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Method & Assumptions

Equations used by this preliminary flight-mechanics tool

Horizontal tail volume

Relates horizontal-tail area and moment arm to the wing reference geometry.

VH = SH · lH / (SW · c̄)

Inverse sizing

A target tail-volume coefficient can be converted into required tail area or tail arm.

SH,req = VH,target · SW · c̄ / lH
lH,req = VH,target · SW · c̄ / SH

Neutral point

The neutral point is estimated from the wing aerodynamic center and horizontal-tail contribution.

xNP/c̄ = xac,W/c̄ + ηHVH(CLα,H/CLα,W)(1 − dε/dα)

Static margin

Positive static margin corresponds to longitudinal static stability in this simplified model.

SM = xNP/c̄ − xCG/c̄

Pitching-moment slope

For the present sign convention, longitudinal static stability corresponds to Cmα < 0.

Cmα = CLα,W(xCG/c̄ − xac,W/c̄) − ηHVHCLα,H(1 − dε/dα)

Model assumptions

  • Linear aerodynamic behavior and small-angle approximation
  • Conventional aft horizontal-tail configuration
  • Constant lift-curve slopes, downwash gradient and tail efficiency
  • Fuselage, propulsion, compressibility and nonlinear stall effects neglected
Preliminary sizing tool only. Verify aerodynamic derivatives, reference positions, downwash assumptions and configuration-specific effects before using results for detailed design or certification.
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Parameters

Geometry, reference positions and aerodynamic derivatives

Wing geometry

Horizontal tail

Reference positions

Example: 0.25 = 25% MAC.

Aerodynamics

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Results

Tail sizing and longitudinal stability
Stability
–
Tail volume VH
–
Neutral point
–
Static margin
–

Longitudinal Stability

Quantity Value Unit
Neutral point xNP/c̄ – –
Static margin SM – –
Pitching-moment slope Cmα – 1/rad
MAC SM AC CG NP

Schematic only. CG, wing AC and neutral point are mapped relative to the mean aerodynamic chord.

Tail Sizing

Quantity Value Unit
Current tail volume VH – –
Required tail area SH,req – m²
Required tail arm lH,req – m
∂VH/∂SH – 1/m²
∂VH/∂lH – 1/m