Endurance of Propeller-Driven Airplane Solution

STEP 0: Pre-Calculation Summary
Formula Used
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))
E = η/c*(CL^1.5)/CD*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
Endurance of Aircraft - (Measured in Second) - Endurance of aircraft is the maximum length of time that an aircraft can spend in cruising flight.
Propeller Efficiency - Propeller Efficiency is defined as power produced (propeller power) divided by power applied (engine power).
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.
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
Specific Fuel Consumption: 0.6 Kilogram per Hour per Watt --> 0.000166666666666667 Kilogram per Second per Watt (Check conversion here)
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
E = η/c*(CL^1.5)/CD*sqrt(2*ρ*S)*((1/W1)^(1/2)-(1/W0)^(1/2)) --> 0.93/0.000166666666666667*(5^1.5)/2*sqrt(2*1.225*5.08)*((1/3000)^(1/2)-(1/5000)^(1/2))
Evaluating ... ...
E = 452.870268891601
STEP 3: Convert Result to Output's Unit
452.870268891601 Second --> No Conversion Required
FINAL ANSWER
452.870268891601 452.8703 Second <-- Endurance of Aircraft
(Calculation completed in 00.004 seconds)

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
Maiarutselvan V has verified this Calculator and 300+ more calculators!

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))
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)
Propeller Efficiency given Preliminary Endurance for Prop-Driven Aircraft
Go Propeller Efficiency = (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))
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

Endurance of Propeller-Driven Airplane Formula

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))
E = η/c*(CL^1.5)/CD*sqrt(2*ρ*S)*((1/W1)^(1/2)-(1/W0)^(1/2))

What is the difference between the range and the endurance of an aircraft?

Endurance is the measure of how long any aerial vehicle can stay aloft, it is a measure of time (hours, minutes, seconds). The range is how far an aerial vehicle can get on a load of fuel, it is a measure of distance (miles, kilometers, yards, and meters).

How to Calculate Endurance of Propeller-Driven Airplane?

Endurance of Propeller-Driven Airplane calculator uses 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)) to calculate the Endurance of Aircraft, The Endurance of Propeller-Driven Airplane is given by the Breguet Endurance formula and is a function of the altitude of aircraft. Endurance of Aircraft is denoted by E symbol.

How to calculate Endurance of Propeller-Driven Airplane using this online calculator? To use this online calculator for Endurance of Propeller-Driven Airplane, enter Propeller Efficiency (η), Specific Fuel Consumption (c), Lift Coefficient (CL), Drag Coefficient (CD), Freestream density ), Reference Area (S), Weight without fuel (W1) & Gross Weight (W0) and hit the calculate button. Here is how the Endurance of Propeller-Driven Airplane calculation can be explained with given input values -> 452.8703 = 0.93/0.000166666666666667*(5^1.5)/2*sqrt(2*1.225*5.08)*((1/3000)^(1/2)-(1/5000)^(1/2)).

FAQ

What is Endurance of Propeller-Driven Airplane?
The Endurance of Propeller-Driven Airplane is given by the Breguet Endurance formula and is a function of the altitude of aircraft and is represented as E = η/c*(CL^1.5)/CD*sqrt(2*ρ*S)*((1/W1)^(1/2)-(1/W0)^(1/2)) or 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)). Propeller Efficiency is defined as power produced (propeller power) divided by power applied (engine power), Specific Fuel Consumption is a characteristic of the engine and defined as the weight of fuel consumed per unit power per unit time, 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 Endurance of Propeller-Driven Airplane?
The Endurance of Propeller-Driven Airplane is given by the Breguet Endurance formula and is a function of the altitude of aircraft is calculated using 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)). To calculate Endurance of Propeller-Driven Airplane, you need Propeller Efficiency (η), Specific Fuel Consumption (c), Lift Coefficient (CL), Drag Coefficient (CD), Freestream density ), Reference Area (S), Weight without fuel (W1) & Gross Weight (W0). With our tool, you need to enter the respective value for Propeller Efficiency, Specific Fuel Consumption, 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.
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