Rudder Deflection Angle given Yawing Moment Coefficient Calculator

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Static Stability and Control

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✖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 Vertical Tail [Q_v]			+10% -10%
✖Dynamic Pressure at Wing Represents the kinetic energy per unit volume of air due to its motion.ⓘ Dynamic Pressure at Wing [Q_w]			+10% -10%
✖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.ⓘ Distance between Rudder Hinge Line and Cg [l_v]			+10% -10%
✖The vertical tail area is the area of the surface of the vertical tail, including the submerged area to the fuselage centerline.ⓘ Vertical Tail Area [S_v]			+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%
✖Wing Reference Area is the planform area, refers to the projected area of the wing, as if viewed directly from above.ⓘ Wing Reference Area [s]			+10% -10%
✖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.ⓘ Lift Coefficient [dCl]			+10% -10%
✖Deviated Rudder Deflection Angle is a lateral force and hence a bigger yawing moment (N), leading to a more pronounced yaw.ⓘ Deviated Rudder Deflection Angle [dδ_r]			+10% -10%
✖Yawing moment coefficient is the coefficient associated with the moment that tends to rotate an airplane about its vertical (or yaw) axis.ⓘ Yawing Moment Coefficient [C_n]			+10% -10%

✖Rudder Deflection Angle is a lateral force and hence a bigger yawing moment (N), leading to a more pronounced yaw.ⓘ Rudder Deflection Angle given Yawing Moment Coefficient [δ_r]

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Formula

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Rudder Deflection Angle given Yawing Moment Coefficient

Formula

`"δ"_{"r"} = -("Q"_{"v"}/"Q"_{"w"})*(("l"_{"v"}*"S"_{"v"})/("b"*"s"))*("dCl"/"dδ"_{"r"})*"C"_{"n"}`

Example

`"7.577497rad"=-("60Pa"/"90Pa")*(("5.5m"*"5m²")/("6.7m"*"8.5m²"))*("-4.25"/"1.3rad")*"7.2"`

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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
δ_r = -(Q_v/Q_w)*((l_v*S_v)/(b*s))*(dCl/dδ_r)*C_n
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

δ_r = -(Q_v/Q_w)*((l_v*S_v)/(b*s))*(dCl/dδ_r)*C_n --> -(60/90)*((5.5*5)/(6.7*8.5))*((-4.25)/1.3)*7.2

Evaluating ... ...

δ_r = 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 00.004 seconds)

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Sri Ramakrishna Engineering College (SREC), COIMBATORE

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< 5 Directional Control Calculators

Yawing Moment Coefficient given Rudder Deflection

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

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 with Rudder Deflection Angle

Go Yawing Moment with Rudder Deflection Angle = -(Vertical Tail Efficiency Factor*Velocity at Tail Plane)*(Change in Coefficient of Lift Refers to Tail Plane/Change in Rudder Deflection Angle)

Yawing Moment given Rudder Deflection

Go Yawing Moment Coefficient = Negative Yawing Moment/Dynamic Pressure at Wing*Wing Reference Area*Wingspan

Rudder Control Effectiveness

Go Yawing Moment Coefficient = Yawing Moment with Rudder Deflection Angle*Rudder Deflection Angle

Rudder Deflection Angle given Yawing Moment Coefficient Formula

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, The Rudder Deflection angle given Yawing Moment Coefficient formula is defined as a movement of a flight control surface used to steer an aircraft. Rudder Deflection Angle is denoted by δ_r 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 (Q_v), Dynamic Pressure at Wing (Q_w), Distance between Rudder Hinge Line and Cg (l_v), Vertical Tail Area (S_v), Wingspan (b), Wing Reference Area (s), Lift Coefficient (dCl), Deviated Rudder Deflection Angle (dδ_r) & Yawing Moment Coefficient (C_n) 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?

The Rudder Deflection angle given Yawing Moment Coefficient formula is defined as a movement of a flight control surface used to steer an aircraft and is represented as δ_r = -(Q_v/Q_w)*((l_v*S_v)/(b*s))*(dCl/dδ_r)*C_n 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?

The Rudder Deflection angle given Yawing Moment Coefficient formula is defined as a movement of a flight control surface used to steer an aircraft 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 (Q_v), Dynamic Pressure at Wing (Q_w), Distance between Rudder Hinge Line and Cg (l_v), Vertical Tail Area (S_v), Wingspan (b), Wing Reference Area (s), Lift Coefficient (dCl), Deviated Rudder Deflection Angle (dδ_r) & Yawing Moment Coefficient (C_n). 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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