Wind Tunnel Model Design

Wind Tunnel Model Design (aerodynamics/wind-tunnel/wind-tunnel-model-design)

Use when the task is designing the scale model and the test setup for a wind tunnel campaign on an aircraft configuration, the pre-test design step that fixes the model geometry and the loads the installation must carry before any runs. The model scale is driven by the smaller of two geometric constraints, the test section blockage limit and the span clearance to the walls; the model reference dimensions follow from the scale; the model Reynolds number at the maximum tunnel speed is compared with the full-scale flight Reynolds number; and the maximum test dynamic pressure and the resulting model load are used to rate the force balance and to size the model support sting. The leaf pairs with the post-test siblings: aerodynamics/wind-tunnel/windtunnel-data-reduction reduces the raw balance readings into coefficients after the runs, and aerodynamics/wind-tunnel/windtunnel-wall-corrections corrects measured coefficients for the test section boundaries; this leaf stops at the pre-test design and reports a Reynolds mismatch flag rather than a corrected result.

The module constants BLOCKAGE_MAX (0.05), SPAN_CLEARANCE (0.8) and STING_ALLOWABLE_STRESS_PA (800 MPa) are documented typical values only: they are program and test specific inputs, and every function and the analyze pass accept explicit overrides. NACA TR-824 frames the compressible-flow context the tunnel operates in; the relations below are standard low-speed model sizing and load estimation methodology, summary-only. Pure Python stdlib, deterministic, offline.

Domain quick reference

• Test section area: A_test = w * h (test_section_area).
• Blockage-limited scale: lambda_blockage = sqrt(blockage_max * A_test / S_full), the scale at which the model wing area equals blockage_max times the test section area (scale_from_blockage).
• Span-limited scale: lambda_span = (w * clearance) / b_full, the largest model that keeps the span inside the available fraction of the section width (scale_from_span).
• Chosen scale: lambda = min(lambda_blockage, lambda_span) (choose_scale). The dict also carries model_wing_area = S_full * lambda^2, model_mac = c_full * lambda, model_span = b_full * lambda, blockage_ratio = S_model / A_test and blocked_ok (the blockage limit is inclusive). choose_scale takes the full-scale MAC as its fifth argument so the model chord is reported; the scale selection itself depends only on the areas and the span.
• Model Reynolds number: Re_model = rho * V * c_model / mu, rho and mu at sea level by default (reynolds_model).
• Reynolds ratio: Re_model / Re_full (reynolds_ratio). The analyze pass reports "reynolds-matched" when the ratio is at least 0.5 and "reynolds-mismatch" below; this is an engineering flag about the tunnel capability, not a pass/fail gate on the campaign.
• Maximum dynamic pressure: q = 0.5 * rho * Vmax^2.
• Model load at the maximum test lift coefficient: L = q * S_model * CL_max_test (model_load_N), the load the balance must carry.
• Balance rating: "balance-ok" when L <= balance_capacity_N, else "balance-overload" (balance_verdict).
• Sting sizing: M = L * sting_arm, then d = (32 * M / (pi * sigma_allow))^(1/3) for the solid circular sting section (sting_diameter_m).
• One-call pass: analyze(inputs) returns the scale selection, model dimensions, blockage ratio, model Reynolds number and ratio, dynamic pressure, load, balance verdict, sting bending moment and diameter in a single dict.
• Units are SI throughout: m, m2, m/s, Pa, N, N m, kg/(m s).

Workflow

1. Gather the test section geometry (test_section_width_m, test_section_height_m, or the area directly), the full-scale reference data (full_span_m, full_wing_area_m2, full_mac_m, full_reynolds), the tunnel maximum speed, and the program specific inputs: max_test_cl (default 1.4), balance_capacity_N, sting_arm_m, sting_allowable_stress_pa, blockage_max and clearance when they differ from the documented typicals.
2. Confirm the test section area with test_section_area, or pass test_section_area_m2 to skip the product.
3. Select the scale with choose_scale and read lambda, the model wing area, MAC and span, the blockage_ratio and blocked_ok from the returned dict; when the span limit binds the model is smaller than the blockage limit allows.
4. Check the tunnel Reynolds capability: reynolds_model at the maximum tunnel speed, then reynolds_ratio against the full-scale flight condition. A ratio below 0.5 flags reynolds-mismatch, the usual low-speed outcome for a large transport, and is reported as a limitation of the campaign, not an error.
5. Compute q = 0.5 * rho * Vmax^2 and the model load at the maximum test lift coefficient with model_load_N, then rate the balance with balance_verdict.
6. Size the sting: the bending moment is the model load times the sting arm (model quarter chord to the sting mount); sting_diameter_m gives the solid circular section diameter at the allowable stress.
7. For the complete setup in one call, run analyze(inputs) and read the whole dict; it applies the same sequence and validates every input.
8. Confirm the deterministic checks with the contract test scripts/test_wind_tunnel_model_design.py.

Worked example

A 2.44 m square test section (area 5.9536 m2) for a full-scale transport: span 34.0 m, wing area 122.6 m2, MAC 4.2 m, full-scale Reynolds number 3.0e7. Tunnel maximum speed 80 m/s, max_test_cl 1.4, balance capacity 5000 N, sting arm 0.35 m, sting allowable stress 800 MPa, default blockage_max 0.05 and clearance 0.8.

• scale_from_blockage: sqrt(0.05 * 5.9536 / 122.6) = 0.04927, the blockage-limited scale.
• scale_from_span: (2.44 * 0.8) / 34.0 = 0.05741. The chosen scale is the smaller, lambda = 0.04927.
• Model dimensions: wing area 122.6 * 0.04927^2 = 0.29761 m2, MAC 4.2 * 0.04927 = 0.20693 m, span 34.0 * 0.04927 = 1.6752 m.
• Blockage ratio: 0.29761 / 5.9536 = 0.04999, within the 0.05 limit, so blocked_ok. The module carries full precision (scale 0.049275, model area 0.29768 m2), which lands the ratio on the limit and the reported anchors within their contract tolerances.
• Model Reynolds at 80 m/s: 1.225 * 80 * 0.20693 / 1.789e-5 = 1.1337e6. Ratio to the full-scale condition: 1.1337e6 / 3.0e7 = 0.03779, far below 0.5, so reynolds_limitation is "reynolds-mismatch": the low-speed model runs at 3.8% of the flight Reynolds number.
• Dynamic pressure: q = 0.5 * 1.225 * 80^2 = 3920 Pa. Model load at max_test_cl 1.4: 3920 * 0.29761 * 1.4 = 1633.3 N, against a 5000 N balance, so the verdict is balance-ok (a 1000 N balance would read balance-overload).
• Sting: bending moment 1633.3 * 0.35 = 571.7 N m; diameter (32 * 571.7 / (pi * 800e6))^(1/3) = 0.01938 m = 19.38 mm at 800 MPa.

Verification

• Confirm choose_scale on the worked example returns scale 0.04927 within 1e-4, model area 0.29761 m2 within 1e-4, model MAC 0.20693 m within 1e-4 and model span 1.6752 m within 2e-4 (the published span anchor is computed from the scale truncated to five decimals).
• Confirm reynolds_model returns 1.1337e6 within 1e3, the ratio 0.03779 within 1e-4, and analyze reports "reynolds-mismatch".
• Confirm model_load_N returns 1633.3 N within 1 N and balance_verdict gives "balance-ok" at 5000 N capacity and "balance-overload" at 1000 N.
• Confirm sting_diameter_m returns 0.01938 m within 0.01 mm.
• Confirm every non-positive width, height, area, span, MAC, Reynolds number, tunnel speed, lift coefficient, balance capacity, sting arm and allowable stress raises ValueError, in the individual functions and in analyze.
• Run the contract test offline: python3 scripts/test_wind_tunnel_model_design.py (35 tests, deterministic, exit 0).

Related leaves

• aerodynamics/wind-tunnel/windtunnel-data-reduction: reduces the raw balance and pressure measurements into coefficients after the runs, with the tare and uncertainty steps this pre-test leaf does not do.
• aerodynamics/wind-tunnel/windtunnel-wall-corrections: applies the closed-wall corrections to the measured coefficients, the post-test counterpart of the pre-test blockage budget fixed here.

Pitfalls

• Taking the blockage limit as the scale without checking the span clearance: choose_scale returns the smaller of lambda_blockage and lambda_span, and in the worked example the span limit would allow 0.05741 while blockage binds at 0.04927 - the reverse case binds on span, so report which constraint drove the choice.
• Treating a reynolds-mismatch flag as a campaign error: a ratio below 0.5 (0.03779 in the worked example) is the usual low-speed outcome for a large transport and is reported as a tunnel-capability limitation, not a pass/fail gate on the model.
• Overriding the documented typical constants without checking the program: BLOCKAGE_MAX, SPAN_CLEARANCE and STING_ALLOWABLE_STRESS_PA are test-specific inputs with defaults; each function and analyze accept explicit overrides, so pass program values rather than assuming the defaults hold.
• Rating the balance on the cruise load: the load that must be carried is q * S_model * CL_max_test at the maximum test lift coefficient (1633 N in the example), and a 1000 N balance reads balance-overload even though the 5000 N rating passes.
• Sizing the sting on force alone: the bending moment is the model load times the sting arm (quarter chord to mount), and the diameter comes from that moment at the allowable stress - an arm change alters the diameter even at fixed load.
• Quoting the rounded scale anchors: the module carries full precision (scale 0.049275 vs the published 0.04927) so the round-trip dimension checks land within tolerance; do not truncate inputs to the published anchors before calling.

Behavior contract (gate 3)

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

python3 scripts/test_wind_tunnel_model_design.py

The test covers the worked example anchors (scale 0.04927, model wing area 0.29761 m2, MAC 0.20693 m, span 1.6752 m, blockage ratio 0.04999, model Reynolds 1.1337e6, Reynolds ratio 0.03779, load 1633.3 N, sting diameter 19.38 mm), scale selection as the minimum of the blockage and span limits with exact dimension round trips, the span-limited case, the balance overload verdict, the reynolds-matched flag above a 0.5 ratio, the default max_test_cl, the direct test section area input, determinism of the analyze pass, and ValueError rejection of every non-positive input class.

Compliance

• Standards referenced, not reproduced: NACA TR-824 is named for the compressible-flow context only; the sizing relations above are standard low-speed wind tunnel methodology, summary-only per standards-map.yaml.
• compliance: STANDARDS-REF, gated: false.