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Landing ground roll distance Formula

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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. Check FAQs

s L = 1.69 \cdot (W^{2}) \cdot (\frac{1}{[g] \cdot ρ ∞ \cdot S \cdot C L,max}) \cdot (\frac{1}{(0.5 \cdot ρ ∞ \cdot ({(0.7 \cdot V T)}^{2}) \cdot S \cdot (C D,0 + (ϕ \cdot \frac{{C L}^{2}}{π \cdot e \cdot AR}))) + (μ r \cdot (W - (0.5 \cdot ρ ∞ \cdot ({(0.7 \cdot V T)}^{2}) \cdot S \cdot C L)))})

s_L - Landing Roll?W - Weight?ρ_∞ - Freestream Density?S - Reference Area?C_L,max - Maximum Lift Coefficient?V_T - Touchdown Velocity?C_D,0 - Zero-Lift Drag Coefficient?ϕ - Ground Effect Factor?C_L - Lift Coefficient?e - Oswald Efficiency Factor?AR - Aspect Ratio of a Wing?μ_r - Coefficient of Rolling Friction?[g] - Gravitational acceleration on Earth?π - Archimedes' constant?

Landing ground roll distance Example

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Here is how the Landing ground roll distance equation looks like with Values.

Here is how the Landing ground roll distance equation looks like with Units.

Here is how the Landing ground roll distance equation looks like.

1.4488 = 1.69 \cdot ({60.5}^{2}) \cdot (\frac{1}{9.8066 \cdot 1.225 \cdot 5.08 \cdot 0.0009}) \cdot (\frac{1}{(0.5 \cdot 1.225 \cdot ({(0.7 \cdot 193)}^{2}) \cdot 5.08 \cdot (0.0161 + (0.4 \cdot \frac{{5.5}^{2}}{3.1416 \cdot 0.5 \cdot 4}))) + (0.1 \cdot (60.5 - (0.5 \cdot 1.225 \cdot ({(0.7 \cdot 193)}^{2}) \cdot 5.08 \cdot 5.5)))})

1.4488m = 1.69 \cdot ({60.5N}^{2}) \cdot (\frac{1}{9.8066m/s² \cdot 1.225kg/m³ \cdot 5.08m² \cdot 0.0009}) \cdot (\frac{1}{(0.5 \cdot 1.225kg/m³ \cdot ({(0.7 \cdot 193m/s)}^{2}) \cdot 5.08m² \cdot (0.0161 + (0.4 \cdot \frac{{5.5}^{2}}{3.1416 \cdot 0.5 \cdot 4}))) + (0.1 \cdot (60.5N - (0.5 \cdot 1.225kg/m³ \cdot ({(0.7 \cdot 193m/s)}^{2}) \cdot 5.08m² \cdot 5.5)))})

1.4488 = 1.69 \cdot ({60.5}^{2}) \cdot (\frac{1}{9.8066 \cdot 1.225 \cdot 5.08 \cdot 0.0009}) \cdot (\frac{1}{(0.5 \cdot 1.225 \cdot ({(0.7 \cdot 193)}^{2}) \cdot 5.08 \cdot (0.0161 + (0.4 \cdot \frac{{5.5}^{2}}{3.1416 \cdot 0.5 \cdot 4}))) + (0.1 \cdot (60.5 - (0.5 \cdot 1.225 \cdot ({(0.7 \cdot 193)}^{2}) \cdot 5.08 \cdot 5.5)))})

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Landing ground roll distance Solution

Follow our step by step solution on how to calculate Landing ground roll distance?

FIRST Step Consider the formula

s L = 1.69 \cdot (W^{2}) \cdot (\frac{1}{[g] \cdot ρ ∞ \cdot S \cdot C L,max}) \cdot (\frac{1}{(0.5 \cdot ρ ∞ \cdot ({(0.7 \cdot V T)}^{2}) \cdot S \cdot (C D,0 + (ϕ \cdot \frac{{C L}^{2}}{π \cdot e \cdot AR}))) + (μ r \cdot (W - (0.5 \cdot ρ ∞ \cdot ({(0.7 \cdot V T)}^{2}) \cdot S \cdot C L)))})

Next Step Substitute values of Variables

∴

s L = 1.69 \cdot ({60.5N}^{2}) \cdot (\frac{1}{[g] \cdot 1.225kg/m³ \cdot 5.08m² \cdot 0.0009}) \cdot (\frac{1}{(0.5 \cdot 1.225kg/m³ \cdot ({(0.7 \cdot 193m/s)}^{2}) \cdot 5.08m² \cdot (0.0161 + (0.4 \cdot \frac{{5.5}^{2}}{π \cdot 0.5 \cdot 4}))) + (0.1 \cdot (60.5N - (0.5 \cdot 1.225kg/m³ \cdot ({(0.7 \cdot 193m/s)}^{2}) \cdot 5.08m² \cdot 5.5)))})

Next Step Substitute values of Constants

∴

s L = 1.69 \cdot ({60.5N}^{2}) \cdot (\frac{1}{9.8066m/s² \cdot 1.225kg/m³ \cdot 5.08m² \cdot 0.0009}) \cdot (\frac{1}{(0.5 \cdot 1.225kg/m³ \cdot ({(0.7 \cdot 193m/s)}^{2}) \cdot 5.08m² \cdot (0.0161 + (0.4 \cdot \frac{{5.5}^{2}}{3.1416 \cdot 0.5 \cdot 4}))) + (0.1 \cdot (60.5N - (0.5 \cdot 1.225kg/m³ \cdot ({(0.7 \cdot 193m/s)}^{2}) \cdot 5.08m² \cdot 5.5)))})

Next Step Prepare to Evaluate

∴

s L = 1.69 \cdot ({60.5}^{2}) \cdot (\frac{1}{9.8066 \cdot 1.225 \cdot 5.08 \cdot 0.0009}) \cdot (\frac{1}{(0.5 \cdot 1.225 \cdot ({(0.7 \cdot 193)}^{2}) \cdot 5.08 \cdot (0.0161 + (0.4 \cdot \frac{{5.5}^{2}}{3.1416 \cdot 0.5 \cdot 4}))) + (0.1 \cdot (60.5 - (0.5 \cdot 1.225 \cdot ({(0.7 \cdot 193)}^{2}) \cdot 5.08 \cdot 5.5)))})

Next Step Evaluate

∴

s L = 1.44883787019799m

LAST Step Rounding Answer

∴

s L = 1.4488m

Landing ground roll distance Formula Elements

Variables

Constants

Landing Roll

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.

Symbol: s_L

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Landing Roll

Weight

Weight Newton is a vector quantity and defined as the product of mass and acceleration acting on that mass.

Symbol: W

Measurement: ForceUnit: N

Note: Value can be positive or negative.

Formulas to find Weight

Freestream Density

Freestream density is the mass per unit volume of air far upstream of an aerodynamic body at a given altitude.

Symbol: ρ_∞

Measurement: DensityUnit: kg/m³

Note: Value can be positive or negative.

Formulas to find Freestream Density

Reference Area

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.

Symbol: S

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Reference Area

Maximum Lift Coefficient

Maximum Lift Coefficient is defined as the lift coefficient of the airfoil at stalling angle of attack.

Symbol: C_L,max

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Maximum Lift Coefficient

Touchdown Velocity

Touchdown Velocity is the instantaneous velocity of an aircraft when it touches the ground during landing.

Symbol: V_T

Measurement: SpeedUnit: m/s

Note: Value should be greater than 0.

Formulas to find Touchdown Velocity

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.

Symbol: C_D,0

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Zero-Lift Drag Coefficient

Ground Effect Factor

Ground effect factor is the ratio of the induced drag in-ground-effect to the induced drag out-of-ground-effect.

Symbol: ϕ

Measurement: NAUnit: Unitless

Note: Value should be less than 1.

Formulas to find Ground Effect Factor

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.

Symbol: C_L

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Lift Coefficient

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.

Symbol: e

Measurement: NAUnit: Unitless

Note: Value should be less than 1.

Formulas to find Oswald Efficiency Factor

Aspect Ratio of a Wing

The Aspect Ratio of a Wing is defined as the ratio of its span to its mean chord.

Symbol: AR

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Aspect Ratio of a Wing

Coefficient of Rolling Friction

Coefficient of Rolling Friction is the ratio of the force of rolling friction to the total weight of the object.

Symbol: μ_r

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Coefficient of Rolling Friction

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

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

Other formulas in Landing category

Go Landing Ground Run

Sg l = (F normal \cdot V TD) + (\frac{W aircraft}{2 \cdot [g]}) \cdot \int (\frac{2 \cdot V ∞}{V TR + D + μ ref \cdot (W aircraft - L)}, x, 0, V TD)

Go Stall velocity for given touchdown velocity

V stall = \frac{V T}{1.3}

How to Evaluate Landing ground roll distance?

Landing ground roll distance evaluator uses Landing Roll = 1.69*(Weight^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-(0.5*Freestream Density*((0.7*Touchdown Velocity)^2)*Reference Area*Lift Coefficient))))) to evaluate the Landing Roll, Landing Ground Roll Distance is a measure of the distance an aircraft travels from touchdown to complete stop, influenced by factors such as aircraft weight, air density, wing design, and friction, allowing pilots and designers to estimate the required runway length for safe landings. Landing Roll is denoted by s_L symbol.

How to evaluate Landing ground roll distance using this online evaluator? To use this online evaluator for Landing ground roll distance, enter Weight (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.

FAQs on Landing ground roll distance

What is the formula to find Landing ground roll distance?

The formula of Landing ground roll distance is expressed as Landing Roll = 1.69*(Weight^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-(0.5*Freestream Density*((0.7*Touchdown Velocity)^2)*Reference Area*Lift Coefficient))))). Here is an example- 1.448838 = 1.69*(60.5^2)*(1/([g]*1.225*5.08*0.000885))*(1/((0.5*1.225*((0.7*193)^2)*5.08*(0.0161+(0.4*(5.5^2)/(pi*0.5*4))))+(0.1*(60.5-(0.5*1.225*((0.7*193)^2)*5.08*5.5))))).

How to calculate Landing ground roll distance?

With Weight (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) we can find Landing ground roll distance using the formula - Landing Roll = 1.69*(Weight^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-(0.5*Freestream Density*((0.7*Touchdown Velocity)^2)*Reference Area*Lift Coefficient))))). This formula also uses Gravitational acceleration on Earth, Archimedes' constant .

Can the Landing ground roll distance be negative?

No, the Landing ground roll distance, measured in Length cannot be negative.

Which unit is used to measure Landing ground roll distance?

Landing ground roll distance is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Landing ground roll distance can be measured.

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Landing ground roll distance Formula

Landing ground roll distance Example

Landing ground roll distance Solution

Landing ground roll distance Formula Elements

Other formulas in Landing category

How to Evaluate Landing ground roll distance?

FAQs on Landing ground roll distance

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