What happens to the lift produced when the velocity in the lift equation is doubled, with all other factors remaining constant?

The lift produced by an airfoil is determined by the lift equation, which can be expressed as:

[ L = \frac{1}{2} \rho V^2 S C_L ]

Where:

• ( L ) is the lift,

• ( \rho ) is the air density,

• ( V ) is the velocity of the air over the wings,

• ( S ) is the wing area,

• ( C_L ) is the lift coefficient.

From this equation, it's evident that lift is proportional to the square of the velocity. Therefore, if the velocity ( V ) is doubled, the new lift can be expressed as:

[ L_{new} = \frac{1}{2} \rho (2V)^2 S C_L ]

[ L_{new} = \frac{1}{2} \rho (4V^2) S C_L ]

[ L_{new} = 4 \left(\frac{1}{2} \rho V^2 S C_L\right) ]

[ L_{new} = 4L ]

This shows that the lift will increase fourfold when the velocity is doubled, assuming all other factors (air density,