# How are wind tunnels used with scale models?

This answer introduced me to the problem of using scaled models in a wind tunnel.

How are wind-tunnels used in practice (for modelling the performance of subsonic airplanes)? In particular:

• Do they used increased air pressure, or another mechanism, to compensate the Reynolds number?
• What scale model is used? A scale of e.g. 70:1 appears to be difficult, because you can't pressurize air that much before it liquifies. So do they use a scale like 10:1? More or less?
• What are the forces (lift and drag) generated on the model? The weight (therefore the lift) of an A380 is about 500 tons. Apparently the lift on a 10:1 scale model would be 50 tons. Is that real? Are they making 10:1 models which cope with 50-ton forces?
• This picture (from Wikipedia's Wind Tunnel article) shows what seems to me to be a 10:1 scale model of a supersonic plane in a subsonic tunnel. The tunnel doesn't seem to me to be built to handle multi-ton forces. What kind of air-speed will they be using, what would they be measuring with that kind of test?
• This is a lot of questions at once, perhaps you could separate them in different questions? For example one asking about the reynolds number, and one about the lift forces Feb 23 '17 at 15:18
• You might be right, OTOH perhaps each question-mark might be answered by a single sentence. I think they're closely-related, maybe one topic. Feb 23 '17 at 15:22
• I'd guess they are mostly investigating things that don't depend that much on the reynolds number. Feb 23 '17 at 15:57
• @ChrisW Well I was about to write a story about Reynolds numbers, but then I saw the other questions and decided not to ;) Feb 23 '17 at 15:59

During development, a lot of different wind tunnels are used. Scales range from full scale to less than 1/100, and sometimes not only the geometric, but also the dynamic and elastic properties of the aircraft to be tested must be modelled correctly.

Today, preliminary work is mostly done in numerical simulations, but before the availability of computers, early wind tunnel models would be between 1/50 to 1/16 scale (depending on the size of the real article and the available wind tunnel), often using modular models on which different engine placements or tail geometries could be tried out. Since wind tunnel testing costs real money, early tests are restricted to small, low-cost tunnels which run at ambient temperature and density. Differences in the Reynolds number between test article and the real aircraft are covered with correction factors and experience.

Only when a design is moving ahead during development, bigger and more expensive tunnels are used. Again, matching the Reynolds number is not possible and not even necessary for some tests: For a spin tunnel the test article must be scaled dynamically (so it has correct moments of inertia), but separated flow is less affected by the Reynolds number, so the precision of a 1/20 scale model is sufficient. Also, a free-falling model in a spin tunnel needs quite a bit of space to move around, so even small models already need test sections with a diameter of several meters.

To reduce cost and avoid the tight schedules of wind tunnels, free-flying or radio controlled models are also used. Watch how Dornier engineers tested the dynamic behavior of the then-new tricycle gear of the Do-335 in this video (starting at 2:00') or ditching characteristics (starting at 2:13').

Only when both Mach and Reynolds number need to be matched, cryogenic and pressurised wind tunnels are used. Due to their energy demand and availability, such tests need to be scheduled years in advance and meticulously planned. Models can run into millions of dollars or Euros, so such tests will mostly narrow down parameters which had been measured previously in simpler tests. Large tunnels like the 9.5x9.5m LLF in Marknesse (the Netherlands) are mostly used for low-speed and high-lift characteristics testing since its 12.6 MW engine can only support a speed of 62 m/s at full power. On the other end of the scale are hypersonic blow-down tubes which support a testing section of 0.5m diameter in which Mach 6 can be achieved for a fraction of a second.

Full-scale testing in a wind tunnel is only possible with small aircraft - see the answers to this question for examples. Even then, the speeds do not match the top speed of the aircraft, so the loads are a fraction of the real loads.

Jan Roskam observes in his book "Roskam's airplane war stories":

It certainly is an unusual luxury for an engineer to have full Reynolds Number tunnel data available.

• 62 m/s is 120 knots which is barely take-off speed for a jetliner. Feb 25 '17 at 15:41
• @ChrisW: Yes, and at the reduced scale the Reynolds number is a tenth or less of what it is in real life. Accordingly, the gaps between flap segments are proportionally bigger on a wind tunnel model to achieve the same flow at high angle of attack. You don't need to match Re exactly, it is enough if you come close and design the model accordingly. Feb 25 '17 at 16:13
• For me your last link ("Roskam's") displays a blanked-out page with the message, "du hast entweder eine Seite erreicht, die nicht angezeicht werden kann, oder die Anzeigebeschrankung fur dieses Buch erreich." It would be better to post a screenshot of the page, as I did in this question. Feb 25 '17 at 23:50
• @ChrisW: I just googled the phrase and that is what came up first. I guess Google is picky about what to show - in Google books many pages will not be displayed. I replaced the link with one to the publisher, but recommend to shop around. My copy of the book is the Kindle edition. Feb 26 '17 at 10:19

Usually, for low subsonic cases, Reynolds number is matched, while for transonic and supersonic cases, the Mach number is matched. In case you only want the Reynolds number similarity, you can go for a water tunnel.

The only way to get both Reynolds and Mach number similarity for models (unless you change the medium) is to use pressurized and/or cryogenic wind tunnel. The cryogenic wind tunnel achieves the required Reynolds number by reducing the viscous forces rather than increasing the inertial forces; even then the actual Reynolds numbers encountered in flight are rarely achieved and one has to resort to scaling laws.

The scale of the model used depends on the application. In some cases (like hypersonic vehicle testing) 1:1 scale models are used, while in other cases like A380 testing, even 200:1 models were used.

Though the force acting on the models would differ by applications (and even approach the actual forces in some cases), the forces acting on the smaller scale models are quite small (note lift and drag scale as square of the dimension provided other parameters are same, which is not even the case here). In general, various scaling laws are used to arrive at the forces experienced by the actual aircraft. For example this video shows the forces in an A380 scale model in the order of Newtons. Usually, you would like to find the lift (or drag) coefficient of the model and use it in actual case.

The Kirsten Wind Tunnel in the image you've linked can measure a maximum lift of slightly more than a ton with the other forces an order of magnitude less than that. Note that this is a quite large subsonic tunnel and smaller tunnels can measure even less. You have to scale the results according to the model. The air speed is given as ~ 90 $ms^{-1}$.

There are a number of things measured and observed in the wind tunnel, which may only be loosely related to force measurements like flow visualization, effect of store jettisoning, wake analysis, among others.

• That A380 test video, for example, which uses a tiny model in a low speed wind tunnel: I guess it didn't try to match the Reynolds number. If it doesn't match the Reynolds number, aren't its measurements completely useless (inaccurate)? Because the Reynolds number affects turbulence (laminar separation over the wing surface etc.), and turbulence is very important? Feb 23 '17 at 16:47
• 1:1 models for hypersonic vehicle testing? I always though hypersonic wind tunnels were shock tubes with test sections smaller than 0.5$m^2$. Do you have any examples? Feb 25 '17 at 7:45

Thanks for the other answers. The last part of my question, i.e. what's the point of testing using small models which don't match the Reynolds number, seems to be answered by the graph in this answer:

Lift coefficient over angle of attack for model and full-scale aircraft, taken from Joseph Chambers' monograph on testing with models (Modeling flight : the role of dynamically scaled free-flight models in support of NASA’s aerospace programs).

This graph shows that the lift coefficient of the model and the full-scale aircraft are identical at ordinary angles of attack; they diverge at steeper angles (maximum lift), as stall becomes imminent (the model stalls more easily); and become identical again post-stall. Even when they're at their furthest apart they're not very different (e.g. the difference is a factor of 2 rather than a factor of 50).

The paper this graph was taken from has a wealth of other information.

Also this video from the European Transonic Windtunnel explains how they achieve realistic Reynolds numbers: by lowering the temperature (e.g. to 110 K, i.e. -160 °C) by evaporating liquid nitrogen after the compressor, without oxygen (which would liquefy), and by increasing the pressure (up to 4.5 bar).

It claims 99% (and better) accuracy.

The largest models it can fit have a wingspan of about 1.6 metres.