Velocity at Maximum Endurance given Preliminary Endurance for Prop-Driven Aircraft Solution

STEP 0: Pre-Calculation Summary
Formula Used
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)
V(Emax) = (LDEmaxratio*η*ln(WL(beg)/WL,end))/(c*E)
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
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.
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.
Endurance of Aircraft - (Measured in Second) - Endurance of aircraft is the maximum length of time that an aircraft can spend in cruising flight.
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)
Endurance of Aircraft: 2000 Second --> 2000 Second No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
V(Emax) = (LDEmaxratio*η*ln(WL(beg)/WL,end))/(c*E) --> (26*0.93*ln(400/300))/(0.000166666666666667*2000)
Evaluating ... ...
V(Emax) = 20.8684575356521
STEP 3: Convert Result to Output's Unit
20.8684575356521 Meter per Second -->40.5650362464079 Knot (Check conversion here)
FINAL ANSWER
40.5650362464079 40.56504 Knot <-- Velocity for Maximum Endurance
(Calculation completed in 00.004 seconds)

Credits

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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

Velocity at Maximum Endurance given Preliminary Endurance for Prop-Driven Aircraft Formula

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

What do you mean by Endurance of Aircraft?

In aviation, endurance is the maximum length of time that an aircraft can spend in 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 Velocity at Maximum Endurance given Preliminary Endurance for Prop-Driven Aircraft?

Velocity at Maximum Endurance given Preliminary Endurance for Prop-Driven Aircraft calculator uses 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) to calculate the Velocity for Maximum Endurance, The Velocity at Maximum Endurance given Preliminary Endurance for Prop-Driven Aircraft formula is the velocity at which the plane can achieve maximum endurance. Velocity for Maximum Endurance is denoted by V(Emax) symbol.

How to calculate Velocity at Maximum Endurance given Preliminary Endurance for Prop-Driven Aircraft using this online calculator? To use this online calculator for Velocity at Maximum Endurance given 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) & Endurance of Aircraft (E) and hit the calculate button. Here is how the Velocity at Maximum Endurance given Preliminary Endurance for Prop-Driven Aircraft calculation can be explained with given input values -> 78.85212 = (26*0.93*ln(400/300))/(0.000166666666666667*2000).

FAQ

What is Velocity at Maximum Endurance given Preliminary Endurance for Prop-Driven Aircraft?
The Velocity at Maximum Endurance given Preliminary Endurance for Prop-Driven Aircraft formula is the velocity at which the plane can achieve maximum endurance and is represented as V(Emax) = (LDEmaxratio*η*ln(WL(beg)/WL,end))/(c*E) or 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). 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 & Endurance of aircraft is the maximum length of time that an aircraft can spend in cruising flight.
How to calculate Velocity at Maximum Endurance given Preliminary Endurance for Prop-Driven Aircraft?
The Velocity at Maximum Endurance given Preliminary Endurance for Prop-Driven Aircraft formula is the velocity at which the plane can achieve maximum endurance is calculated using 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). To calculate Velocity at Maximum Endurance given 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) & Endurance of Aircraft (E). 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 & Endurance of Aircraft 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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