Moreover, the observatory imposes restrictions on how much heat we are allowed to let escape into the air because heated air drifting across the telescope line-of-sight creates image distortion (for other observers), much like the wiggly view over a hot car roof. The goal is to limit the emissions from APOLLO to less than 75 Watts. To put this in perspective, a person typically emits 75--100 W of thermal power all the time. The challenge is then to keep APOLLO's components warm without leaking heat into the telescope dome.
The primary tool we use to fight heat loss is thick insulation. We require the very best rigid foam insulation (about 3 inches thick) to keep the heat loss below 50 W on the coldest of nights. We also have hoses (carrying warm fluid) and electrical conductors to worry about. In addition, we have a cabinet of electronics sitting on the observing floor whose 100 W emission must be ducted away by air.
In short, a great deal of thought and energy has gone into the design of APOLLO to limit its thermal emissions. In the end, we should have a system that has no measurable impact on the telescope performance--both for APOLLO itself, and for other observers.
What follows is an attempt to predict the thermal impact of APOLLO on the telescope dome environment. The relevant temperatures are Ts = the set-point temperature of both the laser enclosure and the electronics cabinet (nominally 10°C); and Tc=the temperature of the (cold) dome air. All figures are given in Watts.
The laser enclosure is constructed out of two layers of insulation: a one-inch-thick Thermax sheathing and a 2.4-inch-thick Thermax finish-board (same as sheathing except with 16.5 mil embossed aluminum facer for durability). Together the effective R-value (in English units) is 24.5, corresponding to a thermal conduction coefficient of 0.020 W/K/m--comparable to that of air! Given the effective enclosure area of 6.6 square meters, the box will leak 1.5 Watts for every 1°C difference between Ts and Tc, or P = 1.5(Ts - Tc).
When the laser is running, the coolant lines are at 30°C. If unprotected, these could alone contribute 150 Watts or more to the dome on the coldest nights. By wrapping the hoses together in a foam envelope, and routing this assembly through a ducted air hose, we can simultaneously curb the heat flow and remove the heat that is generated out of the dome via the ducted air.
There are two cases to consider: laser on (2% of time) and laser off. When the laser is on, the coolant is warmed up to 30°C, and the net leakage to the dome looks like P = 0.256(30 - Tc) Watts. When the laser is off, the coolant returns to Ts (about 10°C, generally), so that the heat loss is P = 0.256(Ts - Tc) Watts. The calculations assume a 6 meter hose length, and a 0.15 m diameter shiny duct/conduit.
The electronics cabinet is to be held at Ts, separated from the cold dome air by one-inch-thick Thermax sheathing with an R-value of 7.2. The effective area of the enclosure is 6.0 square meters, for a heat loss of 4.7 Watts per 1°C differential. For cold temperatures, this would quickly exceed our allowance, so we will enclose the insulated cabinet by a plenum that ducts air past the insulation, carrying the heat it releases down into the intermediate level of the observatory where waste heat is easily removed. The full convective/radiative computation is complex, but based on the materials and geometry used, we get a fit of P = 0.607(Ts - Tc) Watts. A part of this heat is actually residual from the heat being ducted away from the laser coolant hoses. The air that is pulled around the outside of the cabinet insulation is in part drawn through the conduit surrounding the hoses. Thus the air flowing over the cabinet is slightly pre-heated. This in turn warms the outer walls of the plenum and lets off heat into the dome. Because there are two operating conditions for the laser coolant hoses (corresponding to laser on and laser off), one must add 6 Watts to the total emitted from the cabinet when the laser is on (assuming a set-point temperature of 10°C).
Cables traversing from the warm laser enclosure or the warm cabinet enclosure out into the chilly dome air will conduct some heat out. Copper is a very good thermal conductor, but fortunately the cross-sectional area of copper in a typical cable is small. A detailed thermal calculation for a typical co-axial cable indicates a thermal loss of P = 0.008(Ts - Tc) Watts per bulkhead. The thicker laser head cables may be closer to P = 0.1(Ts - Tc) Watts. Assuming two head cables and about 15 RG-58-style co-ax (or thermally similar multi-conductor) cables, we get a total thermal heat output for cables of P = 0.64(Ts - Tc) Watts. Because most of these will be bundled together (rather than having each one exposed to cold on all sides, we should cut this figure at least in half, say to 0.3 Watts per °C.
If we add the contributions above, we get a total of Ptot = 2.66(Ts - Tc) Watts, plus 11.1 Watts when the laser is on. In the worst likely case, with Tc = -15°C, this translates to 66 Watts when the laser is off, and 77 Watts when the laser is on. Temperatures at APO seldom get this low, so most of the time our total emission will be well below 50 Watts. So we have succeeded in keeping the laser emission lower than that of a human even to the coldest expected ambient temperatures---in theory...
