Energy Use in Cars 6: Gasoline Cars vs. Bicycles

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When does a car have the same fuel efficiency as a bicycle?

Big Ideas: 
  • A comparison of the efficiency, air resistance and rolling resistance of bicycles and cars.

When does a car have the same fuel efficiency as a bicycle?

In comparing bicycles and cars, it is tempting to assume that the energy consumption of a cyclist is nearly zero. However, that's not the case. A bicycle is powered by a person, and much like an internal combustion engine that person needs to convert chemical energy into mechanical energy in order to move. Let's consider the case of movement at a steady speed and see how a bicycle stacks up against a standard car. Bicycles and cars will be compared in terms of efficiency, air resistance and rolling resistance.

Efficiency

As we've discussed previously (See Energy Use in Cars 1) much of the chemical energy that is consumed in a car gets converted to heat. On average, only 25% of a car's chemical energy gets turned into useful mechanical energy, the rest being used to heat the surrounding air and exhaust gases. Surprisingly, it turns out that the efficiency of a cyclist is about the same1! A detailed analysis of energy use in cycling shows that people are about 25% efficient in converting food energy into mechanical energy, the rest being used to maintain the function of the body and generate heat. So there is no clear advantage to either form of transportation on the efficiency front.

Air Resistance

Our previous look into air resistance (See Energy Use in Cars 2) shows that the work done against air resistance when travelling a distance d is given by:

$ \textnormal{Work done against air resistance} = \dfrac{1}{2} \rho A C_D d v^2  $ 

So for a given distance, the only values that differ between bikes and cars are the Area (A), Coefficient of Drag (CD), and speed (v). Let's look at the term A x CD. This product is also called the Drag Area, and it's the area of the tube of air that gets dragged along with a moving object.

For a typical family sedan,

$ A = 2 \textnormal{ m} \times 1.5 \textnormal{ m} = 3 \textnormal{ m}^2; \textnormal{ } C_D = 0.33 $

so, the drag area is

$ A \times C_D = (3 \textnormal{ m}^2)(0.33) = 1 \textnormal{ m}^2  $

For a cyclist2,

$ A \approx 1 \textnormal{ m}^2; \textnormal{ }C_D = 0.9 $

 so the drag area is

$ A \times C_D = (1 \textnormal{ m}^2)(0.9) = 0.9 \textnormal{ m}^2  $

This means that if they travel at the same speed, cars and bicycles have nearly the same air resistance. Because cars are so much more streamlined (smaller CD), they have the same air resistance as bicycles despite being so much larger.

However, cars and bicycles rarely travel the same speed. The typical cruising speed for a bicycle is around 20 km/h, and that for a car is around 50 km/h. Going 2.5 times faster means that typically the air resistance for a car will be (2.5)2 = 6.25 times higher.

Rolling Resistance

So, is the higher energy cost of a car solely due to going faster than bicycles? Let's look at the last factor in constant-speed energy consumption: rolling resistance. In a previous article (See Energy Use in Cars 3) we saw that the work done against rolling resistance was given by:

<br />
\begin{eqnarray}<br />
\textnormal{Work done against rolling resistance} &=& \textnormal{Coefficient of Rolling Resistance} \times \textnormal{ mass} \nonumber \\<br />
& &  \times \textnormal{ acceleration of gravity}(g) \times \textnormal{ distance} \nonumber<br />
   \end{eqnarray}<br />

This is where the differences between cars and bicycles really stand out. A car with a mass of 1200 kg will need 187 kJ for each km travelled, whereas a bicycle with a mass of 10 kg will only neeed 4 kJ for each km travelled. This means that even if they travel the same speed, a car will have a much higher energy consumption than a bicycle.

Adding it all up:

The work done against both air resistance and rolling resistance for each km travelled is:

$ \textnormal{Work} = \textnormal{(Coefficient of Rolling Resistance)(mass)(gravity)} + \dfrac{1}{2} \rho A C_D v^2 $

The coefficient of rolling resistance for a bicycle is 0.0053, so the total work done at 20 km/h is:

<br />
\begin{eqnarray}<br />
\textnormal{Work} & =& (0.005)(80 \textnormal{ kg})(9.8 \textnormal{ m/s}^2) + \dfrac{1}{2} (1.3 \textnormal{ kg/m}^3)(1 \textnormal{ m}^2)(0.9)(5.55 \textnormal{m/s})^2 \nonumber \\<br />
	& =& 4 \textnormal{ N} + 18 \textnormal{ N} \nonumber \\<br />
	& =& 22 \textnormal{ N} \nonumber</span></p>
<p>   \end{eqnarray}</p>
<p>

For a car, which has a coefficient of rolling resistance of 0.0154, at 20 km/h this works out to:

<br />
\begin{eqnarray}<br />
\dfrac{\textnormal{Energy}}{\textnormal{distance}} & =& (0.015)(1270 \textnormal{ kg})(9.8 \textnormal{ m/s}^2) + \dfrac{1}{2} (1.3 \textnormal{ kg/m}^3)(3 \textnormal{ m}^2)(0.33)(5.55 \textnormal{m/s})^2 \nonumber \\<br />
& =& 187 \textnormal{ N} + 20 \textnormal{ N} \nonumber \\<br />
& =& 207 \textnormal{ N} \nonumber<br />
   \end{eqnarray}<br />

Summary

So even if the car goes the same speed as a bicycle (or slower), the bicycle will always have better energy economy because of rolling resistance.

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