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The role of mean maximum pressure in specifying cross-country mobility for armoured fighting vehicle design
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 SPECIFYING CROSS-COUNTRY MOBILITY FOR ARMOURED FIGHTING VEHICLE DESIGN* J. G . HETHERINGTON~" a n d 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 T H E 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 W h e n a d d i t i o n a l l o a d is a p p l i e d to a s a t u r a t e d , c o h e s i v e soil, t h e i n c r e m e n t is t r a n s m i t t e d d i r e c t l y t o t h e p o r e w a t e r . T h e soil p a r t i c l e s e x p e r i e n c e n o e x t r a l o a d a n d t h u s t h e s h e a r s t r e n g t h o f t h e soil is u n a f f e c t e d b y t h e a d d i t i o n a l l o a d . V e h i c l e t r a c t i o n d e p e n d s o n soil s h e a r s t r e n g t h a n d so is u n a f f e c t e d b y t h e l o a d i n c r e m e n t . T h e e x t r a l o a d will, h o w e v e r , c a u s e *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. H E T H E R I N G T O N 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
II-
50 FIG. 1.
~5
~0
6'5
70
VEHICLE M A S S ( T )
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.
El Measured . . . . .
200-
Theory (Turnage, Reference 2)
150-
100-
50-
0T FIG. 2.
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).
V E H I C L E W E I G H T A N D 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 . H E T H E R I N G T O N 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
.< ~ 068~
o.4-
i
0.2" 30 FIG. 6.
~0
i
910
120
i
150
180
u°
Whittaker's directional probability variations.
T H E 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
I WHATPERCENTAGEI OFGROUND I
267
of mobiliw
Statement required
ln-situ soil strength
survey ,r
(vc[)
I RCIof weakest soil on which vehicle must operate
~r
MMP= 10.4VC[1 qlW= (MMP).mbV"~ 1.26
40-46%of vehicle mass available for armour
' vehicle front I III Remainder distributed optimally
I Immune
frontal arc
Optimal
armour distribution leads to assessment survivability
I
of
f
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. HETHERINGTONand 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 1.26 W MMP - - -
mb,/
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, 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-STRENGTHMEASUREMENTUSING 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 M A X I M U M 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).
-
801
a z 0 0
60-
8 S 40-
20-
/ 2'o
4'0
6'o
8'0
MEASURED CONE INDEX, PSI
FIG. 8.
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. STATISTICALTREATMENTOF CONEINDEX 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
~
0
0
SOIL:
FINE
GRAINED
SILTY
SAND
180mm
160140 1201OO
•
0--100 mrn
-
8060404 20-
MOISTURE CONTENT % i
10 FIG. 9.
2i0
I ~
3TO
40
510
--
i
6'0
70
Values of cone index against moisture content (controlled site, RMCS).
CONE
E E
INDEX
10 20 30 40 50 60 70 80 90 1OO 110 120 130 140 I
I
r
?
100-
I
L
I
I
I
I
L
i
I
I
o
200 O
300
400-
5CO1CJ
• CONE INDEX
2~0
3'0 MOISTURE CONTENT %
© MOISTURE CONTENT
FIG. 10. Variationof 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-COUNTRYMOBILITY
271
TABLE1.
Sample mean Standard deviation
Sample 1
Sample2
Sample3
Sample4
120 170 190 125 130 145 172 145 185 200 160 202 145 160 190
175 130 180 172 172 167 160 157 145 140 145 180 160 150 145
190 180 175 135 190 130 135 145 180 185 120 150 180 152 170
142 175 157 180 165 175 165 120 150 125 147 175 155 127 142
163
159
161
153
26
13 23 Mean of all sixty data = 158.9 Standard deviation = 21.5
Valuesshown are average of readingstaken at 150mmand 300mmdepth.
19
obtained, and this fact will be used to demonstrate the benefits which accrue from large samples. F o r 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 X2mis evaluated for all as follows:
X2m -
(O - E) 2 - E
and then summed over all the cells to give a value of X2mfor the whole sample. In this case the value of X2mis 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. F r o m the X2 distribution, X~5%)(5) = 11.07. Since the value of the X2 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 . H E T H E R I N G T O N 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 (#): S2
S2
n
n
x - t~/2 x / - - < # < x + t~,2xf--
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 ) < p < p n-1
+ 1.96 x/ p(l - p ) n-1
which for this case gives p lying in the range 80-82%. For the vehicle designer, it is more important to turn the question round as follows: " I f the requirement is for 50 vehicles to traverse a fixed percentage of terrain, what VCIs0 (and therefore MMP) must the vehicle have?" Thus if the requirement is to traverse 87.5% of the terrain of Table 1, the task is to determine the value of cone index above which 87.5% of the population lies. This can be simply achieved by scanning the normal distribution tables for the appropriate entry value for this chosen probability. However, the value thus obtained is again subject to uncertainty which is governed by the number of data in the sample. The effect of this is shown in Fig. 11 which indicates a decision based on a sample size of 15 would be unnecessarily stringent. It will be shown in the following section how such a demand for low VCI has severe implications for vehicle survivability. MEAN MAXIMUM PRESSURE
Recent work by Wong [5, 12, 13] questions the ability of the Rowland expression (MMP = 1.26 W/mbvCp-d) to accurately predict the mean of the peaks of pressure beneath the road wheels of a tracked vehicle. It is argued from the physical standpoint that true MMP must be highly dependent upon terrain characteristics. On a firm terrain the MMP will be higher than on a soft terrain, since the weight of the vehicle will be transmitted to the ground through a reduced zone of contact. Thus Rowland's expression cannot accurately predict the true value of MMP. In ref. [4] Rowland extracted data from the WES trafficability tests and established
MEAN MAXIMUM PRESSURE IN CROSS-COUNTRY MOBILITY
/I
130' ,,x, z
8
120
273
f X - -
110"
100
~b
~
FIG. 1 l.
A
6~
SAMPLES=E
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.
i
(VCi)~° 300.
200
IO0
0
o
2'o
,,'o
[
6o
8'0
,;o
"-
VCI (psO
FIG. 12.
Relationship between MMP and (VCI)j or (VCI)50 (adapted from ref. 4).
274
J.G. HETHERINGTONand 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 pressuresinkage 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. kN/m 2 300-
250 -
200
150-
100
50
0
i
2 3 4 5 5 7 8
cJ x103kNlm 3
TERRAIN STIFFNESS k
FIG. 13.
Variation of the computed value of mean maximum pressure with terrain stiffnessafter 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. H E T H E R I N G T O N and I. LITTLETON
S U R V I V A B I L I T Y 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 M.B.T. 500mmRHA ARMOUR:SPEC~L TERRA~ :FRG RNERVALLEYS THREAT :
100 m < > 80° P
60-
A
S
S
40-
~
PASS
20-
0 50
~o
~%
~o
do
~oo
TRAFFICABIL~Y(%) FIG. 16.
VEHICLE : MBT TERRAIN
: FRGRIVERVALLEYS
CURRENT RANGE OF MBT M A S S
°t 10
50
i 6O
I
710
!
FIG. 17.
go ' ~'o TRAFFICABILITY(%)
MEAN MAXIMUM PRESSURE IN CROSS-COUNTRY MOBILITY VEHICLE : MBT TERRAIN : FRG RIVER VALLEYS No. OF P A S S E S : 5 0
lOOm < _> >
90-
~
co70-
6'0
s'o
~o
9'0
TRAFFICABILITY (%)
FIG. 18.
MICV THREAT =75ram RHA ARMOUR : A L U M I N U M
TB:~RAIN: FRG RIVER VALLEYS
\
1OO m >
80-
LE PASS
D ~9
60,
,4,050 PASS
20-
50
~o
do
~o
lOO
" m A F F ~ A ~ U ' r Y (%)
FIG. 19.
277
278
J . G . H E T H E R I N G T O N and I. L I T T L E T O N VEHICLE : MICV T E R R A I N : FRG RIVER V A L L E Y S No. OF PAS,SES : SINGLE
100
HREAT 75mm HA
60
"'¢>
40
20
50
'
6'0
~
7~3
~
8~0
~
9~0
i
T R A F F I C A B I L I T Y (%)
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
VEHICLE : MICV TERRAIN : FRG RIVER VALLEYS No. OF PASSES : FIFTY
100
60
40'
20
:5O
60
70
80
gO
TRAFFICABILiTY (%)
FIG. 21.
CONCLUSIONS (i) (ii) (iii) (iv) (v)
A q u a n t i t a t i v e r e l a t i o n s h i p has been established between the m o b i l i t y r e q u i r e m e n t a n d the resultant survivability o f A F V s . Excessive d e m a n d s for m o b i l i t y will result in p o o r p r o t e c t i o n a n d vice versa. O n l y b e t t e r a r m o u r m a t e r i a l s o r b e t t e r t r a c k / w h e e l a n d s u s p e n s i o n systems can s i m u l t a n e o u s l y i m p r o v e p r o t e c t i o n a n d mobility. Soil s t r e n g t h d a t a o b t a i n e d with the cone p e n e t r o m e t e r are subject to large inherent v a r i a t i o n s due to inconsistencies in terrain. Statistical analysis o f cone index d a t a enables c o n f i d e n c e levels to be p l a c e d on t e r r a i n assessment - - larger samples p r o v i d i n g 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 . GARBERand 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. WRIGHTand N. H. ROLLO,Survivor; a computer-aidedanalysis of AFV mobilityand survivability. ASC Div I Advanced Study Report, RMCS, Shrivenham, UK (1986). [81 A. A. RULAand 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. GARBERand 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).
0022-4898/8753.00+0.00 Pergamon Journals Ltd. © 1988 ISTVS
THE ROLE OF MEAN MAXIMUM PRESSURE IN SPECIFYING CROSS-COUNTRY MOBILITY FOR ARMOURED FIGHTING VEHICLE DESIGN* J. G . HETHERINGTON~" a n d 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 T H E 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 W h e n a d d i t i o n a l l o a d is a p p l i e d to a s a t u r a t e d , c o h e s i v e soil, t h e i n c r e m e n t is t r a n s m i t t e d d i r e c t l y t o t h e p o r e w a t e r . T h e soil p a r t i c l e s e x p e r i e n c e n o e x t r a l o a d a n d t h u s t h e s h e a r s t r e n g t h o f t h e soil is u n a f f e c t e d b y t h e a d d i t i o n a l l o a d . V e h i c l e t r a c t i o n d e p e n d s o n soil s h e a r s t r e n g t h a n d so is u n a f f e c t e d b y t h e l o a d i n c r e m e n t . T h e e x t r a l o a d will, h o w e v e r , c a u s e *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. H E T H E R I N G T O N 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
II-
50 FIG. 1.
~5
~0
6'5
70
VEHICLE M A S S ( T )
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.
El Measured . . . . .
200-
Theory (Turnage, Reference 2)
150-
100-
50-
0T FIG. 2.
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).
V E H I C L E W E I G H T A N D 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 . H E T H E R I N G T O N 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
.< ~ 068~
o.4-
i
0.2" 30 FIG. 6.
~0
i
910
120
i
150
180
u°
Whittaker's directional probability variations.
T H E 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
I WHATPERCENTAGEI OFGROUND I
267
of mobiliw
Statement required
ln-situ soil strength
survey ,r
(vc[)
I RCIof weakest soil on which vehicle must operate
~r
MMP= 10.4VC[1 qlW= (MMP).mbV"~ 1.26
40-46%of vehicle mass available for armour
' vehicle front I III Remainder distributed optimally
I Immune
frontal arc
Optimal
armour distribution leads to assessment survivability
I
of
f
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. HETHERINGTONand 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 1.26 W MMP - - -
mb,/
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, 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-STRENGTHMEASUREMENTUSING 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 M A X I M U M 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).
-
801
a z 0 0
60-
8 S 40-
20-
/ 2'o
4'0
6'o
8'0
MEASURED CONE INDEX, PSI
FIG. 8.
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. STATISTICALTREATMENTOF CONEINDEX 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
~
0
0
SOIL:
FINE
GRAINED
SILTY
SAND
180mm
160140 1201OO
•
0--100 mrn
-
8060404 20-
MOISTURE CONTENT % i
10 FIG. 9.
2i0
I ~
3TO
40
510
--
i
6'0
70
Values of cone index against moisture content (controlled site, RMCS).
CONE
E E
INDEX
10 20 30 40 50 60 70 80 90 1OO 110 120 130 140 I
I
r
?
100-
I
L
I
I
I
I
L
i
I
I
o
200 O
300
400-
5CO1CJ
• CONE INDEX
2~0
3'0 MOISTURE CONTENT %
© MOISTURE CONTENT
FIG. 10. Variationof 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-COUNTRYMOBILITY
271
TABLE1.
Sample mean Standard deviation
Sample 1
Sample2
Sample3
Sample4
120 170 190 125 130 145 172 145 185 200 160 202 145 160 190
175 130 180 172 172 167 160 157 145 140 145 180 160 150 145
190 180 175 135 190 130 135 145 180 185 120 150 180 152 170
142 175 157 180 165 175 165 120 150 125 147 175 155 127 142
163
159
161
153
26
13 23 Mean of all sixty data = 158.9 Standard deviation = 21.5
Valuesshown are average of readingstaken at 150mmand 300mmdepth.
19
obtained, and this fact will be used to demonstrate the benefits which accrue from large samples. F o r 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 X2mis evaluated for all as follows:
X2m -
(O - E) 2 - E
and then summed over all the cells to give a value of X2mfor the whole sample. In this case the value of X2mis 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. F r o m the X2 distribution, X~5%)(5) = 11.07. Since the value of the X2 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 . H E T H E R I N G T O N 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 (#): S2
S2
n
n
x - t~/2 x / - - < # < x + t~,2xf--
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 ) < p < p n-1
+ 1.96 x/ p(l - p ) n-1
which for this case gives p lying in the range 80-82%. For the vehicle designer, it is more important to turn the question round as follows: " I f the requirement is for 50 vehicles to traverse a fixed percentage of terrain, what VCIs0 (and therefore MMP) must the vehicle have?" Thus if the requirement is to traverse 87.5% of the terrain of Table 1, the task is to determine the value of cone index above which 87.5% of the population lies. This can be simply achieved by scanning the normal distribution tables for the appropriate entry value for this chosen probability. However, the value thus obtained is again subject to uncertainty which is governed by the number of data in the sample. The effect of this is shown in Fig. 11 which indicates a decision based on a sample size of 15 would be unnecessarily stringent. It will be shown in the following section how such a demand for low VCI has severe implications for vehicle survivability. MEAN MAXIMUM PRESSURE
Recent work by Wong [5, 12, 13] questions the ability of the Rowland expression (MMP = 1.26 W/mbvCp-d) to accurately predict the mean of the peaks of pressure beneath the road wheels of a tracked vehicle. It is argued from the physical standpoint that true MMP must be highly dependent upon terrain characteristics. On a firm terrain the MMP will be higher than on a soft terrain, since the weight of the vehicle will be transmitted to the ground through a reduced zone of contact. Thus Rowland's expression cannot accurately predict the true value of MMP. In ref. [4] Rowland extracted data from the WES trafficability tests and established
MEAN MAXIMUM PRESSURE IN CROSS-COUNTRY MOBILITY
/I
130' ,,x, z
8
120
273
f X - -
110"
100
~b
~
FIG. 1 l.
A
6~
SAMPLES=E
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.
i
(VCi)~° 300.
200
IO0
0
o
2'o
,,'o
[
6o
8'0
,;o
"-
VCI (psO
FIG. 12.
Relationship between MMP and (VCI)j or (VCI)50 (adapted from ref. 4).
274
J.G. HETHERINGTONand 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 pressuresinkage 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. kN/m 2 300-
250 -
200
150-
100
50
0
i
2 3 4 5 5 7 8
cJ x103kNlm 3
TERRAIN STIFFNESS k
FIG. 13.
Variation of the computed value of mean maximum pressure with terrain stiffnessafter 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. H E T H E R I N G T O N and I. LITTLETON
S U R V I V A B I L I T Y 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 M.B.T. 500mmRHA ARMOUR:SPEC~L TERRA~ :FRG RNERVALLEYS THREAT :
100 m < > 80° P
60-
A
S
S
40-
~
PASS
20-
0 50
~o
~%
~o
do
~oo
TRAFFICABIL~Y(%) FIG. 16.
VEHICLE : MBT TERRAIN
: FRGRIVERVALLEYS
CURRENT RANGE OF MBT M A S S
°t 10
50
i 6O
I
710
!
FIG. 17.
go ' ~'o TRAFFICABILITY(%)
MEAN MAXIMUM PRESSURE IN CROSS-COUNTRY MOBILITY VEHICLE : MBT TERRAIN : FRG RIVER VALLEYS No. OF P A S S E S : 5 0
lOOm < _> >
90-
~
co70-
6'0
s'o
~o
9'0
TRAFFICABILITY (%)
FIG. 18.
MICV THREAT =75ram RHA ARMOUR : A L U M I N U M
TB:~RAIN: FRG RIVER VALLEYS
\
1OO m >
80-
LE PASS
D ~9
60,
,4,050 PASS
20-
50
~o
do
~o
lOO
" m A F F ~ A ~ U ' r Y (%)
FIG. 19.
277
278
J . G . H E T H E R I N G T O N and I. L I T T L E T O N VEHICLE : MICV T E R R A I N : FRG RIVER V A L L E Y S No. OF PAS,SES : SINGLE
100
HREAT 75mm HA
60
"'¢>
40
20
50
'
6'0
~
7~3
~
8~0
~
9~0
i
T R A F F I C A B I L I T Y (%)
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
VEHICLE : MICV TERRAIN : FRG RIVER VALLEYS No. OF PASSES : FIFTY
100
60
40'
20
:5O
60
70
80
gO
TRAFFICABILiTY (%)
FIG. 21.
CONCLUSIONS (i) (ii) (iii) (iv) (v)
A q u a n t i t a t i v e r e l a t i o n s h i p has been established between the m o b i l i t y r e q u i r e m e n t a n d the resultant survivability o f A F V s . Excessive d e m a n d s for m o b i l i t y will result in p o o r p r o t e c t i o n a n d vice versa. O n l y b e t t e r a r m o u r m a t e r i a l s o r b e t t e r t r a c k / w h e e l a n d s u s p e n s i o n systems can s i m u l t a n e o u s l y i m p r o v e p r o t e c t i o n a n d mobility. Soil s t r e n g t h d a t a o b t a i n e d with the cone p e n e t r o m e t e r are subject to large inherent v a r i a t i o n s due to inconsistencies in terrain. Statistical analysis o f cone index d a t a enables c o n f i d e n c e levels to be p l a c e d on t e r r a i n assessment - - larger samples p r o v i d i n g 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 . GARBERand 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. WRIGHTand N. H. ROLLO,Survivor; a computer-aidedanalysis of AFV mobilityand survivability. ASC Div I Advanced Study Report, RMCS, Shrivenham, UK (1986). [81 A. A. RULAand C. J. NLrrTALL,JR, An Analysis of Ground Mobility Models. Tech Report M-71-4, WES, Vicksburg, MS, USA (1971).
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[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. GARBERand 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).