Pitching Moment Coefficient for Fuselage Contribution Calculator

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Static Stability and Control

Aircraft Design

Aircraft Performance

Introduction and Governing Equations

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Longitudinal Stability

Directional Control

Directional Stability

Lateral Control

Lateral Stability

Longitudinal Control

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Fuselage Contribution

Tail Contribution

Wing-Tail Contribution

✖Final Correction Factor For Body Fitness Ratio can be quantified by the fuselage fineness ratio (FR), defined as the body length divided by its maximum diameter.ⓘ Final Correction Factor For Body Fitness Ratio [k₂]			+10% -10%
✖Initial Correction Factor for body Fitness Ratio can be quantified by the fuselage fineness ratio (FR), defined as the body length divided by its maximum diameter.ⓘ Initial Correction Factor For Body Fitness Ratio [k₁]			+10% -10%
✖The Wing area, S, is the projected area of the planform and is bounded by the leading and trailing edges and the wing tips.ⓘ Wing Area [S]			+10% -10%
✖The mean aerodynamic chord is the average distance from the leading edge to the trailing edge of a wing.ⓘ Mean Aerodynamic Chord [c]			+10% -10%
✖The average width of fuselage refers to the typical diameter or width of the central body structure of an aircraft.ⓘ Average Width Of Fuselage [w_f]			+10% -10%
✖The wing zero lift angle, relative to the fuselage reference line, refers to the angle formed between the chord line of the wing and the reference line of the fuselage.ⓘ Wing Zero Lift Angle [α_0,w]			+10% -10%
✖The incidence of fuselage camber line relative to the fuselage reference line refers to the angle formed between the camber line of the fuselage and the reference line of the fuselage.ⓘ Incidence Of Fuselage Camber Line [i_f]			+10% -10%

✖The moment coefficient for fuselage contribution is the sum of the contributions of each fuselage component, including the nose, cabin, and tailcone.ⓘ Pitching Moment Coefficient for Fuselage Contribution [Cm_0,f]

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Formula

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Pitching Moment Coefficient for Fuselage Contribution

Formula

`"Cm"_{"0,f"} = ("k"_{"2"}-"k"_{"1"})/(36.5*"S"*"c")*int("w"_{"f"}^2*("α"_{"0,w"}+"i"_{"f"}),x,0,"i"_{"f"})`

Example

`"0.000548"=("3"-"2")/(36.5*"184m²"*"5m")*int(("2m")^2*("0.3rad"+"2"),x,0,"2")`

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Pitching Moment Coefficient for Fuselage Contribution Solution

STEP 0: Pre-Calculation Summary

Formula Used

Moment Coefficient For Fuselage Contribution = (Final Correction Factor For Body Fitness Ratio-Initial Correction Factor For Body Fitness Ratio)/(36.5*Wing Area*Mean Aerodynamic Chord)*int(Average Width Of Fuselage^2*(Wing Zero Lift Angle+Incidence Of Fuselage Camber Line),x,0,Incidence Of Fuselage Camber Line)
Cm_0,f = (k₂-k₁)/(36.5*S*c)*int(w_f^2*(α_0,w+i_f),x,0,i_f)
This formula uses 1 Functions, 8 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

Moment Coefficient For Fuselage Contribution - The moment coefficient for fuselage contribution is the sum of the contributions of each fuselage component, including the nose, cabin, and tailcone.
Final Correction Factor For Body Fitness Ratio - Final Correction Factor For Body Fitness Ratio can be quantified by the fuselage fineness ratio (FR), defined as the body length divided by its maximum diameter.
Initial Correction Factor For Body Fitness Ratio - Initial Correction Factor for body Fitness Ratio can be quantified by the fuselage fineness ratio (FR), defined as the body length divided by its maximum diameter.
Wing Area - (Measured in Square Meter) - The Wing area, S, is the projected area of the planform and is bounded by the leading and trailing edges and the wing tips.
Mean Aerodynamic Chord - (Measured in Meter) - The mean aerodynamic chord is the average distance from the leading edge to the trailing edge of a wing.
Average Width Of Fuselage - (Measured in Meter) - The average width of fuselage refers to the typical diameter or width of the central body structure of an aircraft.
Wing Zero Lift Angle - (Measured in Radian) - The wing zero lift angle, relative to the fuselage reference line, refers to the angle formed between the chord line of the wing and the reference line of the fuselage.
Incidence Of Fuselage Camber Line - The incidence of fuselage camber line relative to the fuselage reference line refers to the angle formed between the camber line of the fuselage and the reference line of the fuselage.

STEP 1: Convert Input(s) to Base Unit

Final Correction Factor For Body Fitness Ratio: 3 --> No Conversion Required
Initial Correction Factor For Body Fitness Ratio: 2 --> No Conversion Required
Wing Area: 184 Square Meter --> 184 Square Meter No Conversion Required
Mean Aerodynamic Chord: 5 Meter --> 5 Meter No Conversion Required
Average Width Of Fuselage: 2 Meter --> 2 Meter No Conversion Required
Wing Zero Lift Angle: 0.3 Radian --> 0.3 Radian No Conversion Required
Incidence Of Fuselage Camber Line: 2 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Cm_0,f = (k₂-k₁)/(36.5*S*c)*int(w_f^2*(α_0,w+i_f),x,0,i_f) --> (3-2)/(36.5*184*5)*int(2^2*(0.3+2),x,0,2)

Evaluating ... ...

Cm_0,f = 0.000547945205479452

STEP 3: Convert Result to Output's Unit

0.000547945205479452 --> No Conversion Required

FINAL ANSWER

0.000547945205479452 ≈ 0.000548 <-- Moment Coefficient For Fuselage Contribution

(Calculation completed in 00.004 seconds)

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< 2 Fuselage Contribution Calculators

Pitching Moment Coefficient for Fuselage Contribution

Go Moment Coefficient For Fuselage Contribution = (Final Correction Factor For Body Fitness Ratio-Initial Correction Factor For Body Fitness Ratio)/(36.5*Wing Area*Mean Aerodynamic Chord)*int(Average Width Of Fuselage^2*(Wing Zero Lift Angle+Incidence Of Fuselage Camber Line),x,0,Incidence Of Fuselage Camber Line)

Coefficient of Pitching Moment Respect to Fuselage Contribution

Go Moment Coefficient For Fuselage Contribution = (1/(36.5*Wing Area*Wingspan))*sum(x,0,Wingspan/2,Average Width Of Fuselage^2*(Wing Zero Lift Angle+Incidence Of Fuselage Camber Line)*Length Of Fuselage Increment)

Pitching Moment Coefficient for Fuselage Contribution Formula

What is Moment Coefficient For Fuselage Contribution ?

When an aircraft pitches (rotates about its lateral axis), various aerodynamic surfaces and components contribute to the overall pitching moment. The fuselage, being a significant component of an aircraft, also contributes to this moment. The pitching moment coefficient for fuselage contribution represents this contribution relative to other aerodynamic factors.

How to Calculate Pitching Moment Coefficient for Fuselage Contribution?

Pitching Moment Coefficient for Fuselage Contribution calculator uses Moment Coefficient For Fuselage Contribution = (Final Correction Factor For Body Fitness Ratio-Initial Correction Factor For Body Fitness Ratio)/(36.5*Wing Area*Mean Aerodynamic Chord)*int(Average Width Of Fuselage^2*(Wing Zero Lift Angle+Incidence Of Fuselage Camber Line),x,0,Incidence Of Fuselage Camber Line) to calculate the Moment Coefficient For Fuselage Contribution, The Pitching moment coefficient for fuselage contribution is the sum of the contributions of each fuselage component, including the nose, cabin, and tail cone. Moment Coefficient For Fuselage Contribution is denoted by Cm_0,f symbol.

How to calculate Pitching Moment Coefficient for Fuselage Contribution using this online calculator? To use this online calculator for Pitching Moment Coefficient for Fuselage Contribution, enter Final Correction Factor For Body Fitness Ratio (k₂), Initial Correction Factor For Body Fitness Ratio (k₁), Wing Area (S), Mean Aerodynamic Chord (c), Average Width Of Fuselage (w_f), Wing Zero Lift Angle (α_0,w) & Incidence Of Fuselage Camber Line (i_f) and hit the calculate button. Here is how the Pitching Moment Coefficient for Fuselage Contribution calculation can be explained with given input values -> 0.005898 = (3-2)/(36.5*17.0941593601368*5)*int(2^2*(0.3+2),x,0,2).

FAQ

What is Pitching Moment Coefficient for Fuselage Contribution?

The Pitching moment coefficient for fuselage contribution is the sum of the contributions of each fuselage component, including the nose, cabin, and tail cone and is represented as Cm_0,f = (k₂-k₁)/(36.5*S*c)*int(w_f^2*(α_0,w+i_f),x,0,i_f) or Moment Coefficient For Fuselage Contribution = (Final Correction Factor For Body Fitness Ratio-Initial Correction Factor For Body Fitness Ratio)/(36.5*Wing Area*Mean Aerodynamic Chord)*int(Average Width Of Fuselage^2*(Wing Zero Lift Angle+Incidence Of Fuselage Camber Line),x,0,Incidence Of Fuselage Camber Line). Final Correction Factor For Body Fitness Ratio can be quantified by the fuselage fineness ratio (FR), defined as the body length divided by its maximum diameter, Initial Correction Factor for body Fitness Ratio can be quantified by the fuselage fineness ratio (FR), defined as the body length divided by its maximum diameter, The Wing area, S, is the projected area of the planform and is bounded by the leading and trailing edges and the wing tips, The mean aerodynamic chord is the average distance from the leading edge to the trailing edge of a wing, The average width of fuselage refers to the typical diameter or width of the central body structure of an aircraft, The wing zero lift angle, relative to the fuselage reference line, refers to the angle formed between the chord line of the wing and the reference line of the fuselage & The incidence of fuselage camber line relative to the fuselage reference line refers to the angle formed between the camber line of the fuselage and the reference line of the fuselage.

How to calculate Pitching Moment Coefficient for Fuselage Contribution?

The Pitching moment coefficient for fuselage contribution is the sum of the contributions of each fuselage component, including the nose, cabin, and tail cone is calculated using Moment Coefficient For Fuselage Contribution = (Final Correction Factor For Body Fitness Ratio-Initial Correction Factor For Body Fitness Ratio)/(36.5*Wing Area*Mean Aerodynamic Chord)*int(Average Width Of Fuselage^2*(Wing Zero Lift Angle+Incidence Of Fuselage Camber Line),x,0,Incidence Of Fuselage Camber Line). To calculate Pitching Moment Coefficient for Fuselage Contribution, you need Final Correction Factor For Body Fitness Ratio (k₂), Initial Correction Factor For Body Fitness Ratio (k₁), Wing Area (S), Mean Aerodynamic Chord (c), Average Width Of Fuselage (w_f), Wing Zero Lift Angle (α_0,w) & Incidence Of Fuselage Camber Line (i_f). With our tool, you need to enter the respective value for Final Correction Factor For Body Fitness Ratio, Initial Correction Factor For Body Fitness Ratio, Wing Area, Mean Aerodynamic Chord, Average Width Of Fuselage, Wing Zero Lift Angle & Incidence Of Fuselage Camber Line 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 Moment Coefficient For Fuselage Contribution?

In this formula, Moment Coefficient For Fuselage Contribution uses Final Correction Factor For Body Fitness Ratio, Initial Correction Factor For Body Fitness Ratio, Wing Area, Mean Aerodynamic Chord, Average Width Of Fuselage, Wing Zero Lift Angle & Incidence Of Fuselage Camber Line. We can use 1 other way(s) to calculate the same, which is/are as follows -

Moment Coefficient For Fuselage Contribution = (1/(36.5*Wing Area*Wingspan))*sum(x,0,Wingspan/2,Average Width Of Fuselage^2*(Wing Zero Lift Angle+Incidence Of Fuselage Camber Line)*Length Of Fuselage Increment)

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