MATCH TWO RATIOS
The similarity map
Curves hold B temperature and model size fixed. The white diamond is the full-scale target; A and B are independently calculated. Reynolds number uses a logarithmic axis.
FROM A SMALL MODEL TO A FULL-SIZE AIRCRAFT
Small model.
Same physics?
A miniature aircraft does not automatically fly in miniature air. Change the tunnel conditions, match the important ratios, then examine what the balance can actually measure.
Calculated similarity, prescribed aerodynamics. This lab calculates air properties and dimensionless ratios. Drag coefficient is an explicit teaching input, not a CFD result. Matching Re and M is necessary for the selected effects, but does not prove complete similarity.
ONE REFERENCE / TWO TEST CONFIGURATIONS
On a narrow screen, scroll the diagram sideways. Profiles are magnified separately; the chord ruler shows true relative scale. Moving markers indicate uniform freestream speed, slowed for viewing. They are not a solved flow around the model.
A · baseline saved at start
Start with a comparison, or change any control.
SIZE CHANGES THE SIGNAL
Force and model scale
A and B each retain their own tunnel conditions and prescribed coefficient. Doubling linear size quadruples reference area. This is a force-scaling relation, not a prediction of changing drag coefficient.
A READING IS NOT AN EXACT VALUE
Read the force balance.
Use the measurement controls above to change absolute balance uncertainty, airspeed uncertainty and a signed force offset. A small model can give a precise-looking number with a weak signal.
Bands show ±1 combined standard uncertainty (k = 1). They are not guaranteed bounds or a stated 95% interval. Large relative uncertainty makes this first-order estimate less reliable. Reynolds/Mach mismatch, wall corrections, transition and other model-form errors are excluded.
Compare the complete setup
| Quantity | A · saved | B · live | B − A | Unit |
|---|
A stores the entire setup, including its full-scale reference. If that reference changes, the table makes the change explicit.
Speed alone is not enough
For the same gas state, Reynolds number scales with length and speed. Matching a smaller model by speed alone also changes Mach number. Pressurisation offers another degree of freedom.
Cooling changes more than density
At fixed Mach, lower temperature reduces the speed of sound and tunnel speed. Density rises at fixed pressure, while viscosity falls. Follow all three changes in the comparison table.
A good ratio is not a complete test
Geometry, incidence, roughness, transition, blockage and support interference still matter. A force coefficient is transferable only when the relevant physics and corrections justify it.
EQUATIONS / ASSUMPTIONS / EVIDENCE
Read the model
Air and similarity
Static pressure p [Pa], static temperature T [K], speed V [m/s], chord L [m], density ρ [kg/m³] and dynamic viscosity μ [Pa s]. Dry ideal air: R = 287.05287 J/(kg K), γ = 1.4.
Scale geometry, then force
λ = model chord / full-scale chord. S [m²] is reference area and F [N] is drag. The entered CD is prescribed at both scales for this measurement exercise; it is not inferred from Re or M.
Temperature-dependent viscosity
Sutherland's relation for air, with T in kelvin and μ in Pa s. The full-scale reference uses a dry tropospheric atmosphere from 0 to 11 km. Tunnel inputs are static conditions.
Propagate a measurement uncertainty
First-order propagation for independent F, p, T, V and S measurements. The balance offset moves the reading; it is not included as an estimated random uncertainty.
What this experiment can establish
Algebraic checks verify unit conversion, ideal-gas identities, geometric scaling, exact Re/M matching within the offered ranges and numerical derivatives of the uncertainty calculation. No wind-tunnel data or aircraft-specific calibration is used. The profiles and freestream markers are original explanatory graphics.
The ±1% Re/M indicator is an interface comparison tolerance, not a research acceptance standard. Low-speed tests can sometimes relax Mach matching; this interface still reports both ratios. Ideal air, a constant heat-capacity ratio and Sutherland viscosity are approximations. No shocks, boundary layer, transition, deformation, heat transfer, tunnel walls or force-coefficient dependence on flow are solved.
Read numerical check record ↗ · Model specification ↗