Tail Sizing

Tail Sizing (vehicle-design/sizing/tail-sizing)

Use when the task is empennage sizing from tail volume coefficients: computing the horizontal and vertical tail volume coefficients from the tail areas, tail arms, and wing reference quantities, solving for the required tail area for a target volume coefficient, and checking the result against typical conceptual sizing ranges.

Domain quick reference

• Horizontal tail volume coefficient: V_h = S_h * L_h / (S_w * cbar), with S_h the horizontal tail area (m^2), L_h the horizontal tail arm (m, wing aerodynamic center to tail quarter chord), S_w the wing reference area (m^2), and cbar the wing mean aerodynamic chord (m).
• Vertical tail volume coefficient: V_v = S_v * L_v / (S_w * b), with S_v the vertical tail area (m^2), L_v the vertical tail arm (m), and b the wing span (m).
• Required tail area for a target coefficient: S_h = V_h * S_w * cbar / L_h, and S_v = V_v * S_w * b / L_v; a longer tail arm reduces the required area, a larger wing reference area increases it.
• Typical ranges: V_h from 0.5 to 1.0 (transport category about 0.7), V_v from 0.04 to 0.07 (transport category about 0.06). Both are unitless; all lengths and areas are SI (m and m^2).
• FAR-25 (14 CFR Part 25) and CS-25 set the certification context for transport-category stability and control (tail authority, control surface sizing); the volume coefficient method itself is common conceptual sizing practice.

Workflow

1. Set the wing reference area S_w and the reference lengths: mean aerodynamic chord cbar for the horizontal tail, span b for the vertical tail.
2. Set the tail arms L_h and L_v from the layout: wing aerodynamic center to horizontal tail quarter chord, and to vertical tail quarter chord.
3. Compute V_h and V_v from the candidate tail areas with tail_volume_coefficient.
4. Solve for the required tail area for the target volume coefficient with tail_area_required; this closes the empennage sizing once the tail arms and wing reference quantities are fixed.
5. Judge the pair against the typical ranges with volume_coefficient_verdict; rework the layout (tail arm, tail area) until h_ok and v_ok are both True.

Pitfalls

• Swapping the reference lengths: cbar for the horizontal tail, b for the vertical tail; exchanging them gives a wrong coefficient with no error signal.
• Measuring the tail arm from the wrong point: the arm runs from the wing aerodynamic center to the tail quarter chord, not from the nose or the wing leading edge.
• Using mixed units: keep areas in m^2 and arms in m; a centimeter arm with a meter area silently distorts the coefficient.
• Treating the typical ranges as hard limits: 0.5-1.0 and 0.04-0.07 are sizing guidance, not a certification requirement; the verdict flags outliers for layout rework.
• Passing a zero or negative tail arm to tail_area_required; the module raises ValueError instead of dividing by zero.
• Sizing the vertical tail with the horizontal reference length; the vertical tail volume coefficient uses the span, not the chord.

Behavior contract (gate 3)

The tail volume coefficient relations, the required-area inverse, and the typical-range verdict are exercised by the gate 3 contract test: scripts/test_tail_sizing.py against scripts/tail_sizing_logic.py (stdlib unittest, offline). Run: python3 scripts/test_tail_sizing.py

Compliance

• Standards referenced, not reproduced: FAR-25 is US government work (public domain) and CS-25 is a free EASA download; the tail volume coefficient equations are common conceptual sizing methodology, summary-only per standards-map.yaml.
• compliance: STANDARDS-REF, gated: false.