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

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Velocity for Maximum Endurance is velocity of plane at which a plane can loiter for maximum time i.e. for maximum endurance. Check FAQs

V (Emax) = \frac{LDEmax ratio \cdot η \cdot \ln (\frac{W L(beg)}{W L,end})}{c \cdot E}

V_(Emax) - Velocity for Maximum Endurance?LDEmax_ratio - Lift to Drag Ratio at Maximum Endurance?η - Propeller Efficiency?W_L(beg) - Weight of Aircraft at Beginning of Loiter Phase?W_L,end - Weight of Aircraft at End of Loiter Phase?c - Power Specific Fuel Consumption?E - Endurance of Aircraft?

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

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Here is how the Velocity at Maximum Endurance given Preliminary Endurance for Prop-Driven Aircraft equation looks like with Values.

Here is how the Velocity at Maximum Endurance given Preliminary Endurance for Prop-Driven Aircraft equation looks like with Units.

Here is how the Velocity at Maximum Endurance given Preliminary Endurance for Prop-Driven Aircraft equation looks like.

40.005 = \frac{26 \cdot 0.93 \cdot \ln (\frac{400}{300})}{0.6 \cdot 2028}

40.005kn = \frac{26 \cdot 0.93 \cdot \ln (\frac{400kg}{300kg})}{0.6kg/h/W \cdot 2028s}

40.005 = \frac{26 \cdot 0.93 \cdot \ln (\frac{400}{300})}{0.6 \cdot 2028}

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

Follow our step by step solution on how to calculate Velocity at Maximum Endurance given Preliminary Endurance for Prop-Driven Aircraft?

FIRST Step Consider the formula

V (Emax) = \frac{LDEmax ratio \cdot η \cdot \ln (\frac{W L(beg)}{W L,end})}{c \cdot E}

Next Step Substitute values of Variables

∴

V (Emax) = \frac{26 \cdot 0.93 \cdot \ln (\frac{400kg}{300kg})}{0.6kg/h/W \cdot 2028s}

Next Step Convert Units

∴

V (Emax) = \frac{26 \cdot 0.93 \cdot \ln (\frac{400kg}{300kg})}{0.0002kg/s/W \cdot 2028s}

Next Step Prepare to Evaluate

∴

V (Emax) = \frac{26 \cdot 0.93 \cdot \ln (\frac{400}{300})}{0.0002 \cdot 2028}

Next Step Evaluate

∴

V (Emax) = 20.5803328753966m/s

Next Step Convert to Output's Unit

∴

V (Emax) = 40.0049667124339kn

LAST Step Rounding Answer

∴

V (Emax) = 40.005kn

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

Variables

Functions

Velocity for Maximum Endurance

Velocity for Maximum Endurance is velocity of plane at which a plane can loiter for maximum time i.e. for maximum endurance.

Symbol: V_(Emax)

Measurement: SpeedUnit: kn

Note: Value should be greater than 0.

Formulas to find Velocity 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.

Symbol: LDEmax_ratio

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Lift to Drag Ratio at Maximum Endurance

Propeller Efficiency

Propeller Efficiency is defined as power produced (propeller power) divided by power applied (engine power).

Symbol: η

Measurement: NAUnit: Unitless

Note: Value should be less than 1.

Formulas to find Propeller Efficiency

Weight of Aircraft at Beginning of Loiter Phase

Weight of Aircraft at Beginning of Loiter Phase is considered as the weight of the plane just before going to loiter phase.

Symbol: W_L(beg)

Measurement: WeightUnit: kg

Note: Value should be greater than 0.

Formulas to find Weight of Aircraft at Beginning of Loiter Phase

Weight of Aircraft at End of 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.

Symbol: W_L,end

Measurement: WeightUnit: kg

Note: Value should be greater than 0.

Formulas to find Weight of Aircraft at End of Loiter Phase

Power Specific Fuel Consumption

Power Specific Fuel Consumption is a characteristic of the engine and defined as the weight of fuel consumed per unit power per unit time.

Symbol: c

Measurement: Specific Fuel ConsumptionUnit: kg/h/W

Note: Value should be greater than 0.

Formulas to find Power Specific Fuel Consumption

Endurance of Aircraft

Endurance of Aircraft is the maximum length of time that an aircraft can spend in cruising flight.

Symbol: E

Measurement: TimeUnit: s

Note: Value should be greater than 0.

Formulas to find Endurance of Aircraft

The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function.

Syntax: ln(Number)

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Go Preliminary Take Off Weight Built-up for Manned Aircraft

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Go Fuel Fraction

F f = \frac{FW}{DTW}

How to Evaluate Velocity at Maximum Endurance given Preliminary Endurance for Prop-Driven Aircraft?

Velocity at Maximum Endurance given Preliminary Endurance for Prop-Driven Aircraft evaluator 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 evaluate the Velocity for Maximum Endurance, The Velocity at Maximum Endurance given Preliminary Endurance for Prop-Driven Aircraft formula calculation gives you the velocity at which the aircraft achieves its maximum endurance, allowing for efficient flight planning and optimization of fuel consumption during endurance missions. Velocity for Maximum Endurance is denoted by V_(Emax) symbol.

How to evaluate Velocity at Maximum Endurance given Preliminary Endurance for Prop-Driven Aircraft using this online evaluator? To use this online evaluator for Velocity at Maximum Endurance given Preliminary Endurance for Prop-Driven Aircraft, enter Lift to Drag Ratio at Maximum Endurance (LDEmax_ratio), Propeller Efficiency (η), Weight of Aircraft at Beginning of Loiter Phase (W_L(beg)), Weight of Aircraft at End of Loiter Phase (W_L,end), Power Specific Fuel Consumption (c) & Endurance of Aircraft (E) and hit the calculate button.

FAQs on Velocity at Maximum Endurance given Preliminary Endurance for Prop-Driven Aircraft

What is the formula to find Velocity at Maximum Endurance given Preliminary Endurance for Prop-Driven Aircraft?

The formula of Velocity at Maximum Endurance given Preliminary Endurance for Prop-Driven Aircraft is expressed as 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). Here is an example- 78.85212 = (26*0.93*ln(400/300))/(0.000166666666666667*2028).

How to calculate Velocity at Maximum Endurance given Preliminary Endurance for Prop-Driven Aircraft?

With Lift to Drag Ratio at Maximum Endurance (LDEmax_ratio), Propeller Efficiency (η), Weight of Aircraft at Beginning of Loiter Phase (W_L(beg)), Weight of Aircraft at End of Loiter Phase (W_L,end), Power Specific Fuel Consumption (c) & Endurance of Aircraft (E) we can find Velocity at Maximum Endurance given Preliminary Endurance for Prop-Driven Aircraft using the 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). This formula also uses Natural Logarithm (ln) function(s).

Can the Velocity at Maximum Endurance given Preliminary Endurance for Prop-Driven Aircraft be negative?

No, the Velocity at Maximum Endurance given Preliminary Endurance for Prop-Driven Aircraft, measured in Speed cannot be negative.

Which unit is used to measure Velocity at Maximum Endurance given Preliminary Endurance for Prop-Driven Aircraft?

Velocity at Maximum Endurance given Preliminary Endurance for Prop-Driven Aircraft is usually measured using the Knot[kn] for Speed. Meter per Second[kn], Meter per Minute[kn], Meter per Hour[kn] are the few other units in which Velocity at Maximum Endurance given Preliminary Endurance for Prop-Driven Aircraft can be measured.

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

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

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

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

Other formulas in Preliminary Design category

How to Evaluate Velocity at Maximum Endurance given Preliminary Endurance for Prop-Driven Aircraft?

FAQs on Velocity at Maximum Endurance given Preliminary Endurance for Prop-Driven Aircraft

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