Telescope Mirror Cooling Calculator
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MirrorCooling: A Tool to Evaluate the Cooling of a Telescope Mirror

Introduction
MirrorCooling is a tool that can help to evaluate the thermal behavior of a telescope mirror. The application simulates the temperature evolution in a mirror subject to varying ambient temperature and chosen heat transfer conditions on the front and back surface. It displays a plot of the temperature profile at every time step, and a graph of the evolution of the mirror core, optical surface and air temperature.
Click here to download MirrorCooling. The zip archive contains a single executable file MirrorCooling.exe which runs under Windows.
References to other useful articles about thermal management of Newtonian telescopes can be found at the bottom of this article.
Program Results
The program produces the following graphs:
  • Temperature profile in the mirror glass (optical surface at the left, mirror back at the right).
  • Temperature evolution over time: optical surface temperature, back temperature, core temperature (highest glass temperature) and ambient temperature. The colored bar at the bottom gives a visual indication of the degree of cooling: red is bad, green is OK.

In both graphs you can zoom in by selecting a rectangle with the mouse from upper left corner to lower right corner. Zoom out by selecting a rectangle from upper right to lower left.
The temperature evolution can be exported to a CSV text file for processing in other applications including Excel.
Program Parameters
Mirror Properties Panel
  • Mirror Thickness in mm
  • Initial Mirror Temperature in °C
  • Mirror Material: Pyrex, plate glass, BK7, Fused Silica or Zerodur
  • Mirror Elements: number of finite elements in the mirror model. Any value between 20 and 100 will be fine.
Heat Transfer Properties Panel
  • Front Film Coefficient in W/m²K: The film coefficient indicates the rate at which heat is exchanged between the front surface of the mirror and the ambient air. A high value means that a lot of heat is transferred even when there is a small temperature difference.
    For natural convection without fans the film coefficients lie between 5 and 15 W/m²K. A lot depends on the geometry of the telescope tube or mirror box, how open design the design is, the position of the telescope, even whether there is a breeze. A typical value is 8 or 10 W/m²K.
    For forced cooling with fans the film coefficients lie between 25 and 100 W/m²K. Once again, it is nearly impossible to give a more precise estimation. It all depends on the number, capacity and position of the fans, the geometry of the mirror cell and the position of the telescope.
  • Front Radiation: the emissivity coefficient for radiation of the front (optical) surface into space. Use 0.04 for a standard aluminum coated mirror that is seeing a large part of the sky (truss design). For a mirror in a telescope tube a lower value should be used - probably around 0.01 or even lower.
  • Back Film Coefficient in W/m²K: film coefficient for the back of the mirror.
  • Back Radiation: emissivity coefficient for radiation of the back surface. Usually 0 because the back of the mirror is not facing the sky.
Simulation Panel
  • Initial and Final Air Temperature in °C: the ambient temperature can vary linearly between start and end of the simulation
  • Simulation duration in minutes.
  • Time step in seconds.
How are results computed and how accurate are they?
MirrorCooling uses a one-dimensional finite differences approach to compute the heat transfer in the mirror and between the mirror and the surrounding air. In other words, radial heat flow or losses at the side edge of the mirror are ignored. This is a fairly good approximation for the relatively thin mirrors that are often used in large Newtonian telescopes.
The major uncertainty in the simulation is the heat transfer coefficients (film coefficients and radiation emissivity). It is probably impossible to estimate these with an uncertainty of less than 50% without actually performing temperature measurements of the mirror during cooldown.
How much time does a mirror require to reach equilibrium?
Practically speaking one could say that the mirror is in equilibrium when its temperature is within 1°C of the ambient. If the ambient temperature stays constant the mirror will eventually get colder than the air because of the heat radiation into space - the mirror will be prone to dew forming.
The program will give you a good idea about what happens to the mirror, but do not expect it to tell you exactly when you can start observing. Unless you have actually measured the heat transfer coefficients, you cannot expect very accurate answers.
With the film coefficients and mirror thicknesses found in amateur telescopes, the limiting factor in the cooling process is nearly always the heat transfer between glass and air. The cooling time will vary approximately linearly with the mirror thickness.
Only when the film coefficients are very high (or the mirror is rather thick) the thermal conduction in the glass may become the limiting factor. In that case the cooling time will vary with the square of the thickness.
How to compute a mirror with varying thickness
The program makes a simplified analysis in one dimension - the thickness of the mirror. If the mirror is not cylindrical one should chose an "average" or "equivalent" thickness.
The same applies to very thin, short focal length mirrors that are significantly thinner in the center. For example a 600x40 mm f/3.3 mirror has a central thickness of 29 mm which is significantly less than the 40 mm edge thickness. For the analysis an average thickness of 35 mm could be used.
Some selected Examples


2" (50 mm) thick Pyrex mirror in a closed-design mirror box without cooling fans.

Film coefficients: 8 W/m²K at front and back.

The mirror is initially at 20°C room temperature, the ambient temperature is constant at 10 °C.

It is quite amazing to see how slowly a 2" thick mirror cools without forced ventilation. It takes about 3 hours for the 10 °C initial temperature difference to drop to 1°C.


2" thick mirror with fans blowing at the back.

Film coefficients: 90 W/m²K at back, 15 W/m²K at front.

Mirror initially at 20°C, ambient temperature dropping from 2°C to 0°C over a 3 hours time span.

It takes about 90 minutes to achieve thermal equilibrium.


40 mm (1.6") thick mirror without cooling fans in dropping ambient temperature.

Film coefficients: 10 W/m²K at front and back.

The mirror is initially at 20°C room temperature, the ambient drops from 10°C to 5°C over a 3 hours time span.

Clearly the mirror cannot catch up with the dropping air temperature and never reaches equilibrium. This is quite similar to Anthoney Wesley's experiences (see useful links).


0.8" (20 mm) thick mirror without cooling fans.

Film coefficients: 10 W/m²K at front and back.

The mirror is initially at 20°C room temperature, the ambient temperature is constant at 10°C.

A thinner mirror without forced cooling drops quickly to below the ambient air temperature because of the heat radiation to the sky. There is a risk of dew forming at the surface that is cooler than the surrounding air.
Version history
  • Version 1.0 (20080215)
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