Journal ofTerramechanics, Vol. 24, No. 4, pp. 263-280, 1987. Printed in Great Britain.

0022-4898/8753.00+0.00 Pergamon Journals Ltd.

1988 ISTVS

THE ROLE OF MEAN MAXIMUM PRESSURE IN SPECIFY ING CROSS-COUNTRY MOBIL ITY FOR ARMOURED F IGHTING

VEHICLE DES IGN*

J . G. HETHERINGTON~" and I. LITTLETON~"

Summary--This paper examines the relationship between a military vehicle's mobility and its survivability. The theoretical model governing this relationship is based on a series of steps, each of which is critically examined. The tactical role of the vehicle is translated into a mobility requirement stated in terms of the percentage of ground to be trafficable in specified areas. The assessment of soil strength is achieved using the cone index, the statistical handling of which is described. The link between Vehicle Cone Index and Rowland's Mean Maximum Pressure (MMP) is discussed, as is its role as an indicator of vehicle mobility. Vehicle and armour weight follow directly from Rowland's MMP, leading to an assessment of survivability. Examples are given of the effects of varying the mobility requirement, the threat level and the armour type on the ultimate survivability of the vehicle.

INTRODUCTION

THE MILITARY vehicle designer often refers to the trade-off between mobility and protection. The argument normally runs as follows:

"A high level of protection leads to high vehicle weight which results in poor cross-country performance."

The argument can be developed by examining the influence of protection and mobility on survivability:

"At one extreme one can go for a very light vehicle, which will have a high cross-country mobility, poor protection and therefore a poor chance of surviving an attack. However due to its high mobility, its exposure to attack will be greatly reduced. At the other extreme one can go for a very heavy vehicle, which will have a poor cross-country performance, but a good chance of surviving an attack. However, due to its poor mobility, its exposure to attack will be greatly increased."

It is not immediately clear which of these two options would offer the better chance of survival; indeed for a particular vehicle role there will exist an optimum in this spectrum of choice somewhere between these two extremes. The aim of this paper is to examine these assertions to see what part the effective characterisation of cross-country vehicle mobility can play in enhancing the conceptual design of Armoured Fighting Vehicles (AFVs).

THE EFFECT OF VEHICLE WEIGHT ON CROSS-COUNTRY PERFORMANCE

When add i t iona l load is app l ied to a saturated, cohes ive soil, the inc rement is t ransmi t ted direct ly to the pore water. The soil part ic les exper ience no extra load and thus the shear strength o f the soil is unaf fected by the addi t ional load. Vehicle t ract ion depends on soil shear strength and so is unaf fected by the load increment. The extra load will, however , cause

*Presented at the 4th Annual British Conference, ISTVS, Sutton Bonington, 23-24 September 1986. tRoyal Military College of Science, Shrivenham, Swindon, Wilts. SN6 8LA, U.K.

263

264 3. G. HETHERINGTON and 1. LITTLETON

extra sinkage and therefore extra rolling resistance. This results in the relationship between drawbar pull and weight depicted in Fig. 1.

300-

113 ~ 200-

100 -

0 50 ~5 ~0 6'5 70

I I -

VEHICLE MASS (T)

FIG. 1. Typical relationships for drawbar pull vs vehicle mass on clay.

In a coarse-grained soil an increment of load enhances the inter-particle friction, increasing the shear strength and therefore the derivable traction. In this case, both the traction and the rolling resistance increase, although the increase in traction dominates. Results obtained at model scale for a tracked vehicle on sand at The Royal Military College of Science (RMCS) [1] are compared with the predictions of Turnage [2] in Fig. 2. The contrast in behaviour suggests that whilst extra protection will inevitably reduce cross-country performance on cohesive soils, it is likely that it actually improves performance on purely frictional soils. Of course, this extra potential performance for the very heavily armoured vehicle on sandy soils would only be available if extra power were supplied, and the vehicle would have to be dedicated to operations in the desert. Few armies can afford the luxury of vehicles dedicated to a desert role, and are obliged to operate in regions with cohesive soils.

200-

150-

100-

50-

0

FIG. 2.

El Measured

. . . . . Theory (Turnage, Reference 2)

T I I I I I I I 50 100 150 200 250 300 350 LOAD (N)

Drawbar pull vs load for model track in sand (from ref. 1).

VEHICLE WEIGHT AND PROTECTION

Although detailed designs will show some departure from any generalised statement, it is possible to draw some broad conclusions about the proportion of total vehicle weight which is given over to armour. Analysis of post-war main battle tanks of various nations shows that about 45% of the vehicle all up weight is devoted to protection (Fig. 3). The figure for a

MEAN MAXIMUM PRESSURE IN CROSS-COUNTRY MOBILITY 265

----- PAY'LOA

FIG. 3. Approximate distribution of vehicle mass for main battle tank.

MICV (Mechanised Infantry Combat Vehicle) is nearer 40% (Fig. 4). The assumption of a fixed proportion of vehicle weight being available for armour provides the link between a specified level of mobility and the achievable level of protection.

FIG. 4. Approximate distribution of vehicle mass for MICV.

ARMOUR AND SURVIVABILITY

The evaluation of the survivability of an armoured fighting vehicle is very complex. The range of attacks to which the vehicle may be subjected includes: direct fire [both kinetic energy (KE) and chemical energy (CE)] which attacks the front, rear and sides of the vehicle almost at horizontal; a variety of artillery delivered top attack weapons designed to attack the more lightly armoured areas of the vehicle; and attack to the underneath by mines.

Threat analyses, both present and future, indicate that direct fire KE and CE constitutes the majority threat. Thus, although top attack weapons and mines pose a considerable problem to the armourer, the majority of armour will continue to be provided as protection to horizontal attack. Whittaker [3] analysed the distribution of horizontal attacks on vehicles and developed "Directional Probability Variations" which describe the probability of an attack, sustained by a vehicle, coming from within a specified frontal are + u (Fig. 5). A

266 J .G. HETHERINGTON and 1. LITTLETON

FIG 5. Frontal arc _+ u .

plot of his probability function is given in Fig. 6. Altough the arrival on the scene of hand-held anti-tank guided weapons has shifted some of the attacks from the front to the sides and rear, it is argued that this effect has been neutralized by the further concentration of attack on the front of a vehicle due to the increased range achievable. Whittaker's directional probability variations therefore still provide a realistic description of the distribution of attacks on a vehicle, and show a concentration of attacks to the front. It is unlikely that the weight quota afforded to the armour will provide sufficient armour to make it totally immune to all attacks. It is therefore necessary to provide all-round protection against a lower level of threat whilst providing immunity against the highest level of threat within as big a frontal arc as possible. The aim, therefore, is to maximise the size of the immune frontal arc, to provide the maximum survivability. By evaluating the directional probability variation within this immune frontal arc, a quantitative estimate of survivability can be obtained.

o u_

1.0

~ o.8

.< ~ 06-

8~ o.4-

i 0.2"

i i 30 ~0 910 120 150 180 u

FIG. 6. Whittaker's directional probability variations.

THE CONCEPTUAL DESIGN ROUTE

In practice the design of an armoured fighting vehicle will be a process of evolutionary engineering, with innovations providing gradual improvements in performance. However, if one is seeking to quantify the effect of cross-country performance on survivability, it is instructive to follow a conceptual design route determined principally by off-road performance. A proposed scheme is presented in Fig. 7, in which the tactical decision of field of operation provides the initial step. By specifying the areas of the earth's surface on which the vehicle is required to operate, the number of days of the year on which the vehicle must be

MEAN MAXIMUM PRESSURE IN CROSS-COUNTRY MOBILITY 267

I WHAT PERCENTAGE I OF GROUND I

, r

I RCI of weakest soil on which vehicle must operate

~r

ql-

' vehicle front I I I I

Remainder distributed optimally

I Immune frontal arc

Survivability

I f

Statement of required mobiliw

ln-situ soil strength survey

(vc[)

MMP = 10.4 VC[ 1

W = (MMP).mbV"~ 1.26

40-46% of vehicle mass available for armour

Optimal armour distribution leads to assessment of survivability

FIG. 7.

able to traverse the ground and the percentage of that ground which must be trafficable, a characteristic weakest soil across which the vehicle must be able to travel is specified. The foregoing is a theoretical and highly optimistic statement. Certainly one could specify the tactical requirement very precisely. For example it is essential that a UK main battle tank is

268 J.G. HETHERINGTON and I. LITTLETON

able to traverse river valleys in the Federal Republic of Germany 365 days a year. One is bound to accept a small proportion of the ground as non-trafficable, say 10%, giving a requirement for 90% terrain trafficability. The difficulty lies in translating this precise mobility requirement into a characteristic weakest soil. The dual requirement is for

(a) an efficient system of in situ, soil strength measurement and (b) a comprehensive survey for the variation of this measurement with area and season.

The Bevameter and cone penetrometer are two popular examples of a wide range of devices which have been suggested for in situ soil strength measurement. The cone penetrometer is adopted here and a discussion of the validity of its use will follow later. It is assumed, therefore, that it has been possible to convert the precise tactical mobility requirement into a figure, the remoulded cone index (RCI), which represents the weakest soil over which the vehicle must be able to pass to conform with the tactical mobility requirement [the vehicle cone index, (VCI)]. Rowland [4] developed a conversion from VCI to Mean Maximum Pressure (MMP), and through the Rowland expression

MMP - - -

where W is the weight of the vehicle m is the number of road wheels b is the track breadth p is the track plate length

and d is the diameter of the road wheels,

1.26 W

mb,/

it is possible to relate the permissible weight of the vehicle to the required value of MMP. The validity of Rowland's expression for MMP has been the subject of recent criticism by Garber and Wong [5] and the subject of research by Bowring [1] and Lord [6] and will be discussed in a later section. The vehicle weight is thus determined, provided the geometrical parameters of the track system are fixed, and the armour will occupy a fixed proportion of the vehicle weight. For a threat level specified in terms of the thickness of rolled homogeneous steel armour (RHA) which can be penetrated at normal, the thickness of other armours (e.g. aluminium or complex) which will provide equivalent protection can be found. The front of the vehicle is armoured to provide total immunity to the perceived threat and the remainder of available armour is distributed on the vehicle in such a way as to maximise the directional probability variation within the arc of immunity, and thus the vehicle's survivability. The chain is thus completed and the relationship between mobility and survivability established in quantifiable terms.

As has been indicated above, two links in the chain need more careful examination, and this follows in the subsequent sections. The chain also needs extending, for the term "survivability" used above refers to the chance of a vehicle surviving a sustained hit. As was discussed in the introduction, an important aspect of survivability is cross-country speed and agility, so that exposure to attack is minimised. This extension is the subject of continuing study and will be published shortly by Wright and Rollo [7].

IN SITU SOIL-STRENGTH MEASUREMENT USING THE CONE PENETROMETER The cone penetrometer provides an easy and convenient system for measuring soil

strength in the field and has been used successfully by US Army Waterways Experiment

MEAN MAXIMUM PRESSURE IN CROSS-COUNTRY MOBILITY 269

Station (WES) as a descriptor of soil strength in establishing empirical soil-vehicle relationships [8]. Moreover, Rohani and Baladi [9] have, through analysing the mechanism of penetration, established a correlation between the cone penetrometer readings obtained and the expected value, predicted in terms of conventional soil strength parameters c and qb (see, for example, Fig. 8).

FIG. 8.

- 80-

a z

0 60- 0

8 S

40-

20-

1

/ 2'o 4'0 6'o 8'0

MEASURED CONE INDEX, PSI

Comparison of predicted and measure cone index for clay (tk = 0) after Rohani and Baladi (ref. 9).

Unfortunately, homogeneous soils rarely present themselves in practice, where the natural process of deposition and man's intervention in tillage, result in both lateral and vertical variations in soil gradations, void ratio and moisture content. The lateral variations are described, for strategically important areas, in the NATO Cross Country Mobility (CMM) maps. Rowland et aL [10] have investigated the variation of cone index in the critical layer with area and season within this zone, producing detailed and valuable estimates of the proportion of land surface having a particular strength. By selecting a "critical layer", some of the more intractable problems of handling cone index data are avoided. Figure 9 shows the variation of cone index with moisture content and depth for a well controlled test site. Although at any particular depth there is a discernible relationship between cone index and moisture content, the variation with depth is simply a function of the stratified nature of the soil. Equally problematical are the data of Fig. 10 which shows the variation of cone index and moisture content on a particular day within a small area of a typical North German layered soil.

Soil strength information is fundamental to predicting cross country mobility, however wise selection and handling of the data is vital if meaningful predictions are to result.

STATISTICAL TREATMENT OF CONE INDEX VALUES The inherent variability of cone index readings demands a statistical treatment of field

data. Kogure et al. [11] described the essential statistical techniques which have been

270 J.G. HETHERINGTON and 1. LITTLETON

O O 200

180-

160-

140 -

120-

1OO -

80-

60-

404

20-

FIG. 9.

~ 0 0 SOIL : F INE GRAINED S ILTY SAND

mm

0--100 mrn

MOISTURE CONTENT % i I ~ - - i

10 2i0 3TO 40 510 6'0 70

Values of cone index against moisture content (controlled site, RMCS).

E E

100-

200

300

400-

5CO-

CONE INDEX

10 20 30 40 50 60 70 80 90 1OO 110 120 130 140 I I r ? I L I I I I L i I I

o

O

1CJ 2~0 3'0 MOISTURE CONTENT %

CONE INDEX MOISTURE CONTENT

FIG. 10. Variation of C1 and moisture content with depth -- North German layered soil.

developed below. The techniques will be described in the context of 60 cone index readings taken on a single day within an apparently homogeneous, fiat, silty clay field. Testing was conducted in four batches of fifteen readings, each of which can be treated as a separate sample of size 15 (Table 1).

Each sample consists of 15 independent observations of the variable cone index from the (infinitely large) number of readings which could have been taken from the chosen area. By simply combining the batches in various ways, sample sizes of 15, 30, 45 and 60 data can be

MEAN MAXIMUM PRESSURE IN CROSS-COUNTRY MOBILITY

TABLE 1.

271

Sample 1 Sample 2 Sample 3 Sample 4

120 175 190 142 170 130 180 175 190 180 175 157 125 172 135 180 130 172 190 165 Values shown 145 167 130 175 are average of 172 160 135 165 readings taken 145 157 145 120 at 150mmand 185 145 180 150 300mmdepth. 200 140 185 125 160 145 120 147 202 180 150 175 145 160 180 155 160 150 152 127 190 145 170 142

Sample mean 163 Standard deviation 26

159 161 153

13 23 Mean of all sixty data = 158.9

Standard deviation = 21.5

19

obtained, and this fact will be used to demonstrate the benefits which accrue from large samples. For each sample, the mean and standard deviation have been tabulated in Table 1.

Drawing inferences from the data is greatly facilitated if it can be shown that they follow the normal distribution. The goodness of fit can be investigated using the Chi-squared distribution as follows. The range within which the sixty data of Table 1 fall is divided into a number of cells. Using the mean and standard deviation of the sixty data, the number of data which would be expected to occur in each cell, assuming the data are normally distributed, (E) is calculated and compared with the number which is observed to occur in each cell (O).

A value of X2m is evaluated for all as follows:

(O - E ) 2 X2m - - -

E

and then summed over all the cells to give a value of X2m for the whole sample. In this case the value of X2m is 6.549. Although there were eight cells, the size of the sample, n, the mean, x and the sample standard deviation, S, were used in establishing the expected value in each class, and so there are only 5 degrees of freedom. From the X 2 distribution,

X~5%) (5) = 11.07.

Since the value of the X 2 statistic obtained from the goodness of fit test is less than the value from the X~5~) distribution, it is not possible, at this level of confidence, to reject the hypothesis that the sample comes from a normally distributed population.

Being only in possession of the information afforded by the fifteen readings of sample 1, and wishing to make an estimate of the true mean value of the whole of the chosen area, one would only be able to state, with a specified level of confidence, that the mean lies within certain limits. The larger the sample and the smaller the standard deviation, the smaller will

272 J .G. HETHERINGTON and I. LITTLETON

be the range within which the mean of the population can be said to be, at a specified level of confidence. In fact one can state, with a 100 ( l -a)% level of confidence that the following range includes the population mean (#):

S 2 S 2 x - t~/2 x / - - < # < x + t~,2xf--

n n

where ~ is the mean of the sample, S 2 is the variance of the sample, n is the sample size and t~/2 is obtained from t distribution tables. For example, using the fifteen data available from sample 1 alone, it can be stated with 95% confidence that the range 148-178 includes the population mean whereas including the sixty data available from all four samples, the range within which the population mean can be expected to lie at the same level of confidence is narrowed to between 153 and 164. Thus collecting more data can either enhance the level of confidence one has that the mean lies within a specified range, or reduce the range within which the mean can be expected to lie at a specified level of confidence.

Assuming the data to be normally distributed, the trafficability assessment is simply made by entering the normal distribution with the appropriate value of cone index. The data of Table 1 are for a good, uniform site and therefore provide a somewhat unrealistic example, However, for a low mobility vehicle with a VCIs0 of 140, the probability (p) of encountering soil with strength greater than this (i.e. the percentage of the ground trafficable) is found from the normal distribution tables to be 81%. This statement is itself the subject of uncertainty, due to the variation in the data. At the 95% confidence level, it can be stated that p lies within the range:

p - 1.96 x/p(1 -P )

MEAN MAXIMUM PRESSURE IN CROSS-COUNTRY MOBILITY 273

,,x, z

8

130'

120

110"

100

f X - - /I

~ ~b A 6~ SAMPLE S=E

FIG. 1 l. Effect of sample size on VCI assessment.

the relationship shown in Fig. 12. In the sequence of analysis presented here, this relationship provides the link between Rowland's MMP and the vehicle's ability to traverse ground with a particular value of strength as determined by the RCI. It is acknowledged that the use of Rowland's MMP and the relationship of Fig. 12 may introduce errors, and it may be desirable to introduce a more sophisticated model of soil/vehicle interaction at a later stage.

FIG. 12.

i (VCi)~

300.

200

IO0

0 [ o 2'o ,,'o 6o 8'0 ,;o "-

VCI (psO

Relationship between MMP and (VCI)j or (VCI)50 (adapted from ref. 4).

274 J.G. HETHERINGTON and I. LITTLETON

The Wong model examines the mechanics of the interaction between a tensioned track supported on a system of suspended road wheels and a deforming terrain. The pressure- sinkage response of the soil is characterized by the equation p = kz" for steadily increasing sinkage, with refinements to cope with the cyclic loading which results from a sequence of road wheels. The model is able to accommodate other forms of pressure sinkage relationship. In the formulation, an array of simultaneous equations is developed which are essentially statements of equilibrium and compatibility for the soil-track interface.

The shear stress distribution beneath the track is deduced from the characterisation of the shear stress vs shear strain relationship for the soil, the degree of slip and the normal pressure distribution beneath the track. The solution of the assembled equations by computer yields comprehensive information concerning a specific vehicle's performance over selected terrain. Reference [ 13] presents convincing supportive evidence from instrumented trials for track pressure distributions, drawbar pull and sinkage of a tracked test vehicle on sand, snow and muskeg. The model indicates the importance of both terrain stiffness (Fig. 13) and initial track tension on the pressure distribution: stiffer terrain and lower track tension both result in more pronounced peaks of pressure beneath the wheel stations and therefore higher MMP values. These and numerous other vehicle parameters, omitted by Rowland, are shown to have an effect on the true surface ground pressure distribution.

FIG. 13.

kN/m 2

300-

250 -

200

150-

100

50

0 i 2 3 4 5 5 7 8 cJ x103kNlm 3 TERRAIN STIFFNESS k

Variation of the computed value of mean maximum pressure with terrain stiffness after Wong (ref. 5).

A programme of work at RMCS is seeking to examine the influence of many of these parameters on MMP. A one tenth scale model of the Challenger main battle tank track and suspension system (Fig. 14) has been constructed for testing in the mobility bins. The model offers the opportunity of varying the number of road wheels, road wheel diameter, suspension stiffness, track tension, track plate profile, and track pitch. As part of his study Bowring [1] examined the dependence of MMP on the number of road wheels and road

MEAN MAXIMUM PRESSURE IN CROSS-COUNTRY MOBILITY 275

FIG. 14. One tenth scale model of challenger MBT.

wheel diameter for the model on a uniformly graded sand. Figure 15 demonstrates that the number of wheels significantly affects MMP, whereas wheel diameter is relatively unimportant. An attempt to correlate measured pressure with prediction of the Wong model is in hand.

40.

35-

30-

25-

2o"

15

FIG, 15. Measured values of MMP from one tenth scale model tests, compared with Rowland predictions (at depth of 23 ram) (increase by factor of 1.75 to obtain values at surface).

276 ]. G. HETHERINGTON and I. LITTLETON

SURVIVABILITY ASSESSMENT

The procedure outlined in Fig. 7 has been carried out for (a) a main battle tank (MBT) and (b) a mechanised infantry combat vehicle (MICV), the results being presented in Figs 16-18

100

m < > 80

60-

40-

20-

M.B.T. THREAT : 500mmRHA ARMOUR:SPEC~L

TERRA~ :FRG RNER VALLEYS

P A S S

~ PASS

0 50 ~o ~% ~o do ~oo

TRAFFICABIL~Y (%)

FIG. 16.

t 10 50

VEHICLE : MBT

TERRAIN : FRG RIVER VALLEYS

CURRENT RANGE OF MBT MASS

i I 6O 710

!

FIG. 17.

go ' ~'o TRA FFICABILITY (%)

MEAN MAXIMUM PRESSURE IN CROSS-COUNTRY MOBILITY 277

lOO-

m < 90- _> >

~ co-

70-

VEHICLE : MBT

TERRAIN : FRG RIVER VALLEYS

No. OF PASSES : 50

6'0 ~o

FIG. 18.

s'o 9'0 TRAFFICABILITY (%)

m

>

D ~9

1OO

80-

60,

,4,0-

20-

MICV

THREAT =75ram RHA

ARMOUR : ALUMINUM

TB:~RAIN: FRG RIVER VALLEYS

\ LE PASS

50 PASS

50 ~o do ~o lOO

FIG. 19.

"mAFF~A~U'rY (%)

278 J .G . HETHERINGTON and I. L ITTLETON

VEHICLE : M ICV

TERRAIN : FRG RIVER VALLEYS

No. OF PAS,SES : SINGLE

100 HREAT

75mm

HA

60 "'>

40

20

50 ' 6'0 ~ 7~3 ~ 8~0 ~ 9~0 i

TRAFF ICABIL ITY (%)

FIG. 20.

for MBT and Figs 19-21 for MICV. The demands of mobility are characterised in Fig. 16 and 19 where the requirement for fifty pass trafficability has such a significant protection penalty that survivability is greatly reduced. Figures 17 and 20 explore the single pass case in greater detail by showing the effect of (a) increased threat level and (b) armour type on surviability. The current range of MBT masses will give 60 to 75% trafficability over FRG river valleys and could offer protection to threats in the range of 400-600 mm of RHA, if exclusively special armour were used. The current MICV, however, will offer 75 to 95% single pass trafficability and up to total immunity against threats in the range 75-100 mm RHA. It becomes apparent from Fig. 18 that the combination of multi-pass and high percentage trafficability proves too demanding a requirement for MBTs, leaving the current configuration of tank with insufficient protection to be viable. A similar, though less severe, effect is apparent for MICVs in Fig. 21.

The stark reality of the protection/mobility trade-off as displayed in Figures 16-21 emphasises the importance of careful specification of the mobility requirement. A request for multi-pass capability over a high proportion of the terrain will result in poor protection. The corollary is, of course, that a demand for total immunity will result in a correspondingly poor mobility. Moreover a scarcity of terrain data, when statistically analysed, would lead to an overpessimistic view of potential mobility and again would result in reduced survivability. There are, of course, two ways to break the two handed stranglehold on the AFV designer described above. One is to develop more effective armour materials, which provide better protection for a given weight w the other to develop more efficient track/wheel and suspension systems to provide lower ground pressures for a given vehicle mass.

MEAN MAXIMUM PRESSURE IN CROSS-COUNTRY MOBILITY 279

100

60

VEHICLE : MICV

TERRAIN : FRG RIVER VALLEYS

No. OF PASSES : FIFTY

40'

20

:5O 60 70 80 gO

TRAFFICABILiTY (%)

FIG. 21.

CONCLUSIONS

(i) A quantitat ive relat ionship has been established between the mobi l i ty requirement and the resultant survivabil ity of AFVs.

(ii) Excessive demands for mobi l i ty will result in poor protect ion and vice versa. (iii) Only better a rmour materials or better t rack/wheel and suspension systems can

simultaneously improve protect ion and mobil ity. (iv) Soil strength data obtained with the cone penetrometer are subject to large inherent

variat ions due to inconsistencies in terrain. (v) Statist ical analysis of cone index data enables confidence levels to be placed on terrain

assessment - - larger samples providing better predictions.

REFERENCES

[1] R. A. W. BOWRING, The Construction and Testing of a Model for a Study of the Parameters which Affect Tracked Vehicle Ground Pressure. MSc Thesis, RMCS, Shrivenham, UK (1985).

[2] G. W. TURNAGE, Performance of Soils under Track Loads. Technical Report No M-71-5, US Army Waterways Experimental Station, Vicksburg, MS, USA (1971).

[3] Whittaker's DPV for Tank Hulls. OA Group Note 544, RMCS, Shrivenham, UK (1978). [4] D. ROWLAND, Tracked Vehicle Ground Pressure. MVEE Report No 72031, MVEE, Chertsey, UK (1972). [5] i . GARBER and J. Y. WONG, Prediction of ground pressure distribution under tracked vehicles - - I. An

analytical method for predicting ground pressure distribution, d. Terraraechanics 18 (1) (1981). [6] E.A. LORD, Investigation of Track Vehicle MMP. MSc Thesis, RMCS, Shrivenham, UK (1986). [7] R.A. WRIGHT and N. H. ROLLO, Survivor; a computer-aided analysis of AFV mobility and survivability. ASC

Div I Advanced Study Report, RMCS, Shrivenham, UK (1986). [81 A. A. RULA and C. J. NLrrTALL, JR, An Analysis of Ground Mobility Models. Tech Report M-71-4, WES,

Vicksburg, MS, USA (1971).

280 J .G. HETHERINGTON and I. LITTLETON

[9] B. ROHAN~ and G. Y. BALADI, Correlation of mobility cone index with fundamental engineering properties of soil. Proc. 7th Int. Conf. Int. Soc. for Terrain-Vehicle Systems, Calgary, Canada (1981).

[ 10] D. ROWLAND, H. J. DOVE and G. TORNTON," Terrain Limitations to the Use of Agility. Memo 7525 Defence Operational Analysis Establishment (1976).

[11] K. KOGURE, Y. OHIRA and H. YAMAGUCHI, Basic study of probabilistic approach to prediction of soil trafficability - - statistical characteristics of cone index. J. Terramechanics 22 (3) (1985).

[12] J.Y. WONG, M. GARBER and J. PRESTON-THOMAS, Theoretical prediction and experimental substantiation of the ground pressure distribution and tractive performance of tracked vehicles. Proc. Inst. Mech. Engrs. 19811 (15)(1984).

[ 13] J.Y. WONG and J. PRESTON-THOMAS, Parametric analysis of tracked vehicle performance using an advanced computer simulation model. Proc. Inst. Mech. Engrs 200 (D2) (1986).