Tail Pitching Moment for given Lift Coefficient Calculator

✖The Horizontal Tail Moment Arm is the distance between the lift center of the horizontal tail and the center of gravity of the aircraft.ⓘ Horizontal Tail Moment Arm [𝒍_t]			+10% -10%
✖Tail Lift Coefficient is the lift coefficient associated with the tail (only) of an aircraft. It is a dimensionless quantity.ⓘ Tail Lift Coefficient [CT_lift]			+10% -10%
✖Freestream Density is the mass per unit volume of air far upstream of an aerodynamic body at a given altitude.ⓘ Freestream Density [ρ_∞]			+10% -10%
✖Velocity Tail refers to the airspeed or velocity of the horizontal stabilizer (tail) of an aircraft relative to the surrounding air (relative wind).ⓘ Velocity Tail [V_tail]			+10% -10%
✖The Horizontal Tail Area is the surface area of the horizontal stabilizer on an aircraft, which provides pitch stability and control.ⓘ Horizontal Tail Area [S_t]			+10% -10%

✖Pitching Moment due to Tail is the pitching moment of the tail about the aircraft's center of gravity.ⓘ Tail Pitching Moment for given Lift Coefficient [M_t]

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Formula

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Tail Pitching Moment for given Lift Coefficient

Formula

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

Example

-218.664465 N*m = - \frac{0.801511 m \cdot 0.3 \cdot 1.225 kg/m³ \cdot {28.72 m/s}^{2} \cdot 1.8 m²}{2}

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Tail Pitching Moment for given Lift Coefficient Solution

STEP 0: Pre-Calculation Summary

Formula Used

Pitching Moment due to Tail = -(Horizontal Tail Moment Arm*Tail Lift Coefficient*Freestream Density*Velocity Tail^2*Horizontal Tail Area)/2
M_t = -(𝒍_t*CT_lift*ρ_∞*V_tail^2*S_t)/2
This formula uses 6 Variables

Variables Used

Pitching Moment due to Tail - (Measured in Newton Meter) - Pitching Moment due to Tail is the pitching moment of the tail about the aircraft's center of gravity.
Horizontal Tail Moment Arm - (Measured in Meter) - The Horizontal Tail Moment Arm is the distance between the lift center of the horizontal tail and the center of gravity of the aircraft.
Tail Lift Coefficient - Tail Lift Coefficient is the lift coefficient associated with the tail (only) of an aircraft. It is a dimensionless quantity.
Freestream Density - (Measured in Kilogram per Cubic Meter) - Freestream Density is the mass per unit volume of air far upstream of an aerodynamic body at a given altitude.
Velocity Tail - (Measured in Meter per Second) - Velocity Tail refers to the airspeed or velocity of the horizontal stabilizer (tail) of an aircraft relative to the surrounding air (relative wind).
Horizontal Tail Area - (Measured in Square Meter) - The Horizontal Tail Area is the surface area of the horizontal stabilizer on an aircraft, which provides pitch stability and control.

STEP 1: Convert Input(s) to Base Unit

Horizontal Tail Moment Arm: 0.801511 Meter --> 0.801511 Meter No Conversion Required
Tail Lift Coefficient: 0.3 --> No Conversion Required
Freestream Density: 1.225 Kilogram per Cubic Meter --> 1.225 Kilogram per Cubic Meter No Conversion Required
Velocity Tail: 28.72 Meter per Second --> 28.72 Meter per Second No Conversion Required
Horizontal Tail Area: 1.8 Square Meter --> 1.8 Square Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

M_t = -(𝒍_t*CT_lift*ρ_∞*V_tail^2*S_t)/2 --> -(0.801511*0.3*1.225*28.72^2*1.8)/2

Evaluating ... ...

M_t = -218.664464559509

STEP 3: Convert Result to Output's Unit

-218.664464559509 Newton Meter --> No Conversion Required

FINAL ANSWER

-218.664464559509 ≈ -218.664465 Newton Meter <-- Pitching Moment due to Tail

(Calculation completed in 00.004 seconds)

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Home » Physics » Aircraft Mechanics » Static Stability and Control » Longitudinal Stability » Aerospace » Tail Contribution » Tail Pitching Moment for given Lift Coefficient

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Created by Vinay Mishra

Indian Institute for Aeronautical Engineering and Information Technology (IIAEIT), Pune

Vinay Mishra has created this Calculator and 300+ more calculators!

Verified by Maiarutselvan V

PSG College of Technology (PSGCT), Coimbatore

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< Tail Contribution Calculators

Tail Pitching Moment for given Moment Coefficient

Go Pitching Moment due to Tail = (Tail Pitching Moment Coefficient*Freestream Density*Flight Velocity^2*Reference Area*Mean Aerodynamic Chord)/2

Tail Pitching Moment for given Lift Coefficient

Go Pitching Moment due to Tail = -(Horizontal Tail Moment Arm*Tail Lift Coefficient*Freestream Density*Velocity Tail^2*Horizontal Tail Area)/2

Tail Lift for given Tail Pitching Moment

Go Lift due to Tail = -(Pitching Moment due to Tail/Horizontal Tail Moment Arm)

Pitching Moment due to Tail

Go Pitching Moment due to Tail = -Horizontal Tail Moment Arm*Lift due to Tail

Tail Pitching Moment for given Lift Coefficient Formula

Pitching Moment due to Tail = -(Horizontal Tail Moment Arm*Tail Lift Coefficient*Freestream Density*Velocity Tail^2*Horizontal Tail Area)/2
M_t = -(𝒍_t*CT_lift*ρ_∞*V_tail^2*S_t)/2

Why does aft CG save fuel?

A CG near the aft reduces drag by reducing the necessary downforce that has to be supplied (usually) by the tailplane.

How to Calculate Tail Pitching Moment for given Lift Coefficient?

Tail Pitching Moment for given Lift Coefficient calculator uses Pitching Moment due to Tail = -(Horizontal Tail Moment Arm*Tail Lift Coefficient*Freestream Density*Velocity Tail^2*Horizontal Tail Area)/2 to calculate the Pitching Moment due to Tail, Tail Pitching Moment for given Lift Coefficient is a measure of the rotational force around the lateral axis of an aircraft's tail section, calculated by considering the horizontal tail moment arm, lift coefficient, freestream density, tail velocity, and horizontal tail area, providing a crucial parameter in aircraft design and stability analysis. Pitching Moment due to Tail is denoted by M_t symbol.

How to calculate Tail Pitching Moment for given Lift Coefficient using this online calculator? To use this online calculator for Tail Pitching Moment for given Lift Coefficient, enter Horizontal Tail Moment Arm (𝒍_t), Tail Lift Coefficient (CT_lift), Freestream Density (ρ_∞), Velocity Tail (V_tail) & Horizontal Tail Area (S_t) and hit the calculate button. Here is how the Tail Pitching Moment for given Lift Coefficient calculation can be explained with given input values -> -218.664465 = -(0.801511*0.3*1.225*28.72^2*1.8)/2.

FAQ

What is Tail Pitching Moment for given Lift Coefficient?

Tail Pitching Moment for given Lift Coefficient is a measure of the rotational force around the lateral axis of an aircraft's tail section, calculated by considering the horizontal tail moment arm, lift coefficient, freestream density, tail velocity, and horizontal tail area, providing a crucial parameter in aircraft design and stability analysis and is represented as M_t = -(𝒍_t*CT_lift*ρ_∞*V_tail^2*S_t)/2 or Pitching Moment due to Tail = -(Horizontal Tail Moment Arm*Tail Lift Coefficient*Freestream Density*Velocity Tail^2*Horizontal Tail Area)/2. The Horizontal Tail Moment Arm is the distance between the lift center of the horizontal tail and the center of gravity of the aircraft, Tail Lift Coefficient is the lift coefficient associated with the tail (only) of an aircraft. It is a dimensionless quantity, Freestream Density is the mass per unit volume of air far upstream of an aerodynamic body at a given altitude, Velocity Tail refers to the airspeed or velocity of the horizontal stabilizer (tail) of an aircraft relative to the surrounding air (relative wind) & The Horizontal Tail Area is the surface area of the horizontal stabilizer on an aircraft, which provides pitch stability and control.

How to calculate Tail Pitching Moment for given Lift Coefficient?

Tail Pitching Moment for given Lift Coefficient is a measure of the rotational force around the lateral axis of an aircraft's tail section, calculated by considering the horizontal tail moment arm, lift coefficient, freestream density, tail velocity, and horizontal tail area, providing a crucial parameter in aircraft design and stability analysis is calculated using Pitching Moment due to Tail = -(Horizontal Tail Moment Arm*Tail Lift Coefficient*Freestream Density*Velocity Tail^2*Horizontal Tail Area)/2. To calculate Tail Pitching Moment for given Lift Coefficient, you need Horizontal Tail Moment Arm (𝒍_t), Tail Lift Coefficient (CT_lift), Freestream Density (ρ_∞), Velocity Tail (V_tail) & Horizontal Tail Area (S_t). With our tool, you need to enter the respective value for Horizontal Tail Moment Arm, Tail Lift Coefficient, Freestream Density, Velocity Tail & Horizontal Tail Area and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Pitching Moment due to Tail?

In this formula, Pitching Moment due to Tail uses Horizontal Tail Moment Arm, Tail Lift Coefficient, Freestream Density, Velocity Tail & Horizontal Tail Area. We can use 2 other way(s) to calculate the same, which is/are as follows -

Pitching Moment due to Tail = -Horizontal Tail Moment Arm*Lift due to Tail
Pitching Moment due to Tail = (Tail Pitching Moment Coefficient*Freestream Density*Flight Velocity^2*Reference Area*Mean Aerodynamic Chord)/2

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