# What fuel economy?

Physically, when a car travels in a straight line on a level road, three forces oppose its free movement: the friction of the tires on the road, mechanical friction, and air resistance. From the point of view of speed variation, tire rolling resistance and mechanical friction do not vary. The rolling resistance force of tires, for example, depends on the coefficient of friction (we consider car tires to have a coefficient of resistance of 0.01), the acceleration due to gravity (approximately 9.81 ms -2) and the mass of the vehicle, but not its speed. Above all, these rolling resistance forces will be overcome very quickly by air resistance.

So let’s focus on this air resistance. It will depend on the shape of the vehicle, the frontal surface, the coefficient of drag (shape drag, friction drag, turbulence drag and internal drag) just like the Cx, but also, and this is the problem of the speed at square. To move a vehicle from a certain speed, it is mainly this air resistance that must be overcome. It is this that determines the expenditure of energy (hence of fuel or electric kWh) necessary.

So, with this damn square of speed, going from 50 to 60 km/h adds much less energy to expend than going from 100 to 110 km/h. Back to today’s topic. How much does going from 130 km/h to 110 km/h save fuel? We will reason in percentage of consumption. 110 km/h is 84.6% of 130 km/h. The energy difference of the air resistance (still due to the square of the speed) will therefore be 28.4%.

## 8 minutes more compared to 25% less consumption

In theory, therefore, it takes 28% less energy to drive at 110 km/h than to drive at 130 km/h with the same car, under the same conditions. Obviously this is an approximation and other phenomena come into play such as the engine speed that will not be the same, and aerodynamic phenomena that may vary (turbulence for example). The deformation of the tire carcasses will not be the same and therefore the rolling resistance will not be the same. But, in general, we will have this order of magnitude. In some electric vehicles, the calculation is also distorted by staggering the reducer that can put the electric motor “at the end of its stroke”, further increasing electrical consumption.

Above all, friction other than air has been neglected. At “high” speed, 80 to 90% of the energy required is due to air resistance. A 28.4% drop in this resistance represents approximately a 25% drop in the energy required to drive the vehicle forward (90% of 28.4%).

And by lowering its speed by 15%, the trip lasts… 15% longer (there, instead, it is proportional to the speed). 25% on one side, 15% on the other. In a car that consumes 6 liters of diesel per 100 km at 130 km/h, this gives 1.5 l/100 km less at 110 km/h. With current fuel prices, it is not far from €3 for 100 km, for 8 minutes 25 more to cover 100 km. Now it’s up to you to know if those 8 minutes are worth about €3 (or more if you want in a gasoline vehicle that consumes more than 6 l/100 km on the highway).

## This only applies to the road.

Obviously, for these calculations we made totally physical approximations because we were at more than 110 km/h. The calculation for a speed that would go from 50 km/h to 42.5 km/h (ie -15%) would not give the same variation in consumption at all. The mass component of friction is, at these low speeds, much more important than air resistance.

The same reasoning regarding weight can hold. But, there, we do not vary in relation to its square. Rolling resistance comes mainly from weight, but also from the energy of gravity when you’re on a slope. A vehicle of the same shape, weighing 50% more, will have a rolling resistance force that is 50% greater. However, it will not consume 50% more, air resistance prevailing “quickly” over this tire rolling resistance.

Therefore, the main problem with SUVs is not their weight (contrary to what the weight penalty would have us believe), but rather the larger frontal area and a drag coefficient that is often higher as well. The SCx (the frontal area multiplied by the Drag Coefficient) could be the tool to measure the penalty instead of the weight.