Turn rate for given wing loading Solution

STEP 0: Pre-Calculation Summary
Formula Used
Turn Rate = [g]*(sqrt(Freestream density*Lift Coefficient*Load factor/(2*Wing Loading)))
ฯ‰ = [g]*(sqrt(ฯโˆž*CL*n/(2*WS)))
This formula uses 1 Constants, 1 Functions, 5 Variables
Constants Used
[g] - Gravitational acceleration on Earth Value Taken As 9.80665
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
Turn Rate - (Measured in Radian per Second) - Turn Rate is the rate at which an aircraft executes a turn expressed in degrees per second.
Freestream density - (Measured in Kilogram per Cubic Meter) - Freestream density is the mass per unit volume of air far upstream of an aerodynamic body at a given altitude.
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.
Load factor - Load factor is the ratio of the aerodynamic force on the aircraft to the gross weight of the aircraft.
Wing Loading - (Measured in Pascal) - Wing Loading is the loaded weight of the aircraft divided by the area of the wing.
STEP 1: Convert Input(s) to Base Unit
Freestream density: 1.225 Kilogram per Cubic Meter --> 1.225 Kilogram per Cubic Meter No Conversion Required
Lift Coefficient: 0.002 --> No Conversion Required
Load factor: 1.2 --> No Conversion Required
Wing Loading: 5 Pascal --> 5 Pascal No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
ฯ‰ = [g]*(sqrt(ฯโˆž*CL*n/(2*WS))) --> [g]*(sqrt(1.225*0.002*1.2/(2*5)))
Evaluating ... ...
ฯ‰ = 0.168149020102453
STEP 3: Convert Result to Output's Unit
0.168149020102453 Radian per Second -->9.63422918113278 Degree per Second (Check conversion here)
FINAL ANSWER
9.63422918113278 โ‰ˆ 9.634229 Degree per Second <-- Turn Rate
(Calculation completed in 00.004 seconds)

Credits

Created by Vinay Mishra
Indian Institute for Aeronautical Engineering and Information Technology (IIAEIT), Pune
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Indian Institute of Technology (IIT), Bombay
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25 High Load Factor Maneuver Calculators

Turn rate for given lift coefficient
Go Turn Rate = [g]*(sqrt((Reference Area*Freestream density*Lift Coefficient*Load factor)/(2*Aircraft weight)))
Turn rate for given wing loading
Go Turn Rate = [g]*(sqrt(Freestream density*Lift Coefficient*Load factor/(2*Wing Loading)))
Lift Coefficient for given turn rate
Go Lift Coefficient = 2*Aircraft weight*(Turn Rate^2)/(([g]^2)*Freestream density*Load factor*Reference Area)
Lift Coefficient for given Turn Radius
Go Lift Coefficient = Aircraft weight/(0.5*Freestream density*Reference Area*[g]*Turn Radius)
Radius of turn for given lift coefficient
Go Turn Radius = 2*Aircraft weight/(Freestream density*Reference Area*[g]*Lift Coefficient)
Wing loading for given turn rate
Go Wing Loading = ([g]^2)*Freestream density*Lift Coefficient*Load factor/(2*(Turn Rate^2))
Lift Coefficient for given wing loading and turn radius
Go Lift Coefficient = 2*Wing Loading/(Freestream density*Turn Radius*[g])
Radius of turn for given wing loading
Go Turn Radius = 2*Wing Loading/(Freestream density*Lift Coefficient*[g])
Wing loading for given turn radius
Go Wing Loading = (Turn Radius*Freestream density*Lift Coefficient*[g])/2
Velocity for given pull-up maneuver radius
Go Velocity = sqrt(Turn Radius*[g]*(Load factor-1))
Velocity given Pull-down Maneuver Radius
Go Velocity = sqrt(Turn Radius*[g]*(Load factor+1))
Velocity given Turn Radius for High Load Factor
Go Velocity = sqrt(Turn Radius*Load factor*[g])
Change in Angle of Attack due to Upward Gust
Go Change in Angle of Attack = tan(Gust Velocity/Flight Velocity)
Load Factor given Pull-down Maneuver Radius
Go Load factor = ((Velocity^2)/(Turn Radius*[g]))-1
Load Factor given Pull-UP Maneuver Radius
Go Load factor = 1+((Velocity^2)/(Turn Radius*[g]))
Pull-down maneuver radius
Go Turn Radius = (Velocity^2)/([g]*(Load factor+1))
Pull-up maneuver radius
Go Turn Radius = (Velocity^2)/([g]*(Load factor-1))
Load factor for given turn radius for high-performance fighter aircraft
Go Load factor = (Velocity^2)/([g]*Turn Radius)
Turn radius for high load factor
Go Turn Radius = (Velocity^2)/([g]*Load factor)
Velocity for given pull-up maneuver rate
Go Velocity = [g]*(Load factor-1)/Turn Rate
Load Factor given Pull-Up Maneuver Rate
Go Load factor = 1+(Velocity*Turn Rate/[g])
Pull-down maneuver rate
Go Turn Rate = [g]*(1+Load factor)/Velocity
Pull-up maneuver rate
Go Turn Rate = [g]*(Load factor-1)/Velocity
Load factor for given turn rate for high-performance fighter aircraft
Go Load factor = Velocity*Turn Rate/[g]
Turn rate for high load factor
Go Turn Rate = [g]*Load factor/Velocity

Turn rate for given wing loading Formula

Turn Rate = [g]*(sqrt(Freestream density*Lift Coefficient*Load factor/(2*Wing Loading)))
ฯ‰ = [g]*(sqrt(ฯโˆž*CL*n/(2*WS)))

Can we estimate thrust loading based on wing loading?

Thrust loading and wing loading are one of the crucial parameters of an aircraft design. A designer can find both of them either by estimating thrust loading and then evaluating the wing loading or vice-versa.

How to Calculate Turn rate for given wing loading?

Turn rate for given wing loading calculator uses Turn Rate = [g]*(sqrt(Freestream density*Lift Coefficient*Load factor/(2*Wing Loading))) to calculate the Turn Rate, The Turn rate for given wing loading depends on the altitude, lift coefficient, load factor and wing loading of the aircraft. Turn Rate is denoted by ฯ‰ symbol.

How to calculate Turn rate for given wing loading using this online calculator? To use this online calculator for Turn rate for given wing loading, enter Freestream density (ฯโˆž), Lift Coefficient (CL), Load factor (n) & Wing Loading (WS) and hit the calculate button. Here is how the Turn rate for given wing loading calculation can be explained with given input values -> 552.0007 = [g]*(sqrt(1.225*0.002*1.2/(2*5))).

FAQ

What is Turn rate for given wing loading?
The Turn rate for given wing loading depends on the altitude, lift coefficient, load factor and wing loading of the aircraft and is represented as ฯ‰ = [g]*(sqrt(ฯโˆž*CL*n/(2*WS))) or Turn Rate = [g]*(sqrt(Freestream density*Lift Coefficient*Load factor/(2*Wing Loading))). Freestream density is the mass per unit volume of air far upstream of an aerodynamic body at a given altitude, 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, Load factor is the ratio of the aerodynamic force on the aircraft to the gross weight of the aircraft & Wing Loading is the loaded weight of the aircraft divided by the area of the wing.
How to calculate Turn rate for given wing loading?
The Turn rate for given wing loading depends on the altitude, lift coefficient, load factor and wing loading of the aircraft is calculated using Turn Rate = [g]*(sqrt(Freestream density*Lift Coefficient*Load factor/(2*Wing Loading))). To calculate Turn rate for given wing loading, you need Freestream density (ฯโˆž), Lift Coefficient (CL), Load factor (n) & Wing Loading (WS). With our tool, you need to enter the respective value for Freestream density, Lift Coefficient, Load factor & Wing Loading 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 Turn Rate?
In this formula, Turn Rate uses Freestream density, Lift Coefficient, Load factor & Wing Loading. We can use 4 other way(s) to calculate the same, which is/are as follows -
  • Turn Rate = [g]*Load factor/Velocity
  • Turn Rate = [g]*(sqrt((Reference Area*Freestream density*Lift Coefficient*Load factor)/(2*Aircraft weight)))
  • Turn Rate = [g]*(Load factor-1)/Velocity
  • Turn Rate = [g]*(1+Load factor)/Velocity
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