Aerodynamic Drag
Air resistance a car must overcome, rising with speed squared.
Formula
Variables
Example
ρ=1.2, v=30, C_d=0.3, A=2.2: F_d ≈ 356 N
How it works
Aerodynamic drag is the force required to push air out of the way as a vehicle moves forward. The formula shows that this force grows with the square of speed because doubling speed makes the air’s kinetic impact much larger, and it also depends on how dense the air is, how streamlined the vehicle is, and how much of it faces the airflow. The factor C_dA is often called the drag area, combining shape and size into one measure of how strongly the vehicle resists the air.
When to use it
Use this formula when estimating the air resistance on a car, truck, motorcycle, bike, or any vehicle moving through air at steady speed. It is especially useful for comparing designs, predicting power demand at highway speeds, or analyzing fuel economy and top speed.
Worked example, step by step
Given: ρ = 1.18 kg/m³, v = 25 m/s, C_d = 0.28, A = 2.4 m² Step 1: Square the speed: v² = 25² = 625 Step 2: Substitute into F_d = 1/2 ρv²C_dA F_d = 0.5 × 1.18 × 625 × 0.28 × 2.4 Step 3: Multiply step by step 0.5 × 1.18 = 0.59 0.59 × 625 = 368.75 368.75 × 0.28 = 103.25 103.25 × 2.4 = 247.8 Final answer: F_d ≈ 248 N
Common mistakes to avoid
- Using speed in km/h instead of m/s, which gives the wrong force
- Forgetting that the speed term is squared, not linear
- Mixing up drag force with drag coefficient or frontal area
Did You Know?
Drag dominates fuel use above ~80 km/h, which is why economy plunges on the motorway.
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