How do you derive the square of the desired speed for climb calculations?

The square of the desired speed for climb calculations is derived using the lift equation, which takes into consideration the factors necessary to achieve and maintain climb performance. The correct formulation expresses that a specific amount of lift must be generated to support the aircraft's weight during a climb.

In this context, the lift force (Lift) must equal the weight of the aircraft when climbing at a steady speed. The lift equation can be rearranged to find the speed needed to produce that lift by recognizing that Lift is a function of speed and other aerodynamic parameters. The expression gives us the relationship:

Lift = 0.5 * p * S * Cl * V^2,

where:

• Lift is the lift force needed to counteract the weight,

• p is the air density,

• S is the wing area,

• Cl is the lift coefficient,

• V is the airspeed.

By rearranging this equation to solve for V^2 (the square of the speed), one arrives at:

V^2 = Lift / (0.5 * p * S * Cl).

This mathematically demonstrates how the speed squared is directly tied to lift, air density, wing area, and the lift coefficient. Thus, using this formula allows pilots and flight planners to determine