Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Path: utzoo!watmath!clyde!floyd!harpo!seismo!hao!hplabs!sri-unix!KING@KESTREL From: KING%KESTREL@sri-unix.UUCP Newsgroups: net.physics Subject: Re: Why don't thermostats work? Message-ID: <16485@sri-arpa.UUCP> Date: Tue, 7-Feb-84 12:18:00 EST Article-I.D.: sri-arpa.16485 Posted: Tue Feb 7 12:18:00 1984 Date-Received: Fri, 10-Feb-84 03:17:03 EST Lines: 64 From: Richard M. King2) A closed loop control system (such as a room-thermostat-furnace-room) regulates the "process" by creating an error term. A thermostat is a relatively dumb control unit. There must be an error in room temperature in order for the thermostat to call for heat. The thermostat does not know how much heat is leaving the room, it only knows that there is an error in desired the temperature. The average error will be proportional to the rate of heat loss in the room. So, on colder days, the average room temperature will be lower. I think this is incorrect. It would be correct if the thermostat were "proportionally controlled", which means that it can set the furnace to "partially on" as well as on or off. In a proportionally controlled unit, the heat generated (or, more generally, the equilibrium restoration effort) is proportional to the error term. The human body's temerature control mechanism is proportionally controlled; you don't go from maximum shivering to maximum sweating several times per day. Indeed, as Jeff writes, there are additional inputs besides body temperature. Humans hypothalmi have skin temperature inputs, and I recall in a Scientific American article a few years ago that dogs have exercise transducers (but humans don't). However, a house thermostat has only an on/off setting. Because of this it has to have a hysteresis, or a range of temperatures over which it will not change state. Otherwise it would change state rapidly, reducing contact life and furnace life. If you set the thermostat to 20C, and it has a hysteresis of 1C (a reasonably realistic number), it will start the furnace at 19.5C and turn it off when the temperature has risen to 20.5C. The anticipator is an attempt to account for the heat stored in the radiator or whatever. Assuming that the difference between the indoor and outdoor temperatures is large compared to the width of the hysteresis band, we observe that the temperature will fall at a constand rate within that band when the furnace is off, following which it will rise at a constant rate when the furnace is on. The average temperature is always halfway between the ends of the hysteresis band. So why does the room feel colder when the outside is colder? It has been shown that a major reason is that the walls are colder, and a human loses heat by radiation. The thermostat is comparitively insensitive to radiation for two reasons; the active elements do not give off heat when the furnace is off, so they radiate a lot less than a person, and they are usually enclosed in a little metal box which prevents them from "seeing" the walls. I've always thought that thermostats should be mounted on exterior walls with just the right amount of insulation behind them so they would take (a linear approximation of) the proper amount of notice of this effect. Minor note: if your home is heated by a "heat pump" (a central air conditioning unit that reverses in the winter to bring heat INTO the house rather than take heat OUT) the thermostat has not two but three positions; no heat, heat pump only, and heat pump plus auxiliary electric resistance heaters. In this case, there are two hysteresis bands; the resistance heater might turn off at 20C and on at 19.5C, and the heat pump might turn off at 20.5C and on at 20C. In this case, on a cool day the heat pump might cycle on and off and the resistance heat might never run, making the average room temperature (20+20.5)/2=20.25, and on a frigid day the heat pump might run continuously and the resistance heater cycle, making the average temperature (19.5+20)/2=19.75. This form of heat is relatively rare. Note that it is "closer" to proportional control than the usual thermostat. Dick -------