# Wind scaling and increasing wind speed for wind tunnel problem

1. Sep 19, 2011

### sbalser1

i am making a wind tunnel in order to test aerodynamics of 1/24 scale cars.
i am having two problem:

1. i am not sure what wind speed at that scale to represent 100mph.

2. i am using a fan that has an outlet wind speed of 19.4 mph. i tried to increase wind speed by decreasing the outlet speed of my tunnel from 144 square inches, to 36 square inches. but in doing this i measured the outlet velosity and it was only 9mph. what am i doing wrong? how do i increase wind speed?

2. Sep 19, 2011

The proper scaling parameter you want to use is the Reynolds number. You want the Reynolds number to remain the same regardless of which scale your model is. The Reynolds number is defined as:
$$\mathrm{Re} = \frac{\rho V D}{\mu}$$

Where $\rho$ is density, $$V$$ is velocity, $$D$$ is some characteristic length scale (often the length of the car or diameter of a pipe etc) and $$\mu$$ is viscosity. You want to make sure you have the same Reynolds number on your small model as the full sized car. That leaves you with:
$$\mathrm{Re_{full}} = \mathrm{Re_{scale}}$$
$$\frac{\rho V_{\mathrm{full}} D_{\mathrm{full}}}{\mu} = \frac{\rho V_{\mathrm{scale}} D_{\mathrm{scale}}}{\mu}$$
$$V_{\mathrm{full}} D_{\mathrm{full}}= V_{\mathrm{scale}} D_{\mathrm{scale}}$$
$$V_{\mathrm{scale}}= V_{\mathrm{full}} \frac{D_{\mathrm{full}}}{D_{\mathrm{scale}}}$$

Now, before you said you wanted a 1/24 scale model, so you can use that to get:
$$V_{\mathrm{scale}}= 24V_{\mathrm{full}}$$

In other words, to make a truly scaled model in air, you would need to have the air moving 2400 mph. Of course that doesn't take into account the fact that now you have compressibility effects. What does this mean? it means you can't perfectly scale it. In reality, after a certain Reynolds number most quantities of interest tend to plateau, so you don't always have to match it (and in most cases you can't if you are using a wind tunnel with air as the operating fluid).

So then the question becomes what are you hoping to measure?

3. Sep 20, 2011

### sbalser1

that was the number that i got in doing it but i thought that i was doing it wrong because that makes no sence. it seams that it would be slower because the distance is less from one end of the scale car to the other. so to scale the car to full scale the speed would have to increase to signify the same meters per seconds.

i am trying to measure drag force and down force of wings and such.

4. Sep 20, 2011