## 83 Consideration of Rolling Resistance

As discussed in Chapter 7, the rolling drag on a vehicle Frr is given by:

where irr is the coefficient of rolling resistance. The rolling drag is independent of speed. Power needed to overcome rolling is given by:

The value of ¡xrr varies from 0.015 for a radial ply tyre down to 0.005 for tyres specially developed for electric vehicles. A reduction of rolling resistance to one-third is a substantial benefit, particularly for low speed vehicles such as buggies for the disabled. For low speed vehicles of this type the air resistance is negligible and a reduction of drag to one-third will either triple the vehicle range or cut the battery mass and cost by one-third, a substantial saving both in terms of cost and weight.

Power requirements/speed for an electric vehicle travelling on the flat, with typical drag (Cd = 0.3) and fairly standard tyres (¡xrr = 0.015), with a mass of 1000 kg and a frontal

Frr = Irrmg

Figure 8.4 The power requirements to overcome rolling resistance and aerodynamic drag at different speeds. This is for a fairly ordinary small car, with Cd = 0.3, frontal area 1.5 m2, mass = 1000 kg, and /zrr = 0.015

area of 1.5 m2 is shown in Figure 8.4. The graph, derived from the above equations, shows how much power is required to overcome rolling resistance and aerodynamic drag.

It can be seen clearly in Figure 8.4 that at low speeds, e.g. under 50kph, aerodynamics have very little influence, whereas at high speeds they are the major influence on power requirements. It may be concluded that streamlining is not very important at relatively low speeds, more important at medium speeds and very important at high speeds. So, for example, on a golf cart the aerodynamics are unimportant, whereas for a saloon car intended for motorway driving the aerodynamics are extremely important. (The rolling resistance of a golf buggy wheels on turf will of course be considerably higher than can be expected on hard road surfaces.)

A graph of the total power requirement for two vans is shown in Figure 8.5, where a power/velocity curve for each vehicle is plotted. Both vans have a mass of 1000 kg, frontal area of 2 m2 and a Cd of 0.5. However one has ordinary tyres with a firr of 0.015, whereas the other has low rolling resistance tyres for which firr of 0.005.

It can be concluded that for all electric vehicles a low rolling resistance is desirable and that the choice of tyres is therefore extremely important. A low coefficient of aerodynamic

Figure 8.5 Power requirements for aerodynamic drag and rolling resistance at a range of speeds. This is for two vans, both of mass 1000kg, frontal area 2m2, and Cd = 0.5. However, one has low resistance tyres with /zrr = 0.005, whereas the other has ordinary tyres for which /zrr = 0.015

drag is very important for high speed vehicles, but is less important for town/city delivery vehicles and commuter vehicles. On very low speed vehicles such as electric bicycles, golf buggies and buggies for the disabled, aerodynamic drag has very little influence, whereas rolling resistance certainly does.

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