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Lift given Roll Rate Formula

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Lift with respect to Roll Rate refers to the relationship between the lift force generated by an aircraft's wings and the rate at which the aircraft rolls about its longitudinal axis. Check FAQs

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

L - Lift with respect to Roll Rate?Cl_α - Lift Curve Slope?p - Roll Rate?u₀ - Reference Velocity across X Axis?Q - Pitch Rate?c - Chord?b - Wingspan?

Lift given Roll Rate Example

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Here is how the Lift given Roll Rate equation looks like with Values.

Here is how the Lift given Roll Rate equation looks like with Units.

Here is how the Lift given Roll Rate equation looks like.

770 = - 2 \cdot \int (-0.1 \cdot (\frac{0.5 \cdot x}{50}) \cdot 0.55 \cdot 2.1 \cdot x, x, 0, \frac{200}{2})

770N = - 2 \cdot \int (-0.1 \cdot (\frac{0.5rad/s² \cdot x}{50m/s}) \cdot 0.55rad/s² \cdot 2.1m \cdot x, x, 0, \frac{200m}{2})

770 = - 2 \cdot \int (-0.1 \cdot (\frac{0.5 \cdot x}{50}) \cdot 0.55 \cdot 2.1 \cdot x, x, 0, \frac{200}{2})

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Lift given Roll Rate Solution

Follow our step by step solution on how to calculate Lift given Roll Rate?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

L = - 2 \cdot \int (-0.1 \cdot (\frac{0.5rad/s² \cdot x}{50m/s}) \cdot 0.55rad/s² \cdot 2.1m \cdot x, x, 0, \frac{200m}{2})

Next Step Prepare to Evaluate

∴

L = - 2 \cdot \int (-0.1 \cdot (\frac{0.5 \cdot x}{50}) \cdot 0.55 \cdot 2.1 \cdot x, x, 0, \frac{200}{2})

Next Step Evaluate

∴

L = 770.000000358559N

LAST Step Rounding Answer

∴

L = 770N

Lift given Roll Rate Formula Elements

Variables

Functions

Lift with respect to Roll Rate

Lift with respect to Roll Rate refers to the relationship between the lift force generated by an aircraft's wings and the rate at which the aircraft rolls about its longitudinal axis.

Symbol: L

Measurement: ForceUnit: N

Note: Value can be positive or negative.

Formulas to find Lift with respect to Roll Rate

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

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

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

Pitch Rate

Pitch Rate refers to the rate of change of an aircraft's pitch angle over time.

Symbol: Q

Measurement: Angular AccelerationUnit: rad/s²

Note: Value can be positive or negative.

Formulas to find Pitch Rate

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

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

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 given Roll Rate?

Lift given Roll Rate evaluator uses Lift with 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) to evaluate the Lift with respect to Roll Rate, Lift given Roll Rate typically involves considering the change in lift coefficient with respect to the change in roll rate This relationship helps to understand how the lift generated by an aircraft's wings is affected by its rate of roll, considering factors such as the lift curve slope, roll control, pitch rate, chord control, and wing span. Lift with respect to Roll Rate is denoted by L symbol.

How to evaluate Lift given Roll Rate using this online evaluator? To use this online evaluator for Lift given Roll Rate, enter Lift Curve Slope (Cl_α), Roll Rate (p), Reference Velocity across X Axis (u₀), Pitch Rate (Q), Chord (c) & Wingspan (b) and hit the calculate button.

FAQs on Lift given Roll Rate

What is the formula to find Lift given Roll Rate?

The formula of Lift given Roll Rate is expressed as Lift with 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). Here is an example- 770 = -2*int((-0.1)*((0.5*x)/50)*0.55*2.1*x,x,0,200/2).

How to calculate Lift given Roll Rate?

With Lift Curve Slope (Cl_α), Roll Rate (p), Reference Velocity across X Axis (u₀), Pitch Rate (Q), Chord (c) & Wingspan (b) we can find Lift given Roll Rate using the formula - Lift with 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). This formula also uses Definite Integral (int) function(s).

Can the Lift given Roll Rate be negative?

Yes, the Lift given Roll Rate, measured in Force can be negative.

Which unit is used to measure Lift given Roll Rate?

Lift given Roll Rate is usually measured using the Newton[N] for Force. Exanewton[N], Meganewton[N], Kilonewton[N] are the few other units in which Lift given Roll Rate can be measured.

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Lift given Roll Rate Formula

Lift given Roll Rate Example

Lift given Roll Rate Solution

Lift given Roll Rate Formula Elements

Other formulas in Lateral Control category

How to Evaluate Lift given Roll Rate?

FAQs on Lift given Roll Rate

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