## 85 Consideration of Vehicle Mass

The mass of an electrical vehicle has a critical effect on the performance, range and cost of an electric vehicle. The first effect of the mass on rolling resistance and the power and energy to overcome this has already been discussed in Section 8.3.

There are two other effects of mass. The first concerns a vehicle climbing a hill and the second is the kinetic energy lost when the vehicle is accelerating and decelerating in an urban cycle.

In Chapter 7 equation (7.3) it was seen that the Force Fhc in Newtons along the slope for a car of mass m (kg) climbing a hill of angle f is given by:

It follows that the power Phc in Watts for a vehicle climbing a slope at a velocity v ms-1 is given by:

Figure 8.10 shows the total power needed to travel at a constant 80kph up slopes of varying angles up to 10° for vehicles of two different weights, but otherwise similar. They are based loosely on the GM EV1 electric car studied in Chapter 7. They both have a drag coefficient of 0.19, and tyres with coefficient of rolling resistance of 0.005, and the frontal area is 1.8 m2. We can see that the 1500 kg car, which is approximately the weight of the real GM EV1, has to provide approximately 12 times as much power at 10° than is

Figure 8.10 The total power requirements for two different vehicles moving at 80 kph up a hill of slope angle zero to 10°. In both cases the vehicle has good tyres with /zrr = 0.005, low drag as Cd = 0.19, and a frontal area of 1.8 m2. One car weighs 800kg, the other 1500kg

needed on the flat. With the 800 kg vehicle the power needed increases greatly, but only by about 8 times.

Looking at Figure 8.10 we see why the GM EV1 electric car needs a motor of power about 100 kW. In the SFUDS simulation we noted that the maximum power needed was only 12 kW, as in Figure 7.16. It is taking heavy vehicles up hills that requires high power.

The results shown in the graph send a clear message. Considerable power is required for hill climbing, and such terrain will restrict the range of electric vehicles relying solely on rechargeable batteries. When designing electric vehicles the effect of hills must be taken into account, though there are no agreed 'standard hills' for doing this. It is not too difficult, after a little experience, to add gradients to the simulation driving cycles considered in the last chapter. This is usually done with a specific journey in mind.

The effect of the vehicle mass when accelerating and stopping in town and city conditions is another area where the mass of the electric vehicle will have considerable influence on vehicle performance. There are a variety of simulated urban driving cycles that have already been discussed in Chapter 7. Basically when a vehicle of mass m (kg) is travelling at velocity v (ms-1) its kinetic energy is given by:

If the vehicle brakes this energy is converted into heat. When regenerative braking is used a certain amount of the energy is recovered. This was extensively explored in Chapter 7, Section 7.4.2.3 and Table 7.3. The maximum practical limit on the recovery of kinetic energy is about 40%. In light vehicles the losses associated with continually creating and then losing kinetic energy are much less, and the benefits of regenerative braking are similarly reduced.

Apart from the importance of minimising vehicle weight, it is also important to try to minimise the moment of inertia of rotating components, as these store rotational kinetic energy. The energy stored Er (Joules) of a component with a moment of inertia I (kg.m2) rotating at rn (rad s-1) is given by:

The moment of inertia I is normally expressed as:

i.e. the sum of all the finite masses of a component which lie a distance r from the centre of rotation. In practice most rotating components such as the wheels are purchased as proprietary items, but the energy lost in rotary energy needs to be considered particularly for urban driving conditions. This was addressed in Section 7.2 and equation (7.8). In practice it is often difficult to obtain precise information about the moment of inertia of the rotating parts, and a reasonable approximation is to simply increase the mass in equation (8.9) by 5%, and not use equation (8.10). Notice that this does not need to be done for the mass in the hill climbing equation (8.8).

In the next section we consider the chassis and body design, and how it might be made, and what materials used, in order to achieve this aim of reducing the weight.

## Hybrid Cars The Whole Truth Revealed

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