Calculate theoretical lift-equals-weight airspeed, solve its inverse variables, or estimate dry-air density from ISA pressure. This educational model does not determine operational takeoff or rotation speeds; use the aircraft AFM/POH for flight decisions.

Educational model only. This is lift-equals-weight speed, not an operational takeoff or rotation speed. Use the aircraft AFM/POH for flight decisions.

Illustrative input presets

Original generic examples, not verified aircraft specifications.

Actual CL depends on airfoil, angle of attack and configuration.

Takeoff Velocity Formula

The following equation solves the idealized speed at which aerodynamic lift equals aircraft weight. It is not an operational takeoff-speed model.

V = SQRT (2 × m × g / (CL × A × d))
  • Where V is theoretical lift-balance airspeed (m/s), not groundspeed or certified takeoff speed
  • m is the mass of the aircraft (kg)
  • g is standard gravitational acceleration (9.80665 m/s²)
  • CL is the coefficient of lift
  • A is the surface area of the wings (m^2)
  • d is the density of the air (kg/m^3)

To calculate the takeoff velocity, divide the product of 2 times the mass times g by the product of the coefficient of lift, the surface area of the wings, and the density of the air, then take the square root of the result.

What is a Takeoff Velocity?

Definition:

This formula describes airspeed where idealized lift equals aircraft weight (mass × g), not mass. Operational takeoff speeds depend on aircraft-specific certification, configuration and performance data.

How to Calculate Takeoff Velocity?

Example Problem:

The following example outlines the steps and information needed to calculate Takeoff Velocity.

First, determine the mass of the aircraft. In this example, the mass is found to be 4000 kg.

Next, determine the coefficient of lift. For this problem, the coefficient of lift is found to be .85.

Next, determine the surface area of the wings. In this case, the area is measured to be 100 m^2.

Next, determine the density of the air. For this, the air density is 1.225 kg/m^3.

Finally, calculate the Takeoff Velocity using the formula above:

V = SQRT (2*m*g / (CL*A*d))

V = SQRT (2*4000*9.80665 / (.85*100*1.225))

V ≈ 27.449 m/s (theoretical lift balance)

FAQ

What factors can affect the takeoff velocity of an aircraft?

The takeoff velocity of an aircraft can be affected by several factors including the aircraft’s weight, the wing surface area, the air density (which can vary with altitude and weather conditions), and the coefficient of lift, which can change based on the wing’s design and the angle of attack during takeoff.

How does air density impact aircraft performance during takeoff?

Air density plays a crucial role in aircraft performance during takeoff. Higher air density (found in cooler temperatures or at lower altitudes) increases the air’s resistance against the wing, resulting in higher lift at lower speeds. Conversely, lower air density (found in warmer temperatures or at higher altitudes) reduces lift, requiring higher takeoff velocities to achieve the necessary lift for takeoff.

Can the takeoff velocity formula be applied to any type of aircraft?

The lift equation is useful for education, but it does not establish safe takeoff performance. Use the aircraft AFM/POH for actual takeoff and rotation speeds, runway performance and operating limitations.