Cruise Weight Fraction for Jet Aircraft Calculator

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Propeller-Driven Airplane

✖Range of aircraft is defined as the total distance (measured with respect to ground) traversed by the aircraft on a tank of fuel.ⓘ Range of aircraft [R]			+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 [c]			+10% -10%
✖Velocity at Maximum Lift to Drag Ratio is the velocity when the ratio of lift and drag coefficient is maximum in value. Basically considered for the cruise phase.ⓘ Velocity at Maximum Lift to Drag Ratio [V_L/D,max]			+10% -10%
✖Maximum Lift to Drag ratio of Aircraft while in cruise, the ratio of lift to drag coefficient is maximum in value.ⓘ Maximum Lift to Drag Ratio [LDmax_ratio]			+10% -10%

✖Cruise Weight Fraction is the Ratio of the Weight of Aircraft at the end of cruise phase to the Weight of aircraft at the start of Cruise Phase. The reduction in Weight is due to the fuel consumption.ⓘ Cruise Weight Fraction for Jet Aircraft [F_Wcruise]

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Formula

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Cruise Weight Fraction for Jet Aircraft

Formula

`"F"_{"Wcruise"} = exp(("R"*"c"*(-1))/(0.866*1.32*"V"_{"L/D,max"}*"LDmax"_{"ratio"}))`

Example

`"0.995919"=exp(("7126m"*"0.6kg/h/W"*(-1))/(0.866*1.32*"50m/s"*"5.081"))`

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Cruise Weight Fraction for Jet Aircraft Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
F_Wcruise = exp((R*c*(-1))/(0.866*1.32*V_L/D,max*LDmax_ratio))
This formula uses 1 Functions, 5 Variables

Functions Used

exp - n an exponential function, the value of the function changes by a constant factor for every unit change in the independent variable., exp(Number)

Variables Used

Cruise Weight Fraction - Cruise Weight Fraction is the Ratio of the Weight of Aircraft at the end of cruise phase to the Weight of aircraft at the start of Cruise Phase. The reduction in Weight is due to the fuel consumption.
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.
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.
Velocity at Maximum Lift to Drag Ratio - (Measured in Meter per Second) - Velocity at Maximum Lift to Drag Ratio is the velocity when the ratio of lift and drag coefficient is maximum in value. Basically considered for the cruise phase.
Maximum Lift to Drag Ratio - Maximum Lift to Drag ratio of Aircraft while in cruise, the ratio of lift to drag coefficient is maximum in value.

STEP 1: Convert Input(s) to Base Unit

Range of aircraft: 7126 Meter --> 7126 Meter No Conversion Required
Specific Fuel Consumption: 0.6 Kilogram per Hour per Watt --> 0.000166666666666667 Kilogram per Second per Watt (Check conversion here)
Velocity at Maximum Lift to Drag Ratio: 50 Meter per Second --> 50 Meter per Second No Conversion Required
Maximum Lift to Drag Ratio: 5.081 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

F_Wcruise = exp((R*c*(-1))/(0.866*1.32*V_L/D,max*LDmax_ratio)) --> exp((7126*0.000166666666666667*(-1))/(0.866*1.32*50*5.081))

Evaluating ... ...

F_Wcruise = 0.995918725582708

STEP 3: Convert Result to Output's Unit

0.995918725582708 --> No Conversion Required

FINAL ANSWER

0.995918725582708 ≈ 0.995919 <-- Cruise Weight Fraction

(Calculation completed in 00.004 seconds)

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Created by Vedant Chitte

All India Shri Shivaji Memorials Society's ,College of Engineering (AISSMS COE PUNE), Pune

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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))

Cruise Weight Fraction for Jet Aircraft Formula

What is Cruise Weight Fraction ?

The Cruise Weight Fraction is defined as the Ratio of the weight of Aircraft at the End of Cruise Phase to Weight of Aircraft at Start of the Cruise phase. It depends upon the range of aircraft, the Specific Fuel Consumption of the jet engine, it also depends upon the Carson’s speed which is 32% higher than the speed for maximizing range ( Velocity at max. Lift to Drag ratio ) and the maximum Lift to Drag Ratio itself.
It is basically important for the preliminary estimation of Take Off Weight.

What is Carson's Speed?

The maximum range airspeed may be the most economical way to fly, but it's quite slow. Hence, we may consider the speed for which the ratio fuel flow/knot of airspeed reaches a minimum. That speed, marked by the point where a line from the origin is tangent to the thrust required curve, is called 'Carson's speed'.
It is basically considered 32% more than the maximum range airspeed i.e. 132% of maximum Range airspeed.
For example if maximum range airspeed is 100 knots, The Carson's speed would be 132 Knots.

How to Calculate Cruise Weight Fraction for Jet Aircraft?

Cruise Weight Fraction for Jet Aircraft calculator uses 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)) to calculate the Cruise Weight Fraction, The Cruise Weight Fraction for Jet Aircraft formula is defined as the ratio of the weight of Aircraft at the End of the Cruise Phase to the weight of Aircraft at the start of the Cruise phase. It depends upon the range of aircraft, the Specific Fuel Consumption of the jet engine, it also depends upon Carson’s speed which is 32% higher than the speed for maximizing range ( Velocity at max. Lift to Drag ratio ) and the maximum Lift to Drag Ratio itself. Cruise Weight Fraction is denoted by F_Wcruise symbol.

How to calculate Cruise Weight Fraction for Jet Aircraft using this online calculator? To use this online calculator for Cruise Weight Fraction for Jet Aircraft, enter Range of aircraft (R), Specific Fuel Consumption (c), Velocity at Maximum Lift to Drag Ratio (V_L/D,max) & Maximum Lift to Drag Ratio (LDmax_ratio) and hit the calculate button. Here is how the Cruise Weight Fraction for Jet Aircraft calculation can be explained with given input values -> 0.999308 = exp((7126*0.000166666666666667*(-1))/(0.866*1.32*50*5.081)).

FAQ

What is Cruise Weight Fraction for Jet Aircraft?

The Cruise Weight Fraction for Jet Aircraft formula is defined as the ratio of the weight of Aircraft at the End of the Cruise Phase to the weight of Aircraft at the start of the Cruise phase. It depends upon the range of aircraft, the Specific Fuel Consumption of the jet engine, it also depends upon Carson’s speed which is 32% higher than the speed for maximizing range ( Velocity at max. Lift to Drag ratio ) and the maximum Lift to Drag Ratio itself and is represented as F_Wcruise = exp((R*c*(-1))/(0.866*1.32*V_L/D,max*LDmax_ratio)) or 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)). Range of aircraft is defined as the total distance (measured with respect to ground) traversed by the aircraft on a tank of fuel, Specific Fuel Consumption is a characteristic of the engine and defined as the weight of fuel consumed per unit power per unit time, Velocity at Maximum Lift to Drag Ratio is the velocity when the ratio of lift and drag coefficient is maximum in value. Basically considered for the cruise phase & Maximum Lift to Drag ratio of Aircraft while in cruise, the ratio of lift to drag coefficient is maximum in value.

How to calculate Cruise Weight Fraction for Jet Aircraft?

The Cruise Weight Fraction for Jet Aircraft formula is defined as the ratio of the weight of Aircraft at the End of the Cruise Phase to the weight of Aircraft at the start of the Cruise phase. It depends upon the range of aircraft, the Specific Fuel Consumption of the jet engine, it also depends upon Carson’s speed which is 32% higher than the speed for maximizing range ( Velocity at max. Lift to Drag ratio ) and the maximum Lift to Drag Ratio itself is calculated using 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)). To calculate Cruise Weight Fraction for Jet Aircraft, you need Range of aircraft (R), Specific Fuel Consumption (c), Velocity at Maximum Lift to Drag Ratio (V_L/D,max) & Maximum Lift to Drag Ratio (LDmax_ratio). With our tool, you need to enter the respective value for Range of aircraft, Specific Fuel Consumption, Velocity at Maximum Lift to Drag Ratio & Maximum Lift to Drag Ratio 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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