Bank angle during level turn Calculator

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Introduction and Governing Equations

Static Stability and Control

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✖Aircraft Weight refers to the total mass of an aircraft, including its structure, payload, fuel, and passengers.ⓘ Aircraft Weight [W]			+10% -10%
✖Lift Force is the aerodynamic force exerted on an object, such as an aircraft wing, perpendicular to the oncoming airflow.ⓘ Lift Force [F_L]			+10% -10%

✖Bank angle is the angle between the lift vector and the vertical during a level turn of the aircraft.ⓘ Bank angle during level turn [Φ]

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Formula

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Bank angle during level turn

Formula

`"Φ" = acos("W"/"F"_{"L"})`

Example

`"0.451027rad"=acos("18N"/"20N")`

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Bank angle during level turn Solution

STEP 0: Pre-Calculation Summary

Formula Used

Bank angle = acos(Aircraft Weight/Lift Force)
Φ = acos(W/F_L)
This formula uses 2 Functions, 3 Variables

Functions Used

cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)
acos - The inverse cosine function, is the inverse function of the cosine function. It is the function that takes a ratio as an input and returns the angle whose cosine is equal to that ratio., acos(Number)

Variables Used

Bank angle - (Measured in Radian) - Bank angle is the angle between the lift vector and the vertical during a level turn of the aircraft.
Aircraft Weight - (Measured in Newton) - Aircraft Weight refers to the total mass of an aircraft, including its structure, payload, fuel, and passengers.
Lift Force - (Measured in Newton) - Lift Force is the aerodynamic force exerted on an object, such as an aircraft wing, perpendicular to the oncoming airflow.

STEP 1: Convert Input(s) to Base Unit

Aircraft Weight: 18 Newton --> 18 Newton No Conversion Required
Lift Force: 20 Newton --> 20 Newton No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Φ = acos(W/F_L) --> acos(18/20)

Evaluating ... ...

Φ = 0.451026811796262

STEP 3: Convert Result to Output's Unit

0.451026811796262 Radian --> No Conversion Required

FINAL ANSWER

0.451026811796262 ≈ 0.451027 Radian <-- Bank angle

(Calculation completed in 00.004 seconds)

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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 Shikha Maurya

Indian Institute of Technology (IIT), Bombay

Shikha Maurya has verified this Calculator and 200+ more calculators!

< 13 Turning Flight Calculators

Velocity for given turn radius

Go Flight Velocity = sqrt(Turn Radius*[g]*(sqrt(Load Factor^2-1)))

Load Factor given Turn Radius

Go Load Factor = sqrt(1+(Flight Velocity^2/([g]*Turn Radius))^2)

Turn radius

Go Turn Radius = Flight Velocity^2/([g]*sqrt((Load Factor^2)-1))

Load Factor given Turn Rate

Go Load Factor = sqrt((Flight Velocity*Turn Rate/[g])^2+1)

Velocity for given turn rate

Go Flight Velocity = [g]*sqrt(Load Factor^2-1)/Turn Rate

Turn rate

Go Turn Rate = [g]*sqrt(Load Factor^2-1)/Flight Velocity

Rate of Turn

Go Turn Rate = 1091*tan(Bank angle)/Flight Velocity

Bank angle during level turn

Go Bank angle = acos(Aircraft Weight/Lift Force)

Weight of aircraft during level turn

Go Aircraft Weight = Lift Force*cos(Bank angle)

Lift during level turn

Go Lift Force = Aircraft Weight/cos(Bank angle)

Load factor given Lift Force and Weight of Aircraft

Go Load Factor = Lift Force/Aircraft Weight

Weight for given Load Factor

Go Aircraft Weight = Lift Force/Load Factor

Lift for given load factor

Go Lift Force = Load Factor*Aircraft Weight

Bank angle during level turn Formula

Bank angle = acos(Aircraft Weight/Lift Force)
Φ = acos(W/F_L)

Do planes lose altitude when turning?

Increased drag slows the airplane. Also, in a turn, there's less area of lift under a wing, causing it to lose altitude. However, to compensate, pilots angle the airplane up as well as increase thrust (speed) to maintain a constant altitude during a turn.

How to Calculate Bank angle during level turn?

Bank angle during level turn calculator uses Bank angle = acos(Aircraft Weight/Lift Force) to calculate the Bank angle, The Bank angle during level turn is given by the inverse cosine of the ratio of weight to lift of the aircraft. Bank angle is denoted by Φ symbol.

How to calculate Bank angle during level turn using this online calculator? To use this online calculator for Bank angle during level turn, enter Aircraft Weight (W) & Lift Force (F_L) and hit the calculate button. Here is how the Bank angle during level turn calculation can be explained with given input values -> 0.451027 = acos(18/20).

FAQ

What is Bank angle during level turn?

The Bank angle during level turn is given by the inverse cosine of the ratio of weight to lift of the aircraft and is represented as Φ = acos(W/F_L) or Bank angle = acos(Aircraft Weight/Lift Force). Aircraft Weight refers to the total mass of an aircraft, including its structure, payload, fuel, and passengers & Lift Force is the aerodynamic force exerted on an object, such as an aircraft wing, perpendicular to the oncoming airflow.

How to calculate Bank angle during level turn?

The Bank angle during level turn is given by the inverse cosine of the ratio of weight to lift of the aircraft is calculated using Bank angle = acos(Aircraft Weight/Lift Force). To calculate Bank angle during level turn, you need Aircraft Weight (W) & Lift Force (F_L). With our tool, you need to enter the respective value for Aircraft Weight & Lift Force and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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