Wind and Air: Relative Motion and Drag

Compare air forces while stating which quantities stay fixed.

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In a common drag model, D = 0.5 x rho x Cd x A x v^2. Here v is speed relative to the air. With density rho, reference area A and coefficient Cd fixed, drag scales with v squared. Shape or flow-regime changes can change Cd.

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If relative air speed rises from 5 m/s to 10 m/s with the other factors fixed, the speed ratio is 2 and the drag ratio is 2^2 = 4. This is not a prediction of electrical power.

With density, reference area and drag coefficient held fixed, relative speeds of 5 and 10 meters per second give drag in the ratio 1 to 4. This model is not a universal fixed-coefficient law.

Would you believe it?

At fixed air density and swept area, doubling wind speed gives eight times the available kinetic power in the air. That does not mean a real turbine delivers eight times the electricity.

U.S. Department of Energy: wind power basics

Question 1 In the example, drag changes by what factor? 4 2 8

Question 2 Which speed belongs in the drag model? Only speed relative to the road Only the largest gust ever measured Speed relative to the air

Question 3 An object moves east at 3 m/s while air moves west at 2 m/s. Relative speed is what? 0 m/s 5 m/s 1 m/s

Question 4 Why might changing shape invalidate a fixed-Cd comparison? Shape can change the drag coefficient Shape makes air disappear Every shape has identical drag

Question 5 Does four times drag prove four times turbine electrical output? Yes, force and power are identical Yes, losses never matter No, these are different quantities

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