Cruise Weight Fraction for Prop-Driven Aircraft Solution

STEP 0: Pre-Calculation Summary
Formula Used
Cruise Weight Fraction = exp((Range of aircraft*(-1)*Specific Fuel Consumption)/(Maximum Lift to Drag Ratio*Propeller Efficiency))
FWcruise = exp((R*(-1)*c)/(LDmaxratio*η))
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.
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.
Propeller Efficiency - Propeller Efficiency is defined as power produced (propeller power) divided by power applied (engine power).
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)
Maximum Lift to Drag Ratio: 5.081 --> No Conversion Required
Propeller Efficiency: 0.93 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
FWcruise = exp((R*(-1)*c)/(LDmaxratio*η)) --> exp((7126*(-1)*0.000166666666666667)/(5.081*0.93))
Evaluating ... ...
FWcruise = 0.777757522784892
STEP 3: Convert Result to Output's Unit
0.777757522784892 --> No Conversion Required
FINAL ANSWER
0.777757522784892 0.777758 <-- Cruise Weight Fraction
(Calculation completed in 00.004 seconds)

Credits

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

Cruise Weight Fraction for Prop-Driven Aircraft Formula

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

What is Cruise Weight Fraction?

The Cruise Weight Fraction is defined as the ratio of the weight of the Aircraft at the End of Cruise Phase to the Weight of Aircraft at the Start of Cruise phase. It depends upon the range of aircraft, the Specific Fuel Consumption of the engine, it also depends upon the Propeller Efficiency and the maximum Lift to Drag Ratio itself.
It is Basically important for the preliminary estimation of Take Off Weight.

How to Calculate Cruise Weight Fraction for Prop-Driven Aircraft?

Cruise Weight Fraction for Prop-Driven Aircraft calculator uses Cruise Weight Fraction = exp((Range of aircraft*(-1)*Specific Fuel Consumption)/(Maximum Lift to Drag Ratio*Propeller Efficiency)) to calculate the Cruise Weight Fraction, The Cruise Weight Fraction for Prop-Driven 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. The Propeller efficiency plays important role in Cruise Weight Fraction. Cruise Weight Fraction is denoted by FWcruise symbol.

How to calculate Cruise Weight Fraction for Prop-Driven Aircraft using this online calculator? To use this online calculator for Cruise Weight Fraction for Prop-Driven Aircraft, enter Range of aircraft (R), Specific Fuel Consumption (c), Maximum Lift to Drag Ratio (LDmaxratio) & Propeller Efficiency (η) and hit the calculate button. Here is how the Cruise Weight Fraction for Prop-Driven Aircraft calculation can be explained with given input values -> 0.958325 = exp((7126*(-1)*0.000166666666666667)/(5.081*0.93)).

FAQ

What is Cruise Weight Fraction for Prop-Driven Aircraft?
The Cruise Weight Fraction for Prop-Driven 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. The Propeller efficiency plays important role in Cruise Weight Fraction and is represented as FWcruise = exp((R*(-1)*c)/(LDmaxratio*η)) or Cruise Weight Fraction = exp((Range of aircraft*(-1)*Specific Fuel Consumption)/(Maximum Lift to Drag Ratio*Propeller Efficiency)). 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, Maximum Lift to Drag ratio of Aircraft while in cruise, the ratio of lift to drag coefficient is maximum in value & Propeller Efficiency is defined as power produced (propeller power) divided by power applied (engine power).
How to calculate Cruise Weight Fraction for Prop-Driven Aircraft?
The Cruise Weight Fraction for Prop-Driven 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. The Propeller efficiency plays important role in Cruise Weight Fraction is calculated using Cruise Weight Fraction = exp((Range of aircraft*(-1)*Specific Fuel Consumption)/(Maximum Lift to Drag Ratio*Propeller Efficiency)). To calculate Cruise Weight Fraction for Prop-Driven Aircraft, you need Range of aircraft (R), Specific Fuel Consumption (c), Maximum Lift to Drag Ratio (LDmaxratio) & Propeller Efficiency (η). With our tool, you need to enter the respective value for Range of aircraft, Specific Fuel Consumption, Maximum Lift to Drag Ratio & Propeller Efficiency 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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