Constant Speed Cruise using Range 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

✖Flight Velocity is the speed with which the aircraft moves through the air.ⓘ Flight Velocity [V]			+10% -10%
✖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%
✖Total Thrust is the sum of all the thrusts produced in a system or plant.ⓘ Total Thrust [T_total]			+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%

✖Range of aircraft is defined as the total distance (measured with respect to ground) traversed by the aircraft on a tank of fuel.ⓘ Constant Speed Cruise using Range Equation [R]

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Formula

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Constant Speed Cruise using Range Equation

Formula

`"R" = "V"/("c"_{"t"}*"T"_{"total"})*int(1,x,"W"_{"1"},"W"_{"0"})`

Example

`"71874.58m"="60m/s"/("10.17kg/h/N"*"591N")*int(1,x,"3000kg","5000kg")`

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Constant Speed Cruise using Range Equation Solution

STEP 0: Pre-Calculation Summary

Formula Used

Range of aircraft = Flight Velocity/(Thrust-Specific Fuel Consumption*Total Thrust)*int(1,x,Weight without fuel,Gross Weight)
R = V/(c_t*T_total)*int(1,x,W₁,W₀)
This formula uses 1 Functions, 6 Variables

Functions Used

int - The definite integral can be used to calculate net signed area, which is the area above the x -axis minus the area below the x -axis., int(expr, arg, from, to)

Variables Used

Range of aircraft - (Measured in Meter) - Range of aircraft is defined as the total distance (measured with respect to ground) traversed by the aircraft on a tank of fuel.
Flight Velocity - (Measured in Meter per Second) - Flight Velocity is the speed with which the aircraft moves through the air.
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.
Total Thrust - (Measured in Newton) - Total Thrust is the sum of all the thrusts produced in a system or plant.
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

Flight Velocity: 60 Meter per Second --> 60 Meter per Second No Conversion Required
Thrust-Specific Fuel Consumption: 10.17 Kilogram per Hour per Newton --> 0.002825 Kilogram per Second per Newton (Check conversion here)
Total Thrust: 591 Newton --> 591 Newton 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

R = V/(c_t*T_total)*int(1,x,W₁,W₀) --> 60/(0.002825*591)*int(1,x,3000,5000)

Evaluating ... ...

R = 71874.5788598895

STEP 3: Convert Result to Output's Unit

71874.5788598895 Meter --> No Conversion Required

FINAL ANSWER

71874.5788598895 ≈ 71874.58 Meter <-- Range of aircraft

(Calculation completed in 00.004 seconds)

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Home » Physics » Aircraft Mechanics » Aircraft Performance » Range and Endurance » Jet Airplane » Constant Speed Cruise using Range 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

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< 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))

Constant Speed Cruise using Range Equation Formula

Range of aircraft = Flight Velocity/(Thrust-Specific Fuel Consumption*Total Thrust)*int(1,x,Weight without fuel,Gross Weight)
R = V/(c_t*T_total)*int(1,x,W₁,W₀)

What is Constant speed cruise using range equation ?

The Constant speed cruise using range equation is an essential tool in aircraft performance analysis, particularly for determining the maximum distance an aircraft can travel under specific conditions.

How to Calculate Constant Speed Cruise using Range Equation?

Constant Speed Cruise using Range Equation calculator uses Range of aircraft = Flight Velocity/(Thrust-Specific Fuel Consumption*Total Thrust)*int(1,x,Weight without fuel,Gross Weight) to calculate the Range of aircraft, The Constant speed cruise using range equation formula is defined as an aircraft performance analysis, particularly for determining the maximum distance an aircraft can travel under specific conditions. Range of aircraft is denoted by R symbol.

How to calculate Constant Speed Cruise using Range Equation using this online calculator? To use this online calculator for Constant Speed Cruise using Range Equation, enter Flight Velocity (V), Thrust-Specific Fuel Consumption (c_t), Total Thrust (T_total), Weight without fuel (W₁) & Gross Weight (W₀) and hit the calculate button. Here is how the Constant Speed Cruise using Range Equation calculation can be explained with given input values -> 243654.8 = 60/(0.002825*591)*int(1,x,3000,5000).

FAQ

What is Constant Speed Cruise using Range Equation?

The Constant speed cruise using range equation formula is defined as an aircraft performance analysis, particularly for determining the maximum distance an aircraft can travel under specific conditions and is represented as R = V/(c_t*T_total)*int(1,x,W₁,W₀) or Range of aircraft = Flight Velocity/(Thrust-Specific Fuel Consumption*Total Thrust)*int(1,x,Weight without fuel,Gross Weight). Flight Velocity is the speed with which the aircraft moves through the air, Thrust-specific fuel consumption (TSFC) is the fuel efficiency of an engine design with respect to thrust output, Total Thrust is the sum of all the thrusts produced in a system or plant, 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 Constant Speed Cruise using Range Equation?

The Constant speed cruise using range equation formula is defined as an aircraft performance analysis, particularly for determining the maximum distance an aircraft can travel under specific conditions is calculated using Range of aircraft = Flight Velocity/(Thrust-Specific Fuel Consumption*Total Thrust)*int(1,x,Weight without fuel,Gross Weight). To calculate Constant Speed Cruise using Range Equation, you need Flight Velocity (V), Thrust-Specific Fuel Consumption (c_t), Total Thrust (T_total), Weight without fuel (W₁) & Gross Weight (W₀). With our tool, you need to enter the respective value for Flight Velocity, Thrust-Specific Fuel Consumption, Total Thrust, 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 Range of aircraft?

In this formula, Range of aircraft uses Flight Velocity, Thrust-Specific Fuel Consumption, Total Thrust, Weight without fuel & Gross Weight. We can use 2 other way(s) to calculate the same, which is/are as follows -

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

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