Canard Sizing

Canard Sizing (vehicle-design/sizing/canard-sizing)

Use when the task is sizing the forward canard surface of a canard-configured or three-surface aircraft: the canard area needed for a target canard volume coefficient, the trim lift share carried by the canard in steady level flight, the canard and wing lift coefficients at the trim condition, and the stall precedence check that the canard stalls before the wing so the nose drops rather than pitches up. This leaf implements the conceptual sizing loop in pure Python, stdlib only. It pairs with vehicle-design/sizing/tail-sizing, which owns the conventional aft empennage volume coefficients V_h and V_v, and with flight-mechanics/stability-control/longitudinal-stability for the neutral point and static margin that frame canard trim.

Domain quick reference

• Canard volume coefficient: V_c = S_c * L_c / (S * cbar), with S_c the canard area (m2), L_c the canard arm (m) from the wing aerodynamic center to the canard aerodynamic center, S the wing reference area (m2) and cbar the wing mean aerodynamic chord (m). The convention mirrors V_h for a horizontal tail, but the surface lies forward of the wing.
• Required canard area: S_c = V_c_target * S * cbar / L_c. A canard configuration that must trim at a forward center of gravity with a high nose-down pitching moment needs a large V_c target (0.35 to 0.6 typical at conceptual level).
• Geometry convention: x positive aft, origin at the wing aerodynamic center, canard forward of the wing (x_c < x_w = 0) and the center of gravity between them (x_c < x_cg < x_w).
• Trim lift share: f_c = (x_w - x_cg) / (x_w - x_c), the fraction of weight carried by the canard from the moment balance about the center of gravity with lift up positive. Moving the CG aft lowers the canard share.
• Trim lift coefficients: L_c = f_c * weight, L_w = weight - L_c, then Cl_c = L_c / (q * S_c) and Cl_w = L_w / (q * S_w) at the dynamic pressure q.
• Stall precedence margins: margin_c = Cl_max_c / Cl_c and margin_w = Cl_max_w / Cl_w. The surface with the smaller margin reaches its maximum lift first. A canard layout is pitch-safe only when the canard stalls first, so the nose drops instead of pitching up.
• Units are SI throughout: m, m2, N, Pa, kg/m3, dimensionless coefficients.
• FAR 25 and CS 25 flight characteristics requirements frame the pitch-up avoidance intent; the relations above are standard engineering methodology, summary-only.

Workflow

1. Fix the wing reference quantities (wing_area S, wing_mac cbar) and the canard arm from the layout; pick the target canard volume coefficient for the configuration and the CG envelope.
2. Size the surface: required_canard_area gives the canard area for the target coefficient, or run size_canard for the area plus the echoed coefficient.
3. Verify the chosen area with canard_volume_coefficient, which must return the target (round trip).
4. Compute the trim lift share with canard_lift_share at the CG station of interest; the geometry must satisfy x_c < x_cg < x_w.
5. Resolve the trim condition with trim_lift_coefficients from the weight and dynamic pressure to get the canard and wing lift forces and coefficients.
6. Run the stall precedence check with stall_precedence on the trim coefficients and the surface maximum lift coefficients. The verdict must read canard-stalls-first for the nose to drop rather than pitch up at the stall.
7. Sweep the CG envelope: at the aft CG the canard share falls and the verdict can flip to wing-stalls-first, which flags the pitch up risk and demands a larger V_c or a CG limit.
8. Confirm the deterministic checks with the contract test scripts/test_canard_sizing.py.

Worked example

Canard-configured light aircraft: wing area S = 30 m2, wing MAC cbar = 2.8 m, canard arm L_c = 9 m, target V_c = 0.45. Forward CG case x_cg = -3 m, canard x_c = -9 m, wing x_w = 0 m. Weight = 1200 * g0 N with g0 = 9.80665 m/s2; dynamic pressure q = 0.5 * 1.225 * 45^2 = 1240.3 Pa. Canard Cl_max = 1.7, wing Cl_max = 1.5.

• Required area: S_c = 0.45 * 30 * 2.8 / 9 = 4.2 m2. Round trip: V_c = 4.2 * 9 / (30 * 2.8) = 0.45.
• Forward CG trim share: f_c = (0 - (-3)) / (0 - (-9)) = 3/9 = 0.3333.
• Trim forces and coefficients: L_c = 3922.7 N, L_w = 7845.3 N, Cl_c = 3922.7 / (1240.3 * 4.2) = 0.7526, Cl_w = 7845.3 / (1240.3 *
  30. = 0.2108.
• Stall precedence: margin_c = 1.7 / 0.7526 = 2.259 against margin_w = 1.5 / 0.2108 = 7.116, verdict canard-stalls-first.
• Aft CG case x_cg = -1 m: f_c = 1/9 = 0.1111, Cl_c = 0.2510, Cl_w = 0.2811, margin_c = 6.77 against margin_w = 5.34, verdict wing-stalls-first, which demonstrates the pitch-up risk when the CG moves aft.

Pitfalls

• Declaring pitch safety without the stall precedence check: a canard layout is only pitch-safe when the canard stalls first (margin_c < margin_w); in the worked example the aft CG case flips to wing-stalls-first, so a fixed canard area is not safe across the whole CG envelope.
• Sizing the area and skipping the CG sweep: the trim share f_c = (x_w - x_cg) / (x_w - x_c) falls as the CG moves aft (0.3333 to 0.1111 in the worked example), so the surface must be checked at the aft CG where the pitch-up risk lives.
• Violating the geometry convention: the layout must satisfy x_c < x_cg < x_w with x positive aft; a CG station outside that ordering is rejected and the share formula loses meaning.
• Comparing margins across the wrong surface: the surface with the SMALLER margin (Cl_max / Cl) reaches its maximum lift first, so canard-stalls-first needs margin_c < margin_w, not the larger coefficient.
• Forgetting the coefficient depends on dynamic pressure: Cl_c = L_c / (q * S_c) and Cl_w = L_w / (q * S_w) use the trim q; the stall precedence verdict changes if q changes, so the check belongs at the actual trim condition.
• Treating the canard like a tail: the volume coefficient mirrors V_h but the surface lies FORWARD of the wing and carries upload (positive trim lift), which is the opposite of the download a conventional tail usually carries.

Verification

• Confirm required_canard_area(0.45, 9, 30, 2.8) returns 4.2 m2 and canard_volume_coefficient(4.2, 9, 30, 2.8) recovers 0.45.
• Confirm canard_lift_share(-3, 0, -9) returns 0.3333 and canard_lift_share(-1, 0, -9) returns 0.1111.
• Confirm trim_lift_coefficients at the worked example returns the anchor values above, and that the canard and wing lift forces sum to the weight.
• Confirm stall_precedence returns the canard-stalls-first verdict at the forward CG and wing-stalls-first at the aft CG, with the margin ratios 2.259/7.116 and 6.77/5.34.
• Confirm every non-positive volume coefficient target, area, arm, wing reference quantity, dynamic pressure, weight, maximum lift coefficient and trim lift coefficient raises ValueError, and that any CG station outside x_c < x_cg < x_w is rejected.
• Run the contract test offline: python3 scripts/test_canard_sizing.py (45 tests, deterministic).

Related leaves

• vehicle-design/sizing/tail-sizing: conventional aft empennage volume coefficients V_h and V_v, the alternative layout for the same trim function.
• flight-mechanics/stability-control/longitudinal-stability: the neutral point and static margin that frame where the canard trim share must act.
• vehicle-design/sizing/control-surface-sizing: elevators or control authority on the canard when the surface carries controls.
• vehicle-design/sizing/wing-planform-sizing: wing reference area and chord inputs for the canard volume coefficient.

Behavior contract (gate 3)

Run the deterministic contract test (stdlib unittest, offline):

python3 scripts/test_canard_sizing.py

The test covers the worked example anchors (required canard area 4.2 m2 within 1e-6, volume coefficient round trip within 1e-9, trim lift share 0.3333 at the forward CG and 0.1111 at the aft CG, trim lift coefficients 0.7526 and 0.2108, stall precedence margin ratios and both verdicts), the coefficient scaling laws and lift split identity, the size_canard convenience wrapper, and ValueError rejection of non-positive inputs and of CG stations outside x_c < x_cg < x_w.

Compliance

• Standards referenced, not reproduced: FAR 25 and CS 25 flight characteristics requirements frame the pitch-up avoidance intent for canard configurations; the canard sizing relations above are standard engineering methodology, summary-only per standards-map.yaml.
• compliance: STANDARDS-REF, gated: false.