Take Off Ground Run Calculator

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Aircraft Performance

Aircraft Design

Introduction and Governing Equations

Static Stability and Control

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✖Weight Of Aircraft is a force which is always directed towards the center of the earth.ⓘ Weight Of Aircraft [W]			+10% -10%
✖Velocity of Aircraft is the velocity, or airspeed, at which a plane flies.ⓘ Velocity of Aircraft [V_∞]			+10% -10%
✖Thrust Force in is the force generated by engines or propulsion systems that propels an aircraft forward through the air.ⓘ Thrust Force [T]			+10% -10%
✖Drag force, also known as air resistance, is the aerodynamic force that opposes the motion of an aircraft through the air.ⓘ Drag Force [D]			+10% -10%
✖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.ⓘ Reference Of Rolling Resistance Coefficient [μ_r]			+10% -10%
✖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.ⓘ Lift Force [L]			+10% -10%
✖Aircraft Lift Off Speed is the airspeed at which the aeroplane first becomes airborne.ⓘ Aircraft Lift Off Speed [V_LO]			+10% -10%

✖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.ⓘ Take Off Ground Run [S_g]

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Formula

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Take Off Ground Run

Formula

`"S"_{"g"} = "W"/(2*"[g]")*int((2*"V"_{"∞"})/("T"-"D"-"μ"_{"r"}*("W"-"L")),x,0,"V"_{"LO"})`

Example

`"239.078m"="2000kg"/(2*"[g]")*int((2*"292m/s")/("20000N"-"65N"-"0.004"*("2000kg"-"7N")),x,0,"80m/s")`

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Take Off Ground Run Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
S_g = W/(2*[g])*int((2*V_∞)/(T-D-μ_r*(W-L)),x,0,V_LO)
This formula uses 1 Constants, 1 Functions, 8 Variables

Constants Used

[g] - Gravitational acceleration on Earth Value Taken As 9.80665

Functions Used

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., int(expr, arg, from, to)

Variables Used

Takeoff Ground Run - (Measured in Meter) - 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.
Weight Of Aircraft - (Measured in Kilogram) - Weight Of Aircraft is a force which is always directed towards the center of the earth.
Velocity of Aircraft - (Measured in Meter per Second) - Velocity of Aircraft is the velocity, or airspeed, at which a plane flies.
Thrust Force - (Measured in Newton) - Thrust Force in is the force generated by engines or propulsion systems that propels an aircraft forward through the air.
Drag Force - (Measured in Newton) - Drag force, also known as air resistance, is the aerodynamic force that opposes the motion of an aircraft through the air.
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.
Lift Force - (Measured in Newton) - 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.
Aircraft Lift Off Speed - (Measured in Meter per Second) - Aircraft Lift Off Speed is the airspeed at which the aeroplane first becomes airborne.

STEP 1: Convert Input(s) to Base Unit

Weight Of Aircraft: 2000 Kilogram --> 2000 Kilogram No Conversion Required
Velocity of Aircraft: 292 Meter per Second --> 292 Meter per Second No Conversion Required
Thrust Force: 20000 Newton --> 20000 Newton No Conversion Required
Drag Force: 65 Newton --> 65 Newton No Conversion Required
Reference Of Rolling Resistance Coefficient: 0.004 --> No Conversion Required
Lift Force: 7 Newton --> 7 Newton No Conversion Required
Aircraft Lift Off Speed: 80 Meter per Second --> 80 Meter per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

S_g = W/(2*[g])*int((2*V_∞)/(T-D-μ_r*(W-L)),x,0,V_LO) --> 2000/(2*[g])*int((2*292)/(20000-65-0.004*(2000-7)),x,0,80)

Evaluating ... ...

S_g = 239.078007369332

STEP 3: Convert Result to Output's Unit

239.078007369332 Meter --> No Conversion Required

FINAL ANSWER

239.078007369332 ≈ 239.078 Meter <-- Takeoff Ground Run

(Calculation completed in 00.004 seconds)

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< 15 Take-Off Calculators

Take Off Ground Run

Go 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)

Drag during ground effect

Go Drag Force = (Parasite Drag coefficient+(((Lift Coefficient^2)*Ground effect factor)/(pi*Oswald efficiency factor*Aspect Ratio of a wing)))*(0.5*Freestream density*(Flight Velocity^2)*Reference Area)

Thrust for given liftoff distance

Go Thrust of an aircraft = 1.44*(Weight Newton^2)/([g]*Freestream density*Reference Area*Maximum Lift Coefficient*Liftoff Distance)

Liftoff distance

Go Liftoff Distance = 1.44*(Weight Newton^2)/([g]*Freestream density*Reference Area*Maximum Lift Coefficient*Thrust of an aircraft)

Liftoff velocity for given weight

Go Liftoff velocity = 1.2*(sqrt((2*Weight Newton)/(Freestream density*Reference Area*Maximum Lift Coefficient)))

Stall velocity for given weight

Go Stall Velocity = sqrt((2*Weight Newton)/(Freestream density*Reference Area*Maximum Lift Coefficient))

Maximum Lift coefficient for given liftoff velocity

Go Maximum Lift Coefficient = 2.88*Weight Newton/(Freestream density*Reference Area*(Liftoff velocity^2))

Ground effect factor

Go Ground effect factor = ((16*Height from Ground/Wingspan)^2)/(1+((16*Height from Ground/Wingspan)^2))

Maximum Lift coefficient for given stall velocity

Go Maximum Lift Coefficient = 2*Weight Newton/(Freestream density*Reference Area*(Stall Velocity^2))

Coefficient of rolling friction during ground roll

Go Coefficient of Rolling Friction = Rolling Resistance/(Weight Newton-Lift Force)

Lift acting on aircraft during ground roll

Go Lift Force = Weight Newton-(Rolling Resistance/Coefficient of Rolling Friction)

Weight of aircraft during ground roll

Go Weight Newton = (Rolling Resistance/Coefficient of Rolling Friction)+Lift Force

Resistance force during ground roll

Go Rolling Resistance = Coefficient of Rolling Friction*(Weight Newton-Lift Force)

Liftoff velocity for given stall velocity

Go Liftoff velocity = 1.2*Stall Velocity

Stall velocity for given liftoff velocity

Go Stall Velocity = Liftoff velocity/1.2

Take Off Ground Run Formula

what is Take Off Ground Run?

A takeoff ground run, also known as a take-off roll or ground roll, is the distance an aircraft travels from the beginning of its takeoff to the point when it leaves the ground or water. It's the portion of the takeoff procedure where the aircraft accelerates from a standstill to an airspeed that provides enough lift to become airborne.

How to Calculate Take Off Ground Run?

Take Off Ground Run calculator 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 calculate the Takeoff Ground Run, take off ground run also known as a take-off roll or ground roll, is the distance an aircraft travels from the beginning of its takeoff to the point when it leaves the ground or water. Takeoff Ground Run is denoted by S_g symbol.

How to calculate Take Off Ground Run using this online calculator? To use this online calculator for Take Off Ground Run, enter Weight Of Aircraft (W), Velocity of Aircraft (V_∞), Thrust Force (T), Drag Force (D), Reference Of Rolling Resistance Coefficient (μ_r), Lift Force (L) & Aircraft Lift Off Speed (V_LO) and hit the calculate button. Here is how the Take Off Ground Run calculation can be explained with given input values -> 2.38983 = 2000/(2*[g])*int((2*292)/(20000-65-0.004*(2000-7)),x,0,80).

FAQ

What is Take Off Ground Run?

take off ground run also known as a take-off roll or ground roll, is the distance an aircraft travels from the beginning of its takeoff to the point when it leaves the ground or water and is represented as S_g = W/(2*[g])*int((2*V_∞)/(T-D-μ_r*(W-L)),x,0,V_LO) or 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). Weight Of Aircraft is a force which is always directed towards the center of the earth, Velocity of Aircraft is the velocity, or airspeed, at which a plane flies, Thrust Force in is the force generated by engines or propulsion systems that propels an aircraft forward through the air, Drag force, also known as air resistance, is the aerodynamic force that opposes the motion of an aircraft through the air, 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, 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 & Aircraft Lift Off Speed is the airspeed at which the aeroplane first becomes airborne.

How to calculate Take Off Ground Run?

take off ground run also known as a take-off roll or ground roll, is the distance an aircraft travels from the beginning of its takeoff to the point when it leaves the ground or water is calculated using 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 calculate Take Off Ground Run, you need Weight Of Aircraft (W), Velocity of Aircraft (V_∞), Thrust Force (T), Drag Force (D), Reference Of Rolling Resistance Coefficient (μ_r), Lift Force (L) & Aircraft Lift Off Speed (V_LO). With our tool, you need to enter the respective value for Weight Of Aircraft, Velocity of Aircraft, Thrust Force, Drag Force, Reference Of Rolling Resistance Coefficient, Lift Force & Aircraft Lift Off Speed and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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