Lightweight Electric/Hybrid Vehicle Design

Design for optimum body-structural and running-gear performance efficiency 227
tabular approach to gravimetric analysis is combined with moment equations to determine axle
loadings; the numbers locating the main assemblies on the vehicle correspond with the first column
of the table and go on to include front wing (5), front suspension (6), power unit (7) and on to
(51)/(52) as shown. The alignment charts are nomograms which represent the weight of a given
material as a function of the surface area or length and help in the estimation of body structural
weight, a surprisingly large percentage of the total on conventional cars. Successful prediction of
body weight distribution is key to the early fixing of centre-of-gravity position upon which
performance prediction depends.
The importance of vehicle weight is made clear by Taborek 9 who points out that a key relationship
in performance considerations is that tractive force P is equal to load on the driving axle W times
tyre-to-ground adhesion coefficient μ. But, while W for a static vehicle can easily be found by a
moment calculation, the dynamic axle reactions of a moving vehicle are more difficult to work
out. The dynamic weight transfer:
dW = (H/L)(T d /r −fW) and P = (T e RE)/r
where T d is torque at drive axle, T e torque at engine, R total reduction ratio, E transmission efficiency
and r rolling radius. H is height of vehicle centre of gravity (CG) above ground, L the wheelbase
and f the symbol for rolling resistance coefficient.
With front and rear-wheel drive, dynamic front axle load = W(L r + fH)/(L + μH) where L r is the
distance from CG to rear axle and μ is adhesion coefficient; this leads to the maximum transferable
tractive force as
P f,max = μW[(L r + fH)/(L + μH)]
the square-bracketed term being the weight distribution factor dW/W = w so that W df = W wf P max =
μW wf and P r.max = μWdr
With four-wheel-drive, P 4.max = μW and w 4 = 1; otherwise the chart at (c) can be used to determine
the relative distributions. The weight distributions derived above are dimensionless, being derived
from ratios, and the chart also contains only dimensionless factors, with the weight of the vehicle
being eliminated by dividing the tractive force equation by W, giving P max /W = μw.
The dotted line shows an example for a vehicle with h/L = 0.35 and L f /L = 0.45 defining its CG
position, for which it is required to find maximum transferable tractive force and the maximum
engine torque for a low gear reduction factor of RE/r = 7.3 – given also μ = 0.6 for the adhesion
coefficient. Starting in the lower left quadrant, the intersection of the m = 0.6 line cuts curves for
front and rear wheel drive at h/L = 0.35. Horizontal projections from those points similarly lead to
the P max /W scale. Values thus obtained give the first solution while projecting into the top left
quadrant gives the second. For a vehicle weight of 4000 kg, P max = 1620 kg and T e.max = 224 kNm
(front drive) or 840 kg and 112 kNm (rear drive).
In predicting performance, Fig. 8.16, this data can be used in a chart, such as at (a), to obtain
available vehicle speeds on different gradients. The chart plots maximum values of tractive force
at the wheel, as functions of speed, in different gears. Also on the chart, gradient slopes are plotted
against vehicle weight. The 0% line is drawn at a slope designating a rolling resistance of 35.4 lb/
ton (80 kg/tonne). Propelling force P lines are obtained by graphical subtraction of wind resistance
from maximum tractive force, in this method due to Goldschmidt and Hadar of the Israel Institute
of Metals. Dotted lines illustrate worked examples for vehicles weighing 1910 and 1875 lb
respectively. The first is shown to be able to climb a slope of 10% at 36 mph reducing to 9% at the
same speed if that speed is maintained. The second climbs an 8% slope at 43.5 and 38.5 mph in