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Endurance of Propeller-Driven Airplane Formula

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Endurance of Propeller Aircraft is the maximum length of time that an aircraft can spend in cruising flight. Check FAQs

E prop = \frac{η}{c} \cdot \frac{{C L}^{1.5}}{C D} \cdot \sqrt{2 \cdot ρ ∞ \cdot S} \cdot ({(\frac{1}{W 1})}^{\frac{1}{2}} - {(\frac{1}{W 0})}^{\frac{1}{2}})

E_prop - Endurance of Propeller Aircraft?η - Propeller Efficiency?c - Specific Fuel Consumption?C_L - Lift Coefficient?C_D - Drag Coefficient?ρ_∞ - Freestream Density?S - Reference Area?W₁ - Weight without Fuel?W₀ - Gross Weight?

Endurance of Propeller-Driven Airplane Example

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Here is how the Endurance of Propeller-Driven Airplane equation looks like with Values.

Here is how the Endurance of Propeller-Driven Airplane equation looks like with Units.

Here is how the Endurance of Propeller-Driven Airplane equation looks like.

454.2055 = \frac{0.93}{0.6} \cdot \frac{5^{1.5}}{2} \cdot \sqrt{2 \cdot 1.225 \cdot 5.11} \cdot ({(\frac{1}{3000})}^{\frac{1}{2}} - {(\frac{1}{5000})}^{\frac{1}{2}})

454.2055s = \frac{0.93}{0.6kg/h/W} \cdot \frac{5^{1.5}}{2} \cdot \sqrt{2 \cdot 1.225kg/m³ \cdot 5.11m²} \cdot ({(\frac{1}{3000kg})}^{\frac{1}{2}} - {(\frac{1}{5000kg})}^{\frac{1}{2}})

454.2055 = \frac{0.93}{0.6} \cdot \frac{5^{1.5}}{2} \cdot \sqrt{2 \cdot 1.225 \cdot 5.11} \cdot ({(\frac{1}{3000})}^{\frac{1}{2}} - {(\frac{1}{5000})}^{\frac{1}{2}})

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Endurance of Propeller-Driven Airplane Solution

Follow our step by step solution on how to calculate Endurance of Propeller-Driven Airplane?

FIRST Step Consider the formula

E prop = \frac{η}{c} \cdot \frac{{C L}^{1.5}}{C D} \cdot \sqrt{2 \cdot ρ ∞ \cdot S} \cdot ({(\frac{1}{W 1})}^{\frac{1}{2}} - {(\frac{1}{W 0})}^{\frac{1}{2}})

Next Step Substitute values of Variables

∴

E prop = \frac{0.93}{0.6kg/h/W} \cdot \frac{5^{1.5}}{2} \cdot \sqrt{2 \cdot 1.225kg/m³ \cdot 5.11m²} \cdot ({(\frac{1}{3000kg})}^{\frac{1}{2}} - {(\frac{1}{5000kg})}^{\frac{1}{2}})

Next Step Convert Units

∴

E prop = \frac{0.93}{0.0002kg/s/W} \cdot \frac{5^{1.5}}{2} \cdot \sqrt{2 \cdot 1.225kg/m³ \cdot 5.11m²} \cdot ({(\frac{1}{3000kg})}^{\frac{1}{2}} - {(\frac{1}{5000kg})}^{\frac{1}{2}})

Next Step Prepare to Evaluate

∴

E prop = \frac{0.93}{0.0002} \cdot \frac{5^{1.5}}{2} \cdot \sqrt{2 \cdot 1.225 \cdot 5.11} \cdot ({(\frac{1}{3000})}^{\frac{1}{2}} - {(\frac{1}{5000})}^{\frac{1}{2}})

Next Step Evaluate

∴

E prop = 454.205515825231s

LAST Step Rounding Answer

∴

E prop = 454.2055s

Endurance of Propeller-Driven Airplane Formula Elements

Variables

Functions

Endurance of Propeller Aircraft

Endurance of Propeller Aircraft is the maximum length of time that an aircraft can spend in cruising flight.

Symbol: E_prop

Measurement: TimeUnit: s

Note: Value should be greater than 0.

Formulas to find Endurance of Propeller Aircraft

Propeller Efficiency

Propeller Efficiency is defined as power produced (propeller power) divided by power applied (engine power).

Symbol: η

Measurement: NAUnit: Unitless

Note: Value should be less than 1.

Formulas to find Propeller Efficiency

Specific Fuel Consumption

Specific Fuel Consumption is a characteristic of the engine and defined as the weight of fuel consumed per unit power per unit time.

Symbol: c

Measurement: Specific Fuel ConsumptionUnit: kg/h/W

Note: Value should be greater than 0.

Formulas to find Specific Fuel Consumption

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

Drag Coefficient

Drag Coefficient is a dimensionless quantity that is used to quantify the drag or resistance of an object in a fluid environment, such as air or water.

Symbol: C_D

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Drag Coefficient

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

Weight without Fuel

Weight without Fuel is the total weight of the airplane without fuel.

Symbol: W₁

Measurement: WeightUnit: kg

Note: Value should be greater than 0.

Formulas to find Weight without Fuel

Gross Weight

The Gross Weight of the airplane is the weight with full fuel and payload.

Symbol: W₀

Measurement: WeightUnit: kg

Note: Value should be greater than 0.

Formulas to find Gross Weight

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

Other formulas in Propeller Driven Airplane category

Go Range of Propeller-Driven Airplane

R prop = (\frac{η}{c}) \cdot (\frac{C L}{C D}) \cdot (\ln (\frac{W 0}{W 1}))

Go Propeller Efficiency for given Range of Propeller-Driven Airplane

η = R prop \cdot c \cdot \frac{C D}{C L \cdot \ln (\frac{W 0}{W 1})}

How to Evaluate Endurance of Propeller-Driven Airplane?

Endurance of Propeller-Driven Airplane evaluator uses Endurance of Propeller Aircraft = Propeller Efficiency/Specific Fuel Consumption*(Lift Coefficient^1.5)/Drag Coefficient*sqrt(2*Freestream Density*Reference Area)*((1/Weight without Fuel)^(1/2)-(1/Gross Weight)^(1/2)) to evaluate the Endurance of Propeller Aircraft, Endurance of Propeller-Driven Airplane is a measure of the time an aircraft can stay aloft, which depends on factors such as propeller efficiency, specific fuel consumption, lift coefficient, drag coefficient, and aircraft weight. Endurance of Propeller Aircraft is denoted by E_prop symbol.

How to evaluate Endurance of Propeller-Driven Airplane using this online evaluator? To use this online evaluator for Endurance of Propeller-Driven Airplane, enter Propeller Efficiency (η), Specific Fuel Consumption (c), Lift Coefficient (C_L), Drag Coefficient (C_D), Freestream Density (ρ_∞), Reference Area (S), Weight without Fuel (W₁) & Gross Weight (W₀) and hit the calculate button.

FAQs on Endurance of Propeller-Driven Airplane

What is the formula to find Endurance of Propeller-Driven Airplane?

The formula of Endurance of Propeller-Driven Airplane is expressed as Endurance of Propeller Aircraft = Propeller Efficiency/Specific Fuel Consumption*(Lift Coefficient^1.5)/Drag Coefficient*sqrt(2*Freestream Density*Reference Area)*((1/Weight without Fuel)^(1/2)-(1/Gross Weight)^(1/2)). Here is an example- 454.2055 = 0.93/0.000166666666666667*(5^1.5)/2*sqrt(2*1.225*5.11)*((1/3000)^(1/2)-(1/5000)^(1/2)).

How to calculate Endurance of Propeller-Driven Airplane?

With Propeller Efficiency (η), Specific Fuel Consumption (c), Lift Coefficient (C_L), Drag Coefficient (C_D), Freestream Density (ρ_∞), Reference Area (S), Weight without Fuel (W₁) & Gross Weight (W₀) we can find Endurance of Propeller-Driven Airplane using the formula - Endurance of Propeller Aircraft = Propeller Efficiency/Specific Fuel Consumption*(Lift Coefficient^1.5)/Drag Coefficient*sqrt(2*Freestream Density*Reference Area)*((1/Weight without Fuel)^(1/2)-(1/Gross Weight)^(1/2)). This formula also uses Square Root Function function(s).

Can the Endurance of Propeller-Driven Airplane be negative?

No, the Endurance of Propeller-Driven Airplane, measured in Time cannot be negative.

Which unit is used to measure Endurance of Propeller-Driven Airplane?

Endurance of Propeller-Driven Airplane is usually measured using the Second[s] for Time. Millisecond[s], Microsecond[s], Nanosecond[s] are the few other units in which Endurance of Propeller-Driven Airplane can be measured.

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Endurance of Propeller-Driven Airplane Formula

Endurance of Propeller-Driven Airplane Example

Endurance of Propeller-Driven Airplane Solution

Endurance of Propeller-Driven Airplane Formula Elements

Other formulas in Propeller Driven Airplane category

How to Evaluate Endurance of Propeller-Driven Airplane?

FAQs on Endurance of Propeller-Driven Airplane

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