Power required at Altitude Solution

STEP 0: Pre-Calculation Summary
Formula Used
Power required at an altitude = sqrt((2*Weight of body^3*Drag Coefficient^2)/(Density*Reference Area*Lift Coefficient^3))
PR,alt = sqrt((2*Wbody^3*CD^2)/(ρ0*S*CL^3))
This formula uses 1 Functions, 6 Variables
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).
Weight of body - (Measured in Newton) - Weight of body is the force acting on the object due to gravity.
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.
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.
Reference Area - (Measured in Square Meter) - 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.
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.
STEP 1: Convert Input(s) to Base Unit
Weight of body: 750 Newton --> 750 Newton No Conversion Required
Drag Coefficient: 1.134 --> No Conversion Required
Density: 997 Kilogram per Cubic Meter --> 997 Kilogram per Cubic Meter No Conversion Required
Reference Area: 91.05 Square Meter --> 91.05 Square Meter No Conversion Required
Lift Coefficient: 0.29 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
PR,alt = sqrt((2*Wbody^3*CD^2)/(ρ0*S*CL^3)) --> sqrt((2*750^3*1.134^2)/(997*91.05*0.29^3))
Evaluating ... ...
PR,alt = 700.060213980307
STEP 3: Convert Result to Output's Unit
700.060213980307 Watt --> No Conversion Required
FINAL ANSWER
700.060213980307 700.0602 Watt <-- Power required at an altitude
(Calculation completed in 00.004 seconds)

Credits

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
Maiarutselvan V has verified this Calculator and 300+ more calculators!

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 Formula

Power required at an altitude = sqrt((2*Weight of body^3*Drag Coefficient^2)/(Density*Reference Area*Lift Coefficient^3))
PR,alt = sqrt((2*Wbody^3*CD^2)/(ρ0*S*CL^3))

How fast can you go in a commercial airliner?

For civil aircraft, there is an airspeed limit of Mach 1 which is 667 knots or around 767 miles per hour.

How to Calculate Power required at Altitude?

Power required at Altitude calculator uses Power required at an altitude = sqrt((2*Weight of body^3*Drag Coefficient^2)/(Density*Reference Area*Lift Coefficient^3)) to calculate the Power required at an altitude, The Power required at Altitude for an aircraft is a function of the weight, reference area, aerodynamic coefficients of the aircraft, and the density of air at that altitude. Power required at an altitude is denoted by PR,alt symbol.

How to calculate Power required at Altitude using this online calculator? To use this online calculator for Power required at Altitude, enter Weight of body (Wbody), Drag Coefficient (CD), Density 0), Reference Area (S) & Lift Coefficient (CL) and hit the calculate button. Here is how the Power required at Altitude calculation can be explained with given input values -> 699.8681 = sqrt((2*750^3*1.134^2)/(997*91.05*0.29^3)).

FAQ

What is Power required at Altitude?
The Power required at Altitude for an aircraft is a function of the weight, reference area, aerodynamic coefficients of the aircraft, and the density of air at that altitude and is represented as PR,alt = sqrt((2*Wbody^3*CD^2)/(ρ0*S*CL^3)) or Power required at an altitude = sqrt((2*Weight of body^3*Drag Coefficient^2)/(Density*Reference Area*Lift Coefficient^3)). Weight of body is the force acting on the object due to gravity, 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, 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, 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 & 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.
How to calculate Power required at Altitude?
The Power required at Altitude for an aircraft is a function of the weight, reference area, aerodynamic coefficients of the aircraft, and the density of air at that altitude is calculated using Power required at an altitude = sqrt((2*Weight of body^3*Drag Coefficient^2)/(Density*Reference Area*Lift Coefficient^3)). To calculate Power required at Altitude, you need Weight of body (Wbody), Drag Coefficient (CD), Density 0), Reference Area (S) & Lift Coefficient (CL). With our tool, you need to enter the respective value for Weight of body, Drag Coefficient, Density, Reference Area & Lift Coefficient 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 Weight of body, Drag Coefficient, Density, Reference Area & Lift Coefficient. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Power required at an altitude = Power required at sea-level*sqrt([Std-Air-Density-Sea]/Density)
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