Re: [ATM] basic questions about cooling fans

[Mark Holm <mdholm@telerama.com>]

Thomas A Simmons wrote:

>I was wondering how long it would take before someone commented
>on Bryan Greer's articles.

Actually, on the very same day the May issue arrived in my mail box, I wrote a strongly worded message to the list suggesting (almost demanding) that every atm should read these articles.

I am going to take this opportunity to recap something I wrote a few months back, because I notice that confusion/ignorance over this point is common.

The optical distortion caused by "tube currents", mirror boundary layer and atmospheric "turbulence" is caused by non uniform refractive index of the air along the path that light travels to get from a celestial object to our eye.  It is exactly the same effect as if you put pieces of clear and well polished, but different refractive index glass in the light path.  Light traveling through each region of different refractive index takes a slightly different time to pass through.  After passage, light waves that had a certain phase relationship, imposed when they left the celestial object, now have a different phase relationship that bears only a scrambled version of the original relationship.

An aside:  We are often told that the speed of light is a constant.  This is true if you are talking about the speed of light in a vacuum.  When light passes through materials, it slows down.  The amount by which it slows down depends on the electromagnetic environment inside the material, and is exactly equal to the number we call the refractive index.

The refractive index of air is close to 1.  That is, it isn't too terribly different from the refractive index of a vacuum, but it isn't exactly 1.

The refractive index of air depends on the chemical composition of air and on its density (how many molecules are in a given volume).  Except for water vapor content, the chemical composition of air is pretty uniform both on small and large scales.  Water vapor content usually is pretty constant on small scales, so changing water vapor content usually isn't a big player in degrading telescope images.

Density, the other player in air's refractive index is given to a rather good approximation by the universal gas law

PV = nRT

Density, for this purpose, is number of molecules per volume of air, so the equation rearranges to

n/V = P/RT

n/V is the number of molecules per volume
R is a constant (called the universal gas constant.  It shows up in a lot of chemical thermodynamic equations.)

So, the factors that influence air's refractive index on a small scale are Pressure, P, and Temperature, T.

Notice that velocity is nowhere to be found in these equations.  It does not matter whether the air is moving or not.  Turbulence (chaotic motion) of air does not cause bad seeing, unless it involves pressure gradients or temperature gradients.

The thing about pressure is that pressure differences in air even out very quickly on small scales.  Pressure differences propagate at the speed of sound and bulk pressure differences rapidly induce air movement that quickly damps out the pressure differences.  Pressure differences are of course associated with all air movement, but the amount of pressure difference associated with low speed air movement on small scales is very small.  Running a fan in front of a telescope mirror induces pressure differences in the vicinity of the fan blades, but 1. those pressure differences are small, and 2. they damp out very quickly, so that, a short distance from the fan (millimeters) the pressure differences have dropped to a small level.  Thus, unless you have a monster fan at work, the pressure differences caused by the fan will cause only quite small refractive index differences in the air.

Temperature is a different story.  Heat propagates slowly through air.  It is quite possible (and quite common) to have significant temperature differences across small distances, and for those temperature differences to take a long time to dissipate.

When we see atmospheric distortion of telescope images, whether the source is inside the scope or up in the sky, we are seeing primarily the effect of different air temperatures along the light path.  The distortions are usually in motion, because the air is usually in motion, moving the different temperature parcels of air about in the light path.  It isn't the motion per se that causes the distortion, it is the temperature differences.  If we froze the motion, we would still have distortion because the air column would still be non uniform in temperature.  Freezing the motion would just give a static distortion instead of dynamic.

To eliminate the distortion one needs to eliminate the temperature differences.  This is where fans become our ally.  Moving air and mixing it up is the quickest way to even out temperature differences in it.  We can homogenize the air inside our telescopes, and immediately in front of the mirrors to a very great extent using fans.  We can also greatly speed the equilibration of solids (mirrors) with the surrounding air temperature, thus greatly reducing a big cause of air temperature difference in our telescopes.

To minimize the temperature differences in the atmosphere outside our telescopes, our only hope is finding a good observing site.  It doesn't have to be Mona Kea to be an improvement.  Grassy fields are better than parking lots.  Heated buildings are bad.  The top of a hill is usually better than a valley (cold air pools in valleys).  The top of a hill is usually better than the side of a hill (cold air flows down the side of hills.)

It is often true that, at night, the greatest temperature differences in air are found in the first couple of meters above the ground.  A lot of that nasty seeing is happening only a few feet over your head!!!  Get up on a hilltop, or build an observing platform a meter or two tall, and a lot of bad seeing will be put under your feet.

Mark Holm
mdholm@telerama.com


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