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Power required at Altitude Formula

GoPower required at Altitude given Power at sea-level Formula

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Power Required at Altitude is the power required for an aircraft to fly with a specific velocity at an altitude for a given altitude (or density). Check FAQs

P R,alt = \sqrt{\frac{2 \cdot {W body}^{3} \cdot {C D}^{2}}{ρ 0 \cdot S \cdot {C L}^{3}}}

P_R,alt - Power Required at Altitude?W_body - Weight of Body?C_D - Drag Coefficient?ρ₀ - Density?S - Reference Area?C_L - Lift Coefficient?

Power required at Altitude Example

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Here is how the Power required at Altitude equation looks like with Values.

Here is how the Power required at Altitude equation looks like with Units.

Here is how the Power required at Altitude equation looks like.

700.0602 = \sqrt{\frac{2 \cdot 750^{3} \cdot {1.134}^{2}}{997 \cdot 91.05 \cdot {0.29}^{3}}}

700.0602W = \sqrt{\frac{2 \cdot {750N}^{3} \cdot {1.134}^{2}}{997kg/m³ \cdot 91.05m² \cdot {0.29}^{3}}}

700.0602 = \sqrt{\frac{2 \cdot 750^{3} \cdot {1.134}^{2}}{997 \cdot 91.05 \cdot {0.29}^{3}}}

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Power required at Altitude Solution

Follow our step by step solution on how to calculate Power required at Altitude?

FIRST Step Consider the formula

P R,alt = \sqrt{\frac{2 \cdot {W body}^{3} \cdot {C D}^{2}}{ρ 0 \cdot S \cdot {C L}^{3}}}

Next Step Substitute values of Variables

∴

P R,alt = \sqrt{\frac{2 \cdot {750N}^{3} \cdot {1.134}^{2}}{997kg/m³ \cdot 91.05m² \cdot {0.29}^{3}}}

Next Step Prepare to Evaluate

∴

P R,alt = \sqrt{\frac{2 \cdot 750^{3} \cdot {1.134}^{2}}{997 \cdot 91.05 \cdot {0.29}^{3}}}

Next Step Evaluate

∴

P R,alt = 700.060213980307W

LAST Step Rounding Answer

∴

P R,alt = 700.0602W

Power required at Altitude Formula Elements

Variables

Functions

Power Required at Altitude

Power Required at Altitude is the power required for an aircraft to fly with a specific velocity at an altitude for a given altitude (or density).

Symbol: P_R,alt

Measurement: PowerUnit: W

Note: Value should be greater than 0.

Formulas to find Power Required at Altitude

Weight of Body

Weight of Body is the force acting on the object due to gravity.

Symbol: W_body

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Weight of Body

Drag Coefficient

Drag Coefficient is a dimensionless quantity that is used to quantify the drag or resistance of an object in a fluid environment, such as air or water.

Symbol: C_D

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Drag Coefficient

Density

The Density of a material shows the denseness of that material in a specific given area. This is taken as mass per unit volume of a given object.

Symbol: ρ₀

Measurement: DensityUnit: kg/m³

Note: Value should be greater than 0.

Formulas to find Density

Reference Area

The Reference Area is arbitrarily an area that is characteristic of the object being considered. For an aircraft wing, the wing's planform area is called the reference wing area or simply wing area.

Symbol: S

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Reference Area

Lift Coefficient

The Lift Coefficient is a dimensionless coefficient that relates the lift generated by a lifting body to the fluid density around the body, the fluid velocity and an associated reference area.

Symbol: C_L

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Lift Coefficient

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

Other Formulas to find Power Required at Altitude

Go Power required at Altitude given Power at sea-level

P R,alt = P R,0 \cdot \sqrt{\frac{[Std-Air-Density-Sea]}{ρ 0}}

Other formulas in Preliminary Aerodynamics category

Go Velocity at Sea-Level given Lift Coefficient

V 0 = \sqrt{\frac{2 \cdot W body}{[Std-Air-Density-Sea] \cdot S \cdot C L}}

Go Power required at sea-level conditions

P R,0 = \sqrt{\frac{2 \cdot {W body}^{3} \cdot {C D}^{2}}{[Std-Air-Density-Sea] \cdot S \cdot {C L}^{3}}}

Go Velocity at Altitude

V alt = \sqrt{2 \cdot \frac{W body}{ρ 0 \cdot S \cdot C L}}

Go Velocity at Altitude given Velocity at Sea-Level

V alt = V 0 \cdot \sqrt{\frac{[Std-Air-Density-Sea]}{ρ 0}}

How to Evaluate Power required at Altitude?

Power required at Altitude evaluator uses Power Required at Altitude = sqrt((2*Weight of Body^3*Drag Coefficient^2)/(Density*Reference Area*Lift Coefficient^3)) to evaluate the Power Required at Altitude, Power required at Altitude is a measure of the minimum power needed by an aircraft to overcome the drag forces and maintain a steady altitude, influenced by factors such as body weight, drag coefficient, air density, and lift coefficient. Power Required at Altitude is denoted by P_R,alt symbol.

How to evaluate Power required at Altitude using this online evaluator? To use this online evaluator for Power required at Altitude, enter Weight of Body (W_body), Drag Coefficient (C_D), Density (ρ₀), Reference Area (S) & Lift Coefficient (C_L) and hit the calculate button.

FAQs on Power required at Altitude

What is the formula to find Power required at Altitude?

The formula of Power required at Altitude is expressed as Power Required at Altitude = sqrt((2*Weight of Body^3*Drag Coefficient^2)/(Density*Reference Area*Lift Coefficient^3)). Here is an example- 699.8681 = sqrt((2*750^3*1.134^2)/(997*91.05*0.29^3)).

How to calculate Power required at Altitude?

With Weight of Body (W_body), Drag Coefficient (C_D), Density (ρ₀), Reference Area (S) & Lift Coefficient (C_L) we can find Power required at Altitude using the formula - Power Required at Altitude = sqrt((2*Weight of Body^3*Drag Coefficient^2)/(Density*Reference Area*Lift Coefficient^3)). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Power Required at Altitude?

Here are the different ways to Calculate Power Required at Altitude-

Power Required at Altitude=Power Required at Sea-level*sqrt([Std-Air-Density-Sea]/Density)

Can the Power required at Altitude be negative?

No, the Power required at Altitude, measured in Power cannot be negative.

Which unit is used to measure Power required at Altitude?

Power required at Altitude is usually measured using the Watt[W] for Power. Kilowatt[W], Milliwatt[W], Microwatt[W] are the few other units in which Power required at Altitude can be measured.

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Power required at Altitude Formula

​GoPower required at Altitude given Power at sea-level Formula

Power required at Altitude Example

Power required at Altitude Solution

Power required at Altitude Formula Elements

Other Formulas to find Power Required at Altitude

Other formulas in Preliminary Aerodynamics category

How to Evaluate Power required at Altitude?

FAQs on Power required at Altitude

Variable Name

GoPower required at Altitude given Power at sea-level Formula