bearing copocity I 130% of static rear axle weight
;
= 1
r
,
o
I i
~•
0
i
~o
o
2
3
~
5
Total tractor weight
6
7
Mp 6
F]~. 16. Rear tyres used by the tractors of different weights in Fig. 14; comparison of static rear axle loads encountered with these tyres on the assumption of a 30 per cent increase in axle weight at the maximum bearing capacity of the tyres at an inflation pressure of 1"0 atm. Bearing capacity of tyres (kp) and tyre diameter of rear wheels (ram) vs total tractor weight (Mp). (Crosses) Calculated from bearing capacity equation L = 1850 D2b; (Circles) From data in maker's catalogues; (Area between curves) Reserve of bearing capacity; (Lower curve) 130 per cent of static rear axle weight. With a tractor weight of 7'6 Mp the 24"5-32 tyre has no reserve of bearing capacity. It would be adequate for a tractor of 5-6 Mp weight and still have the same reserve of bearing capacity, the 7"6 Mp tractor needed 28-32 tyres.
(3) Moreover, for considerations of soil compaction, soil-plastic flow and depth of the rut the axle weight in the field should not exceed a certain level. This acceptable axle weight depends in each case on the moisture content and type of soil and its resistance to compression. The weights of 3000 kp per axle and power transmissions of 80-100 h.p. per axle, mentioned previously as maxima, have already been exceeded by some recent tractor models. The axle weight could be increased further by use of large tyres with low inflation pressure. However, it will then be even more difficult to accommodate such tyres. (4) In accordance with road traffic regulations, the tractor width must not exceed 2.5 m. This sets a limit of 6 Mp (Fig. 17) if the width is not being restricted. For considerations of road loading the rear axle weight must not exceed 10 Mp. The weight limits imposed by road traffic regulations are well above the future size range of farm tractors and may be ignored in the present paper. The above considerations clearly show that there is an as yet unknown maximum of weight and horsepower for conventional rear-wheel drive tractors for physical
22
w. S/SaNE
TABLE 2. LIMITATION OF WEIGHT AND PERFORMANCE OF TRACTORS WITH REAR-WHEEL DRIVE THROUGH THE ROW SPACING OR FURROW WIDTH WHEN OPERATING ON LEVEL GROUND
Max. acceptable tyre size
Bearing capacity (kp)
Dead weight of tractor* (kp)
Weight per unit horsepower
Tractor performance (h.p.)
(kp/h.p.)
Row width of potatoes 62"5 cm 75 cm Row width of beet 45 cm 50 cm Working width o f plough
9-5/ 9-36 AS 12"4/11-38 AS
730 1100
1520 2280
49 40
31 57
11'2/10-28 AS 12'4/11-38 AS
800 1100
1660 2280
46 40
36 57
14"9/13-30 AS
1350
2800
39
72
body1"
14 in.
*At a rear axle weight of 65 per cent of tractor dead weight and 67"5 per cent utilization of bearing capacity at dead weight of the tractor. #The max. acceptable tyre width depends on the shape of the body, the clearance of the furrow depending on it, type and moisture content of soil and crop.
i
8010
m. Length of tractor /[m]=215+8,4,#S[Mpj
I, ~°//
t,
#~ ,/
S
"
/
/
/
I
o/"
.
5010
t
! Limit for moximum width by rood troffic 0¢t$I
,/'/
;
;~Y//.×:~///////////////HA I •
~.~"~
~''] i
5010 J
8010
"o 2 l:l
+.~
Width of troctor b[a]=/,25+o,2oo6Np]
P 7
0
FIG. 17.
I
2
4 6' Weight o f t r a c t o r 6
8
Mp
10
Length (upper curve) and width of tractor (m) vs. tractor weight G (Mp).
FOUR-WHEEL DRIVE OR REAR-WHEEL DRIVE
23
reasons, which must not be exceeded. Bekker has shown that the "train" concept, i.e. splitting up o£ vehicles into several linked members is able to overcome these limits [5, 6]. In fact the four-wheel drive tractor with front and rear wheels of equal size represents the first step in this direction, because it enables the critical limits in the size of tractor wheels to be considerably extended. The same applies to a tandem tractor, in which a possible critical size of engine can also be avoided by splitting it up into two units. Starting from the specific weights indicated in Fig. 3 by a dotted line, the tractor dry weights shown in Fig. 18 as a function of engine power, will be obtained. From ,
I
o
.~
,r
,
I
,
i
i
ii I L,,,'G/ 110
.
20
I1
II
II
I,J,
J
J
;~r /
I/
,
.
J
;/
,4
"'Yi ~
I 30
;
!
-,l'rTIi,
I ! Hiu 40
60
I :
~00 700
I
,20011,tb300
I/
--Rearwheeldrli~
. . . . ,-w,,,,., ..,,,,, UUU L¢~-
I
U -~
'-.~
FIG. 18. Dead weight of tractor (lower limit curve), weight of tractor with ballast and plough (upper limit curve), and weight on driving axle (Mp) when ploughing with rear-wheel drive (full bold line) and four-wheel drive (dashed bold line) vs. engine horsepower, as well as the required tyre dimensions in both cases. this were calculated the tractor weight with ballast and plough on the assumptions that at dry weights o£ up to 3 Mp they constitute 155 per cent of the dry weight, whereas for tractors between 3 and 10 Mp they are reduced from 155 to 135 per cent of the dry weights. When ploughing with mounted or semi-mounted ploughs the rear wheel axle weight of a standard tractor can be increased by the weight of the plough and the resultant soil forces on the plough to a level exceeding the dry weight of the tractor. On these assumptions, the bearing capacity of the 12.4/11-36 tyres is exceeded at an output of 53 h.p. and that of 14.0/13-30 tyres at 73 h.p.* By using four-wheel ~The h i g h e r m a x i m a given b y t h e a u t h o r in a n earlier p a p e r [7] h a v e b e e n calculated o n t h e basis o f a h i g h e r utilization o f t h e tyres at dry weight.
24
W. SOHNE
drive with wheels of equal size the total load when ploughing can be distributed evenly to both axles, such that in a static condition about 40 per cent of lhe tractor weight is supported on the rear axle and 60 per cent on the front axle. In order to keep weight transfer between the axles to a minimum, the wheelbase of four-wheel drive tractors should be relatively large. The limit for 14.9/13-30 tyres is then not reached until 120 h.p. Since in the future no tyres should run in the furrow at such a power output, tyres larger than 14-9/13-30 can be used. The four-wheel drive tractor thus offers a fair amount of scope for development. COMPARISON BETWEEN DIFFERENT GROUND DRIVE SYSTEMS Tractors with rear-wheel drive There is no doubt that the conventional rear-wheel drive is the simplest and fol all but very high horsepowers the cheapest form of power transmission. Moreover, as stated above, when ploughing with a mounted plough the rear axle can be additionally loaded by the weight of the plough and the soil forces acting on the plough, so that under certain conditions a rear axle weight equalling the total weight of the tractor may be obtained. Trailed implements and trailers also impose a considerable additional load on the rear axle. Under favourable soil conditions the differences in m a x i m u m drawbar pull, in the power balance and in efficiency ot power transmission compared with those of four-wheel drive are not very great. If under unfavourable soil conditions the drawbar pull of the standard rear-wheel driven tractor is not adequate, it can be increased by the following auxiliary means [8, 9] : the rear axle weight can be increased considerably by use of wheel weights or water ballasting; on frictional soils such as sand, sandy loam and light loam, the drawbar pull increases about linearly with rear axle weight. Tyre chains and strakes are not as effective on frictional soils. Dual tyres on their own also have little effect, but water ballasted dual tyres can more than double the rear axle weight and drawbar pull. A tyre girdle increases the traction coefficient on frictional soils by about 40 per cent [9]. On heavy wet loam and clay soil the traction coefficient m a y decrease with increasing rear axle weight. Only with water-ballasted dual tyres can the traction coefficient be increased slightly, and hence also the drawbar pull, in accordance with the higher load. Cage wheels can improve the traction coefficient by over 100 per cent, while about 50 per cent increases in the traction coefficient can be achieved with tyre girdles, though they tend to lead to smearing of the soil. A precondition for the use of traction aids in practice is that they do not have an adverse effect on road transport and can be easily removed. In view of this, on heavy, wet soil the use of tyres in conjunction with strakes which are easily retractable offers at present the best solution [9]. All these aids involve additional costs and extra work for fitting and removing ol retracting the strakes. It should therefore be examined whether in the 75 h.p. class a tractor of conventional design with power-driven small front wheels would not be more favourable. Four-wheel drive with small steered front wheels and large rear wheels This type of tractor can only be considered, as mentioned above, for those horsepower classes for which the rear wheels do not exceed certain sizes, as specified in
FOUR-WHEEL DRIVE OR REAR-WHEEL DRIVE
25
Table 2. The choice of whether such a tractor is to be preferred to a conventional rear-wheel driven tractor of the same or higher performance depends on the soil conditions under which the tractor is to be predominantly employed, possibly on the slope of the land and on the relationship between the extra cost of drive to the front wheels and that for a tractor of higher horsepower having the same drawbar pull under the relevant soil conditions, as well as on the respective running costs of these two tractors. If a tractor model is produced with or without front-wheel dlive, use of wide-rim tyres with low inflation pressure is recommended for front-wheel drive.
Four-wheel drive with wheels of equal size With tractors of high horsepower the rear wheels of which would become too large, four-wheel drive with wheels of equal size might be used. When at rest, 60-65 per cent of the weight should then be supported by the front wheels and 35-40 pet cent by the rear wheels, so that when a heavy load is being pulled an approximately equal weight distribution is obtained. The choice of steering is of decisive importance for the conception of these tractors. The conventional Ackermann steering of the front wheels is not likely to permit an adequate lock with the large tyres. In that case there are the following solutions : (1) (2)
articulated steering four-wheel steering.
With articulated steering the tractor frame is divided exactly in the centre between front and rear axle, the two parts being linked by a universal joint. Power steering is effected by means of hydraulic cylinders about this joint. The front and rear wheels always run in the same track, so that there is no straining of the front against the rear tyres when travelling through a bend and the rolling resistance in the bend is reduced. Articulate steering has disadvantages when tillage implements are mounted at the front. With four-wheel steering each wheel is driven and steered through a ball-andsocket joint. Apart from conventional steering in which only the front wheels are being deflected, the front and rear wheels can be turned in opposite directions, so that smaller turning radii can be achieved. Front and rear wheels can also be turned in the same direction. By this means it is possible to prevent pushing of the tractor on the slope. It also makes the tractor more manoeuvrable in narrow farmyards.
The tandem tractor Finally, the tandem tractor offers a special form of four-wheel drive and in the form of two 50 h.p. tractors it has gained some importance. With the tandem trac:tor two tractors without front axles are joined by a ball-and-socket joint and this articulated steering is operated hydraulically. The driver engages the transmissions at the front and rear simultaneously and operates the accelerator by remote control. In the case of a semi-tandem tractor the front axle remains on the front tractor and is used for steering. An advantage of this type is the use of two identical engines and the same conventional rear wheels of 50 h.p. tractors in mass production. In the long term it is unlikely that two engines will be used if the same performance can be achieved with a single engine. It may in fact be assumed that this is a transitionary
26
w. SOHNE
solution, because true tractors with an output of 100 h.p. were not available a few years ago when the tandem tractors first appeared. A further possible advantage considered was that by combining tractors of different horsepowers, e.g. 35 and 50 h.p., the following powers might be achieved : as individual tractor as tandem tractor
35 and 50 h.p. 35 + 3 5 - 70 h.p. 35 + 50--85 h.p. 50 + 50 = 100 h.p.
Although this possibility of combination appears at first very promising, it is doubtful whether the farmer will take the trouble to use two tractors either singly or joined together as tandem tractors as required. He is likely to prefer to use a more powerful tractor and an older used tractor of lower horsepower.
Track-laying tractors Although on heavy soils track-laying tractors were traditionally used as a highpowered tractor for normal field work, they are being replaced by four-wheel drive tractors in m a n y cases. Their disadvantages, such as low working speed, high primary cost, high maintenance costs due to wear of the tracks, great weight, difficult steering and inadequate ability to travel on the road, must be considered against the lower cost, higher forward speed and easier steering of the wheel tractor at the same high drawbar performance. The case is different in the earthmoving industry, where track-laying tractors are employed predominantly where high power for pushing or pulling is needed at low speed and over short distances. FURTHER ARGUMENTS FOR AND AGAINST FOUR-WHEEL DRIVE As already pointed out by Sonnen E13, four-wheel drive is particularly useful for tractors with front loaders because the axle below the loader supports a high additional load. Therefore four-wheel driven vehicles are used predominantly for tractor loaders in the building industry. Another advantage of four-wheel drive is an improved steerability on the slope. The steered and driven front wheels pull the tractor in the desired direction. An important disadvantage of four-wheel drive tractors are the high costs for an additional drive axle with differential gear and for the articulated or four-wheel steering, as well as for an overload protection or third differential between the axles. These costs can be more readily justified for tractors of high horsepower than for tractors up to 75 h.p. and partly absorbed. On a track with good adhesion characteristics the drive to the steered front wheels has to be disengaged in order to avoid twisting of the axles in relation to each other. Hydraulic power steering is essential for four-wheel drive tractors, both those with articulate and those with four-wheel steering, as well as for rear-wheel drive tractors of high horsepower and great weight. The development costs for tractors of high horsepower with four-wheel drive are relatively high and their sales are likely to be low as yet in view of the small number of large holdings in central Europe. It thus depends on such tractors being used
FOUR-WHEEL DRIVE OR REAR-WHEEL DRIVE
27
outside agriculture, particularly as special machines in the building industry, which is willing an able to bear higher costs of such machines than agriculture and forestry. As already stated by Franke [10], it therefore depends on whether the designer is able to create a basic type with many applications. An example of this is the Unimog which is being used extensively in other industries outside farming as a crosscountry vehicle with four-wheel drive and high speed. In Fig. 19 an attempt has been made to estimate the transfer of tractors with rear wheel drive to those with four-wheel drive in relation to tractor power. There is no
I
too
0
0
ao g .~.
{ oo k. ~3
i
"d qll
100
I
50
Hp / / e.
Tractor engine h o r s e p o ~ r
FAG. 19. Estimated transition from the region of tractors with rear wheel drive to that of four-wheel drive tractors depending o n engine horsepower. The transition from rear-wheel drive (upper section of graph) to four-wheel drive (lower section) will have to take place earlier for tractors operating predomi nantly on heavy clay soils (upper curve) than for those employed predominantly on sandy soils.
doubt that up to 75 h.p. the rear wheel drive tractor will predominate also in future in view of its great simplicity. Only for unfavourable soil conditions will there be a relatively small, but perhaps increasing proportion of four-wheel drive tractors, predominantly with small, steered front wheels and large rear wheels, With farm tractors of high horsepower the four-wheel drive tractor with wheels of equal size and articulated or four-wheel steering will predominate. The transfer from rear wheel to four-wheel drive tractors will take place earlier for soft, wet loam or clay soils than for less sensitive frictional soils, as shown in Fig. 19. The relationship between four-wheel drive and rear-wheel drive tractor may change if hydrostatic transmissions should become more widely used, it can also change if greater demands are made with respect to ride comfort at increasing working speeds, which can be achieved only by providing suspension on all four wheels.
[1] [2] [3] [4]
REFERENCES F . J . SONt~EN. Zur Frage des Allradantriebes yon Ackerschleppern. (On the question of four-wheel drive tractors.) Land techn. Forsch., 12, 1 (1962). R. FRAre~E. Four-wheel drives. Paper presented at an Open Meeting on 15th Jan. 1963. C.B. RICHEY. Traction tests of a tandem-tractor. Trans AS,4E, 2~ 16 (1959). J. F. REED, A. W. COOPER and C. A. REAVES. Effects of two-wheel and tandem drives on traction and soil comFacting stresses. Trans ,4SAE, 2, 22 (1959).
2s [5] [6] [7] [8] [9] [10] [11] [12] [13]
w. SO'HNE M. G. BEKKER. Theory of land locomotion. The mechanics of vehicle mobility. The University of Michigan Press, Ann Arbor (1956). M . G . BEKKER.Off-the-road locomotion. Research and development in terramechanics. The University of Michigan Press, A n n Arbor (1960). W. S6HNE. Beitrag zur Mechanik des Systems Fahrzeug-Boden unter besonderer Beriicksichtigung des Ackerschleppers. (Contribution to the mechanics of the system vehicle-soil with special reference to farm tractors.) Grundl. Landtech., 17, 5 (1963). P . H . SOtrrHWELL. An investigation of traction and traction aids. ASAE Paper No. 62-622. Winter Meeting 1962, American Society of Agricultural Engineers. P . H . BAILEY.The comparative performance of some traction aids. J. agric. Engng Res., 1, 12 (1956). R. FRANKE. Der Allradantrieb f[ir Ackerschlepper. (Four-wheel drive for farm tractors.) Grundl. Landtech., 18, 580 (1963). F. BUCKINGHAM.Four-wheel drive. Implement and Tractor, 21, 46 (1963). W . F . BUCHELE. Design and operation of MSU tandem tractor. Trans ASAE, 2, 11 (1959). W. SOHNE and R. M()LLER. ~ b e r den Entwurf yon Streichblechen unter besonderer Beriicksichtigung yon Streichblechen fiir h6here Geschwindigkeit. (On the designing of mouldboards with special reference of mouldboards for higher speeds.) Grundl. Landtech., 15, 15 (1962).