Takeoff Velocity Calculator

Formula

To calculate the Takeoff Velocity (V):

\[ V = \sqrt{\frac{2 \cdot m \cdot g}{CL \cdot A \cdot d}} \]

Where:

\(V\) is the Takeoff Velocity (m/s)
\(m\) is the Mass of the Aircraft (kg)
\(g\) is the Acceleration due to Gravity (9.81 m/s\(^2\))
\(CL\) is the Coefficient of Lift
\(A\) is the Surface Area of the Wings (m\(^2\))
\(d\) is the Density of the Air (kg/m\(^3\))

What is Takeoff Velocity?

Takeoff velocity describes the speed at which the lift force is equal to the mass of the aircraft. It is the minimum speed required for an aircraft to become airborne, ensuring that the lift generated by the wings is sufficient to counteract the weight of the aircraft.

Example Calculation

Let's assume the following values:

Mass of the Aircraft (\(m\)) = 5000 kg
Coefficient of Lift (\(CL\)) = 1.5
Surface Area of the Wings (\(A\)) = 50 m\(^2\)
Density of the Air (\(d\)) = 1.225 kg/m\(^3\)

Using the formula:

\[ V = \sqrt{\frac{2 \cdot 5000 \cdot 9.81}{1.5 \cdot 50 \cdot 1.225}} = \sqrt{\frac{98100}{91.875}} = \sqrt{1067.78} = 32.67 \text{ m/s} \]

The Takeoff Velocity is 32.67 m/s.