Rudder Deflection Angle given Yawing Moment Coefficient Solution

STEP 0: Pre-Calculation Summary
Formula Used
Rudder Deflection Angle = -(Dynamic Pressure at Vertical Tail/Dynamic Pressure at Wing)*((Distance between Rudder Hinge Line and Cg*Vertical Tail Area)/(Wingspan*Wing Reference Area))*(Lift Coefficient/Deviated Rudder Deflection Angle)*Yawing Moment Coefficient
δr = -(Qv/Qw)*((lv*Sv)/(b*s))*(dCl/r)*Cn
This formula uses 10 Variables
Variables Used
Rudder Deflection Angle - (Measured in Radian) - Rudder Deflection Angle is a lateral force and hence a bigger yawing moment (N), leading to a more pronounced yaw.
Dynamic Pressure at Vertical Tail - (Measured in Pascal) - The Dynamic Pressure at Vertical Tail of an aircraft is the pressure exerted by the air flowing past the tail due to the aircraft's forward motion.
Dynamic Pressure at Wing - (Measured in Pascal) - Dynamic Pressure at Wing Represents the kinetic energy per unit volume of air due to its motion.
Distance between Rudder Hinge Line and Cg - (Measured in Meter) - Distance between Rudder Hinge Line and Cg is the geometric property which define the moment arm of the rudder force, affecting the overall yawing moment produced.
Vertical Tail Area - (Measured in Square Meter) - The vertical tail area is the area of the surface of the vertical tail, including the submerged area to the fuselage centerline.
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.
Wing Reference Area - (Measured in Square Meter) - Wing Reference Area is the planform area, refers to the projected area of the wing, as if viewed directly from above.
Lift Coefficient - lift coefficient is a dimensionless quantity that relates the lift generated by a lifting body to the fluid density around the body, the fluid velocity, and an associated reference area.
Deviated Rudder Deflection Angle - (Measured in Radian) - Deviated Rudder Deflection Angle is a lateral force and hence a bigger yawing moment (N), leading to a more pronounced yaw.
Yawing Moment Coefficient - Yawing moment coefficient is the coefficient associated with the moment that tends to rotate an airplane about its vertical (or yaw) axis.
STEP 1: Convert Input(s) to Base Unit
Dynamic Pressure at Vertical Tail: 60 Pascal --> 60 Pascal No Conversion Required
Dynamic Pressure at Wing: 90 Pascal --> 90 Pascal No Conversion Required
Distance between Rudder Hinge Line and Cg: 5.5 Meter --> 5.5 Meter No Conversion Required
Vertical Tail Area: 5 Square Meter --> 5 Square Meter No Conversion Required
Wingspan: 6.7 Meter --> 6.7 Meter No Conversion Required
Wing Reference Area: 8.5 Square Meter --> 8.5 Square Meter No Conversion Required
Lift Coefficient: -4.25 --> No Conversion Required
Deviated Rudder Deflection Angle: 1.3 Radian --> 1.3 Radian No Conversion Required
Yawing Moment Coefficient: 7.2 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
δr = -(Qv/Qw)*((lv*Sv)/(b*s))*(dCl/dδr)*Cn --> -(60/90)*((5.5*5)/(6.7*8.5))*((-4.25)/1.3)*7.2
Evaluating ... ...
δr = 7.57749712973594
STEP 3: Convert Result to Output's Unit
7.57749712973594 Radian --> No Conversion Required
FINAL ANSWER
7.57749712973594 7.577497 Radian <-- Rudder Deflection Angle
(Calculation completed in 00.010 seconds)

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Created by Sastika Ilango
Sri Ramakrishna Engineering College (SREC), COIMBATORE
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Directional Control Calculators

Yawing Moment Coefficient given Rudder Deflection
​ LaTeX ​ Go Yawing Moment Coefficient = -(Dynamic Pressure at Vertical Tail/Dynamic Pressure at Wing)*((Distance between Rudder Hinge Line and Cg*Vertical Tail Area)/(Wingspan*Wing Reference Area))*(Coefficient of Lift/Deviated Rudder Deflection Angle)*Rudder Deflection Angle
Rudder Deflection Angle given Yawing Moment Coefficient
​ LaTeX ​ Go Rudder Deflection Angle = -(Dynamic Pressure at Vertical Tail/Dynamic Pressure at Wing)*((Distance between Rudder Hinge Line and Cg*Vertical Tail Area)/(Wingspan*Wing Reference Area))*(Lift Coefficient/Deviated Rudder Deflection Angle)*Yawing Moment Coefficient
Yawing Moment given Rudder Deflection
​ LaTeX ​ Go Yawing Moment Coefficient = Negative Yawing Moment/Dynamic Pressure at Wing*Wing Reference Area*Wingspan
Rudder Control Effectiveness
​ LaTeX ​ Go Yawing Moment Coefficient = Yawing Moment with Rudder Deflection Angle*Rudder Deflection Angle

Rudder Deflection Angle given Yawing Moment Coefficient Formula

​LaTeX ​Go
Rudder Deflection Angle = -(Dynamic Pressure at Vertical Tail/Dynamic Pressure at Wing)*((Distance between Rudder Hinge Line and Cg*Vertical Tail Area)/(Wingspan*Wing Reference Area))*(Lift Coefficient/Deviated Rudder Deflection Angle)*Yawing Moment Coefficient
δr = -(Qv/Qw)*((lv*Sv)/(b*s))*(dCl/r)*Cn

What is Rudder Deflection Angle?

The rudder deflection angle is the angle at which the rudder, a hinged control surface located at the rear of the vertical stabilizer of an aircraft, is turned from its neutral position. It is a crucial factor in controlling the aircraft's yaw, which is the rotation of the aircraft about its vertical axis.

How to Calculate Rudder Deflection Angle given Yawing Moment Coefficient?

Rudder Deflection Angle given Yawing Moment Coefficient calculator uses Rudder Deflection Angle = -(Dynamic Pressure at Vertical Tail/Dynamic Pressure at Wing)*((Distance between Rudder Hinge Line and Cg*Vertical Tail Area)/(Wingspan*Wing Reference Area))*(Lift Coefficient/Deviated Rudder Deflection Angle)*Yawing Moment Coefficient to calculate the Rudder Deflection Angle, Rudder Deflection Angle given Yawing Moment Coefficient is a measure of the angle at which the rudder deflects in response to a yawing moment, influenced by the dynamic pressure, distance between the rudder hinge line and center of gravity, vertical tail area, wingspan, and lift coefficient, this angle is critical in understanding the behavior of an aircraft's rudder and its impact on flight dynamics. Rudder Deflection Angle is denoted by δr symbol.

How to calculate Rudder Deflection Angle given Yawing Moment Coefficient using this online calculator? To use this online calculator for Rudder Deflection Angle given Yawing Moment Coefficient, enter Dynamic Pressure at Vertical Tail (Qv), Dynamic Pressure at Wing (Qw), Distance between Rudder Hinge Line and Cg (lv), Vertical Tail Area (Sv), Wingspan (b), Wing Reference Area (s), Lift Coefficient (dCl), Deviated Rudder Deflection Angle (dδr) & Yawing Moment Coefficient (Cn) and hit the calculate button. Here is how the Rudder Deflection Angle given Yawing Moment Coefficient calculation can be explained with given input values -> 7.648815 = -(60/90)*((5.5*5)/(6.7*8.5))*((-4.25)/1.3)*7.2.

FAQ

What is Rudder Deflection Angle given Yawing Moment Coefficient?
Rudder Deflection Angle given Yawing Moment Coefficient is a measure of the angle at which the rudder deflects in response to a yawing moment, influenced by the dynamic pressure, distance between the rudder hinge line and center of gravity, vertical tail area, wingspan, and lift coefficient, this angle is critical in understanding the behavior of an aircraft's rudder and its impact on flight dynamics and is represented as δr = -(Qv/Qw)*((lv*Sv)/(b*s))*(dCl/dδr)*Cn or Rudder Deflection Angle = -(Dynamic Pressure at Vertical Tail/Dynamic Pressure at Wing)*((Distance between Rudder Hinge Line and Cg*Vertical Tail Area)/(Wingspan*Wing Reference Area))*(Lift Coefficient/Deviated Rudder Deflection Angle)*Yawing Moment Coefficient. The Dynamic Pressure at Vertical Tail of an aircraft is the pressure exerted by the air flowing past the tail due to the aircraft's forward motion, Dynamic Pressure at Wing Represents the kinetic energy per unit volume of air due to its motion, Distance between Rudder Hinge Line and Cg is the geometric property which define the moment arm of the rudder force, affecting the overall yawing moment produced, The vertical tail area is the area of the surface of the vertical tail, including the submerged area to the fuselage centerline, The Wingspan (or just span) of a bird or an airplane is the distance from one wingtip to the other wingtip, Wing Reference Area is the planform area, refers to the projected area of the wing, as if viewed directly from above, lift coefficient is a dimensionless quantity that relates the lift generated by a lifting body to the fluid density around the body, the fluid velocity, and an associated reference area, Deviated Rudder Deflection Angle is a lateral force and hence a bigger yawing moment (N), leading to a more pronounced yaw & Yawing moment coefficient is the coefficient associated with the moment that tends to rotate an airplane about its vertical (or yaw) axis.
How to calculate Rudder Deflection Angle given Yawing Moment Coefficient?
Rudder Deflection Angle given Yawing Moment Coefficient is a measure of the angle at which the rudder deflects in response to a yawing moment, influenced by the dynamic pressure, distance between the rudder hinge line and center of gravity, vertical tail area, wingspan, and lift coefficient, this angle is critical in understanding the behavior of an aircraft's rudder and its impact on flight dynamics is calculated using Rudder Deflection Angle = -(Dynamic Pressure at Vertical Tail/Dynamic Pressure at Wing)*((Distance between Rudder Hinge Line and Cg*Vertical Tail Area)/(Wingspan*Wing Reference Area))*(Lift Coefficient/Deviated Rudder Deflection Angle)*Yawing Moment Coefficient. To calculate Rudder Deflection Angle given Yawing Moment Coefficient, you need Dynamic Pressure at Vertical Tail (Qv), Dynamic Pressure at Wing (Qw), Distance between Rudder Hinge Line and Cg (lv), Vertical Tail Area (Sv), Wingspan (b), Wing Reference Area (s), Lift Coefficient (dCl), Deviated Rudder Deflection Angle (dδr) & Yawing Moment Coefficient (Cn). With our tool, you need to enter the respective value for Dynamic Pressure at Vertical Tail, Dynamic Pressure at Wing, Distance between Rudder Hinge Line and Cg, Vertical Tail Area, Wingspan, Wing Reference Area, Lift Coefficient, Deviated Rudder Deflection Angle & Yawing Moment Coefficient 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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