It’s All Relative: How Time, Distance, and Wind Speed Relate in the Wind Tunnel

By Yarrow Fewless, Principal, CPP Wind Engineering

Time, distance, and wind speed are intrinsically linked in the wind tunnel, as they are in the real world. So how can you relate a building tested at a scale of 1:300 in the wind tunnel to the real-world building? The answer is that the relationship of distance (D), time (t), and wind speed (U) is the same at model scale as it is at full scale.

A simple analogy is a race car going around a track. If you want to model the race car and track at a scale of 1:10 and have the car go around the track in the same amount of time as at full scale then the speed must also be reduced by a factor of ten, just like the model scale. If you do this and watch the model-scale and full-scale events side by side they should look the same. Both model and full-scale cars starting at the same time will finish at the same time, despite the small car traveling only 1/10th the distance as the full-scale car.

In this example time is constant. The car takes the same amount of time to get around at model scale as it does in full scale. But what if you run the model car at the full-scale speed? It only has 1/10th the distance to travel so it will finish in 1/10th the time! Is the simulation worth anything? Well it is if you know how to treat the data.

Let’s say we record the lap with a video camera and call the video the ‘data’. A typical video camera has a frame rate of about 30 frames (images) per second, meaning it captures an image every 1/30th of a second. We’ve already established that if we have a model scale of 1:10 and we run the model car at 1/10th the speed of the real car then to the viewer or camera everything looks right. The model-scale and full-scale frame rates are the same.

Running the model car at the full-scale speed produces a video where the model car finishes ten times faster than the real thing, so how can we correct for this? The solution comes back to the original relationship: If the model speed is ten times too fast, then model-scale time is also off by a factor of ten. We’d have to slow the video down by a factor of ten to make it look right. Then the time between frames would be 1/3rd of a second instead of 1/30th of a second. The model car takes the right amount of time to get around the track, and aside from perhaps a slightly choppy looking video the model race looks like the full-scale race.

The same principle applies to a building tested in the wind tunnel except it’s the wind speed that matters instead of the car speed in the example. For a building tested at a scale of 1:300 with a wind tunnel speed that is 1/3rd of the design wind speed, one second in the wind tunnel represents 100 seconds in full scale. Bonus! Now we can get an hour of full-scale data in just 36 seconds in the wind tunnel!

This critical relationship is why you can run a model-scale wind tunnel test of a building with a very small model and a slower wind speed and get the right answer in the end.