Energy Use in Cars 3: Rolling Resistance

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Why does Natural Resources Canada recommend keeping your tires inflated to conserve gasoline?

Big Ideas: 
  • Rolling resistance affects the motion of a car.
  • Underinflated tires affect the fuel consumption of a car.

Natural Resources Canada recommends keeping your tires inflated to their maximum pressure to conserve gasoline. Why does this matter? A rough calculation of rolling resistance in cars explores the impact of having underinflated tires.

First, a quick review: When you are driving a car, the energy from the fuel goes into four main places:

  1. Accelerating the car up to its cruising speed. A moving car has kinetic energy, and it needs to get this energy from the engine. Once we are at a constant speed, this doesn't take any more energy, but we still need our foot on the gas because of the next two issues.
  2. Air resistance. Driving a car makes the air around it swirl around, and this takes energy. Driving faster makes the air swirl much more.
  3. Rolling resistance. This accounts for all of the small bits of friction within the car, as well as resistance due to the tires on the road.
  4. Heat. Burning fuel doesn't make the car move directly. It creates a lot of heat, and then the engine has to convert that heat into motion. However, there is still a lot of heat in the exhaust gases that gets pumped out the back of the car, so not ALL of it gets converted into motion.

So if we are traveling at a constant speed, we don't need to worry about #1 on the list. We have already accelerated up to speed, so that part is taken care of. However, we need to figure out how to understand the other ways that energy is used.

Item number 4 is taken care of by the notion of the efficiency of the car's engine. For a typical gasoline engine, only around 25% of the heat energy from the fuel gets converted into mechanical energy which gets used for the first three items on this list1. The energy content of gasoline is about 32 x 106 J/litre, but because of the engine efficiency only 25% of that gets converted to mechanical energy2.

So what about Rolling Resistance?

In cars rolling resistance comes from the fact that the tires are soft, and get deformed as we drive forward, costing the car some energy. The effect of this depends on the inflation of the tire, what kind of tire you have, and how fast you are going, BUT a common approximation which is reasonably accurate is just that the rolling resistance is a constant frictional force that depends on the weight of the car (similar to any other kind of friction).

Force due to Rolling Resistance (FRR)= (Coefficient of Rolling Resistance (μRR)) (Mass of vehicle) (Acceleration of gravity (g))

The Coefficient of Rolling Resistance is usually written as μRR, and it has different values for different types of vehicles. Some example values of rolling resistance are given in the table below3.

<br />
\begin{tabular}{ c c }<br />
\hline<br />
  Tire Type & Coefficient of Rolling Friction \\ \hline<br />
  Low rolling resistance car tire & 0.006 - 0.01  \\<br />
  Ordinary car tire & 0.015  \\<br />
Truck tire & 0.006 - 0.01 \\<br />
Train wheel & 0.001 \\<br />
\hline<br />
\end{tabular}<br />

So what does this tell us? In order to figure out how this force impacts our fuel economy we need to figure out how much energy is required to overcome it. For this we use the Work-Energy principle, which tells us how much energy a force will add to a system.

$ \textnormal{Work = (Force)(Distance)} $

Because the rolling friction opposes the motion of the car, it actually subtracts energy from the car. This energy needs to be made up by burning more fuel.

A typical sedan has a mass of around 1200 kg. For this car, plus a single driver (70 kg) the force of rolling resistance will be:

<br />
\begin{eqnarray}<br />
   F_{RR} & =& \mu_{RR} m g \nonumber \\<br />
   & =& (0.015)(1270 \textnormal{ kg})(9.8 \textnormal{ m/s}^2) \nonumber \\<br />
   & =& 187 \textnormal{ Newtons} \nonumber<br />
   \end{eqnarray}<br />

Over the course of driving one kilometre, this will require extra energy given by:

<br />
\begin{eqnarray}<br />
   W & =& (F_{RR})(\textnormal{Distance}) \nonumber \\<br />
   & =& (187 \textnormal {N}) (1000 \textnormal{ m}) \nonumber \\<br />
   & =& 187,000 \textnormal{ N•m} \nonumber \\<br />
   & =& 187 \textnormal{ kJ for each kilometre driven} \nonumber<br />
   \end{eqnarray}<br />

We can figure out how much fuel is required to drive one kilometre by using the efficiency formula:

<br />
\begin{eqnarray}<br />
\textnormal{Efficiency} & =& \dfrac{\textnormal{Work Output}}{\textnormal{Work Input}} \nonumber \\<br />
& =& \dfrac{\textnormal{Work Output}}{\textnormal{Fuel Energy Input}} \nonumber \\<br />
\textnormal{Fuel Energy Input} &=& \dfrac{\textnormal{Work Output}}{\textnormal{Efficiency}} \nonumber \\<br />
& =& \dfrac{187 \textnormal{ kJ}} {25 \%} \nonumber \\<br />
& =& 748 \textnormal{ kJ} \nonumber<br />
   \end{eqnarray}<br />

And to provide this amount of energy we need to use

<br />
\begin{eqnarray}<br />
\textnormal{Energy per litre} & =& \dfrac{\textnormal{\# of Joules}}{\textnormal{\# of litres}} \nonumber \\<br />
\textnormal{\# of litres} & =& \dfrac{\textnormal{\# of Joules}}{\textnormal{Energy per litre}} \nonumber \\<br />
& =& \dfrac{748 \textnormal{ kJ}}{32 \textnormal{ MJ/L}} \nonumber \\<br />
& =& 0.023 \textnormal{ L} \nonumber<br />
\end{eqnarray}<br />

So, 0.023 L of fuel is required to drive 1 km.

Remember, this result is just to overcome the rolling friction. If we add this to the 0.064 L/km highway mileage we calculated in Constant Speed Cruising (taking air drag into acount) this comes out to a total of 0.087 L/km. This is a little bit higher than the reported average of 0.076 L/km4, which seems reasonable as the highway mileage was calculated at a speed of 100 km/h which is perhaps a bit fast.

So, now what would be the impact of having low air pressure in our tires? Let's imagine that having your air pressure reduced by 5% would result in a 5% increase in the coefficient of rolling resistance. A typical car's tires are inflated to around 40 psi, so this would correspond to being 2 psi lower than average. A 5% increase in the Coefficient of Rolling Resistance would bring it up to 0.01575, and the associated fuel consumption would increase to 0.024 L/km. This is an extra 0.01 L/km, or approximately an extra 1% of fuel mileage. This corresponds closely with the guidelines published by Natural Resources Canada1.

This extra drag starts to add up when your tires are really low on air. If they are 10 psi low, that would correspond to an extra 5% fuel mileage!

Take Home Experiment: 
Energy Use in Cars Take-Home Experiment


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