Roll Damping Coefficient Calculator

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Static Stability and Control

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Introduction and Governing Equations

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Lateral Control

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✖Derivative of wing lift coefficient is the lift curve slope, which is a measure of how much lift changes when the angle of attack of an aircraft changes.ⓘ Derivative of Wing Lift Coefficient [C_lαw]			+10% -10%
✖The Wing area, S, is the projected area of the planform and is bounded by the leading and trailing edges and the wing tips.ⓘ Wing Area [S]			+10% -10%
✖The Wingspan (or just span) of a bird or an airplane is the distance from one wingtip to the other wingtip.ⓘ Wingspan [b]			+10% -10%
✖The chord the distance between the trailing edge and the point where the chord intersects the leading edge.ⓘ Chord [c]			+10% -10%

✖Roll damping coefficient is the airplane's rolling-moment response to a roll rate.ⓘ Roll Damping Coefficient [Cl_p]

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Formula

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Roll Damping Coefficient

Formula

`"Cl"_{"p"} = -(4*"C"_{"lαw"})/("S"*"b"^2)*int("c"*x^2,x,0,"b"/2)`

Example

`"-0.947059"=-(4*"0.23")/("17m²"*("200m")^2)*int("2.1m"*x^2,x,0,"200m"/2)`

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Roll Damping Coefficient Solution

STEP 0: Pre-Calculation Summary

Formula Used

Roll Damping Coefficient = -(4*Derivative of Wing Lift Coefficient)/(Wing Area*Wingspan^2)*int(Chord*x^2,x,0,Wingspan/2)
Cl_p = -(4*C_lαw)/(S*b^2)*int(c*x^2,x,0,b/2)
This formula uses 1 Functions, 5 Variables

Functions Used

int - The definite integral can be used to calculate net signed area, which is the area above the x -axis minus the area below the x -axis., int(expr, arg, from, to)

Variables Used

Roll Damping Coefficient - Roll damping coefficient is the airplane's rolling-moment response to a roll rate.
Derivative of Wing Lift Coefficient - Derivative of wing lift coefficient is the lift curve slope, which is a measure of how much lift changes when the angle of attack of an aircraft changes.
Wing Area - (Measured in Square Meter) - The Wing area, S, is the projected area of the planform and is bounded by the leading and trailing edges and the wing tips.
Wingspan - (Measured in Meter) - The Wingspan (or just span) of a bird or an airplane is the distance from one wingtip to the other wingtip.
Chord - (Measured in Meter) - The chord the distance between the trailing edge and the point where the chord intersects the leading edge.

STEP 1: Convert Input(s) to Base Unit

Derivative of Wing Lift Coefficient: 0.23 --> No Conversion Required
Wing Area: 17 Square Meter --> 17 Square Meter No Conversion Required
Wingspan: 200 Meter --> 200 Meter No Conversion Required
Chord: 2.1 Meter --> 2.1 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Cl_p = -(4*C_lαw)/(S*b^2)*int(c*x^2,x,0,b/2) --> -(4*0.23)/(17*200^2)*int(2.1*x^2,x,0,200/2)

Evaluating ... ...

Cl_p = -0.947058823529875

STEP 3: Convert Result to Output's Unit

-0.947058823529875 --> No Conversion Required

FINAL ANSWER

-0.947058823529875 ≈ -0.947059 <-- Roll Damping Coefficient

(Calculation completed in 00.601 seconds)

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< 10+ Lateral Control Calculators

Aileron Deflection Given Aileron Lift Coefficient

Go Lift Coefficient Roll Control = (2*Derivative of Wing Lift Coefficient*Flap Effectiveness Parameter*Deflection of Aileron)/(Wing Area*Wingspan)*int(Chord*x,x,Initial Length,Final Length)

Lift Coefficient with respect to Roll Rate

Go Lift Coefficient Respect to Roll Rate = -((2*Roll Rate)/(Wing Reference Area*Wingspan*Reference Velocity Across X Axis))*int(Lift Curve Slope*Chord*x^2,x,0,Wingspan/2)

Roll Control Power

Go Roll Control Power = (2*Derivative of Wing Lift Coefficient*Flap Effectiveness Parameter)/(Wing Area*Wingspan)*int(Chord*x,x,Initial Length,Final Length)

Lift given Roll Rate

Go Lift Respect to Roll Rate = -2*int(Lift Curve Slope*((Roll Rate*x)/Reference Velocity Across X Axis)*Pitch Rate*Chord*x,x,0,Wingspan/2)

Roll Damping Coefficient

Go Roll Damping Coefficient = -(4*Derivative of Wing Lift Coefficient)/(Wing Area*Wingspan^2)*int(Chord*x^2,x,0,Wingspan/2)

Aileron Section lift Coefficient given Aileron Deflection

Go Lift Coefficient Roll Control = Lift Coefficient Slope Roll Control*(Rate of change of Angle of Attack/Rate of change of Deflection of Aileron)*Deflection of Aileron

Aileron Control Effectiveness given Aileron Deflection

Go Flap Effectiveness Parameter = Lift Coefficient Roll Control/(Lift Coefficient Slope Roll Control*Deflection of Aileron)

Deflection Angle given Lift Coefficient

Go Deflection of Aileron = Lift Coefficient Roll Control/(Lift Coefficient Slope Roll Control*Flap Effectiveness Parameter)

Lift Coefficient Slope Roll Control

Go Lift Coefficient Slope Roll Control = Lift Coefficient Roll Control/(Deflection of Aileron*Flap Effectiveness Parameter)

Aileron Section Lift Coefficient given Control Effectiveness

Go Lift Coefficient Roll Control = Lift Coefficient Slope Roll Control*Flap Effectiveness Parameter*Deflection of Aileron

Roll Damping Coefficient Formula

Roll Damping Coefficient = -(4*Derivative of Wing Lift Coefficient)/(Wing Area*Wingspan^2)*int(Chord*x^2,x,0,Wingspan/2)
Cl_p = -(4*C_lαw)/(S*b^2)*int(c*x^2,x,0,b/2)

What is Roll damping coefficient?

Roll damping is the airplane's rolling-moment response to a roll rate. It depends on how the lift of the wings changes with roll rate.

What is roll damping moment

The rolling motion induces an AOA increase on the down-going wing, and an AOA decrease on the up-going wing which creates an opposing moment known as the roll damping moment.

How to Calculate Roll Damping Coefficient?

Roll Damping Coefficient calculator uses Roll Damping Coefficient = -(4*Derivative of Wing Lift Coefficient)/(Wing Area*Wingspan^2)*int(Chord*x^2,x,0,Wingspan/2) to calculate the Roll Damping Coefficient, The Roll Damping Coefficient formula is defined as the airplane's rolling-moment response to a roll rate. Roll Damping Coefficient is denoted by Cl_p symbol.

How to calculate Roll Damping Coefficient using this online calculator? To use this online calculator for Roll Damping Coefficient, enter Derivative of Wing Lift Coefficient (C_lαw), Wing Area (S), Wingspan (b) & Chord (c) and hit the calculate button. Here is how the Roll Damping Coefficient calculation can be explained with given input values -> -0.094706 = -(4*0.23)/(17*200^2)*int(2.1*x^2,x,0,200/2).

FAQ

What is Roll Damping Coefficient?

The Roll Damping Coefficient formula is defined as the airplane's rolling-moment response to a roll rate and is represented as Cl_p = -(4*C_lαw)/(S*b^2)*int(c*x^2,x,0,b/2) or Roll Damping Coefficient = -(4*Derivative of Wing Lift Coefficient)/(Wing Area*Wingspan^2)*int(Chord*x^2,x,0,Wingspan/2). Derivative of wing lift coefficient is the lift curve slope, which is a measure of how much lift changes when the angle of attack of an aircraft changes, The Wing area, S, is the projected area of the planform and is bounded by the leading and trailing edges and the wing tips, The Wingspan (or just span) of a bird or an airplane is the distance from one wingtip to the other wingtip & The chord the distance between the trailing edge and the point where the chord intersects the leading edge.

How to calculate Roll Damping Coefficient?

The Roll Damping Coefficient formula is defined as the airplane's rolling-moment response to a roll rate is calculated using Roll Damping Coefficient = -(4*Derivative of Wing Lift Coefficient)/(Wing Area*Wingspan^2)*int(Chord*x^2,x,0,Wingspan/2). To calculate Roll Damping Coefficient, you need Derivative of Wing Lift Coefficient (C_lαw), Wing Area (S), Wingspan (b) & Chord (c). With our tool, you need to enter the respective value for Derivative of Wing Lift Coefficient, Wing Area, Wingspan & Chord 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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