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Optimum Range for Prop-Driven Aircraft in Cruising Phase Formula

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Optimum Range of Aircraft is defined as the total distance (measured with respect to ground) traversed by the aircraft on a tank of fuel. Check FAQs

R opt = \frac{η \cdot LDmax ratio}{c} \cdot \ln (\frac{W i}{W f})

R_opt - Optimum Range of Aircraft?η - Propeller Efficiency?LDmax_ratio - Maximum Lift-to-Drag Ratio of Aircraft?c - Power Specific Fuel Consumption?W_i - Weight of Aircraft at Beginning of Cruise Phase?W_f - Weight of Aircraft at End of Cruise Phase?

Optimum Range for Prop-Driven Aircraft in Cruising Phase Example

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Here is how the Optimum Range for Prop-Driven Aircraft in Cruising Phase equation looks like with Values.

Here is how the Optimum Range for Prop-Driven Aircraft in Cruising Phase equation looks like with Units.

Here is how the Optimum Range for Prop-Driven Aircraft in Cruising Phase equation looks like.

42.2435 = \frac{0.93 \cdot 19.7}{0.6} \cdot \ln (\frac{514}{350})

42.2435km = \frac{0.93 \cdot 19.7}{0.6kg/h/W} \cdot \ln (\frac{514kg}{350kg})

42.2435 = \frac{0.93 \cdot 19.7}{0.6} \cdot \ln (\frac{514}{350})

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Optimum Range for Prop-Driven Aircraft in Cruising Phase Solution

Follow our step by step solution on how to calculate Optimum Range for Prop-Driven Aircraft in Cruising Phase?

FIRST Step Consider the formula

R opt = \frac{η \cdot LDmax ratio}{c} \cdot \ln (\frac{W i}{W f})

Next Step Substitute values of Variables

∴

R opt = \frac{0.93 \cdot 19.7}{0.6kg/h/W} \cdot \ln (\frac{514kg}{350kg})

Next Step Convert Units

∴

R opt = \frac{0.93 \cdot 19.7}{0.0002kg/s/W} \cdot \ln (\frac{514kg}{350kg})

Next Step Prepare to Evaluate

∴

R opt = \frac{0.93 \cdot 19.7}{0.0002} \cdot \ln (\frac{514}{350})

Next Step Evaluate

∴

R opt = 42243.4747386756m

Next Step Convert to Output's Unit

∴

R opt = 42.2434747386757km

LAST Step Rounding Answer

∴

R opt = 42.2435km

Optimum Range for Prop-Driven Aircraft in Cruising Phase Formula Elements

Variables

Functions

Optimum Range of Aircraft

Optimum Range of Aircraft is defined as the total distance (measured with respect to ground) traversed by the aircraft on a tank of fuel.

Symbol: R_opt

Measurement: LengthUnit: km

Note: Value can be positive or negative.

Formulas to find Optimum Range of Aircraft

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

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.

Symbol: LDmax_ratio

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Maximum Lift-to-Drag Ratio of Aircraft

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

Weight of Aircraft at Beginning of Cruise Phase

Weight of Aircraft at Beginning of Cruise Phase is the weight of the plane just before going to cruise phase of the mission.

Symbol: W_i

Measurement: WeightUnit: kg

Note: Value should be greater than 0.

Formulas to find Weight of Aircraft at Beginning of Cruise Phase

Weight of Aircraft at End of Cruise Phase

Weight of Aircraft at End of Cruise Phase is the weight before the loitering/descent/action phase of the mission plan.

Symbol: W_f

Measurement: WeightUnit: kg

Note: Value should be greater than 0.

Formulas to find Weight of Aircraft at End of Cruise Phase

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}

Go Preliminary Take off Weight Built-Up for Manned Aircraft given Fuel and Empty Weight Fraction

DTW = \frac{PYL + W c}{1 - F f - E f}

Go Optimum Range for Jet Aircraft in Cruising Phase

R = \frac{V L/D(max) \cdot LDmax ratio}{c} \cdot \ln (\frac{W i}{W f})

How to Evaluate Optimum Range for Prop-Driven Aircraft in Cruising Phase?

Optimum Range for Prop-Driven Aircraft in Cruising Phase evaluator 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 evaluate 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 evaluate Optimum Range for Prop-Driven Aircraft in Cruising Phase using this online evaluator? To use this online evaluator 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.

FAQs on Optimum Range for Prop-Driven Aircraft in Cruising Phase

What is the formula to find Optimum Range for Prop-Driven Aircraft in Cruising Phase?

The formula of Optimum Range for Prop-Driven Aircraft in Cruising Phase is expressed as 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). Here is an example- 42243.47 = (0.93*19.7)/0.000166666666666667*ln(514/350).

How to calculate Optimum Range for Prop-Driven Aircraft in Cruising Phase?

With 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) we can find Optimum Range for Prop-Driven Aircraft in Cruising Phase using the formula - 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). This formula also uses Natural Logarithm (ln) function(s).

Can the Optimum Range for Prop-Driven Aircraft in Cruising Phase be negative?

Yes, the Optimum Range for Prop-Driven Aircraft in Cruising Phase, measured in Length can be negative.

Which unit is used to measure Optimum Range for Prop-Driven Aircraft in Cruising Phase?

Optimum Range for Prop-Driven Aircraft in Cruising Phase is usually measured using the Kilometer[km] for Length. Meter[km], Millimeter[km], Decimeter[km] are the few other units in which Optimum Range for Prop-Driven Aircraft in Cruising Phase can be measured.

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Optimum Range for Prop-Driven Aircraft in Cruising Phase Formula

Optimum Range for Prop-Driven Aircraft in Cruising Phase Example

Optimum Range for Prop-Driven Aircraft in Cruising Phase Solution

Optimum Range for Prop-Driven Aircraft in Cruising Phase Formula Elements

Other formulas in Preliminary Design category

How to Evaluate Optimum Range for Prop-Driven Aircraft in Cruising Phase?

FAQs on Optimum Range for Prop-Driven Aircraft in Cruising Phase

Variable Name