Landing ground roll distance Calculator

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✖Weight Newton is a vector quantity and defined as the product of mass and acceleration acting on that mass.ⓘ Weight Newton [W]			+10% -10%
✖Freestream density is the mass per unit volume of air far upstream of an aerodynamic body at a given altitude.ⓘ Freestream density [ρ_∞]			+10% -10%
✖The Reference Area is arbitrarily an area that is characteristic of the object being considered. For an aircraft wing, the wing's planform area is called the reference wing area or simply wing area.ⓘ Reference Area [S]			+10% -10%
✖Maximum Lift Coefficient is defined as the lift coefficient of the airfoil at stalling angle of attack.ⓘ Maximum Lift Coefficient [C_L,max]			+10% -10%
✖Touchdown Velocity is the instantaneous velocity of an aircraft when it touches the ground during landing.ⓘ Touchdown Velocity [V_T]			+10% -10%
✖The Zero-lift drag coefficient is a dimensionless parameter that relates an aircraft's zero-lift drag force to its size, speed, and flying altitude.ⓘ Zero-lift drag coefficient [C_D,0]			+10% -10%
✖Ground effect factor is the ratio of the induced drag in-ground-effect to the induced drag out-of-ground-effect.ⓘ Ground effect factor [ϕ]			+10% -10%
✖The Lift Coefficient is a dimensionless coefficient that relates the lift generated by a lifting body to the fluid density around the body, the fluid velocity and an associated reference area.ⓘ Lift Coefficient [C_L]			+10% -10%
✖The Oswald efficiency factor is a correction factor that represents the change in drag with lift of a three-dimensional wing or airplane, as compared with an ideal wing having the same aspect ratio.ⓘ Oswald efficiency factor [e]			+10% -10%
✖The Aspect Ratio of a wing is defined as the ratio of its span to its mean chord.ⓘ Aspect Ratio of a wing [AR]			+10% -10%
✖Coefficient of Rolling Friction is the ratio of the force of rolling friction to the total weight of the object.ⓘ Coefficient of Rolling Friction [μ_r]			+10% -10%

✖The Landing Roll distance is the distance covered when the aircraft touches down, is brought down to taxi speed, and eventually comes to a complete stop.ⓘ Landing ground roll distance [s_L]

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Formula

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Landing ground roll distance

Formula

`"s"_{"L"} = 1.69*("W"^2)*(1/("[g]"*"ρ"_{"∞"}*"S"*"C"_{"L,max"}))*(1/((0.5*"ρ"_{"∞"}*((0.7*"V"_{"T"})^2)*"S"*("C"_{"D,0"}+("ϕ"*("C"_{"L"}^2)/(pi*"e"*"AR"))))+("μ"_{"r"}*("W"-(0.5*"ρ"_{"∞"}*((0.7*"V"_{"T"})^2)*"S"*"C"_{"L"})))))`

Example

`"0.000773m"=1.69*(("60.34N")^2)*(1/("[g]"*"1.225kg/m³"*"5.08m²"*"1.65"))*(1/((0.5*"1.225kg/m³"*((0.7*"193m/s")^2)*"5.08m²"*("0.0161"+("0.4"*(("5.5")^2)/(pi*"0.5"*"4"))))+("0.1"*("60.34N"-(0.5*"1.225kg/m³"*((0.7*"193m/s")^2)*"5.08m²"*"5.5")))))`

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Landing ground roll distance Solution

STEP 0: Pre-Calculation Summary

Formula Used

Landing Roll = 1.69*(Weight Newton^2)*(1/([g]*Freestream density*Reference Area*Maximum Lift Coefficient))*(1/((0.5*Freestream density*((0.7*Touchdown Velocity)^2)*Reference Area*(Zero-lift drag coefficient+(Ground effect factor*(Lift Coefficient^2)/(pi*Oswald efficiency factor*Aspect Ratio of a wing))))+(Coefficient of Rolling Friction*(Weight Newton-(0.5*Freestream density*((0.7*Touchdown Velocity)^2)*Reference Area*Lift Coefficient)))))
s_L = 1.69*(W^2)*(1/([g]*ρ_∞*S*C_L,max))*(1/((0.5*ρ_∞*((0.7*V_T)^2)*S*(C_D,0+(ϕ*(C_L^2)/(pi*e*AR))))+(μ_r*(W-(0.5*ρ_∞*((0.7*V_T)^2)*S*C_L)))))
This formula uses 2 Constants, 12 Variables

Constants Used

[g] - Gravitational acceleration on Earth Value Taken As 9.80665
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Landing Roll - (Measured in Meter) - The Landing Roll distance is the distance covered when the aircraft touches down, is brought down to taxi speed, and eventually comes to a complete stop.
Weight Newton - (Measured in Newton) - Weight Newton is a vector quantity and defined as the product of mass and acceleration acting on that mass.
Freestream density - (Measured in Kilogram per Cubic Meter) - Freestream density is the mass per unit volume of air far upstream of an aerodynamic body at a given altitude.
Reference Area - (Measured in Square Meter) - The Reference Area is arbitrarily an area that is characteristic of the object being considered. For an aircraft wing, the wing's planform area is called the reference wing area or simply wing area.
Maximum Lift Coefficient - Maximum Lift Coefficient is defined as the lift coefficient of the airfoil at stalling angle of attack.
Touchdown Velocity - (Measured in Meter per Second) - Touchdown Velocity is the instantaneous velocity of an aircraft when it touches the ground during landing.
Zero-lift drag coefficient - The Zero-lift drag coefficient is a dimensionless parameter that relates an aircraft's zero-lift drag force to its size, speed, and flying altitude.
Ground effect factor - Ground effect factor is the ratio of the induced drag in-ground-effect to the induced drag out-of-ground-effect.
Lift Coefficient - The Lift Coefficient is a dimensionless coefficient that relates the lift generated by a lifting body to the fluid density around the body, the fluid velocity and an associated reference area.
Oswald efficiency factor - The Oswald efficiency factor is a correction factor that represents the change in drag with lift of a three-dimensional wing or airplane, as compared with an ideal wing having the same aspect ratio.
Aspect Ratio of a wing - The Aspect Ratio of a wing is defined as the ratio of its span to its mean chord.
Coefficient of Rolling Friction - Coefficient of Rolling Friction is the ratio of the force of rolling friction to the total weight of the object.

STEP 1: Convert Input(s) to Base Unit

Weight Newton: 60.34 Newton --> 60.34 Newton No Conversion Required
Freestream density: 1.225 Kilogram per Cubic Meter --> 1.225 Kilogram per Cubic Meter No Conversion Required
Reference Area: 5.08 Square Meter --> 5.08 Square Meter No Conversion Required
Maximum Lift Coefficient: 1.65 --> No Conversion Required
Touchdown Velocity: 193 Meter per Second --> 193 Meter per Second No Conversion Required
Zero-lift drag coefficient: 0.0161 --> No Conversion Required
Ground effect factor: 0.4 --> No Conversion Required
Lift Coefficient: 5.5 --> No Conversion Required
Oswald efficiency factor: 0.5 --> No Conversion Required
Aspect Ratio of a wing: 4 --> No Conversion Required
Coefficient of Rolling Friction: 0.1 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

s_L = 1.69*(W^2)*(1/([g]*ρ_∞*S*C_L,max))*(1/((0.5*ρ_∞*((0.7*V_T)^2)*S*(C_D,0+(ϕ*(C_L^2)/(pi*e*AR))))+(μ_r*(W-(0.5*ρ_∞*((0.7*V_T)^2)*S*C_L))))) --> 1.69*(60.34^2)*(1/([g]*1.225*5.08*1.65))*(1/((0.5*1.225*((0.7*193)^2)*5.08*(0.0161+(0.4*(5.5^2)/(pi*0.5*4))))+(0.1*(60.34-(0.5*1.225*((0.7*193)^2)*5.08*5.5)))))

Evaluating ... ...

s_L = 0.000772999238247418

STEP 3: Convert Result to Output's Unit

0.000772999238247418 Meter --> No Conversion Required

FINAL ANSWER

0.000772999238247418 ≈ 0.000773 Meter <-- Landing Roll

(Calculation completed in 00.004 seconds)

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Created by Vinay Mishra

Indian Institute for Aeronautical Engineering and Information Technology (IIAEIT), Pune

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Verified by Sanjay Krishna

Amrita School of Engineering (ASE), Vallikavu

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< 5 Landing Calculators

Landing ground roll distance

Go Landing Roll = 1.69*(Weight Newton^2)*(1/([g]*Freestream density*Reference Area*Maximum Lift Coefficient))*(1/((0.5*Freestream density*((0.7*Touchdown Velocity)^2)*Reference Area*(Zero-lift drag coefficient+(Ground effect factor*(Lift Coefficient^2)/(pi*Oswald efficiency factor*Aspect Ratio of a wing))))+(Coefficient of Rolling Friction*(Weight Newton-(0.5*Freestream density*((0.7*Touchdown Velocity)^2)*Reference Area*Lift Coefficient)))))

Landing Ground Run

Go Landing Ground Run = (Normal Force*Velocity at Touchdown Point)+(Weight Of Aircraft/(2*[g]))*int((2*Velocity of Aircraft)/(Reverse Thrust+Drag Force+Reference Of Rolling Resistance Coefficient*(Weight Of Aircraft-Lift Force)),x,0,Velocity at Touchdown Point)

Touchdown velocity

Go Touchdown Velocity = 1.3*(sqrt(2*Weight Newton/(Freestream density*Reference Area*Maximum Lift Coefficient)))

Touchdown velocity for given stall velocity

Go Touchdown Velocity = 1.3*Stall Velocity

Stall velocity for given touchdown velocity

Go Stall Velocity = Touchdown Velocity/1.3

Landing ground roll distance Formula

How many kilometers is a runway?

Runway dimensions vary from as small as 245 m (804 ft) long and 8 m (26 ft) wide in smaller general aviation airports to 5,500 m (18,045 ft) long and 80 m (262 ft) wide at large international airports.

How to Calculate Landing ground roll distance?

Landing ground roll distance calculator uses Landing Roll = 1.69*(Weight Newton^2)*(1/([g]*Freestream density*Reference Area*Maximum Lift Coefficient))*(1/((0.5*Freestream density*((0.7*Touchdown Velocity)^2)*Reference Area*(Zero-lift drag coefficient+(Ground effect factor*(Lift Coefficient^2)/(pi*Oswald efficiency factor*Aspect Ratio of a wing))))+(Coefficient of Rolling Friction*(Weight Newton-(0.5*Freestream density*((0.7*Touchdown Velocity)^2)*Reference Area*Lift Coefficient))))) to calculate the Landing Roll, Landing ground roll distance is a function of weight, freestream density, maximum lift coefficient, touchdown velocity, coefficient of rolling friction (between the tires and ground), ground effect factor, lift and drag of the aircraft. Landing Roll is denoted by s_L symbol.

How to calculate Landing ground roll distance using this online calculator? To use this online calculator for Landing ground roll distance, enter Weight Newton (W), Freestream density (ρ_∞), Reference Area (S), Maximum Lift Coefficient (C_L,max), Touchdown Velocity (V_T), Zero-lift drag coefficient (C_D,0), Ground effect factor (ϕ), Lift Coefficient (C_L), Oswald efficiency factor (e), Aspect Ratio of a wing (AR) & Coefficient of Rolling Friction (μ_r) and hit the calculate button. Here is how the Landing ground roll distance calculation can be explained with given input values -> 0.000773 = 1.69*(60.34^2)*(1/([g]*1.225*5.08*1.65))*(1/((0.5*1.225*((0.7*193)^2)*5.08*(0.0161+(0.4*(5.5^2)/(pi*0.5*4))))+(0.1*(60.34-(0.5*1.225*((0.7*193)^2)*5.08*5.5))))).

FAQ

What is Landing ground roll distance?

Landing ground roll distance is a function of weight, freestream density, maximum lift coefficient, touchdown velocity, coefficient of rolling friction (between the tires and ground), ground effect factor, lift and drag of the aircraft and is represented as s_L = 1.69*(W^2)*(1/([g]*ρ_∞*S*C_L,max))*(1/((0.5*ρ_∞*((0.7*V_T)^2)*S*(C_D,0+(ϕ*(C_L^2)/(pi*e*AR))))+(μ_r*(W-(0.5*ρ_∞*((0.7*V_T)^2)*S*C_L))))) or Landing Roll = 1.69*(Weight Newton^2)*(1/([g]*Freestream density*Reference Area*Maximum Lift Coefficient))*(1/((0.5*Freestream density*((0.7*Touchdown Velocity)^2)*Reference Area*(Zero-lift drag coefficient+(Ground effect factor*(Lift Coefficient^2)/(pi*Oswald efficiency factor*Aspect Ratio of a wing))))+(Coefficient of Rolling Friction*(Weight Newton-(0.5*Freestream density*((0.7*Touchdown Velocity)^2)*Reference Area*Lift Coefficient))))). Weight Newton is a vector quantity and defined as the product of mass and acceleration acting on that mass, Freestream density is the mass per unit volume of air far upstream of an aerodynamic body at a given altitude, The Reference Area is arbitrarily an area that is characteristic of the object being considered. For an aircraft wing, the wing's planform area is called the reference wing area or simply wing area, Maximum Lift Coefficient is defined as the lift coefficient of the airfoil at stalling angle of attack, Touchdown Velocity is the instantaneous velocity of an aircraft when it touches the ground during landing, The Zero-lift drag coefficient is a dimensionless parameter that relates an aircraft's zero-lift drag force to its size, speed, and flying altitude, Ground effect factor is the ratio of the induced drag in-ground-effect to the induced drag out-of-ground-effect, The Lift Coefficient is a dimensionless coefficient that relates the lift generated by a lifting body to the fluid density around the body, the fluid velocity and an associated reference area, The Oswald efficiency factor is a correction factor that represents the change in drag with lift of a three-dimensional wing or airplane, as compared with an ideal wing having the same aspect ratio, The Aspect Ratio of a wing is defined as the ratio of its span to its mean chord & Coefficient of Rolling Friction is the ratio of the force of rolling friction to the total weight of the object.

How to calculate Landing ground roll distance?

Landing ground roll distance is a function of weight, freestream density, maximum lift coefficient, touchdown velocity, coefficient of rolling friction (between the tires and ground), ground effect factor, lift and drag of the aircraft is calculated using Landing Roll = 1.69*(Weight Newton^2)*(1/([g]*Freestream density*Reference Area*Maximum Lift Coefficient))*(1/((0.5*Freestream density*((0.7*Touchdown Velocity)^2)*Reference Area*(Zero-lift drag coefficient+(Ground effect factor*(Lift Coefficient^2)/(pi*Oswald efficiency factor*Aspect Ratio of a wing))))+(Coefficient of Rolling Friction*(Weight Newton-(0.5*Freestream density*((0.7*Touchdown Velocity)^2)*Reference Area*Lift Coefficient))))). To calculate Landing ground roll distance, you need Weight Newton (W), Freestream density (ρ_∞), Reference Area (S), Maximum Lift Coefficient (C_L,max), Touchdown Velocity (V_T), Zero-lift drag coefficient (C_D,0), Ground effect factor (ϕ), Lift Coefficient (C_L), Oswald efficiency factor (e), Aspect Ratio of a wing (AR) & Coefficient of Rolling Friction (μ_r). With our tool, you need to enter the respective value for Weight Newton, Freestream density, Reference Area, Maximum Lift Coefficient, Touchdown Velocity, Zero-lift drag coefficient, Ground effect factor, Lift Coefficient, Oswald efficiency factor, Aspect Ratio of a wing & Coefficient of Rolling Friction 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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