At land speed record velocities, a vehicle must push through air so fast that aerodynamic drag becomes the main force opposing motion. Drag is not just a small resistance force at these speeds because it grows with the square of speed. Doubling speed makes the drag force about four times larger if the shape and air density stay the same.
This is why record cars are shaped more like aircraft or missiles than ordinary automobiles.
Key Facts
- Aerodynamic drag force: Fd = 1/2 rho Cd A v^2
- Power needed to overcome drag: P = Fd v = 1/2 rho Cd A v^3
- If speed doubles, drag force increases by a factor of 4 when rho, Cd, and A stay constant.
- If speed doubles, power needed for drag increases by a factor of 8 when rho, Cd, and A stay constant.
- Dynamic pressure: q = 1/2 rho v^2, so high speed creates very large pressure loads on the body.
- Near and above the speed of sound, shock waves and compressibility can greatly increase drag and stability challenges.
Vocabulary
- Aerodynamic drag
- Aerodynamic drag is the force of air resistance that acts opposite the motion of a vehicle moving through air.
- Drag coefficient
- The drag coefficient, Cd, is a dimensionless number that describes how strongly a shape resists airflow.
- Frontal area
- Frontal area, A, is the projected area of the vehicle seen from directly ahead.
- Dynamic pressure
- Dynamic pressure is the pressure associated with moving air and is calculated as q = 1/2 rho v^2.
- Shock wave
- A shock wave is a thin region where air pressure, density, and speed change suddenly, often forming near vehicles moving close to or faster than sound.
Common Mistakes to Avoid
- Treating drag as proportional to speed is wrong because high speed aerodynamic drag is proportional to v^2, not v.
- Forgetting that power grows faster than force is wrong because drag power equals Fd v, so it increases with v^3.
- Using a low drag coefficient but ignoring frontal area is wrong because the product Cd A determines much of the drag force.
- Ignoring compressibility near the speed of sound is wrong because shock waves and pressure changes can increase drag and affect stability.
Practice Questions
- 1 A land speed vehicle has Cd = 0.20, frontal area A = 1.8 m^2, air density rho = 1.2 kg/m^3, and speed v = 300 m/s. Calculate the aerodynamic drag force using Fd = 1/2 rho Cd A v^2.
- 2 Using the drag force from the previous question, calculate the power needed just to overcome aerodynamic drag at 300 m/s using P = Fd v.
- 3 A designer can reduce either Cd or A by 10 percent, but not both. Explain why either change gives the same percentage reduction in drag force when speed and air density are unchanged.