Breguet Endurance Equation Calculator

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Aircraft Performance

Aircraft Design

Introduction and Governing Equations

Static Stability and Control

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Propeller-Driven Airplane

✖Thrust-specific fuel consumption (TSFC) is the fuel efficiency of an engine design with respect to thrust output.ⓘ Thrust-Specific Fuel Consumption [c_t]			+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%
✖The Gross Weight of the airplane is the weight with full fuel and payload.ⓘ Gross Weight [W₀]			+10% -10%
✖Weight without fuel is the total weight of the airplane without fuel.ⓘ Weight without fuel [W₁]			+10% -10%

✖Endurance of aircraft is the maximum length of time that an aircraft can spend in cruising flight.ⓘ Breguet Endurance Equation [E]

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Formula

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Breguet Endurance Equation

Formula

`"E" = (1/"c"_{"t"})*("C"_{"L"}/"C"_{"D"})*ln("W"_{"0"}/"W"_{"1"})`

Example

`"452.0581s"=(1/"10.17kg/h/N")*("5"/"2")*ln("5000kg"/"3000kg")`

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Breguet Endurance Equation Solution

STEP 0: Pre-Calculation Summary

Formula Used

Endurance of Aircraft = (1/Thrust-Specific Fuel Consumption)*(Lift Coefficient/Drag Coefficient)*ln(Gross Weight/Weight without fuel)
E = (1/c_t)*(C_L/C_D)*ln(W₀/W₁)
This formula uses 1 Functions, 6 Variables

Functions Used

ln - The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function., ln(Number)

Variables Used

Endurance of Aircraft - (Measured in Second) - Endurance of aircraft is the maximum length of time that an aircraft can spend in cruising flight.
Thrust-Specific Fuel Consumption - (Measured in Kilogram per Second per Newton) - Thrust-specific fuel consumption (TSFC) is the fuel efficiency of an engine design with respect to thrust output.
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.
Gross Weight - (Measured in Kilogram) - The Gross Weight of the airplane is the weight with full fuel and payload.
Weight without fuel - (Measured in Kilogram) - Weight without fuel is the total weight of the airplane without fuel.

STEP 1: Convert Input(s) to Base Unit

Thrust-Specific Fuel Consumption: 10.17 Kilogram per Hour per Newton --> 0.002825 Kilogram per Second per Newton (Check conversion here)
Lift Coefficient: 5 --> No Conversion Required
Drag Coefficient: 2 --> No Conversion Required
Gross Weight: 5000 Kilogram --> 5000 Kilogram No Conversion Required
Weight without fuel: 3000 Kilogram --> 3000 Kilogram No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

E = (1/c_t)*(C_L/C_D)*ln(W₀/W₁) --> (1/0.002825)*(5/2)*ln(5000/3000)

Evaluating ... ...

E = 452.058074129195

STEP 3: Convert Result to Output's Unit

452.058074129195 Second --> No Conversion Required

FINAL ANSWER

452.058074129195 ≈ 452.0581 Second <-- Endurance of Aircraft

(Calculation completed in 00.004 seconds)

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Home » Physics » Aircraft Mechanics » Aircraft Performance » Range and Endurance » Jet Airplane » Breguet Endurance Equation

Credits

Created by Sastika Ilango

Sri Ramakrishna Engineering College (SREC), COIMBATORE

Sastika Ilango has created this Calculator and 9 more calculators!

Verified by Harsh Raj

Indian Institute of Technology, Kharagpur (IIT KGP), West Bengal

Harsh Raj has verified this Calculator and 25+ more calculators!

< 18 Jet Airplane Calculators

Thrust-Specific Fuel Consumption for given Range of Jet Airplane

Go Thrust-Specific Fuel Consumption = (sqrt(8/(Freestream density*Reference Area)))*(1/(Range of aircraft*Drag Coefficient))*(sqrt(Lift Coefficient))*((sqrt(Gross Weight))-(sqrt(Weight without fuel)))

Range of Jet Airplane

Go Range of aircraft = (sqrt(8/(Freestream density*Reference Area)))*(1/(Thrust-Specific Fuel Consumption*Drag Coefficient))*(sqrt(Lift Coefficient))*((sqrt(Gross Weight))-(sqrt(Weight without fuel)))

Maximum Lift to Drag Ratio given Range for Jet Aircraft

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

Specific Fuel Consumption given Range for Jet Aircraft

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

Breguet Range

Go Range of aircraft = (Lift-to-drag ratio*Flight Velocity*ln(Initial Weight/Final Weight))/([g]*Thrust-Specific Fuel Consumption)

Breguet Endurance Equation

Go Endurance of Aircraft = (1/Thrust-Specific Fuel Consumption)*(Lift Coefficient/Drag Coefficient)*ln(Gross Weight/Weight without fuel)

Thrust-Specific Fuel Consumption for given Endurance of Jet Airplane

Go Thrust-Specific Fuel Consumption = Lift Coefficient*(ln(Gross Weight/Weight without fuel))/(Drag Coefficient*Endurance of Aircraft)

Endurance of Jet Airplane

Go Endurance of Aircraft = Lift Coefficient*(ln(Gross Weight/Weight without fuel))/(Drag Coefficient*Thrust-Specific Fuel Consumption)

Cruise Weight Fraction for Jet Aircraft

Go Cruise Weight Fraction = exp((Range of aircraft*Specific Fuel Consumption*(-1))/(0.866*1.32*Velocity at Maximum Lift to Drag Ratio*Maximum Lift to Drag Ratio))

Constant Speed Cruise using Range Equation

Go Range of aircraft = Flight Velocity/(Thrust-Specific Fuel Consumption*Total Thrust)*int(1,x,Weight without fuel,Gross Weight)

Lift-to-Drag ratio for given Range of Propeller-Driven Airplane

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

Maximum Lift to Drag Ratio given Preliminary Endurance for Jet Aircraft

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

Specific Fuel Consumption given Preliminary Endurance for Jet Aircraft

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

Thrust-Specific Fuel Consumption for given Endurance and Lift-to-Drag ratio of Jet Airplane

Go Thrust-Specific Fuel Consumption = (1/Endurance of Aircraft)*Lift-to-drag ratio*ln(Gross Weight/Weight without fuel)

Endurance for given Lift-to-Drag ratio of Jet Airplane

Go Endurance of Aircraft = (1/Thrust-Specific Fuel Consumption)*Lift-to-drag ratio*ln(Gross Weight/Weight without fuel)

Lift-to-Drag ratio for given Endurance of Jet Airplane

Go Lift-to-drag ratio = Thrust-Specific Fuel Consumption*Endurance of Aircraft/(ln(Gross Weight/Weight without fuel))

Loiter Weight Fraction for Jet Aircraft

Go Loiter weight Fraction for Jet aircraft = exp(((-1)*Endurance of Aircraft*Specific Fuel Consumption)/Maximum Lift to Drag Ratio)

Average Value Range Equation

Go Average Value Range Equation = Weight/(Thrust-Specific Fuel Consumption*(Drag Force/Flight Velocity))

Breguet Endurance Equation Formula

Endurance of Aircraft = (1/Thrust-Specific Fuel Consumption)*(Lift Coefficient/Drag Coefficient)*ln(Gross Weight/Weight without fuel)
E = (1/c_t)*(C_L/C_D)*ln(W₀/W₁)

What is Breguet Endurance Equation ?

The Breguet Endurance Equation, often attributed to French aviation pioneer Louis Breguet, is a fundamental formula used to estimate the endurance (time aloft) of an aircraft on a still-air trip. While the original equation dealt with propeller-driven aircraft, it can be adapted to incorporate integral aerodynamics for modern jet engines.

How to Calculate Breguet Endurance Equation?

Breguet Endurance Equation calculator uses Endurance of Aircraft = (1/Thrust-Specific Fuel Consumption)*(Lift Coefficient/Drag Coefficient)*ln(Gross Weight/Weight without fuel) to calculate the Endurance of Aircraft, The Breguet endurance equation formula is defined as an aircraft's endurance (time aloft) to its initial weight, fuel consumption, and aerodynamic properties. Endurance of Aircraft is denoted by E symbol.

How to calculate Breguet Endurance Equation using this online calculator? To use this online calculator for Breguet Endurance Equation, enter Thrust-Specific Fuel Consumption (c_t), Lift Coefficient (C_L), Drag Coefficient (C_D), Gross Weight (W₀) & Weight without fuel (W₁) and hit the calculate button. Here is how the Breguet Endurance Equation calculation can be explained with given input values -> 1532.477 = (1/0.002825)*(5/2)*ln(5000/3000).

FAQ

What is Breguet Endurance Equation?

The Breguet endurance equation formula is defined as an aircraft's endurance (time aloft) to its initial weight, fuel consumption, and aerodynamic properties and is represented as E = (1/c_t)*(C_L/C_D)*ln(W₀/W₁) or Endurance of Aircraft = (1/Thrust-Specific Fuel Consumption)*(Lift Coefficient/Drag Coefficient)*ln(Gross Weight/Weight without fuel). Thrust-specific fuel consumption (TSFC) is the fuel efficiency of an engine design with respect to thrust output, 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, The Gross Weight of the airplane is the weight with full fuel and payload & Weight without fuel is the total weight of the airplane without fuel.

How to calculate Breguet Endurance Equation?

The Breguet endurance equation formula is defined as an aircraft's endurance (time aloft) to its initial weight, fuel consumption, and aerodynamic properties is calculated using Endurance of Aircraft = (1/Thrust-Specific Fuel Consumption)*(Lift Coefficient/Drag Coefficient)*ln(Gross Weight/Weight without fuel). To calculate Breguet Endurance Equation, you need Thrust-Specific Fuel Consumption (c_t), Lift Coefficient (C_L), Drag Coefficient (C_D), Gross Weight (W₀) & Weight without fuel (W₁). With our tool, you need to enter the respective value for Thrust-Specific Fuel Consumption, Lift Coefficient, Drag Coefficient, Gross Weight & Weight without fuel 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 Endurance of Aircraft?

In this formula, Endurance of Aircraft uses Thrust-Specific Fuel Consumption, Lift Coefficient, Drag Coefficient, Gross Weight & Weight without fuel. We can use 2 other way(s) to calculate the same, which is/are as follows -

Endurance of Aircraft = Lift Coefficient*(ln(Gross Weight/Weight without fuel))/(Drag Coefficient*Thrust-Specific Fuel Consumption)
Endurance of Aircraft = (1/Thrust-Specific Fuel Consumption)*Lift-to-drag ratio*ln(Gross Weight/Weight without fuel)

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