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Landing Ground Run Formula

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Landing Ground Run typically refers to the distance a aircraft requires to come to a complete stop after landing on a runway. Check FAQs

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)

Sg_l - Landing Ground Run?F_normal - Normal Force?V_TD - Velocity at Touchdown Point?W_aircraft - Weight Of Aircraft?V_∞ - Velocity of Aircraft?V_TR - Reverse Thrust?D - Drag Force?μ_ref - Reference Of Rolling Resistance Coefficient?L - Lift Force?[g] - Gravitational acceleration on Earth?

Landing Ground Run Example

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

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

Here is how the Landing Ground Run equation looks like.

2042.1746 = (0.3 \cdot 23) + (\frac{2000}{2 \cdot 9.8066}) \cdot \int (\frac{2 \cdot 292}{600 + 65 + 0.004 \cdot (2000 - 7)}, x, 0, 23)

2042.1746m = (0.3N \cdot 23m/s) + (\frac{2000kg}{2 \cdot 9.8066m/s²}) \cdot \int (\frac{2 \cdot 292m/s}{600N + 65N + 0.004 \cdot (2000kg - 7N)}, x, 0, 23m/s)

2042.1746 = (0.3 \cdot 23) + (\frac{2000}{2 \cdot 9.8066}) \cdot \int (\frac{2 \cdot 292}{600 + 65 + 0.004 \cdot (2000 - 7)}, x, 0, 23)

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Landing Ground Run Solution

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

FIRST Step Consider the formula

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)

Next Step Substitute values of Variables

∴

Sg l = (0.3N \cdot 23m/s) + (\frac{2000kg}{2 \cdot [g]}) \cdot \int (\frac{2 \cdot 292m/s}{600N + 65N + 0.004 \cdot (2000kg - 7N)}, x, 0, 23m/s)

Next Step Substitute values of Constants

∴

Sg l = (0.3N \cdot 23m/s) + (\frac{2000kg}{2 \cdot 9.8066m/s²}) \cdot \int (\frac{2 \cdot 292m/s}{600N + 65N + 0.004 \cdot (2000kg - 7N)}, x, 0, 23m/s)

Next Step Prepare to Evaluate

∴

Sg l = (0.3 \cdot 23) + (\frac{2000}{2 \cdot 9.8066}) \cdot \int (\frac{2 \cdot 292}{600 + 65 + 0.004 \cdot (2000 - 7)}, x, 0, 23)

Next Step Evaluate

∴

Sg l = 2042.17459875292m

LAST Step Rounding Answer

∴

Sg l = 2042.1746m

Landing Ground Run Formula Elements

Variables

Constants

Functions

Landing Ground Run

Landing Ground Run typically refers to the distance a aircraft requires to come to a complete stop after landing on a runway.

Symbol: Sg_l

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Landing Ground Run

Normal Force

Normal Force is the reaction force exerted by the ground on the aircraft through its landing gear, counteracting the aircraft's weight.

Symbol: F_normal

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Normal Force

Velocity at Touchdown Point

Velocity at Touchdown Point represents the touchdown speed of the aircraft.

Symbol: V_TD

Measurement: SpeedUnit: m/s

Note: Value should be greater than 0.

Formulas to find Velocity at Touchdown Point

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

Reverse Thrust

Reverse thrust is a mechanism used by jet engines, particularly on aircraft, to help slow down the aircraft after landing.

Symbol: V_TR

Measurement: ForceUnit: N

Note: Value can be positive or negative.

Formulas to find Reverse Thrust

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

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 Landing category

Go Stall velocity for given touchdown velocity

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

Go Touchdown velocity for given stall velocity

V T = 1.3 \cdot V stall

How to Evaluate Landing Ground Run?

Landing Ground Run evaluator uses 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) to evaluate the Landing Ground Run, Landing Ground Run is a measure of the distance an aircraft travels on the ground from touchdown to complete stop, influenced by factors such as the aircraft's weight, aerodynamics, and rolling resistance, as well as the thrust reversal and drag forces acting upon it. Landing Ground Run is denoted by Sg_l symbol.

How to evaluate Landing Ground Run using this online evaluator? To use this online evaluator for Landing Ground Run, enter Normal Force (F_normal), Velocity at Touchdown Point (V_TD), Weight Of Aircraft (W_aircraft), Velocity of Aircraft (V_∞), Reverse Thrust (V_TR), Drag Force (D), Reference Of Rolling Resistance Coefficient (μ_ref) & Lift Force (L) and hit the calculate button.

FAQs on Landing Ground Run

What is the formula to find Landing Ground Run?

The formula of Landing Ground Run is expressed as 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). Here is an example- 2042.175 = (0.3*23)+(2000/(2*[g]))*int((2*292)/(600+65+0.004*(2000-7)),x,0,23).

How to calculate Landing Ground Run?

With Normal Force (F_normal), Velocity at Touchdown Point (V_TD), Weight Of Aircraft (W_aircraft), Velocity of Aircraft (V_∞), Reverse Thrust (V_TR), Drag Force (D), Reference Of Rolling Resistance Coefficient (μ_ref) & Lift Force (L) we can find Landing Ground Run using the formula - 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). This formula also uses Gravitational acceleration on Earth constant(s) and Definite Integral (int) function(s).

Can the Landing Ground Run be negative?

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

Which unit is used to measure Landing Ground Run?

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

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Landing Ground Run Formula

Landing Ground Run Example

Landing Ground Run Solution

Landing Ground Run Formula Elements

Other formulas in Landing category

How to Evaluate Landing Ground Run?

FAQs on Landing Ground Run

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