Tail Volume Coefficient Calculator

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⚠️ Note: This tool provides rough estimates for initial sizing only.

About This Tool

The Tail Volume Coefficient Calculator is a precision design tool for sizing horizontal and vertical tail surfaces on aircraft. It uses industry-standard volume coefficient methods to ensure proper longitudinal and directional static stability.

This calculator is based on the work of Sadraey (Aircraft Design: A Systems Engineering Approach) and Raymer (Aircraft Design: A Conceptual Approach), which are widely used references in aerospace engineering. The volume coefficient method provides a reliable first-order approximation for tail sizing during the preliminary design phase.

Key Features:

When to Use This Tool: Use this calculator during the conceptual and preliminary design phases to establish initial tail surface dimensions. Results should be validated with more detailed stability analysis and flight testing.

Inputs

Assumes rectangular wing (Area=b⋅c). If wing is tapered, input Mean Aerodynamic Chord (MAC).

Volume Coefficients

Aspect Ratios

Results

Horizontal Tail

Required Area (S_h): sq. in.

Suggested Span: in.

Suggested Chord: in.

Vertical Tail

Required Area (S_v): sq. in.

Suggested Span: in.

Suggested Chord: in.

Formula Derivation

Horizontal Tail Volume Coefficient (\(V_h\))

The horizontal tail volume coefficient is a non-dimensional number that represents the sizing of the horizontal stabilizer relative to the main wing. It is a key parameter for ensuring longitudinal static stability (pitch stability).

\[V_h = \frac{L_h S_h}{c S_{ref}}\]

  • \(L_h\): Moment arm from the aircraft's center of gravity to the horizontal tail's aerodynamic center.
  • \(S_h\): Area of the horizontal tail.
  • \(c\): Mean aerodynamic chord of the main wing.
  • \(S_{ref}\): Reference area of the main wing.

A higher \(V_h\) value generally implies greater stability, but also more drag and weight. For most conventional aircraft, this value is between 0.5 and 0.7.

Vertical Tail Volume Coefficient (\(V_v\))

The vertical tail volume coefficient is a non-dimensional number for the vertical stabilizer, crucial for directional static stability (yaw stability).

\[V_v = \frac{L_v S_v}{b S_{ref}}\]

  • \(L_v\): Moment arm from the aircraft's center of gravity to the vertical tail's aerodynamic center.
  • \(S_v\): Area of the vertical tail.
  • \(b\): Span of the main wing.
  • \(S_{ref\): Reference area of the main wing.

Similar to \(V_h\), a larger \(V_v\) provides more stability against yawing motions but at the cost of increased drag. Typical values range from 0.05 to 0.07.