Lift Coefficient with respect to Roll Rate Calculator

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Static Stability and Control

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✖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%
✖Wing Reference Area, S, is the projected area of the planform and is bounded by the leading and trailing edges and the wing tips.ⓘ Wing Reference Area [S_r]			+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%
✖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%
✖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%
✖The chord the distance between the trailing edge and the point where the chord intersects the leading edge.ⓘ Chord [c]			+10% -10%

✖Lift Coefficient 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.ⓘ Lift Coefficient with respect to Roll Rate [Cl]

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Formula

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Lift Coefficient with respect to Roll Rate

Formula

`"Cl" = -((2*"p")/("S"_{"r"}*"b"*"u"_{"0"}))*int("Cl"_{"α"}*"c"*x^2,x,0,"b"/2)`

Example

`"0.038043"=-((2*"0.5rad/s²")/("184m²"*"200m"*"50m/s"))*int("-0.1"*"2.1m"*x^2,x,0,"200m"/2)`

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Lift Coefficient with respect to Roll Rate Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
Cl = -((2*p)/(S_r*b*u₀))*int(Cl_α*c*x^2,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 Coefficient Respect to Roll Rate - Lift Coefficient 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.
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.
Wing Reference Area - (Measured in Square Meter) - Wing Reference 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.
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.
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.
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

Roll Rate: 0.5 Radian per Square Second --> 0.5 Radian per Square Second No Conversion Required
Wing Reference Area: 184 Square Meter --> 184 Square Meter No Conversion Required
Wingspan: 200 Meter --> 200 Meter No Conversion Required
Reference Velocity Across X Axis: 50 Meter per Second --> 50 Meter per Second No Conversion Required
Lift Curve Slope: -0.1 --> No Conversion Required
Chord: 2.1 Meter --> 2.1 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Cl = -((2*p)/(S_r*b*u₀))*int(Cl_α*c*x^2,x,0,b/2) --> -((2*0.5)/(184*200*50))*int((-0.1)*2.1*x^2,x,0,200/2)

Evaluating ... ...

Cl = 0.0380434782609357

STEP 3: Convert Result to Output's Unit

0.0380434782609357 --> No Conversion Required

FINAL ANSWER

0.0380434782609357 ≈ 0.038043 <-- Lift Coefficient Respect to Roll Rate

(Calculation completed in 00.492 seconds)

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Lift Coefficient with respect to Roll Rate Formula

What is Lift Coefficient Respect to Roll Rate ?

The Lift Coefficient Respect to Roll Rate refers to the derivative of the lift coefficient with respect to the aircraft's roll rate. It represents how changes in the roll rate of an aircraft affect the lift coefficient, which is a dimensionless coefficient representing the lift generated by the wings relative to the aircraft's size, speed, and angle of attack.

How to Calculate Lift Coefficient with respect to Roll Rate?

Lift Coefficient with respect to Roll Rate calculator uses 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) to calculate the Lift Coefficient 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. Lift Coefficient Respect to Roll Rate is denoted by Cl symbol.

How to calculate Lift Coefficient with respect to Roll Rate using this online calculator? To use this online calculator 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. Here is how the Lift Coefficient with respect to Roll Rate calculation can be explained with given input values -> 0.038043 = -((2*0.5)/(184*200*50))*int((-0.1)*2.1*x^2,x,0,200/2).

FAQ

What is 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 and is represented as Cl = -((2*p)/(S_r*b*u₀))*int(Cl_α*c*x^2,x,0,b/2) or 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 rate refers to the rate at which an aircraft rotates around its longitudinal axis, causing it to tilt or bank to one side, Wing Reference 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, Reference Velocity Across X Axis typically refers to the velocity component along the x-axis (horizontal axis) of a coordinate system, 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 & The chord the distance between the trailing edge and the point where the chord intersects the leading edge.

How to calculate 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 is calculated using 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). To calculate Lift Coefficient with respect to Roll Rate, you need Roll Rate (p), Wing Reference Area (S_r), Wingspan (b), Reference Velocity Across X Axis (u₀), Lift Curve Slope (Cl_α) & Chord (c). With our tool, you need to enter the respective value for Roll Rate, Wing Reference Area, Wingspan, Reference Velocity Across X Axis, Lift Curve Slope & 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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