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Lift Coefficient with respect to Roll Rate Formula

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Lift Coefficient with respect to Roll Rate refers to a parameter in aerodynamics that describes the change in lift coefficient with respect to the rate of roll of an aircraft. Check FAQs

Cl = - (\frac{2 \cdot p}{S r \cdot b \cdot u 0}) \cdot \int (Cl α \cdot c \cdot x^{2}, x, 0, \frac{b}{2})

Cl - Lift Coefficient with respect to Roll Rate?p - Roll Rate?S_r - Wing reference Area?b - Wingspan?u₀ - Reference Velocity across X Axis?Cl_α - Lift Curve Slope?c - Chord?

Lift Coefficient with respect to Roll Rate Example

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Here is how the Lift Coefficient with respect to Roll Rate equation looks like with Values.

Here is how the Lift Coefficient with respect to Roll Rate equation looks like with Units.

Here is how the Lift Coefficient with respect to Roll Rate equation looks like.

0.038 = - (\frac{2 \cdot 0.5}{184 \cdot 200 \cdot 50}) \cdot \int (-0.1 \cdot 2.1 \cdot x^{2}, x, 0, \frac{200}{2})

0.038 = - (\frac{2 \cdot 0.5rad/s²}{184m² \cdot 200m \cdot 50m/s}) \cdot \int (-0.1 \cdot 2.1m \cdot x^{2}, x, 0, \frac{200m}{2})

0.038 = - (\frac{2 \cdot 0.5}{184 \cdot 200 \cdot 50}) \cdot \int (-0.1 \cdot 2.1 \cdot x^{2}, x, 0, \frac{200}{2})

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Lift Coefficient with respect to Roll Rate Solution

Follow our step by step solution on how to calculate Lift Coefficient with respect to Roll Rate?

FIRST Step Consider the formula

Cl = - (\frac{2 \cdot p}{S r \cdot b \cdot u 0}) \cdot \int (Cl α \cdot c \cdot x^{2}, x, 0, \frac{b}{2})

Next Step Substitute values of Variables

∴

Cl = - (\frac{2 \cdot 0.5rad/s²}{184m² \cdot 200m \cdot 50m/s}) \cdot \int (-0.1 \cdot 2.1m \cdot x^{2}, x, 0, \frac{200m}{2})

Next Step Prepare to Evaluate

∴

Cl = - (\frac{2 \cdot 0.5}{184 \cdot 200 \cdot 50}) \cdot \int (-0.1 \cdot 2.1 \cdot x^{2}, x, 0, \frac{200}{2})

Next Step Evaluate

∴

Cl = 0.0380434782609357

LAST Step Rounding Answer

∴

Cl = 0.038

Lift Coefficient with respect to Roll Rate Formula Elements

Variables

Functions

Lift Coefficient with respect to Roll Rate

Lift Coefficient with respect to Roll Rate refers to a parameter in aerodynamics that describes the change in lift coefficient with respect to the rate of roll of an aircraft.

Symbol: Cl

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Lift Coefficient with respect to Roll Rate

Roll Rate

Roll Rate refers to the rate at which an aircraft rotates around its longitudinal axis, causing it to tilt or bank to one side.

Symbol: p

Measurement: Angular AccelerationUnit: rad/s²

Note: Value can be positive or negative.

Formulas to find Roll Rate

Wing reference Area

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

Symbol: S_r

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Wing reference 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

Reference Velocity across X Axis

Reference Velocity across X Axis typically refers to the velocity component along the x-axis (horizontal axis) of a coordinate system.

Symbol: u₀

Measurement: SpeedUnit: m/s

Note: Value can be positive or negative.

Formulas to find Reference Velocity across X Axis

Lift Curve Slope

The Lift Curve Slope refers to a characteristic parameter in aerodynamics that quantifies the change in lift coefficient with respect to the change in angle of attack of an airfoil or wing.

Symbol: Cl_α

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Lift Curve Slope

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)

How to Evaluate Lift Coefficient with respect to Roll Rate?

Lift Coefficient with respect to Roll Rate evaluator uses Lift Coefficient with 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) to evaluate the Lift Coefficient with respect to Roll Rate, Lift Coefficient with respect to Roll Rate refers to a parameter in aerodynamics that describes the change in lift coefficient with respect to the rate of roll of an aircraft. It quantifies how the lift generated by the wings of an aircraft changes as the aircraft rolls or banks to one side, influenced by the roll rate, wing reference area, wingspan, and air velocity, providing insight into the roll-induced lift forces acting on an aircraft or wing. Lift Coefficient with respect to Roll Rate is denoted by Cl symbol.

How to evaluate Lift Coefficient with respect to Roll Rate using this online evaluator? To use this online evaluator for Lift Coefficient with respect to Roll Rate, enter Roll Rate (p), Wing reference Area (S_r), Wingspan (b), Reference Velocity across X Axis (u₀), Lift Curve Slope (Cl_α) & Chord (c) and hit the calculate button.

FAQs on Lift Coefficient with respect to Roll Rate

What is the formula to find Lift Coefficient with respect to Roll Rate?

The formula of Lift Coefficient with respect to Roll Rate is expressed as Lift Coefficient with 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). Here is an example- 0.038043 = -((2*0.5)/(184*200*50))*int((-0.1)*2.1*x^2,x,0,200/2).

How to calculate Lift Coefficient with respect to Roll Rate?

With Roll Rate (p), Wing reference Area (S_r), Wingspan (b), Reference Velocity across X Axis (u₀), Lift Curve Slope (Cl_α) & Chord (c) we can find Lift Coefficient with respect to Roll Rate using the formula - Lift Coefficient with 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). This formula also uses Definite Integral (int) function(s).

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Lift Coefficient with respect to Roll Rate Formula

Lift Coefficient with respect to Roll Rate Example

Lift Coefficient with respect to Roll Rate Solution

Lift Coefficient with respect to Roll Rate Formula Elements

Other formulas in Lateral Control category

How to Evaluate Lift Coefficient with respect to Roll Rate?

FAQs on Lift Coefficient with respect to Roll Rate

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