Question 9 of 13: Maximum Sustainable Cycling Speed from Drag Data

Question 9: Maximum Sustainable Cycling Speed from Drag Data (5 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given (from attachment Table 6.1, "Racing (Fully Crouched)" row — the standard racing bicycle with no added aerodynamic components):

Find. The maximum speed the cyclist can sustain for the full 2-hour race, neglecting rolling resistance.

Approach. A cyclist riding at constant speed converts all of their sustained power into aerodynamic-drag power. Compute the sustainable power from the given empirical formula at t = 120 min, then solve the cubic drag-power relation for V.

1. Sustainable power at t = 120 min: $$P = 0.373 - 0.097\log_{10}(120) = 0.373 - 0.097(2.079) = \boxed{0.1713\ \text{kW} = 171.3\ \text{W}}$$
2. Power balance (drag power = sustained power; rolling resistance neglected per the question): $$P = F_D V = \left(\tfrac{1}{2}\rho C_D A V^2\right)V = \tfrac{1}{2}\rho C_D A\,V^3$$
3. Solve for V: $$V=\left(\frac{2P}{\rho C_D A}\right)^{1/3}=\left(\frac{2(171.3)}{1.21(0.88)(0.36)}\right)^{1/3}=\boxed{9.63\ \text{m/s}}$$
4. Convert to km/h: $$V = 9.63\times3.6=\boxed{34.7\ \text{km/h}}$$