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Pitching Moment Coefficient for Fuselage Contribution Formula

GoCoefficient of Pitching Moment Respect to Fuselage Contribution Formula

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The Moment Coefficient for Fuselage Contribution is the sum of the contributions of each fuselage component, including the nose, cabin, and tail cone. Check FAQs

Cm 0,f = \frac{k 2 - k 1}{36.5 \cdot S w \cdot c ma} \cdot \int ({w f}^{2} \cdot (α 0,w + i f), x, 0, i f)

Cm_0,f - Moment Coefficient for Fuselage Contribution?k₂ - Final Correction Factor for Body Fitness Ratio?k₁ - Initial Correction Factor for Body Fitness Ratio?S_w - Wing Area?c_ma - Mean Aerodynamic Chord?w_f - Average Width of Fuselage?α_0,w - Wing Zero Lift Angle?i_f - Incidence of Fuselage Camber Line?

Pitching Moment Coefficient for Fuselage Contribution Example

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Here is how the Pitching Moment Coefficient for Fuselage Contribution equation looks like with Values.

Here is how the Pitching Moment Coefficient for Fuselage Contribution equation looks like with Units.

Here is how the Pitching Moment Coefficient for Fuselage Contribution equation looks like.

0.0126 = \frac{10.1 - 10}{36.5 \cdot 184 \cdot 0.2} \cdot \int ({3.45}^{2} \cdot (0.31 + 3.62), x, 0, 3.62)

0.0126 = \frac{10.1 - 10}{36.5 \cdot 184m² \cdot 0.2m} \cdot \int ({3.45m}^{2} \cdot (0.31rad + 3.62), x, 0, 3.62)

0.0126 = \frac{10.1 - 10}{36.5 \cdot 184 \cdot 0.2} \cdot \int ({3.45}^{2} \cdot (0.31 + 3.62), x, 0, 3.62)

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Pitching Moment Coefficient for Fuselage Contribution Solution

Follow our step by step solution on how to calculate Pitching Moment Coefficient for Fuselage Contribution?

FIRST Step Consider the formula

Cm 0,f = \frac{k 2 - k 1}{36.5 \cdot S w \cdot c ma} \cdot \int ({w f}^{2} \cdot (α 0,w + i f), x, 0, i f)

Next Step Substitute values of Variables

∴

Cm 0,f = \frac{10.1 - 10}{36.5 \cdot 184m² \cdot 0.2m} \cdot \int ({3.45m}^{2} \cdot (0.31rad + 3.62), x, 0, 3.62)

Next Step Prepare to Evaluate

∴

Cm 0,f = \frac{10.1 - 10}{36.5 \cdot 184 \cdot 0.2} \cdot \int ({3.45}^{2} \cdot (0.31 + 3.62), x, 0, 3.62)

Next Step Evaluate

∴

Cm 0,f = 0.0126066190068493

LAST Step Rounding Answer

∴

Cm 0,f = 0.0126

Pitching Moment Coefficient for Fuselage Contribution Formula Elements

Variables

Functions

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 tail cone.

Symbol: Cm_0,f

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Moment Coefficient for Fuselage Contribution

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.

Symbol: k₂

Measurement: NAUnit: Unitless