## Lift given Roll Rate Solution

STEP 0: Pre-Calculation Summary
Formula Used
Lift 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(Clα*((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 Respect to Roll Rate - (Measured in Newton) - Lift 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 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(Clα*((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
770.000000358559 770 Newton <-- Lift Respect to Roll Rate
(Calculation completed in 00.066 seconds)
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## < 10+ Lateral Control Calculators

Aileron Deflection Given Aileron Lift Coefficient
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)
Lift Coefficient with respect to Roll Rate
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 Control Power
Roll Control Power = (2*Derivative of Wing Lift Coefficient*Flap Effectiveness Parameter)/(Wing Area*Wingspan)*int(Chord*x,x,Initial Length,Final Length)
Lift given Roll Rate
Lift 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)
Roll Damping Coefficient
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
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
Flap Effectiveness Parameter = Lift Coefficient Roll Control/(Lift Coefficient Slope Roll Control*Deflection of Aileron)
Deflection Angle given Lift Coefficient
Deflection of Aileron = Lift Coefficient Roll Control/(Lift Coefficient Slope Roll Control*Flap Effectiveness Parameter)
Lift Coefficient Slope Roll Control
Lift Coefficient Slope Roll Control = Lift Coefficient Roll Control/(Deflection of Aileron*Flap Effectiveness Parameter)
Aileron Section Lift Coefficient given Control Effectiveness
Lift Coefficient Roll Control = Lift Coefficient Slope Roll Control*Flap Effectiveness Parameter*Deflection of Aileron

## Lift given Roll Rate Formula

Lift 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(Clα*((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 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 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. Lift 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 (Clα), 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 and is represented as L = -2*int(Clα*((p*x)/u0)*Q*c*x,x,0,b/2) or Lift 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 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 is calculated using Lift 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 (Clα), 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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