Model similarity-measurement-v1. Authored 23 October 2026 UTC. All illustrations are original; no manufacturer data or aircraft performance claim.
Boundary and variables
Two independent, steady freestream states: a full-scale reference and a generic tunnel. No spatial flow is solved. Full-scale geometry is prescribed through chord L and reference area S; a geometrically similar model has Lm = λLf and Sm = λ²Sf. The sketches are separately magnified. The ruler alone displays their true relative chord. Particles show a uniform external freestream, with one common visual time scale; no boundary layer or local velocity field is implied.
All calculation uses SI. User pressure is static absolute kPa, temperature is static K, altitude is pressure/geopotential altitude in m, and Mach is dimensionless. Motion is left to right. R = 287.05287 J/(kg K); γ = 1.4.
Air properties and matching
Dry tropospheric reference for 0 ≤ h ≤ 11,000 m:
- T = 288.15 − 0.0065h.
- p = 101325(T/288.15)^[9.80665/(R·0.0065)].
- ρ = p/(RT); a = sqrt(γRT); V = Ma.
- μ = 1.458×10⁻⁶ T^(3/2)/(T+110.4) Pa s.
- Re = ρVL/μ; q = ρV²/2.
For fixed model scale and tunnel T, matching flight Mach determines V. Matching Re then requires p = Re_f μ RT/(V Lm). The button applies both only if the calculated pressure is within 20–1,500 kPa. Otherwise it leaves the setup unchanged and reports the required pressure. The ±1% UI indicator is a display tolerance, not a wind-tunnel acceptance criterion.
The atmosphere and constant-property air model approximate actual conditions. Tunnel temperature range 180–330 K and pressure range 20–1,500 kPa are teaching bounds, not an actual facility envelope. No humidity, real-gas effects, wall corrections, roughness, transition, aeroelastic or dynamic similarity is established. Re/M matching alone is not sufficient for all experiments.
Synthetic measurement
Drag coefficient CD is a prescribed input; it does not depend on Re or M in this exercise. Fideal = q Sm CD, Freading = Fideal + signed offset, CDreading = Freading/(q Sm). These are synthetic values. The model does not claim a reliable transfer of actual force coefficients between unmatched flows. A negative reading is possible with a large negative offset; it is retained as an instrument-offset example, not negative true drag.
For independent measured inputs F, p, T, V, S, the first-order combined standard uncertainty is the square root of the sum of squared sensitivity-weighted input uncertainties. Input uF is absolute N, uV is the user percentage of V, up = 0.5% p, uT = 0.2% T and uS = 1% S. The speed measurement is independent of the static T measurement for this uncertainty calculation; Mach is a nominal setup parameter. Covariances are assumed zero. The offset is a known imposed bias, not an estimated random contribution. ±1u (k = 1) is not a guaranteed interval or 95% coverage claim. Large relative uncertainty may make first-order propagation unreliable; no nonlinearity correction is applied.
Interaction and verification
A saves all parameters, including the full-scale reference and measurement assumptions. B remains editable. The similarity map can change Mach/pressure directly; its drag axis bounds freeze during a gesture. Sliders and arrow keys provide alternatives. CSV contains both input sets, result tables and scale sweeps. Share links contain bounded numerical inputs only.
node verify.js writes verification.json. Checks include sea-level/11 km reference states, length/area/force scaling, pressure scaling, q = γpM²/2, algebraic simultaneous matching, bias identity, independent finite-difference uncertainty sensitivities and bounded input grids. This is implementation verification, not experimental validation or facility qualification.