Lift given Roll Rate Calculator

✖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.ⓘ Lift Curve Slope [Cl_α]			+10% -10%
✖Roll Rate refers to the rate at which an aircraft rotates around its longitudinal axis, causing it to tilt or bank to one side.ⓘ Roll Rate [p]			+10% -10%
✖Reference Velocity across X Axis typically refers to the velocity component along the x-axis (horizontal axis) of a coordinate system.ⓘ Reference Velocity across X Axis [u₀]			+10% -10%
✖Pitch Rate refers to the rate of change of an aircraft's pitch angle over time.ⓘ Pitch Rate [Q]			+10% -10%
✖The Chord is the distance between the trailing edge and the point where the chord intersects the leading edge.ⓘ Chord [c]			+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%

✖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.ⓘ Lift given Roll Rate [L]

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Formula

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Lift given Roll Rate

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})

Example

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

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Lift given Roll Rate Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
L = -2*int(Cl_α*((p*x)/u₀)*Q*c*x,x,0,b/2)
This formula uses 1 Functions, 7 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

Lift with respect to Roll Rate - (Measured in Newton) - 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.
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.
Roll Rate - (Measured in Radian per Square Second) - Roll Rate refers to the rate at which an aircraft rotates around its longitudinal axis, causing it to tilt or bank to one side.
Reference Velocity across X Axis - (Measured in Meter per Second) - Reference Velocity across X Axis typically refers to the velocity component along the x-axis (horizontal axis) of a coordinate system.
Pitch Rate - (Measured in Radian per Square Second) - Pitch Rate refers to the rate of change of an aircraft's pitch angle over time.
Chord - (Measured in Meter) - The Chord is the distance between the trailing edge and the point where the chord intersects the leading edge.
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.

STEP 1: Convert Input(s) to Base Unit

Lift Curve Slope: -0.1 --> No Conversion Required
Roll Rate: 0.5 Radian per Square Second --> 0.5 Radian per Square Second No Conversion Required
Reference Velocity across X Axis: 50 Meter per Second --> 50 Meter per Second No Conversion Required
Pitch Rate: 0.55 Radian per Square Second --> 0.55 Radian per Square Second No Conversion Required
Chord: 2.1 Meter --> 2.1 Meter No Conversion Required
Wingspan: 200 Meter --> 200 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

L = -2*int(Cl_α*((p*x)/u₀)*Q*c*x,x,0,b/2) --> -2*int((-0.1)*((0.5*x)/50)*0.55*2.1*x,x,0,200/2)

Evaluating ... ...

L = 770.000000358559

STEP 3: Convert Result to Output's Unit

770.000000358559 Newton --> No Conversion Required

FINAL ANSWER

770.000000358559 ≈ 770 Newton <-- Lift with respect to Roll Rate

(Calculation completed in 00.066 seconds)

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< 5 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)

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)

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)

Lift given Roll Rate 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)
L = -2*int(Cl_α*((p*x)/u₀)*Q*c*x,x,0,b/2)

What is Lift Respect to Roll Rate ?

Lift Respect to Roll Rate" refers to the aerodynamic phenomenon in which changes in the roll rate of an aircraft affect the lift force generated by its wings. When an aircraft rolls, its wings experience a change in angle of attack relative to the airflow, resulting in variations in lift.

How to Calculate Lift given Roll Rate?

Lift given Roll Rate calculator 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 calculate 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 calculate Lift given Roll Rate using this online calculator? To use this online calculator 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. Here is how the Lift given Roll Rate calculation can be explained with given input values -> 770 = -2*int((-0.1)*((0.5*x)/50)*0.55*2.1*x,x,0,200/2).

FAQ

What is Lift given 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 and is represented as L = -2*int(Cl_α*((p*x)/u₀)*Q*c*x,x,0,b/2) or 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). 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, Roll Rate refers to the rate at which an aircraft rotates around its longitudinal axis, causing it to tilt or bank to one side, Reference Velocity across X Axis typically refers to the velocity component along the x-axis (horizontal axis) of a coordinate system, Pitch Rate refers to the rate of change of an aircraft's pitch angle over time, The Chord is the distance between the trailing edge and the point where the chord intersects the leading edge & The Wingspan (or just span) of a bird or an airplane is the distance from one wingtip to the other wingtip.

How to calculate Lift given 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 is calculated using 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 calculate Lift given Roll Rate, you need Lift Curve Slope (Cl_α), Roll Rate (p), Reference Velocity across X Axis (u₀), Pitch Rate (Q), Chord (c) & Wingspan (b). With our tool, you need to enter the respective value for Lift Curve Slope, Roll Rate, Reference Velocity across X Axis, Pitch Rate, Chord & Wingspan 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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