What is the effect of doubling the speed on drag?

What is the effect of doubling the speed on drag?

• A. It produces no change in drag
• B. It produces four times the drag
• C. It produces twice the drag
• D. It decreases the drag

Answer: (B)

Doubling the speed of an aircraft has a significant impact on drag due to the relationship between velocity and drag force, as described by the drag equation. The drag force experienced by an object moving through a fluid is proportional to the square of the velocity. This means that if the speed is doubled, the drag force will increase by the square of that change in speed. To elaborate, the drag force can be expressed mathematically as: \[ D = \frac{1}{2} \rho V^2 C_d A \] where: - \( D \) is the drag force, - \( \rho \) is the air density, - \( V \) is the velocity, - \( C_d \) is the drag coefficient, and - \( A \) is the reference area. When the velocity \( V \) is doubled, the new drag force becomes: \[ D' = \frac{1}{2} \rho (2V)^2 C_d A = \frac{1}{2} \rho (4V^2) C_d A = 4 \times \left( \frac{1}{2} \rho V^2 C_d A \right) = 4D \] Thus

Doubling the speed of an aircraft has a significant impact on drag due to the relationship between velocity and drag force, as described by the drag equation. The drag force experienced by an object moving through a fluid is proportional to the square of the velocity. This means that if the speed is doubled, the drag force will increase by the square of that change in speed.

To elaborate, the drag force can be expressed mathematically as:

[ D = \frac{1}{2} \rho V^2 C_d A ]

where:

• ( D ) is the drag force,

• ( \rho ) is the air density,

• ( V ) is the velocity,

• ( C_d ) is the drag coefficient, and

• ( A ) is the reference area.

When the velocity ( V ) is doubled, the new drag force becomes:

[ D' = \frac{1}{2} \rho (2V)^2 C_d A = \frac{1}{2} \rho (4V^2) C_d A = 4 \times \left( \frac{1}{2} \rho V^2 C_d A \right) = 4D ]

Thus