Ws Tw Trade

W/S and T/W Matching (vehicle-design/sizing/ws-tw-trade)

Use when the task is wing loading and thrust to weight matching for conceptual sizing: the stall, takeoff distance, climb gradient, and cruise constraints that draw the sizing matching chart, and the binding constraint that sets the minimum thrust to weight at a given wing loading.

Domain quick reference

• Wing loading W/S is in N/m^2, thrust to weight T/W is unitless, air density rho in kg/m^3 (default 1.225 kg/m^3, sea-level ISA), speeds in m/s, takeoff distance in m, flight path angle gamma in rad, and g = 9.80665 m/s^2.
• Stall constraint (maximum wing loading): W/S = 0.5 * rho * CLmax * VS^2, from lift equal to weight at the stall speed VS.
• Takeoff distance constraint (required T/W): T/W = 1.21 * (W/S) / (rho * g * CLmax * s_TO), with s_TO the takeoff distance in m.
• Climb gradient constraint (required T/W): T/W = 1/LD + gamma, the level-flight drag term plus the small-angle climb term, gamma in rad.
• Cruise constraint (required T/W at speed V): T/W = 0.5 * rho * V^2
  • CD0 / (W/S) + k * (W/S) / (0.5 * rho * V^2), the zero-lift drag term plus the lift-induced drag term, k = 1/(pi * e * AR).
• The matching chart plots required T/W against W/S, one curve per constraint; at a given wing loading the binding constraint is the curve with the largest required T/W, which sets the minimum thrust to weight for the propulsion sizing.
• FAR-25 (14 CFR Part 25) and CS-25 set the certification context (stall speed, takeoff field length, and climb gradients for transport-category aeroplanes); the constraint equations are common conceptual sizing practice.

Workflow

1. Set the design point: stall speed, maximum lift coefficient, air density, takeoff distance, lift-to-drag ratio, climb gradient, cruise speed, zero-lift drag coefficient, and induced drag factor k.
2. Compute the maximum wing loading allowed by the stall speed with stall_constraint.
3. Compute the required T/W from the takeoff distance with takeoff_constraint.
4. Compute the required T/W from the climb gradient with climb_constraint.
5. Compute the required T/W at the cruise speed with cruise_constraint.
6. Sweep candidate wing loadings and find the binding constraint with feasible_min_tw; the returned min_tw is the required thrust to weight that sizes the propulsion system.

Pitfalls

• Mixing units: wing loading in kg/m^2 instead of N/m^2, or gamma in degrees with the small-angle formula; keep everything SI with gamma in rad.
• Forgetting the density default: rho defaults to 1.225 kg/m^3 (sea level); at altitude the lower density tightens the takeoff and climb constraints.
• Treating the climb term as 1/LD only: the gamma term is the climb gradient itself; dropping it understates the required T/W.
• Averaging the constraint T/W values instead of taking the maximum: the binding constraint is the maximum, not the mean, and it defines the feasible design point on the matching chart.
• Using the stall constraint as a required T/W curve: it gives a maximum wing loading boundary, not a thrust requirement.
• Passing an empty constraints dict to feasible_min_tw; the module raises ValueError instead of guessing.

Behavior contract (gate 3)

The stall, takeoff distance, climb gradient, and cruise constraints plus the binding-constraint minimum T/W logic are exercised by the gate 3 contract test: scripts/test_ws_tw_trade.py against scripts/ws_tw_trade_logic.py (stdlib unittest, offline). Run: python3 scripts/test_ws_tw_trade.py

Compliance

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