A scale model lies to you

Why a smaller model does not behave like a smaller version of the real thing.

A scale model lies to you because shrinking a shape changes the balance between the forces air exerts on it in a way that shrinking the geometry alone does not account for, so a small model tested in ordinary air can produce a different kind of airflow from the one the full-size car will experience, instead of a smaller copy of it.

Inertia, stickiness and what shrinking does to the balance

Airflow around any shape is governed by a balance between two effects: the air's inertia, its tendency to keep moving in whatever direction it is already travelling, and its viscosity, the internal stickiness that resists one layer of air sliding past another. Which one dominates depends on the shape's size combined with the speed of the flow and the fluid's own thickness. Shrinking a shape without speeding up the air past it, or changing the fluid, shifts the balance toward viscosity mattering more than it did at full size. That shift is captured by the Reynolds number, the single figure engineers use to compare how the balance sits for two different flows. A small model can therefore behave as though it were moving through a thicker, stickier fluid than the full-size car does, even though both sit in the same ordinary air. The model has been built perfectly well; ordinary air simply keeps its stickiness whether it flows past a large car or a small model.

A pebble and a boulder in the same pond

Throw a small pebble into a still pond and it makes a delicate splash, fine droplets and ripples dominated by surface tension pulling the disturbance back toward stillness almost as quickly as it appeared. Throw a large boulder into the same pond and it makes a violent, churning plume, where the water's inertia does almost all the work and spray is thrown high into the air. The water is unchanged and only the size of the object differs, yet the character of the disturbance changes along with its scale, just as a small aerodynamic model can see a different kind of airflow from the full-size car. A flat skimming stone of the pebble's size produces yet another pattern, a reminder that scale is one of several factors deciding what kind of flow results.

Making up for size with speed

With the same air, the Reynolds number rises in step with size multiplied by speed. A half-scale model therefore needs air moving past it at twice the full-size car's speed to match, and a quarter-scale model of a car that runs at 60 km/h needs 240 km/h in the tunnel. The fix has its own ceiling. A tenth-scale model of a car at 100 km/h would need 1,000 km/h, most of the way to the speed of sound, where air starts to compress ahead of the model and misbehaves for an entirely new reason. Very small models are therefore stuck with some mismatch however fast the tunnel runs. The mismatch is worst when a model is shrunk a great deal and tested at a similar or lower airspeed than the real car, and least for a model only modestly smaller, or one run correspondingly faster. That is why a serious wind tunnel is judged partly by the top airspeed it can sustain as well as the space inside it, since a tunnel limited to modest speeds pushes every model into a regime the full-size car will never experience.

Asking a model which of two shapes is better

A shape that shows attached, well-behaved flow on a small, slow model can separate on the real car despite being geometrically identical, because the real car's larger size and higher speed put it in a different flow regime. Results from scaled testing need real caution before being scaled up by the same ratio the model was built to. Comparing two design options tested under the same scaled conditions is far more trustworthy than the absolute figures either produces, since whatever mismatch exists between model and full scale tends to push both options in roughly the same direction. A student team without a large, fast tunnel is therefore better served asking a scale model which of two shapes performs better than asking it how much downforce or drag the finished car will produce.