Specific Fuel Consumption for given Endurance of Propeller-Driven Airplane Calculator

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Aircraft Performance

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Introduction and Governing Equations

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Propeller-Driven Airplane

Jet Airplane

✖Propeller Efficiency is defined as power produced (propeller power) divided by power applied (engine power).ⓘ Propeller Efficiency [η]			+10% -10%
✖Endurance of aircraft is the maximum length of time that an aircraft can spend in cruising flight.ⓘ Endurance of Aircraft [E]			+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%
✖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.ⓘ Drag Coefficient [C_D]			+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%
✖Weight without fuel is the total weight of the airplane without fuel.ⓘ Weight without fuel [W₁]			+10% -10%
✖The Gross Weight of the airplane is the weight with full fuel and payload.ⓘ Gross Weight [W₀]			+10% -10%

✖Specific Fuel Consumption is a characteristic of the engine and defined as the weight of fuel consumed per unit power per unit time.ⓘ Specific Fuel Consumption for given Endurance of Propeller-Driven Airplane [c]

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Formula

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Specific Fuel Consumption for given Endurance of Propeller-Driven Airplane

Formula

`"c" = "η"/"E"*"C"_{"L"}^1.5/"C"_{"D"}*sqrt(2*"ρ"_{"∞"}*"S")*((1/"W"_{"1"})^(1/2)-(1/"W"_{"0"})^(1/2))`

Example

`"0.599996kg/h/W"="0.93"/"452.873s"*("5")^1.5/"2"*sqrt(2*"1.225kg/m³"*"5.08m²")*((1/"3000kg")^(1/2)-(1/"5000kg")^(1/2))`

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Specific Fuel Consumption for given Endurance of Propeller-Driven Airplane Solution

STEP 0: Pre-Calculation Summary

Formula Used

Specific Fuel Consumption = Propeller Efficiency/Endurance of Aircraft*Lift Coefficient^1.5/Drag Coefficient*sqrt(2*Freestream density*Reference Area)*((1/Weight without fuel)^(1/2)-(1/Gross Weight)^(1/2))
c = η/E*C_L^1.5/C_D*sqrt(2*ρ_∞*S)*((1/W₁)^(1/2)-(1/W₀)^(1/2))
This formula uses 1 Functions, 9 Variables

Functions Used

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., sqrt(Number)

Variables Used

Specific Fuel Consumption - (Measured in Kilogram per Second per Watt) - Specific Fuel Consumption is a characteristic of the engine and defined as the weight of fuel consumed per unit power per unit time.
Propeller Efficiency - Propeller Efficiency is defined as power produced (propeller power) divided by power applied (engine power).
Endurance of Aircraft - (Measured in Second) - Endurance of aircraft is the maximum length of time that an aircraft can spend in cruising flight.
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.
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.
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.
Weight without fuel - (Measured in Kilogram) - Weight without fuel is the total weight of the airplane without fuel.
Gross Weight - (Measured in Kilogram) - The Gross Weight of the airplane is the weight with full fuel and payload.

STEP 1: Convert Input(s) to Base Unit

Propeller Efficiency: 0.93 --> No Conversion Required
Endurance of Aircraft: 452.873 Second --> 452.873 Second No Conversion Required
Lift Coefficient: 5 --> No Conversion Required
Drag Coefficient: 2 --> 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
Weight without fuel: 3000 Kilogram --> 3000 Kilogram No Conversion Required
Gross Weight: 5000 Kilogram --> 5000 Kilogram No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

c = η/E*C_L^1.5/C_D*sqrt(2*ρ_∞*S)*((1/W₁)^(1/2)-(1/W₀)^(1/2)) --> 0.93/452.873*5^1.5/2*sqrt(2*1.225*5.08)*((1/3000)^(1/2)-(1/5000)^(1/2))

Evaluating ... ...

c = 0.000166665661562072

STEP 3: Convert Result to Output's Unit

0.000166665661562072 Kilogram per Second per Watt -->0.599996381623459 Kilogram per Hour per Watt (Check conversion here)

FINAL ANSWER

0.599996381623459 ≈ 0.599996 Kilogram per Hour per Watt <-- Specific Fuel Consumption

(Calculation completed in 00.004 seconds)

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Home » Physics » Aircraft Mechanics » Aircraft Performance » Range and Endurance » Propeller-Driven Airplane » Specific Fuel Consumption for given Endurance of Propeller-Driven Airplane

Credits

Created by Vinay Mishra

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

Vinay Mishra has created this Calculator and 300+ more calculators!

Verified by Maiarutselvan V

PSG College of Technology (PSGCT), Coimbatore

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< 21 Propeller-Driven Airplane Calculators

Propeller Efficiency for given Endurance of Propeller-Driven Airplane

Go 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))))

Endurance of Propeller-Driven Airplane

Go Endurance of 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))

Specific Fuel Consumption for given Endurance of Propeller-Driven Airplane

Go Specific Fuel Consumption = Propeller Efficiency/Endurance of Aircraft*Lift Coefficient^1.5/Drag Coefficient*sqrt(2*Freestream density*Reference Area)*((1/Weight without fuel)^(1/2)-(1/Gross Weight)^(1/2))

Propeller Efficiency given Preliminary Endurance for Prop-Driven Aircraft

Go Propeller Efficiency = (Preliminary Endurance of Aircraft*Velocity for Maximum Endurance*Specific Fuel Consumption)/(Lift to Drag Ratio at Maximum Endurance*ln(Weight at Start of Loiter Phase/Weight at End of Loiter Phase))

Lift to Drag for Maximum Endurance given Preliminary Endurance for Prop-Driven Aircraft

Go Lift to Drag Ratio at Maximum Endurance = (Endurance of Aircraft*Velocity for Maximum Endurance*Specific Fuel Consumption)/(Propeller Efficiency*ln(Weight at Start of Loiter Phase/Weight at End of Loiter Phase))

Specific Fuel Consumption given Preliminary Endurance for Prop-Driven Aircraft

Go Specific Fuel Consumption = (Lift to Drag Ratio at Maximum Endurance*Propeller Efficiency*ln(Weight at Start of Loiter Phase/Weight at End of Loiter Phase))/(Endurance of Aircraft*Velocity for Maximum Endurance)

Specific Fuel Consumption for given Range of Propeller-Driven Airplane

Go Specific Fuel Consumption = (Propeller Efficiency/Range of aircraft)*(Lift Coefficient/Drag Coefficient)*(ln(Gross Weight/Weight without fuel))

Range of Propeller-Driven Airplane

Go Range of aircraft = (Propeller Efficiency/Specific Fuel Consumption)*(Lift Coefficient/Drag Coefficient)*(ln(Gross Weight/Weight without fuel))

Propeller Efficiency for given Range of Propeller-Driven Airplane

Go Propeller Efficiency = Range of aircraft*Specific Fuel Consumption*Drag Coefficient/(Lift Coefficient*ln(Gross Weight/Weight without fuel))

Maximum Lift to Drag Ratio given Range for Prop-driven Aircraft

Go Maximum Lift to Drag Ratio = (Range of aircraft*Specific Fuel Consumption)/(Propeller Efficiency*ln(Weight at Start of Cruise Phase/Weight at End of Cruise Phase))

Propeller Efficiency given Range for Prop-Driven Aircraft

Go Propeller Efficiency = (Range of aircraft*Specific Fuel Consumption)/(Maximum Lift to Drag Ratio*ln(Weight at Start of Cruise Phase/Weight at End of Cruise Phase))

Specific Fuel Consumption given Range for Prop-Driven Aircraft

Go Specific Fuel Consumption = (Propeller Efficiency*Maximum Lift to Drag Ratio*ln(Weight at Start of Cruise Phase/Weight at End of Cruise Phase))/Range of aircraft

Specific Fuel Consumption for given Range and lift-to-drag ratio of Propeller-Driven Airplane

Go Specific Fuel Consumption = (Propeller Efficiency/Range of aircraft)*(Lift-to-drag ratio)*(ln(Gross Weight/Weight without fuel))

Range of Propeller-Driven Airplane for given lift-to-drag ratio

Go Range of aircraft = (Propeller Efficiency/Specific Fuel Consumption)*(Lift-to-drag ratio)*(ln(Gross Weight/Weight without fuel))

Propeller Efficiency for given Range and lift-to-drag ratio of Propeller-Driven Airplane

Go Propeller Efficiency = Range of aircraft*Specific Fuel Consumption/(Lift-to-drag ratio*(ln(Gross Weight/Weight without fuel)))

Cruise Weight Fraction for Prop-Driven Aircraft

Go Cruise Weight Fraction = exp((Range of aircraft*(-1)*Specific Fuel Consumption)/(Maximum Lift to Drag Ratio*Propeller Efficiency))

Propeller efficiency for reciprocating engine-propeller combination

Go Propeller Efficiency = Available Power/Brake Power

Shaft brake power for reciprocating engine-propeller combination

Go Brake Power = Available Power/Propeller Efficiency

Power available for reciprocating engine-propeller combination

Go Available Power = Propeller Efficiency*Brake Power

Lift to Drag Ratio for Maximum Endurance given Max Lift to Drag Ratio for Prop-driven Aircraft

Go Lift to Drag Ratio at Maximum Endurance = 0.866*Maximum Lift to Drag Ratio

Maximum Lift to Drag Ratio given Lift to Drag Ratio for Max Endurance of Prop-Driven Aircraft

Go Maximum Lift to Drag Ratio = Lift to Drag Ratio at Maximum Endurance/0.866

Specific Fuel Consumption for given Endurance of Propeller-Driven Airplane Formula

What is the best endurance speed?

The speed which gives the minimum drag for given aircraft weight and altitude is called best endurance speed. Flying at higher speeds than the best endurance speed increases the drag and the fuel flow, and therefore reduces the endurance.

How to Calculate Specific Fuel Consumption for given Endurance of Propeller-Driven Airplane?

Specific Fuel Consumption for given Endurance of Propeller-Driven Airplane calculator uses Specific Fuel Consumption = Propeller Efficiency/Endurance of Aircraft*Lift Coefficient^1.5/Drag Coefficient*sqrt(2*Freestream density*Reference Area)*((1/Weight without fuel)^(1/2)-(1/Gross Weight)^(1/2)) to calculate the Specific Fuel Consumption, The Specific Fuel Consumption for given Endurance of Propeller-Driven Airplane can be obtained from the Breguet endurance formula and is a function of the altitude of aircraft. Specific Fuel Consumption is denoted by c symbol.

How to calculate Specific Fuel Consumption for given Endurance of Propeller-Driven Airplane using this online calculator? To use this online calculator for Specific Fuel Consumption for given Endurance of Propeller-Driven Airplane, enter Propeller Efficiency (η), Endurance of Aircraft (E), 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. Here is how the Specific Fuel Consumption for given Endurance of Propeller-Driven Airplane calculation can be explained with given input values -> 1461.243 = 0.93/452.873*5^1.5/2*sqrt(2*1.225*5.08)*((1/3000)^(1/2)-(1/5000)^(1/2)).

FAQ

What is Specific Fuel Consumption for given Endurance of Propeller-Driven Airplane?

The Specific Fuel Consumption for given Endurance of Propeller-Driven Airplane can be obtained from the Breguet endurance formula and is a function of the altitude of aircraft and is represented as c = η/E*C_L^1.5/C_D*sqrt(2*ρ_∞*S)*((1/W₁)^(1/2)-(1/W₀)^(1/2)) or Specific Fuel Consumption = Propeller Efficiency/Endurance of Aircraft*Lift Coefficient^1.5/Drag Coefficient*sqrt(2*Freestream density*Reference Area)*((1/Weight without fuel)^(1/2)-(1/Gross Weight)^(1/2)). Propeller Efficiency is defined as power produced (propeller power) divided by power applied (engine power), Endurance of aircraft is the maximum length of time that an aircraft can spend in cruising flight, 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, 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, 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, Weight without fuel is the total weight of the airplane without fuel & The Gross Weight of the airplane is the weight with full fuel and payload.

How to calculate Specific Fuel Consumption for given Endurance of Propeller-Driven Airplane?

The Specific Fuel Consumption for given Endurance of Propeller-Driven Airplane can be obtained from the Breguet endurance formula and is a function of the altitude of aircraft is calculated using Specific Fuel Consumption = Propeller Efficiency/Endurance of Aircraft*Lift Coefficient^1.5/Drag Coefficient*sqrt(2*Freestream density*Reference Area)*((1/Weight without fuel)^(1/2)-(1/Gross Weight)^(1/2)). To calculate Specific Fuel Consumption for given Endurance of Propeller-Driven Airplane, you need Propeller Efficiency (η), Endurance of Aircraft (E), Lift Coefficient (C_L), Drag Coefficient (C_D), Freestream density (ρ_∞), Reference Area (S), Weight without fuel (W₁) & Gross Weight (W₀). With our tool, you need to enter the respective value for Propeller Efficiency, Endurance of Aircraft, Lift Coefficient, Drag Coefficient, Freestream density, Reference Area, Weight without fuel & Gross Weight and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Specific Fuel Consumption?

In this formula, Specific Fuel Consumption uses Propeller Efficiency, Endurance of Aircraft, Lift Coefficient, Drag Coefficient, Freestream density, Reference Area, Weight without fuel & Gross Weight. We can use 4 other way(s) to calculate the same, which is/are as follows -

Specific Fuel Consumption = (Propeller Efficiency/Range of aircraft)*(Lift Coefficient/Drag Coefficient)*(ln(Gross Weight/Weight without fuel))
Specific Fuel Consumption = (Propeller Efficiency/Range of aircraft)*(Lift-to-drag ratio)*(ln(Gross Weight/Weight without fuel))
Specific Fuel Consumption = (Propeller Efficiency*Maximum Lift to Drag Ratio*ln(Weight at Start of Cruise Phase/Weight at End of Cruise Phase))/Range of aircraft
Specific Fuel Consumption = (Lift to Drag Ratio at Maximum Endurance*Propeller Efficiency*ln(Weight at Start of Loiter Phase/Weight at End of Loiter Phase))/(Endurance of Aircraft*Velocity for Maximum Endurance)

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