Preliminary Endurance for Prop-Driven Aircraft Solution

STEP 0: Pre-Calculation Summary
Formula Used
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)
E = (LDEmaxratio*η*ln(WL(beg)/WL,end))/(c*V(Emax))
This formula uses 1 Functions, 7 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
Endurance of Aircraft - (Measured in Second) - Endurance of aircraft is the maximum length of time that an aircraft can spend in cruising flight.
Lift to Drag Ratio at Maximum Endurance - Lift to Drag Ratio at Maximum Endurance is the ratio of Lift to Drag at which the plane can fly (or Loiter) for maximum time.
Propeller Efficiency - Propeller efficiency is defined as power produced (propeller power) divided by power applied (engine power).
Weight of Aircraft at Beginning of Loiter Phase - (Measured in Kilogram) - Weight of Aircraft at Beginning of Loiter Phase is considered as the weight of the plane just before going to loiter phase.
Weight of Aircraft at End of Loiter Phase - (Measured in Kilogram) - Weight of Aircraft at End of Loiter Phase is considered for the Preliminary Endurance Calculation. For the calculation of preliminary endurance, the loiter phase is considered.
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.
Velocity for Maximum Endurance - (Measured in Meter per Second) - Velocity for Maximum Endurance is velocity of plane at which a plane can loiter for maximum time i.e. for maximum endurance.
STEP 1: Convert Input(s) to Base Unit
Lift to Drag Ratio at Maximum Endurance: 26 --> No Conversion Required
Propeller Efficiency: 0.93 --> No Conversion Required
Weight of Aircraft at Beginning of Loiter Phase: 400 Kilogram --> 400 Kilogram No Conversion Required
Weight of Aircraft at End of Loiter Phase: 300 Kilogram --> 300 Kilogram No Conversion Required
Power Specific Fuel Consumption: 0.6 Kilogram per Hour per Watt --> 0.000166666666666667 Kilogram per Second per Watt (Check conversion here)
Velocity for Maximum Endurance: 40 Knot --> 20.5777777777778 Meter per Second (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
E = (LDEmaxratio*η*ln(WL(beg)/WL,end))/(c*V(Emax)) --> (26*0.93*ln(400/300))/(0.000166666666666667*20.5777777777778)
Evaluating ... ...
E = 2028.2518123204
STEP 3: Convert Result to Output's Unit
2028.2518123204 Second --> No Conversion Required
FINAL ANSWER
2028.2518123204 2028.252 Second <-- Endurance of Aircraft
(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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Shri Govindram Seksaria Institute of Technology and Science (SGSITS), Indore
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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

Preliminary Endurance for Prop-Driven Aircraft Formula

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)
E = (LDEmaxratio*η*ln(WL(beg)/WL,end))/(c*V(Emax))

What do you mean by Endurance of Aircraft?

In aviation, endurance is the maximum length of time that an aircraft can spend in a cruising flight. In other words, it is the amount of time an aircraft can stay in the air with one load of fuel. Endurance is different from range, which is a measure of distance flown. For example, a typical sailplane exhibits high endurance characteristics but poor range characteristics. Endurance can factor into aviation design in a number of ways. Some aircraft, require high endurance characteristics as part of their mission profile (often referred to as loiter time). Endurance plays a prime factor in finding out the fuel fraction for an aircraft. Endurance, like range, is also related to fuel efficiency; fuel-efficient aircraft will tend to exhibit good endurance characteristics.

How to Calculate Preliminary Endurance for Prop-Driven Aircraft?

Preliminary Endurance for Prop-Driven Aircraft calculator uses 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) to calculate the Endurance of Aircraft, The Preliminary endurance for Prop-Driven Aircraft formula is defined as the length of time that an aircraft can remain airborne for a given expenditure of fuel and for a specified set of flight conditions. Here it is for propeller-driven aircraft. Endurance of Aircraft is denoted by E symbol.

How to calculate Preliminary Endurance for Prop-Driven Aircraft using this online calculator? To use this online calculator for Preliminary Endurance for Prop-Driven Aircraft, enter Lift to Drag Ratio at Maximum Endurance (LDEmaxratio), Propeller Efficiency (η), Weight of Aircraft at Beginning of Loiter Phase (WL(beg)), Weight of Aircraft at End of Loiter Phase (WL,end), Power Specific Fuel Consumption (c) & Velocity for Maximum Endurance (V(Emax)) and hit the calculate button. Here is how the Preliminary Endurance for Prop-Driven Aircraft calculation can be explained with given input values -> 2028.252 = (26*0.93*ln(400/300))/(0.000166666666666667*20.5777777777778).

FAQ

What is Preliminary Endurance for Prop-Driven Aircraft?
The Preliminary endurance for Prop-Driven Aircraft formula is defined as the length of time that an aircraft can remain airborne for a given expenditure of fuel and for a specified set of flight conditions. Here it is for propeller-driven aircraft and is represented as E = (LDEmaxratio*η*ln(WL(beg)/WL,end))/(c*V(Emax)) or 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). Lift to Drag Ratio at Maximum Endurance is the ratio of Lift to Drag at which the plane can fly (or Loiter) for maximum time, Propeller efficiency is defined as power produced (propeller power) divided by power applied (engine power), Weight of Aircraft at Beginning of Loiter Phase is considered as the weight of the plane just before going to loiter phase, Weight of Aircraft at End of Loiter Phase is considered for the Preliminary Endurance Calculation. For the calculation of preliminary endurance, the loiter phase is considered, Power Specific Fuel Consumption is a characteristic of the engine and defined as the weight of fuel consumed per unit power per unit time & Velocity for Maximum Endurance is velocity of plane at which a plane can loiter for maximum time i.e. for maximum endurance.
How to calculate Preliminary Endurance for Prop-Driven Aircraft?
The Preliminary endurance for Prop-Driven Aircraft formula is defined as the length of time that an aircraft can remain airborne for a given expenditure of fuel and for a specified set of flight conditions. Here it is for propeller-driven aircraft is calculated using 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). To calculate Preliminary Endurance for Prop-Driven Aircraft, you need Lift to Drag Ratio at Maximum Endurance (LDEmaxratio), Propeller Efficiency (η), Weight of Aircraft at Beginning of Loiter Phase (WL(beg)), Weight of Aircraft at End of Loiter Phase (WL,end), Power Specific Fuel Consumption (c) & Velocity for Maximum Endurance (V(Emax)). With our tool, you need to enter the respective value for Lift to Drag Ratio at Maximum Endurance, Propeller Efficiency, Weight of Aircraft at Beginning of Loiter Phase, Weight of Aircraft at End of Loiter Phase, Power Specific Fuel Consumption & Velocity for Maximum Endurance 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 Endurance of Aircraft?
In this formula, Endurance of Aircraft uses Lift to Drag Ratio at Maximum Endurance, Propeller Efficiency, Weight of Aircraft at Beginning of Loiter Phase, Weight of Aircraft at End of Loiter Phase, Power Specific Fuel Consumption & Velocity for Maximum Endurance. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • 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
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