When does a car have the same fuel efficiency as a bicycle?
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 same[note]P.E. di Prampero, G. Cortili, P. Mognoni and F. Saibene, J Appl Physiol 47: 201-206, 1979.[/note]! 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 traveling a distance $d$ is given by:
$\text{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 ($C_D$), and speed ($v$). Let’s look at the term $A \times C_D$. 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,
$A = 2 \text{ m} \times 1.5 \text{ m} = 3 \text{ m}^2;\ C_D = 0.33$
so, the drag area is
$A \times C_D = (3 \text{ m}^2)\times(0.33) = 1 \text{ m}^2$
For a cyclist[note]MacKay DJC. Drag Coefficients: Sustainable Energy Without the Hot Air (online). UIT Cambridge. p. 257 http://www.inference.phy.cam.ac.uk/withouthotair/cA/page_257.shtml [4 November 2009].[/note],
$A \approx 1 \text{ m}^2; \ C_D = 0.9$
ย so the drag area is
$A \times C_D = (1 \text{ m}^2)\times(0.9) = 0.9 \text{ 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 $C_D$), 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:
\begin{eqnarray}
\text{Work done against rolling resistance} &=& \text{Coefficient of Rolling Resistance } \times \text{ mass} \nonumber \\
& & \times \text{ acceleration of gravity}(g) \times \text{ distance} \nonumber
\end{eqnarray}
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 traveled, whereas a bicycle with a mass of 10 kg will only need 4 kJ for each km traveled. 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 traveled is:
$\text{Work} = \text{(Coefficient of Rolling Resistance)(mass)(gravity)} + \dfrac{1}{2} \rho A C_D v^2$
The coefficient of rolling resistance for a bicycle is 0.005[note]Wikimedia Foundation Inc. Rolling Resistance (Online). http://en.wikipedia.org/wiki/Rolling_resistance [12 May 2010].[/note], so the total work done at 20 km/h is:
\begin{eqnarray}
\text{Work} & =& (0.005)(80 \text{ kg})(9.8 \text{ m/s}^2) + \dfrac{1}{2} (1.3 \text{ kg/m}^3)(1 \text{ m}^2)(0.9)(5.55 \text{m/s})^2 \nonumber \\
& =& 4 \text{ N} + 18 \text{ N} \nonumber \\
& =& 22 \text{ N} \nonumber\end{eqnarray}
For a car, which has a coefficient of rolling resistance of 0.015[note]Rolling Friction Coefficients: http://auto.howstuffworks.com/tire4.htm [4 November 2009].[/note], at 20 km/h this works out to:
\begin{eqnarray}
\dfrac{\text{Energy}}{\text{distance}} & =& (0.015)(1270 \text{ kg})(9.8 \text{ m/s}^2) + \dfrac{1}{2} (1.3 \text{ kg/m}^3)(3 \text{ m}^2)(0.33)(5.55 \text{m/s})^2 \nonumber \\
& =& 187 \text{ N} + 20 \text{ N} \nonumber \\
& =& 207 \text{ N} \nonumber
\end{eqnarray}
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.
