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Roll Damping Coefficient Formula

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Roll Damping Coefficient is the measure of damping in airplane's rolling-moment response to a roll rate. Check FAQs

Cl p = - \frac{4 \cdot C lαw}{S \cdot b^{2}} \cdot \int (c \cdot x^{2}, x, 0, \frac{b}{2})

Cl_p - Roll Damping Coefficient?C_lαw - Derivative of Wing Lift Coefficient?S - Wing Area?b - Wingspan?c - Chord?

Roll Damping Coefficient Example

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Here is how the Roll Damping Coefficient equation looks like with Values.

Here is how the Roll Damping Coefficient equation looks like with Units.

Here is how the Roll Damping Coefficient equation looks like.

-0.9471 = - \frac{4 \cdot 0.23}{17 \cdot 200^{2}} \cdot \int (2.1 \cdot x^{2}, x, 0, \frac{200}{2})

-0.9471 = - \frac{4 \cdot 0.23}{17m² \cdot {200m}^{2}} \cdot \int (2.1m \cdot x^{2}, x, 0, \frac{200m}{2})

-0.9471 = - \frac{4 \cdot 0.23}{17 \cdot 200^{2}} \cdot \int (2.1 \cdot x^{2}, x, 0, \frac{200}{2})

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Roll Damping Coefficient Solution

Follow our step by step solution on how to calculate Roll Damping Coefficient?

FIRST Step Consider the formula

Cl p = - \frac{4 \cdot C lαw}{S \cdot b^{2}} \cdot \int (c \cdot x^{2}, x, 0, \frac{b}{2})

Next Step Substitute values of Variables

∴

Cl p = - \frac{4 \cdot 0.23}{17m² \cdot {200m}^{2}} \cdot \int (2.1m \cdot x^{2}, x, 0, \frac{200m}{2})

Next Step Prepare to Evaluate

∴

Cl p = - \frac{4 \cdot 0.23}{17 \cdot 200^{2}} \cdot \int (2.1 \cdot x^{2}, x, 0, \frac{200}{2})

Next Step Evaluate

∴

Cl p = -0.947058823529875

LAST Step Rounding Answer

∴

Cl p = -0.9471

Roll Damping Coefficient Formula Elements

Variables

Functions

Roll Damping Coefficient

Roll Damping Coefficient is the measure of damping in airplane's rolling-moment response to a roll rate.

Symbol: Cl_p

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Roll Damping Coefficient

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.

Symbol: C_lαw

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Derivative of Wing Lift Coefficient

Wing Area

The Wing Area, S, is the projected area of the planform and is bounded by the leading and trailing edges and the wing tips.

Symbol: S

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Wing Area

Wingspan

The Wingspan (or just span) of a bird or an airplane is the distance from one wingtip to the other wingtip.

Symbol: b

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Wingspan

Chord

The Chord is the distance between the trailing edge and the point where the chord intersects the leading edge.

Symbol: c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Chord

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.

Syntax: int(expr, arg, from, to)

Other formulas in Lateral Control category

Go Aileron Section lift Coefficient given Aileron Deflection

C l = C lα \cdot (\frac{dα}{dδ a}) \cdot δ a

Go Aileron Deflection given Aileron Lift Coefficient

C l = \frac{2 \cdot C lαw \cdot τ \cdot δ a}{S \cdot b} \cdot \int (c \cdot x, x, y 1, y 2)

Go Aileron Control Effectiveness given Aileron Deflection

τ = \frac{C l}{C lα \cdot δ a}

Go Roll Control Power

Cl δα = \frac{2 \cdot C lαw \cdot τ}{S \cdot b} \cdot \int (c \cdot x, x, y 1, y 2)

How to Evaluate Roll Damping Coefficient?

Roll Damping Coefficient evaluator uses Roll Damping Coefficient = -(4*Derivative of Wing Lift Coefficient)/(Wing Area*Wingspan^2)*int(Chord*x^2,x,0,Wingspan/2) to evaluate the Roll Damping Coefficient, Roll Damping Coefficient is a measure of the resistance to rolling motion of an aircraft, it is calculated by combining the derivative of wing lift coefficient, wing area, and wing span, integrating the chord length over half the wing span, this coefficient helps aircraft designers and engineers to optimize wing design for better roll control and overall aircraft performance, it is a critical factor in ensuring the stability and maneuverability of an aircraft. Roll Damping Coefficient is denoted by Cl_p symbol.

How to evaluate Roll Damping Coefficient using this online evaluator? To use this online evaluator for Roll Damping Coefficient, enter Derivative of Wing Lift Coefficient (C_lαw), Wing Area (S), Wingspan (b) & Chord (c) and hit the calculate button.

FAQs on Roll Damping Coefficient

What is the formula to find Roll Damping Coefficient?

The formula of Roll Damping Coefficient is expressed as Roll Damping Coefficient = -(4*Derivative of Wing Lift Coefficient)/(Wing Area*Wingspan^2)*int(Chord*x^2,x,0,Wingspan/2). Here is an example- -0.947059 = -(4*0.23)/(17*200^2)*int(2.1*x^2,x,0,200/2).

How to calculate Roll Damping Coefficient?

With Derivative of Wing Lift Coefficient (C_lαw), Wing Area (S), Wingspan (b) & Chord (c) we can find Roll Damping Coefficient using the formula - Roll Damping Coefficient = -(4*Derivative of Wing Lift Coefficient)/(Wing Area*Wingspan^2)*int(Chord*x^2,x,0,Wingspan/2). This formula also uses Definite Integral (int) function(s).

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Roll Damping Coefficient Formula

Roll Damping Coefficient Example

Roll Damping Coefficient Solution

Roll Damping Coefficient Formula Elements

Other formulas in Lateral Control category

How to Evaluate Roll Damping Coefficient?

FAQs on Roll Damping Coefficient

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