Optimum Range for Prop-Driven Aircraft in Cruising Phase Calculator

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✖Propeller Efficiency is defined as power produced (propeller power) divided by power applied (engine power).ⓘ Propeller Efficiency [η]			+10% -10%
✖Maximum Lift-to-Drag Ratio of Aircraft refers to the highest ratio of lift force to drag force. It represents the optimal balance between lift and drag for maximum efficiency in level flight.ⓘ Maximum Lift-to-Drag Ratio of Aircraft [LDmax_ratio]			+10% -10%
✖Power Specific Fuel Consumption is a characteristic of the engine and defined as the weight of fuel consumed per unit power per unit time.ⓘ Power Specific Fuel Consumption [c]			+10% -10%
✖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 Beginning of Cruise Phase [W_i]			+10% -10%
✖Weight of Aircraft at End of Cruise Phase is the weight before the loitering/descent/action phase of the mission plan.ⓘ Weight of Aircraft at End of Cruise Phase [W_f]			+10% -10%

✖Optimum Range of Aircraft is defined as the total distance (measured with respect to ground) traversed by the aircraft on a tank of fuel.ⓘ Optimum Range for Prop-Driven Aircraft in Cruising Phase [R_opt]

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Formula

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Optimum Range for Prop-Driven Aircraft in Cruising Phase

Formula

`"R"_{"opt"} = ("η"*"LDmax"_{"ratio"})/"c"*ln("W"_{"i"}/"W"_{"f"})`

Example

`"42.24347km"=("0.93"*"19.7")/"0.6kg/h/W"*ln("514kg"/"350kg")`

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Optimum Range for Prop-Driven Aircraft in Cruising Phase Solution

STEP 0: Pre-Calculation Summary

Formula Used

Optimum 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_opt = (η*LDmax_ratio)/c*ln(W_i/W_f)
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

Optimum Range of Aircraft - (Measured in Meter) - Optimum 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 refers to the highest ratio of lift force to drag force. It represents the optimal balance between lift and drag for maximum efficiency in level flight.
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: 19.7 --> 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: 514 Kilogram --> 514 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_opt = (η*LDmax_ratio)/c*ln(W_i/W_f) --> (0.93*19.7)/0.000166666666666667*ln(514/350)

Evaluating ... ...

R_opt = 42243.4747386756

STEP 3: Convert Result to Output's Unit

42243.4747386756 Meter -->42.2434747386757 Kilometer (Check conversion here)

FINAL ANSWER

42.2434747386757 ≈ 42.24347 Kilometer <-- Optimum Range of Aircraft

(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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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 Optimum 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 Preliminary 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 = Harmonic Range-Range Increment of Aircraft

Optimum Range for Prop-Driven Aircraft in Cruising Phase Formula

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 Optimum 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 Optimum Range of Aircraft, The Optimum Range for Prop-Driven Aircraft in Cruising Phase refers to the maximum distance the aircraft can travel while minimizing fuel consumption, it represents the most fuel-efficient flight regime where the aircraft achieves the greatest distance for a given amount of fuel. Optimum Range of Aircraft is denoted by R_opt 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 (LDmax_ratio), Power Specific Fuel Consumption (c), Weight of Aircraft at Beginning of Cruise Phase (W_i) & Weight of Aircraft at End of Cruise Phase (W_f) 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 -> 42243.47 = (0.93*19.7)/0.000166666666666667*ln(514/350).

FAQ

What is Optimum Range for Prop-Driven Aircraft in Cruising Phase?

The Optimum Range for Prop-Driven Aircraft in Cruising Phase refers to the maximum distance the aircraft can travel while minimizing fuel consumption, it represents the most fuel-efficient flight regime where the aircraft achieves the greatest distance for a given amount of fuel and is represented as R_opt = (η*LDmax_ratio)/c*ln(W_i/W_f) or Optimum 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 refers to the highest ratio of lift force to drag force. It represents the optimal balance between lift and drag for maximum efficiency in level flight, 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 refers to the maximum distance the aircraft can travel while minimizing fuel consumption, it represents the most fuel-efficient flight regime where the aircraft achieves the greatest distance for a given amount of fuel is calculated using Optimum 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 (LDmax_ratio), Power Specific Fuel Consumption (c), Weight of Aircraft at Beginning of Cruise Phase (W_i) & Weight of Aircraft at End of Cruise Phase (W_f). 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.

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