Power required at Altitude given Power at sea-level Calculator

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Introduction and Governing Equations

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✖Power required at sea-level is the power required by an aircraft to fly at the sea-level condition.ⓘ Power required at sea-level [P_R,0]			+10% -10%
✖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.ⓘ Density [ρ₀]			+10% -10%

✖Power required at an altitude is the power required for an aircraft to fly with a specific velocity at an altitude for a given altitude (or density).ⓘ Power required at Altitude given Power at sea-level [P_R,alt]

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Formula

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Power required at Altitude given Power at sea-level

Formula

`"P"_{"R,alt"} = "P"_{"R,0"}*sqrt("[Std-Air-Density-Sea]"/"ρ"_{"0"})`

Example

`"700.0894W"="19940W"*sqrt("[Std-Air-Density-Sea]"/"997kg/m³")`

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Power required at Altitude given Power at sea-level Solution

STEP 0: Pre-Calculation Summary

Formula Used

Power required at an altitude = Power required at sea-level*sqrt([Std-Air-Density-Sea]/Density)
P_R,alt = P_R,0*sqrt([Std-Air-Density-Sea]/ρ₀)
This formula uses 1 Constants, 1 Functions, 3 Variables

Constants Used

[Std-Air-Density-Sea] - Standard air density at sea-level conditions Value Taken As 1.229

Functions Used

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., sqrt(Number)

Variables Used

Power required at an altitude - (Measured in Watt) - Power required at an altitude is the power required for an aircraft to fly with a specific velocity at an altitude for a given altitude (or density).
Power required at sea-level - (Measured in Watt) - Power required at sea-level is the power required by an aircraft to fly at the sea-level condition.
Density - (Measured in Kilogram per Cubic Meter) - 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.

STEP 1: Convert Input(s) to Base Unit

Power required at sea-level: 19940 Watt --> 19940 Watt No Conversion Required
Density: 997 Kilogram per Cubic Meter --> 997 Kilogram per Cubic Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

P_R,alt = P_R,0*sqrt([Std-Air-Density-Sea]/ρ₀) --> 19940*sqrt([Std-Air-Density-Sea]/997)

Evaluating ... ...

P_R,alt = 700.08942285968

STEP 3: Convert Result to Output's Unit

700.08942285968 Watt --> No Conversion Required

FINAL ANSWER

700.08942285968 ≈ 700.0894 Watt <-- Power required at an altitude

(Calculation completed in 00.004 seconds)

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Created by Vinay Mishra

Indian Institute for Aeronautical Engineering and Information Technology (IIAEIT), Pune

Vinay Mishra has created this Calculator and 300+ more calculators!

Verified by Maiarutselvan V

PSG College of Technology (PSGCT), Coimbatore

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< 17 Preliminary Aerodynamics Calculators

Power required at sea-level conditions

Go Power required at sea-level = sqrt((2*Weight of body^3*Drag Coefficient^2)/([Std-Air-Density-Sea]*Reference Area*Lift Coefficient^3))

Mach Number-2

Go Mach number 2 = sqrt(((((Heat Capacity Ratio-1)*Mach Number^(2)+2))/(2*Heat Capacity Ratio*Mach Number^(2)-(Heat Capacity Ratio-1))))

Power required at Altitude

Go Power required at an altitude = sqrt((2*Weight of body^3*Drag Coefficient^2)/(Density*Reference Area*Lift Coefficient^3))

Velocity at Sea-level given Lift Coefficient

Go Velocity at sea-level = sqrt((2*Weight of body)/([Std-Air-Density-Sea]*Reference Area*Lift Coefficient))

Dynamic pressure given gas constant

Go Dynamic Pressure = 1/2*Ambient air density*Mach Number^2*Specific Heat of Air*Gas Constant*Temperature

Velocity at Altitude

Go Velocity at an altitude = sqrt(2*Weight of body/(Density*Reference Area*Lift Coefficient))

Power required at Altitude given Power at sea-level

Go Power required at an altitude = Power required at sea-level*sqrt([Std-Air-Density-Sea]/Density)

Velocity at Altitude given Velocity at Sea-Level

Go Velocity at an altitude = Velocity at sea-level*sqrt([Std-Air-Density-Sea]/Density)

Dynamic pressure given induced drag

Go Dynamic Pressure = Lift Force^2/(pi*Induced Drag*Lateral plane span^2)

Dynamic pressure given mach number

Go Dynamic Pressure = 1/2*Ambient air density*(Mach Number*Sonic speed)^2

Dynamic pressure given normal pressure

Go Dynamic Pressure = 1/2*Specific Heat of Air*Pressure*Mach Number^2

Flight speed given dynamic pressure

Go Flight speed = sqrt((2*Dynamic Pressure)/Ambient air density)

Dynamic pressure aircraft

Go Dynamic Pressure = 1/2*Ambient air density*Flight speed^2

Dynamic pressure given lift coefficient

Go Dynamic Pressure = Lift Force/Lift Coefficient

Dynamic pressure given drag coefficient

Go Dynamic Pressure = Drag Force/Drag Coefficient

Aerodynamic force

Go Aerodynamic Force = Drag Force+Lift Force

Mach number of moving object

Go Mach Number = Velocity/Speed of Sound

Power required at Altitude given Power at sea-level Formula

Power required at an altitude = Power required at sea-level*sqrt([Std-Air-Density-Sea]/Density)
P_R,alt = P_R,0*sqrt([Std-Air-Density-Sea]/ρ₀)

How Do Airplanes Fly Faster?

To go “faster”, airplanes have two options: increase thrust or decrease drag. Thrust is created by the engine and drag is created by anything that produces wind resistance.

How to Calculate Power required at Altitude given Power at sea-level?

Power required at Altitude given Power at sea-level calculator uses Power required at an altitude = Power required at sea-level*sqrt([Std-Air-Density-Sea]/Density) to calculate the Power required at an altitude, The Power required at Altitude given Power at sea-level is a function of the density of air at that altitude. Power required at an altitude is denoted by P_R,alt symbol.

How to calculate Power required at Altitude given Power at sea-level using this online calculator? To use this online calculator for Power required at Altitude given Power at sea-level, enter Power required at sea-level (P_R,0) & Density (ρ₀) and hit the calculate button. Here is how the Power required at Altitude given Power at sea-level calculation can be explained with given input values -> 700.581 = 19940*sqrt([Std-Air-Density-Sea]/997).

FAQ

What is Power required at Altitude given Power at sea-level?

The Power required at Altitude given Power at sea-level is a function of the density of air at that altitude and is represented as P_R,alt = P_R,0*sqrt([Std-Air-Density-Sea]/ρ₀) or Power required at an altitude = Power required at sea-level*sqrt([Std-Air-Density-Sea]/Density). Power required at sea-level is the power required by an aircraft to fly at the sea-level condition & 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.

How to calculate Power required at Altitude given Power at sea-level?

The Power required at Altitude given Power at sea-level is a function of the density of air at that altitude is calculated using Power required at an altitude = Power required at sea-level*sqrt([Std-Air-Density-Sea]/Density). To calculate Power required at Altitude given Power at sea-level, you need Power required at sea-level (P_R,0) & Density (ρ₀). With our tool, you need to enter the respective value for Power required at sea-level & Density and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Power required at an altitude?

In this formula, Power required at an altitude uses Power required at sea-level & Density. We can use 1 other way(s) to calculate the same, which is/are as follows -

Power required at an altitude = sqrt((2*Weight of body^3*Drag Coefficient^2)/(Density*Reference Area*Lift Coefficient^3))

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