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Take Off Ground Run Formula

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A takeoff ground run is the distance an airplane travels from the beginning of takeoff to the point when it leaves the ground or water. Check FAQs

S g = \frac{W aircraft}{2 \cdot [g]} \cdot \int (\frac{2 \cdot V ∞}{N - D - μ ref \cdot (W aircraft - L)}, x, 0, V LOS)

S_g - Takeoff Ground Run?W_aircraft - Weight Of Aircraft?V_∞ - Velocity of Aircraft?N - Thrust Force?D - Drag Force?μ_ref - Reference Of Rolling Resistance Coefficient?L - Lift Force?V_LOS - Aircraft Lift Off Speed?[g] - Gravitational acceleration on Earth?

Take Off Ground Run Example

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Here is how the Take Off Ground Run equation looks like with Values.

Here is how the Take Off Ground Run equation looks like with Units.

Here is how the Take Off Ground Run equation looks like.

239.4067 = \frac{2000}{2 \cdot 9.8066} \cdot \int (\frac{2 \cdot 292}{20000 - 65 - 0.004 \cdot (2000 - 7)}, x, 0, 80.11)

239.4067m = \frac{2000kg}{2 \cdot 9.8066m/s²} \cdot \int (\frac{2 \cdot 292m/s}{20000N - 65N - 0.004 \cdot (2000kg - 7N)}, x, 0, 80.11m/s)

239.4067 = \frac{2000}{2 \cdot 9.8066} \cdot \int (\frac{2 \cdot 292}{20000 - 65 - 0.004 \cdot (2000 - 7)}, x, 0, 80.11)

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Take Off Ground Run Solution

Follow our step by step solution on how to calculate Take Off Ground Run?

FIRST Step Consider the formula

S g = \frac{W aircraft}{2 \cdot [g]} \cdot \int (\frac{2 \cdot V ∞}{N - D - μ ref \cdot (W aircraft - L)}, x, 0, V LOS)

Next Step Substitute values of Variables

∴

S g = \frac{2000kg}{2 \cdot [g]} \cdot \int (\frac{2 \cdot 292m/s}{20000N - 65N - 0.004 \cdot (2000kg - 7N)}, x, 0, 80.11m/s)

Next Step Substitute values of Constants

∴

S g = \frac{2000kg}{2 \cdot 9.8066m/s²} \cdot \int (\frac{2 \cdot 292m/s}{20000N - 65N - 0.004 \cdot (2000kg - 7N)}, x, 0, 80.11m/s)

Next Step Prepare to Evaluate

∴

S g = \frac{2000}{2 \cdot 9.8066} \cdot \int (\frac{2 \cdot 292}{20000 - 65 - 0.004 \cdot (2000 - 7)}, x, 0, 80.11)

Next Step Evaluate

∴

S g = 239.406739629465m

LAST Step Rounding Answer

∴

S g = 239.4067m

Take Off Ground Run Formula Elements

Variables

Constants

Functions

Takeoff Ground Run

A takeoff ground run is the distance an airplane travels from the beginning of takeoff to the point when it leaves the ground or water.

Symbol: S_g

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Takeoff Ground Run

Weight Of Aircraft

Weight Of Aircraft is a force which is always directed towards the center of the earth.

Symbol: W_aircraft

Measurement: WeightUnit: kg

Note: Value should be greater than 0.

Formulas to find Weight Of Aircraft

Velocity of Aircraft

Velocity of Aircraft is the velocity, or airspeed, at which a plane flies.

Symbol: V_∞

Measurement: SpeedUnit: m/s

Note: Value should be greater than 0.

Formulas to find Velocity of Aircraft

Thrust Force

Thrust Force in is the force generated by engines or propulsion systems that propels an aircraft forward through the air.

Symbol: N

Measurement: ForceUnit: N

Note: Value can be positive or negative.

Formulas to find Thrust Force

Drag Force

Drag force, also known as air resistance, is the aerodynamic force that opposes the motion of an aircraft through the air.

Symbol: D

Measurement: ForceUnit: N

Note: Value can be positive or negative.

Formulas to find Drag Force

Reference Of Rolling Resistance Coefficient

The Reference Of Rolling Resistance Coefficient is the ratio of the rolling resistance force to the wheel load, it's a basic resistance when moving objects.

Symbol: μ_ref

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Reference Of Rolling Resistance Coefficient

Lift Force

Lift Force is the upward force that holds an aircraft in the air, generated by the interaction of the aircraft with a fluid, such as air.

Symbol: L

Measurement: ForceUnit: N

Note: Value can be positive or negative.

Formulas to find Lift Force

Aircraft Lift Off Speed

Aircraft Lift Off Speed is the airspeed at which the aeroplane first becomes airborne.

Symbol: V_LOS

Measurement: SpeedUnit: m/s

Note: Value should be greater than 0.

Formulas to find Aircraft Lift Off Speed

Gravitational acceleration on Earth

Gravitational acceleration on Earth means that the velocity of an object in free fall will increase by 9.8 m/s2 every second.

Symbol: [g]

Value: 9.80665 m/s²

int

The definite integral can be used to calculate net signed area, which is the area above the x -axis minus the area below the x -axis.

Syntax: int(expr, arg, from, to)

Other formulas in Take Off category

Go Resistance force during ground roll

R = μ r \cdot (W - F L)

Go Coefficient of rolling friction during ground roll

μ r = \frac{R}{W - F L}

How to Evaluate Take Off Ground Run?

Take Off Ground Run evaluator uses Takeoff Ground Run = Weight Of Aircraft/(2*[g])*int((2*Velocity of Aircraft)/(Thrust Force-Drag Force-Reference Of Rolling Resistance Coefficient*(Weight Of Aircraft-Lift Force)),x,0,Aircraft Lift Off Speed) to evaluate the Takeoff Ground Run, Take Off Ground Run is a measure of the distance required by an aircraft to take off from a standstill to lift-off, considering the aircraft's weight, aerodynamics, thrust, drag, and rolling resistance, it represents the ground run required to build up sufficient speed for the aircraft to lift off the ground, ensuring a safe takeoff. Takeoff Ground Run is denoted by S_g symbol.

How to evaluate Take Off Ground Run using this online evaluator? To use this online evaluator for Take Off Ground Run, enter Weight Of Aircraft (W_aircraft), Velocity of Aircraft (V_∞), Thrust Force (N), Drag Force (D), Reference Of Rolling Resistance Coefficient (μ_ref), Lift Force (L) & Aircraft Lift Off Speed (V_LOS) and hit the calculate button.

FAQs on Take Off Ground Run

What is the formula to find Take Off Ground Run?

The formula of Take Off Ground Run is expressed as Takeoff Ground Run = Weight Of Aircraft/(2*[g])*int((2*Velocity of Aircraft)/(Thrust Force-Drag Force-Reference Of Rolling Resistance Coefficient*(Weight Of Aircraft-Lift Force)),x,0,Aircraft Lift Off Speed). Here is an example- 239.3769 = 2000/(2*[g])*int((2*292)/(20000-65-0.004*(2000-7)),x,0,80.11).

How to calculate Take Off Ground Run?

With Weight Of Aircraft (W_aircraft), Velocity of Aircraft (V_∞), Thrust Force (N), Drag Force (D), Reference Of Rolling Resistance Coefficient (μ_ref), Lift Force (L) & Aircraft Lift Off Speed (V_LOS) we can find Take Off Ground Run using the formula - Takeoff Ground Run = Weight Of Aircraft/(2*[g])*int((2*Velocity of Aircraft)/(Thrust Force-Drag Force-Reference Of Rolling Resistance Coefficient*(Weight Of Aircraft-Lift Force)),x,0,Aircraft Lift Off Speed). This formula also uses Gravitational acceleration on Earth constant(s) and Definite Integral (int) function(s).

Can the Take Off Ground Run be negative?

No, the Take Off Ground Run, measured in Length cannot be negative.

Which unit is used to measure Take Off Ground Run?

Take Off Ground Run is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Take Off Ground Run can be measured.

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Take Off Ground Run Formula

Take Off Ground Run Example

Take Off Ground Run Solution

Take Off Ground Run Formula Elements

Other formulas in Take Off category

How to Evaluate Take Off Ground Run?

FAQs on Take Off Ground Run

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