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Tail Pitching Moment Coefficient Formula

GoTail Pitching Moment Coefficient for given Tail Efficiency Formula

GoTail Pitching Moment Coefficient for given Tail Volume Ratio Formula

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Tail Pitching Moment Coefficient is the coefficient of pitching moment associated with the horizontal tail of an aircraft. Check FAQs

Cm t = \frac{M t}{0.5 \cdot ρ ∞ \cdot V^{2} \cdot S \cdot c ma}

Cm_t - Tail Pitching Moment Coefficient?M_t - Pitching Moment due to Tail?ρ_∞ - Freestream Density?V - Flight Velocity?S - Reference Area?c_ma - Mean Aerodynamic Chord?

Tail Pitching Moment Coefficient Example

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Here is how the Tail Pitching Moment Coefficient equation looks like with Values.

Here is how the Tail Pitching Moment Coefficient equation looks like with Units.

Here is how the Tail Pitching Moment Coefficient equation looks like.

-0.3904 = \frac{-218.6644}{0.5 \cdot 1.225 \cdot 30^{2} \cdot 5.08 \cdot 0.2}

-0.3904 = \frac{-218.6644N*m}{0.5 \cdot 1.225kg/m³ \cdot {30m/s}^{2} \cdot 5.08m² \cdot 0.2m}

-0.3904 = \frac{-218.6644}{0.5 \cdot 1.225 \cdot 30^{2} \cdot 5.08 \cdot 0.2}

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Tail Pitching Moment Coefficient Solution

Follow our step by step solution on how to calculate Tail Pitching Moment Coefficient?

FIRST Step Consider the formula

Cm t = \frac{M t}{0.5 \cdot ρ ∞ \cdot V^{2} \cdot S \cdot c ma}

Next Step Substitute values of Variables

∴

Cm t = \frac{-218.6644N*m}{0.5 \cdot 1.225kg/m³ \cdot {30m/s}^{2} \cdot 5.08m² \cdot 0.2m}

Next Step Prepare to Evaluate

∴

Cm t = \frac{-218.6644}{0.5 \cdot 1.225 \cdot 30^{2} \cdot 5.08 \cdot 0.2}

Next Step Evaluate

∴

Cm t = -0.39042333993965

LAST Step Rounding Answer

∴

Cm t = -0.3904

Tail Pitching Moment Coefficient Formula Elements

Variables

Tail Pitching Moment Coefficient

Tail Pitching Moment Coefficient is the coefficient of pitching moment associated with the horizontal tail of an aircraft.

Symbol: Cm_t

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Tail Pitching Moment Coefficient

Pitching Moment due to Tail

Pitching Moment due to Tail is the pitching moment of the tail about the aircraft's center of gravity.

Symbol: M_t

Measurement: Moment of ForceUnit: N*m

Note: Value can be positive or negative.

Formulas to find Pitching Moment due to Tail

Freestream Density

Freestream Density is the mass per unit volume of air far upstream of an aerodynamic body at a given altitude.

Symbol: ρ_∞

Measurement: DensityUnit: kg/m³

Note: Value can be positive or negative.

Formulas to find Freestream Density

Flight Velocity

Flight Velocity refers to the speed at which an aircraft moves through the air.

Symbol: V

Measurement: SpeedUnit: m/s

Note: Value can be positive or negative.

Formulas to find Flight Velocity

Reference Area

The Reference Area is arbitrarily an area that is characteristic of the object being considered. For an aircraft wing, the wing's planform area is called the reference wing area or simply wing area.

Symbol: S

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Reference Area

Mean Aerodynamic Chord

The Mean Aerodynamic Chord is a two-dimensional representation of the whole wing.

Symbol: c_ma

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Mean Aerodynamic Chord

Other Formulas to find Tail Pitching Moment Coefficient

Go Tail Pitching Moment Coefficient for given Tail Efficiency

Cm t = - \frac{η \cdot S t \cdot 𝒍 t \cdot CT lift}{S \cdot c ma}

Go Tail Pitching Moment Coefficient for given Tail Volume Ratio

Cm t = - V H \cdot η \cdot CT lift

Other formulas in Tail Contribution category

Go Tail Pitching Moment for given Lift Coefficient

M t = - \frac{𝒍 t \cdot CT lift \cdot ρ ∞ \cdot {V tail}^{2} \cdot S t}{2}

Go Tail Lift for given Tail Pitching Moment

L t = - (\frac{M t}{𝒍 t})

Go Pitching Moment due to Tail

M t = - 𝒍 t \cdot L t

Go Tail Pitching Moment for given Moment Coefficient

M t = \frac{Cm t \cdot ρ ∞ \cdot V^{2} \cdot S \cdot c ma}{2}

How to Evaluate Tail Pitching Moment Coefficient?

Tail Pitching Moment Coefficient evaluator uses Tail Pitching Moment Coefficient = Pitching Moment due to Tail/(0.5*Freestream Density*Flight Velocity^2*Reference Area*Mean Aerodynamic Chord) to evaluate the Tail Pitching Moment Coefficient, Tail Pitching Moment Coefficient is a measure of the rotational force around the vertical axis of an aircraft's tail, normalized by the freestream dynamic density and reference area, it represents the stabilizing or destabilizing effect of the tail on the aircraft's pitch, providing a critical indicator of the aircraft's stability and control characteristics. Tail Pitching Moment Coefficient is denoted by Cm_t symbol.

How to evaluate Tail Pitching Moment Coefficient using this online evaluator? To use this online evaluator for Tail Pitching Moment Coefficient, enter Pitching Moment due to Tail (M_t), Freestream Density (ρ_∞), Flight Velocity (V), Reference Area (S) & Mean Aerodynamic Chord (c_ma) and hit the calculate button.

FAQs on Tail Pitching Moment Coefficient

What is the formula to find Tail Pitching Moment Coefficient?

The formula of Tail Pitching Moment Coefficient is expressed as Tail Pitching Moment Coefficient = Pitching Moment due to Tail/(0.5*Freestream Density*Flight Velocity^2*Reference Area*Mean Aerodynamic Chord). Here is an example- -0.390423 = (-218.6644)/(0.5*1.225*30^2*5.08*0.2).

How to calculate Tail Pitching Moment Coefficient?

With Pitching Moment due to Tail (M_t), Freestream Density (ρ_∞), Flight Velocity (V), Reference Area (S) & Mean Aerodynamic Chord (c_ma) we can find Tail Pitching Moment Coefficient using the formula - Tail Pitching Moment Coefficient = Pitching Moment due to Tail/(0.5*Freestream Density*Flight Velocity^2*Reference Area*Mean Aerodynamic Chord).

What are the other ways to Calculate Tail Pitching Moment Coefficient?

Here are the different ways to Calculate Tail Pitching Moment Coefficient-

Tail Pitching Moment Coefficient=-(Tail Efficiency*Horizontal Tail Area*Horizontal Tail Moment Arm*Tail Lift Coefficient)/(Reference Area*Mean Aerodynamic Chord)
Tail Pitching Moment Coefficient=-Horizontal Tail Volume Ratio*Tail Efficiency*Tail Lift Coefficient

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Tail Pitching Moment Coefficient Formula

​GoTail Pitching Moment Coefficient for given Tail Efficiency Formula

​GoTail Pitching Moment Coefficient for given Tail Volume Ratio Formula

Tail Pitching Moment Coefficient Example

Tail Pitching Moment Coefficient Solution

Tail Pitching Moment Coefficient Formula Elements

Other Formulas to find Tail Pitching Moment Coefficient

Other formulas in Tail Contribution category

How to Evaluate Tail Pitching Moment Coefficient?

FAQs on Tail Pitching Moment Coefficient

Variable Name

GoTail Pitching Moment Coefficient for given Tail Efficiency Formula

GoTail Pitching Moment Coefficient for given Tail Volume Ratio Formula