Optimum Range for Prop-Driven Aircraft in Cruising Phase Solution

STEP 0: Pre-Calculation Summary
Formula Used
Range of Aircraft = (Propeller Efficiency*Maximum Lift to Drag Ratio of Aircraft)/Power Specific Fuel Consumption*ln(Weight of Aircraft at Beginning of Cruise Phase/Weight of Aircraft at End of Cruise Phase)
R = (η*LDmaxratio)/c*ln(Wi/Wf)
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
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.
Propeller Efficiency - Propeller efficiency is defined as power produced (propeller power) divided by power applied (engine power).
Maximum Lift to Drag Ratio of Aircraft - Maximum Lift to Drag ratio of Aircraft while in cruise, the ratio of lift to drag coefficient is maximum in value.
Power Specific Fuel Consumption - (Measured in Kilogram per Second per Watt) - Power Specific Fuel Consumption is a characteristic of the engine and defined as the weight of fuel consumed per unit power per unit time.
Weight of Aircraft at Beginning of Cruise Phase - (Measured in Kilogram) - Weight of Aircraft at Beginning of Cruise Phase is the weight of the plane just before going to cruise phase of the mission.
Weight of Aircraft at End of Cruise Phase - (Measured in Kilogram) - Weight of Aircraft at End of Cruise Phase is the weight before the loitering/descent/action phase of the mission plan.
STEP 1: Convert Input(s) to Base Unit
Propeller Efficiency: 0.93 --> No Conversion Required
Maximum Lift to Drag Ratio of Aircraft: 30 --> No Conversion Required
Power Specific Fuel Consumption: 0.6 Kilogram per Hour per Watt --> 0.000166666666666667 Kilogram per Second per Watt (Check conversion here)
Weight of Aircraft at Beginning of Cruise Phase: 450 Kilogram --> 450 Kilogram No Conversion Required
Weight of Aircraft at End of Cruise Phase: 350 Kilogram --> 350 Kilogram No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
R = (η*LDmaxratio)/c*ln(Wi/Wf) --> (0.93*30)/0.000166666666666667*ln(450/350)
Evaluating ... ...
R = 42070.0352942236
STEP 3: Convert Result to Output's Unit
42070.0352942236 Meter -->42.0700352942236 Kilometer (Check conversion here)
FINAL ANSWER
42.0700352942236 42.07004 Kilometer <-- Range of Aircraft
(Calculation completed in 00.020 seconds)

Credits

Created by Vedant Chitte
All India Shri Shivaji Memorials Society's ,College of Engineering (AISSMS COE PUNE), Pune
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National Institute Of Technology (NIT), Hamirpur
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25 Preliminary Design Calculators

Velocity at Maximum Endurance given Preliminary Endurance for Prop-Driven Aircraft
Go Velocity for Maximum Endurance = (Lift to Drag Ratio at Maximum Endurance*Propeller Efficiency*ln(Weight of Aircraft at Beginning of Loiter Phase/Weight of Aircraft at End of Loiter Phase))/(Power Specific Fuel Consumption*Endurance of Aircraft)
Preliminary Endurance for Prop-Driven Aircraft
Go Endurance of Aircraft = (Lift to Drag Ratio at Maximum Endurance*Propeller Efficiency*ln(Weight of Aircraft at Beginning of Loiter Phase/Weight of Aircraft at End of Loiter Phase))/(Power Specific Fuel Consumption*Velocity for Maximum Endurance)
Velocity for Maximizing Range given Range for Jet Aircraft
Go Velocity at Maximum Lift to Drag Ratio = (Range of Aircraft*Power Specific Fuel Consumption)/(Maximum Lift to Drag Ratio of Aircraft*ln(Weight of Aircraft at Beginning of Cruise Phase/Weight of Aircraft at End of Cruise Phase))
Optimum Range for Jet Aircraft in Cruising Phase
Go Range of Aircraft = (Velocity at Maximum Lift to Drag Ratio*Maximum Lift to Drag Ratio of Aircraft)/Power Specific Fuel Consumption*ln(Weight of Aircraft at Beginning of Cruise Phase/Weight of Aircraft at End of Cruise Phase)
Optimum Range for Prop-Driven Aircraft in Cruising Phase
Go Range of Aircraft = (Propeller Efficiency*Maximum Lift to Drag Ratio of Aircraft)/Power Specific Fuel Consumption*ln(Weight of Aircraft at Beginning of Cruise Phase/Weight of Aircraft at End of Cruise Phase)
Preliminary Endurance for Jet Aircraft
Go Endurance of Aircraft = (Maximum Lift to Drag Ratio of Aircraft*ln(Weight of Aircraft at Beginning of Cruise Phase/Weight of Aircraft at End of Cruise Phase))/Power Specific Fuel Consumption
Maximum Lift over Drag
Go Maximum Lift to Drag Ratio of Aircraft = Landing Mass Fraction*((Aspect Ratio of a Wing)/(Aircraft Wetted Area/Reference Area))^(0.5)
Preliminary Take Off Weight Built-up for Manned Aircraft
Go Desired Takeoff Weight = Payload Carried+Operating Empty Weight+Fuel Weight to be Carried+Crew Weight
Payload Weight given Takeoff Weight
Go Payload Carried = Desired Takeoff Weight-Operating Empty Weight-Crew Weight-Fuel Weight to be Carried
Empty Weight given Takeoff Weight
Go Operating Empty Weight = Desired Takeoff Weight-Fuel Weight to be Carried-Payload Carried-Crew Weight
Crew Weight given Takeoff Weight
Go Crew Weight = Desired Takeoff Weight-Payload Carried-Fuel Weight to be Carried-Operating Empty Weight
Fuel Weight given Takeoff Weight
Go Fuel Weight to be Carried = Desired Takeoff Weight-Operating Empty Weight-Payload Carried-Crew Weight
Preliminary Take off Weight Built-Up for Manned Aircraft given Fuel and Empty Weight Fraction
Go Desired Takeoff Weight = (Payload Carried+Crew Weight)/(1-Fuel Fraction-Empty Weight Fraction)
Fuel Fraction given Takeoff Weight and Empty Weight Fraction
Go Fuel Fraction = 1-Empty Weight Fraction-(Payload Carried+Crew Weight)/Desired Takeoff Weight
Empty Weight Fraction given Takeoff Weight and Fuel Fraction
Go Empty Weight Fraction = 1-Fuel Fraction-(Payload Carried+Crew Weight)/Desired Takeoff Weight
Payload Weight given Fuel and Empty Weight Fractions
Go Payload Carried = Desired Takeoff Weight*(1-Empty Weight Fraction-Fuel Fraction)-Crew Weight
Crew Weight given Fuel and Empty Weight Fraction
Go Crew Weight = Desired Takeoff Weight*(1-Empty Weight Fraction-Fuel Fraction)-Payload Carried
Takeoff Weight given Empty Weight Fraction
Go Desired Takeoff Weight = Operating Empty Weight/Empty Weight Fraction
Empty Weight given Empty Weight Fraction
Go Operating Empty Weight = Empty Weight Fraction*Desired Takeoff Weight
Empty Weight Fraction
Go Empty Weight Fraction = Operating Empty Weight/Desired Takeoff Weight
Winglet Friction Coefficient
Go Coefficient of Friction = 4.55/(log10(Winglet Reynolds Number^2.58))
Takeoff Weight given Fuel Fraction
Go Desired Takeoff Weight = Fuel Weight to be Carried/Fuel Fraction
Fuel Weight given Fuel Fraction
Go Fuel Weight to be Carried = Fuel Fraction*Desired Takeoff Weight
Fuel Fraction
Go Fuel Fraction = Fuel Weight to be Carried/Desired Takeoff Weight
Design range given range increment
Go Design range = Range increment of aircraft+Harmonic range

Optimum Range for Prop-Driven Aircraft in Cruising Phase Formula

Range of Aircraft = (Propeller Efficiency*Maximum Lift to Drag Ratio of Aircraft)/Power Specific Fuel Consumption*ln(Weight of Aircraft at Beginning of Cruise Phase/Weight of Aircraft at End of Cruise Phase)
R = (η*LDmaxratio)/c*ln(Wi/Wf)

What is Range of Aircraft?

The maximal total range is the maximum distance an aircraft can fly between takeoff and landing, as limited by fuel capacity in powered aircraft, or cross-country speed and environmental conditions in unpowered aircraft. The range can be seen as the cross-country ground speed multiplied by the maximum time in the air. The fuel time limit for powered aircraft is fixed by the fuel load and rate of consumption. When all fuel is consumed, the engines stop and the aircraft will lose its propulsion.

How to Calculate Optimum Range for Prop-Driven Aircraft in Cruising Phase?

Optimum Range for Prop-Driven Aircraft in Cruising Phase calculator uses Range of Aircraft = (Propeller Efficiency*Maximum Lift to Drag Ratio of Aircraft)/Power Specific Fuel Consumption*ln(Weight of Aircraft at Beginning of Cruise Phase/Weight of Aircraft at End of Cruise Phase) to calculate the Range of Aircraft, The Optimum Range for Prop-Driven Aircraft in Cruising Phase formula is defined as the maximum distance traveled by a propeller-driven plane covered only during the cruise phase of the mission. it is considered that plane is cruising at the maximum lift to drag ratio. Range of Aircraft is denoted by R symbol.

How to calculate Optimum Range for Prop-Driven Aircraft in Cruising Phase using this online calculator? To use this online calculator for Optimum Range for Prop-Driven Aircraft in Cruising Phase, enter Propeller Efficiency (η), Maximum Lift to Drag Ratio of Aircraft (LDmaxratio), Power Specific Fuel Consumption (c), Weight of Aircraft at Beginning of Cruise Phase (Wi) & Weight of Aircraft at End of Cruise Phase (Wf) and hit the calculate button. Here is how the Optimum Range for Prop-Driven Aircraft in Cruising Phase calculation can be explained with given input values -> 0.04207 = (0.93*30)/0.000166666666666667*ln(450/350).

FAQ

What is Optimum Range for Prop-Driven Aircraft in Cruising Phase?
The Optimum Range for Prop-Driven Aircraft in Cruising Phase formula is defined as the maximum distance traveled by a propeller-driven plane covered only during the cruise phase of the mission. it is considered that plane is cruising at the maximum lift to drag ratio and is represented as R = (η*LDmaxratio)/c*ln(Wi/Wf) or Range of Aircraft = (Propeller Efficiency*Maximum Lift to Drag Ratio of Aircraft)/Power Specific Fuel Consumption*ln(Weight of Aircraft at Beginning of Cruise Phase/Weight of Aircraft at End of Cruise Phase). Propeller efficiency is defined as power produced (propeller power) divided by power applied (engine power), Maximum Lift to Drag ratio of Aircraft while in cruise, the ratio of lift to drag coefficient is maximum in value, Power Specific Fuel Consumption is a characteristic of the engine and defined as the weight of fuel consumed per unit power per unit time, Weight of Aircraft at Beginning of Cruise Phase is the weight of the plane just before going to cruise phase of the mission & Weight of Aircraft at End of Cruise Phase is the weight before the loitering/descent/action phase of the mission plan.
How to calculate Optimum Range for Prop-Driven Aircraft in Cruising Phase?
The Optimum Range for Prop-Driven Aircraft in Cruising Phase formula is defined as the maximum distance traveled by a propeller-driven plane covered only during the cruise phase of the mission. it is considered that plane is cruising at the maximum lift to drag ratio is calculated using Range of Aircraft = (Propeller Efficiency*Maximum Lift to Drag Ratio of Aircraft)/Power Specific Fuel Consumption*ln(Weight of Aircraft at Beginning of Cruise Phase/Weight of Aircraft at End of Cruise Phase). To calculate Optimum Range for Prop-Driven Aircraft in Cruising Phase, you need Propeller Efficiency (η), Maximum Lift to Drag Ratio of Aircraft (LDmaxratio), Power Specific Fuel Consumption (c), Weight of Aircraft at Beginning of Cruise Phase (Wi) & Weight of Aircraft at End of Cruise Phase (Wf). With our tool, you need to enter the respective value for Propeller Efficiency, Maximum Lift to Drag Ratio of Aircraft, Power Specific Fuel Consumption, Weight of Aircraft at Beginning of Cruise Phase & Weight of Aircraft at End of Cruise Phase 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 Propeller Efficiency, Maximum Lift to Drag Ratio of Aircraft, Power Specific Fuel Consumption, Weight of Aircraft at Beginning of Cruise Phase & Weight of Aircraft at End of Cruise Phase. We can use 2 other way(s) to calculate the same, which is/are as follows -
  • Range of Aircraft = (Velocity at Maximum Lift to Drag Ratio*Maximum Lift to Drag Ratio of Aircraft)/Power Specific Fuel Consumption*ln(Weight of Aircraft at Beginning of Cruise Phase/Weight of Aircraft at End of Cruise Phase)
  • Range of Aircraft = 270*Weight of Fuel/Aircraft Weight *Lift Coefficient/Drag Coefficient*Rotor efficiency*(Coefficient of Power loss)/Power Specific Fuel Consumption
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