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Preliminary Endurance for Prop-Driven Aircraft Formula

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

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

E - Endurance of Aircraft?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?V_(Emax) - Velocity for Maximum Endurance?

Preliminary Endurance for Prop-Driven Aircraft Example

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

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

Here is how the Preliminary Endurance for Prop-Driven Aircraft equation looks like.

2028.2518 = \frac{26 \cdot 0.93 \cdot \ln (\frac{400}{300})}{0.6 \cdot 40}

2028.2518s = \frac{26 \cdot 0.93 \cdot \ln (\frac{400kg}{300kg})}{0.6kg/h/W \cdot 40kn}

2028.2518 = \frac{26 \cdot 0.93 \cdot \ln (\frac{400}{300})}{0.6 \cdot 40}

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Preliminary Endurance for Prop-Driven Aircraft Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

E = \frac{26 \cdot 0.93 \cdot \ln (\frac{400kg}{300kg})}{0.6kg/h/W \cdot 40kn}

Next Step Convert Units

∴

E = \frac{26 \cdot 0.93 \cdot \ln (\frac{400kg}{300kg})}{0.0002kg/s/W \cdot 20.5778m/s}

Next Step Prepare to Evaluate

∴

E = \frac{26 \cdot 0.93 \cdot \ln (\frac{400}{300})}{0.0002 \cdot 20.5778}

Next Step Evaluate

∴

E = 2028.2518123204s

LAST Step Rounding Answer

∴

E = 2028.2518s

Preliminary Endurance for Prop-Driven Aircraft Formula Elements

Variables

Functions

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

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

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

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

Syntax: ln(Number)

Other formulas in Preliminary Design category

Go Preliminary Take Off Weight Built-up for Manned Aircraft

DTW = PYL + OEW + FW + W c

Go Fuel Fraction

F f = \frac{FW}{DTW}

How to Evaluate Preliminary Endurance for Prop-Driven Aircraft?

Preliminary Endurance for Prop-Driven Aircraft evaluator 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 evaluate the Endurance of Aircraft, The Preliminary endurance for Prop-Driven Aircraft formula provides an estimate of the maximum amount of time the propeller-driven aircraft can remain in flight on a single fuel load under normal operating conditions, this formula calculates the endurance of the aircraft by multiplying various factors related to aerodynamic efficiency, propeller efficiency, weight change during flight, and engine fuel consumption characteristics. Endurance of Aircraft is denoted by E symbol.

How to evaluate Preliminary Endurance for Prop-Driven Aircraft using this online evaluator? To use this online evaluator for 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) & Velocity for Maximum Endurance (V_(Emax)) and hit the calculate button.

FAQs on Preliminary Endurance for Prop-Driven Aircraft

What is the formula to find Preliminary Endurance for Prop-Driven Aircraft?

The formula of Preliminary Endurance for Prop-Driven Aircraft is expressed as 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). Here is an example- 2028.252 = (26*0.93*ln(400/300))/(0.000166666666666667*20.5777777777778).

How to calculate 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) & Velocity for Maximum Endurance (V_(Emax)) we can find Preliminary Endurance for Prop-Driven Aircraft using the 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). This formula also uses Natural Logarithm (ln) function(s).

Can the Preliminary Endurance for Prop-Driven Aircraft be negative?

No, the Preliminary Endurance for Prop-Driven Aircraft, measured in Time cannot be negative.

Which unit is used to measure Preliminary Endurance for Prop-Driven Aircraft?

Preliminary Endurance for Prop-Driven Aircraft is usually measured using the Second[s] for Time. Millisecond[s], Microsecond[s], Nanosecond[s] are the few other units in which Preliminary Endurance for Prop-Driven Aircraft can be measured.

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Preliminary Endurance for Prop-Driven Aircraft Formula

Preliminary Endurance for Prop-Driven Aircraft Example

Preliminary Endurance for Prop-Driven Aircraft Solution

Preliminary Endurance for Prop-Driven Aircraft Formula Elements

Other formulas in Preliminary Design category

How to Evaluate Preliminary Endurance for Prop-Driven Aircraft?

FAQs on Preliminary Endurance for Prop-Driven Aircraft

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