Liftoff Velocity For Given Weight Calculator

Liftoff Velocity Formula:

\[ V_{LO} = 1.2 \times \sqrt{\frac{2 \times W}{\rho_{\infty} \times S \times C_{L,max}}} \]

Weight (W):

Newton

Freestream Density (ρ∞):

kg/m³

Reference Area (S):

m²

Maximum Lift Coefficient (CL,max):

Liftoff Velocity (VLO):

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1. What is the Liftoff Velocity Formula?

The liftoff velocity formula calculates the velocity at which an aircraft first becomes airborne. It considers the aircraft's weight, freestream density, reference area, and maximum lift coefficient to determine the minimum speed required for takeoff.

2. How Does the Calculator Work?

The calculator uses the liftoff velocity equation:

\[ V_{LO} = 1.2 \times \sqrt{\frac{2 \times W}{\rho_{\infty} \times S \times C_{L,max}}} \]

Where:

\( V_{LO} \) — Liftoff velocity (m/s)
\( W \) — Weight (Newton)
\( \rho_{\infty} \) — Freestream density (kg/m³)
\( S \) — Reference area (m²)
\( C_{L,max} \) — Maximum lift coefficient

Explanation: The formula accounts for the 1.2 safety factor to ensure safe takeoff margin above stall speed, and calculates the velocity where lift equals weight.

3. Importance of Liftoff Velocity Calculation

Details: Accurate liftoff velocity calculation is crucial for aircraft design, runway length requirements, and ensuring safe takeoff performance under various operating conditions.

4. Using the Calculator

Tips: Enter weight in Newtons, freestream density in kg/m³, reference area in m², and maximum lift coefficient. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: Why is there a 1.2 factor in the formula?
A: The 1.2 factor provides a safety margin above the stall speed to ensure safe takeoff operations and account for various operational uncertainties.

Q2: What is freestream density?
A: Freestream density is the mass per unit volume of air far upstream of the aircraft, typically at the given altitude and atmospheric conditions.

Q3: How is reference area defined for aircraft?
A: For aircraft, reference area typically refers to the wing planform area, which is the projected area of the wing when viewed from above.

Q4: What affects the maximum lift coefficient?
A: Maximum lift coefficient is affected by wing design, airfoil shape, high-lift devices (flaps/slats), and angle of attack.

Q5: How does altitude affect liftoff velocity?
A: Higher altitudes have lower air density, which increases the required liftoff velocity for the same aircraft weight and configuration.