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Propeller Efficiency for given Endurance of Propeller-Driven Airplane Formula

GoPropeller Efficiency for given Range of Propeller-Driven Airplane Formula

GoPropeller Efficiency for given Range and Lift-to-Drag Ratio of Propeller-Driven Airplane Formula

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

η = \frac{E}{(\frac{1}{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}}))}

η - Propeller Efficiency?E - Endurance of Aircraft?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?

Propeller Efficiency for given Endurance of Propeller-Driven Airplane Example

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

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

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

0.9256 = \frac{452.0581}{(\frac{1}{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}}))}

0.9256 = \frac{452.0581s}{(\frac{1}{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}}))}

0.9256 = \frac{452.0581}{(\frac{1}{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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Home » Physics » Aerospace » Aircraft Mechanics » Propeller Efficiency for given Endurance of Propeller-Driven Airplane

Propeller Efficiency for given Endurance of Propeller-Driven Airplane Solution

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

FIRST Step Consider the formula

η = \frac{E}{(\frac{1}{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

∴

η = \frac{452.0581s}{(\frac{1}{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

∴

η = \frac{452.0581s}{(\frac{1}{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

∴

η = \frac{452.0581}{(\frac{1}{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

∴

η = 0.925603098932348

LAST Step Rounding Answer

∴

η = 0.9256

Propeller Efficiency for given Endurance of Propeller-Driven Airplane Formula Elements

Variables

Functions

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.

Endurance of Aircraft

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

Symbol: E

Measurement: TimeUnit: s

Note: Value should be greater than 0.

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.

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.

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.

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.

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.

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.

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.

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)

Credits

Created by Vinay Mishra

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

Vinay Mishra has created this Formula and 300+ more formulas!

Verified by Maiarutselvan V

PSG College of Technology (PSGCT), Coimbatore

Maiarutselvan V has verified this Formula and 300+ more formulas!

Other Formulas to find Propeller Efficiency

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})}

Go Propeller Efficiency for given Range and Lift-to-Drag Ratio of Propeller-Driven Airplane

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

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 Specific Fuel Consumption for given Range of Propeller-Driven Airplane

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

How to Evaluate Propeller Efficiency for given Endurance of Propeller-Driven Airplane?

Propeller Efficiency for given Endurance of Propeller-Driven Airplane evaluator uses Propeller Efficiency = Endurance of Aircraft/((1/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 Propeller Efficiency, Propeller Efficiency for given Endurance of Propeller-Driven Airplane is a measure of the effectiveness of a propeller in converting engine power into useful thrust, taking into account the endurance range of the airplane, specific fuel consumption, lift and drag coefficients, free stream density, reference area, and gross weight. Propeller Efficiency is denoted by η symbol.

How to evaluate Propeller Efficiency for given Endurance of Propeller-Driven Airplane using this online evaluator? To use this online evaluator for Propeller Efficiency for given Endurance of Propeller-Driven Airplane, enter Endurance of Aircraft (E), 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 Propeller Efficiency for given Endurance of Propeller-Driven Airplane

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

The formula of Propeller Efficiency for given Endurance of Propeller-Driven Airplane is expressed as Propeller Efficiency = Endurance of Aircraft/((1/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- 0.925484 = 452.0581/((1/0.000166666666666667)*((5^1.5)/2)*(sqrt(2*1.225*5.11))*(((1/3000)^(1/2))-((1/5000)^(1/2)))).

How to calculate Propeller Efficiency for given Endurance of Propeller-Driven Airplane?

With Endurance of Aircraft (E), 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 Propeller Efficiency for given Endurance of Propeller-Driven Airplane using the formula - Propeller Efficiency = Endurance of Aircraft/((1/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 (sqrt) function(s).

What are the other ways to Calculate Propeller Efficiency?

Here are the different ways to Calculate Propeller Efficiency-

Propeller Efficiency=Range of Propeller Aircraft*Specific Fuel Consumption*Drag Coefficient/(Lift Coefficient*ln(Gross Weight/Weight without Fuel))
Propeller Efficiency=Range of Propeller Aircraft*Specific Fuel Consumption/(Lift-to-Drag Ratio*(ln(Gross Weight/Weight without Fuel)))
Propeller Efficiency=Available Power/Brake Power

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Propeller Efficiency for given Endurance of Propeller-Driven Airplane Formula

​GoPropeller Efficiency for given Range of Propeller-Driven Airplane Formula

​GoPropeller Efficiency for given Range and Lift-to-Drag Ratio of Propeller-Driven Airplane Formula

Propeller Efficiency for given Endurance of Propeller-Driven Airplane Example

Propeller Efficiency for given Endurance of Propeller-Driven Airplane Solution

Propeller Efficiency for given Endurance of Propeller-Driven Airplane Formula Elements

Credits

Other Formulas to find Propeller Efficiency

Other formulas in Propeller Driven Airplane category

How to Evaluate Propeller Efficiency for given Endurance of Propeller-Driven Airplane?

FAQs on Propeller Efficiency for given Endurance of Propeller-Driven Airplane

Variable Name

GoPropeller Efficiency for given Range of Propeller-Driven Airplane Formula

GoPropeller Efficiency for given Range and Lift-to-Drag Ratio of Propeller-Driven Airplane Formula