Bicycle Rider’s Air Resistance In Example 3.9, we made the order-of-magnitude approximation that a person can produce 100–200 W of power while exercising. Based on the upper value of 200 W, estimate the speed at which a person can ride a bicycle at that level of exertion and still overcome air resistance (Figure 6.24). Express your answer in the dimensions of mph. In the calculation, neglect rolling resistance between the bicycle’s tires and the road, as well as the friction in the bearings, chain, and sprockets. A mathematical expression for power is P = Fv, where Fis a force’s magnitude and vis the speed of the object to which the force is applied.
To find the speed, we assume that the only resistance that the rider encounters is air drag. The drag force is given by Equation (6.14), and Table 6.4 lists C_{D}=0.9 with a frontal area of A=4.0 ft ^{2} for a cyclist in racing position. To calculate the drag force, we need the numerical value for the density of air, which is given as 2.33 \times 10^{-3} \text { slugs } / ft ^{3} in Table 6.1.
F_{ D }=\frac{1}{2} \rho A v^{2} C_{ D } (Equation 6.14)
| Table 6.4 Numerical Values of the Drag Coefficient and Frontal Area for Different Systems | |||
| System | Frontal Area, A | Drag | |
| ft2 | m2 | Coefficient, CD | |
| Economy sedan (60 mph) | 20.8 | 1.9 | 0.34 |
| Sports car (60 mph) | 22.4 | 2.1 | 0.29 |
| Sport-utility vehicle (60 mph) | 29.1 | 2.7 | 0.45 |
| Bicycle and rider (racing) | 4.0 | 0.37 | 0.9 |
| Bicycle and rider (upright) | 5.7 | 0.53 | 1.1 |
| Person (standing) | 6.7 | 0.62 | 1.2 |
| Table 6.1 Density and Viscosity Values for Sevweral Gases and Liquid at Room Temperature and Pressure | ||||
| Air | 1.20 | 2.33 × 10-3 | 1.8 × 10-5 | 3.8 × 10-7 |
| Helium | 0.182 | 3.53 × 10-4 | 1.9 × 10-5 | 4.1 × 10-7 |
| Freshwter | 1000 | 1.94 | 1.0 × 10-3 | 2.1 × 10-5 |
| Seawater | 1026 | 1.99 | 1.2 × 10-3 | 2.5 × 10-5 |
| Gasoline | 680 | 1.32 | 2.9 × 10-4 | 6.1 × 10-6 |
| SAE 30 oil | 917 | 1.78 | 0.26 | 5.4 × 10-3 |
