Necessity is the mother … Now that fuel has become relatively expensive, engineers are expected to design more efficient automobiles, buildings, pacemakers, and so forth. But some of our government officials should first set their own goals in order. For example: They keep increasing highway speed limits, unaware that the maximum speed the human nervous system can *safely* handle is 60 miles/hour (100 kilometers/hour). So we continue to happily zoom along at high speeds, wasting fuel, automobile engines, and human lives.

This essay is concerned with another aspect of inefficient behavior: Our energy czars should be constantly reminding us, via headlines in the media, to Shut Off That Heater (or Air Conditioning) Unit when we are away from home!

Let’s first talk about heating. Most people know about weather stripping, installing storm windows, or escaping to Florida. But a substantial proportion—perhaps the majority—believe that “shutting it off” doesn’t make sense. Their argument runs something like this: “What you advocate doesn’t seem to be correct because my heater is a living genie. It gobbles up huge quantities of Home Heating Oil (HHO); it breathes in oxygen and puts out carbon dioxide, just like we do; it suffers from halitosis; it makes a frightening variety of gurgling noises; and I think it should be allowed to rest for a while after working at top speed for, say, 30 minutes.” That smacks of the fuzzy math which accompanies an emotional, anthropomorphic attachment. The fact is that an appreciable amount of HHO is wasted because many people feel that “it is bad to overwork the heater; it gets overheated, and that can cause it to burn out.”

This is unscientific for several reasons, but perhaps there is a better way to view the problem. Consider the following simple and logical basic principle, which follows from the Law of Conservation of Energy:* You pay to put back, into your home, the heat lost to the outside world.* [This can include the heat energy (watt-seconds, or joules) inadvertently donated to your cheapskate common-wall neighbors, who keep their thermostats set to 60°F.]

Please forget about overworking the genie; it has built-in automatic devices to keep it from overheating. In fact, the genie is happiest when it is working full-time; the most inefficient and damaging way to operate equipment (generally) is to have it frequently turn on-and-off (exactly like driving in stop-and-go traffic is for an automobile). It is most efficient to take the heater out for a highway drive by letting it run, when you return home, full speed ahead. When the temperature reaches 68°F (20°C), say, the system goes into a thermostatically-controlled on-and-off mode; it is less efficient, but that is the price you pay for comfort. The heater is most efficient when the house is cold, because more of the heat output then goes into the house and less is wasted going up the chimney. A hot house is characterized by a hot chimney.

Let’s return to “you pay to put back, into your home, the heat lost to the outside world.” Heat is like water in the sense that, if you lose it, it has to be replaced, and that is what you are paying for. (In fact, before a scientific explanation for heat was discovered, heat energy was believed to be in the form of phlogiston, which is analogous to the flow of water.) Obviously, if you shut off that heater, allowing your house to cool down, it will lose a lot less heat to the outside, after it cools down, than if you keep it at 68°F all day. (Set a reasonable minimum temperature, of course, to keep water pipes, animals, and plants from freezing.) But we are all different; some stalwarts arrive home to a 50°F setting, and find it invigorating as they exercise, steam pouring forth with each exhalation, until the house warms up. Others find this scenario deadly, and must have 68°F when they walk in, but are clever enough to use a timer to turn the heater on at a propitious moment. That’s much better, of course, than leaving it on all day.

Most people lower the thermostat temperature setting at night, believing, quite correctly, that it saves fuel.

And what shall we say about an air conditioner? What we shall say is a negative paraphrase of the arguments re a heating unit: For air conditioners, our energy czars should be screaming “Shut Off That Air Conditioner when you leave the house.” In this case, *you pay to remove, from your home, the heat gained from the outside world.* For example: suppose that the thermostat is set to 78°F (25.6°C), and the outside temperature is much hotter than this. If you shut off the air conditioner, the house will warm up, and the reduced inside-outside differential will decrease the heat (watt-seconds) gained from the outside; that corresponds to the money that you save. When you turn on the unit, it will work at maximum efficiency to generate cold air, but it will not “get tired.” A low-cost ceiling fan may be a welcome accessory.

Another example of waste: During our early (8 AM) walks, my wife and I frequently pass stores that have heavily “steamed-up” windows. The manager has set the air-conditioner on full blast the night before, so the customers (or the manager, at least) will feel cool the next morning. The external air-conditioning compressor thus contributes 12 hours to global warming, when a fraction of this time would be sufficient.

Alas, I have no illusions that the above simple analyses will convince anybody. For years, I was in charge of shutting off the pool water heater, which is set to 84°F (28.9°C), when the air temperature forecast is that it will be too cool to swim (less than 68°F). This is a typical condominium outdoor swimming pool in Florida (or anywhere else in the South). During the summertime, we frequently reach triple synchronization: The water temperature is 84°F, the air temperature is 84°F, and the people in the pool are 84. During the winter, however, the air temperature can remain below 68°F for a week. In most cases, the maintenance man can’t be bothered with turning the heater off and on– it is not his money that is being wasted.

But all of this talk, about shutting off the pool heater, can get the environmentally-conscientious pool handler into a heap of trouble. Imagine this riotous scene: The pool heater has been off for a week, but S.D. turned it on yesterday because a temperature maximum of 70°F was predicted for today. At 2 PM, the faithful, buoyed up by a week’s worth of pent-up energy, arrive at the pool. “The water is icy cold,” announces the ring-leader, R.D. Sure enough, the thermometer registers 80°F! Glee turns to consternation; R.D. threatens you-know-who, and S.D. is drowned out (if not drowned deliberately) as he declares that each person gives off 100 watts, so please get in and do your bit to warm up the place.

I could go on and on—each lengthy shut-down is accompanied by anxious telephone calls demanding a guarantee that the water will be at 84°F, “as specified by the rules and regulations.” My main point, of course, is that one must have a suitable schedule for turning the heater on again.

To do this scientifically requires that measurements be made of how fast the temperature drops, and how fast it rises. Every pool and pool heater is different, of course, but from the example given below one can, hopefully, extract some guiding principles.

Rising and falling temperature curves have an “exponential” shape. The rising curve is easy—measurements that I made, of the Oakhurst pool, when the heater was ON and approaching 84°F, revealed a rise of 0.5 degree/hour. In Fig. 1(a), this is shown as a straight-line rise from 70° to 84°F in 28 hours. A linear approximation in place of an exponential is acceptable in this case because the temperature, of the entering hot water, was much higher than 84°F.

Fig. 1- Rising and falling data and curves for the Oakhurst pool. (a)Temperature rise measurement shows 0.5°F per hour. (b)Three temperature fall measurements as indicated by three dots. (c)Calculated exponential, using equations derived in the Appendix, that fit the three measurements.

Here, also, there is a wasteful controversy. For maximum efficiency, with regard to the heater, the water should flow through the pipes as rapidly as possible. Maximum heat energy is transferred from the flame to the fluid if the fluid is cool. The Directors, of course, were of the reverse opinion—the water entering the pool should be hot enough to make a good cup of tea, as one of them put it. A slow but sure way to waste energy. This illustrates a Grand Illusion that shows how wrong opinions can be without accurate measurements. The heat energy entering the pool is the product of temperature change and volume. The “cup of tea” represents water flowing so slowly that the volume is inadequate. Speed it up by a factor of 10; it will still be warmer than 84°F, and be felt at the other end of the pool compared to that “cup of tea’s” local hot spot.

In Fig. 1(a), an ideal thermostatic control is illustrated with a flat line at 84°F. In reality, this line fluctuates between 84° and 85°F as the heater turns on and off. (The thermometer-watchers would never let it go below 84°F.)

The three cooling measurements are shown by the three dots in Fig. 1(b). Based on a prediction of several days of cold weather (*average* substantially below 68°F), the heater was shut off at T = 84°F, at time = 2 PM. This is called “t = 0”, in Fig. 1, to simplify the arithmetic. From this point on, there is a great deal of make-believe. The exponential drop is influenced by air temperature, wind, sun, and temperature of the ground surrounding the pool. As the curve shows, however, the temperature drops slowly, taking an average of all of these fluctuations. This is the best that can be done without making the “science of minimum pool heating” so complicated that nobody will pay attention to the details.

The second measurement was made at T2 = 78°F, t2 = 18.4 hours (the actual time was 8:24 AM); third measurement at T3 = 73°F, t3 = 41 hours (the actual time was 7:00 AM). Three readings are sufficient to define the exponential [the curve of Fig. 1(c)]; if they are reasonably far apart in temperature and time, as these were, the exponential should be fairly accurate.

An “exact” solution requires trial-and-error work on a computer, but a good approximation is derived in the Appendix. The net result, for the Oakhurst pool, is the exponential plotted in Fig. 1(c), where the arithmetic is considerably simplified because temperature is given relative to the 84°F starting point. After t = 200 hours (8 days + 8 hours), the temperature drops down to 84° – 24.6°, or 59.4°F. Eventually, at t = infinity, the temperature would reach 84° – 26.3°, or 57.7°F. Various calculated values are given in Table 1.

Table 1- Various calculated values of the exponential, time versus temperature drop, for the Oakhurst pool. This depends upon typical average ambient conditions; it may be quite inaccurate, but it is better than nothing.

Are the curves of Fig. 1(c) and the values of Table 1 realistic? Yes – for daily fluctuations from 40 to 60°F, some sun, and relatively warm ground. Are the taking of data and calculating the values worth the trouble? Yes – if you have fun doing it, and it only has to be done once.

“Only once” is summarized in the Oakhurst Pool Sequence of Table 2. It was fun applying Table 2 (luckily, the 4:00 AM event never occurred), and I did quite well in keeping ahead of the supreme thermometer-readers. But eventually, and perhaps inevitably, the axe fell and I was fired from my unpaid volunteer job!

Table 2- Oakhurst Pool TURN ON Sequence. The forecast is for a high of less than 68°F tomorrow (DAY 1). Therefore, turn the heater OFF at 4:00 PM today (DAY 0).

If the forecast is for cold wave to end (i.e., high over 68°F) on

The “youth” (70 years old) have recently taken over. In my opinion, they are youthless. I was told, not too politely, “Deutsch, your services are no longer required. The lock has been changed. You were wearing out the switch by turning it off and on, and we don’t like the way you overwork the heater when you turn it on and, anyway, it uses more fuel that way.” And so forth.

The mental attitude toward energy conservation is slowly beginning to improve, in the United States, thanks to the increase in oil prices. [The rest of the world is much more conservation-conscious than we are. When I lived abroad, gasoline cost $4 a gallon, compared to (at that time) the United States $1 a gallon.] Needless to add, science and math from kindergarten up are essential to combat the “new age” pseudoscientific mentality. But environmental groups should get the message out: “To save fuel, shut off the heater (or air conditioning) unit when you leave the house, and turn off the pool heater when it is too cold to swim.” They should also press for 24-hour on-off timers to be mandatory on commercial heating and air-conditioning installations.

**Appendix**

The arithmetic is considerably simplified if the exponential starts at temperature T = time t = 0, as is true for the curve of Fig. 1(c). The curve is then given by

T = T_{0}[1 – exp(-ct)],

where T_{0} = temperature at t = infinity,

c = an unknown constant.

Substituting the measured values T_{2}, t_{2}, T_{3}, and t_{3}, and eliminating T_{0}, we get

T_{2}[1 – exp(-ct_{3})] = T_{3}[1 – exp(-ct_{2})].

One can solve for c, using trial-and-error, with the aid of a computer. A good approximation is given, however, by using the first three terms of the infinite-series expression for exp(-x):

exp(-x) = 1-x + 0.5x^{2}.

If this is substituted into the above, there results

2T_{2}t_{3}-cT_{2}t_{3}^{2} = 2T_{3}t_{2}-cT_{3}t_{2}^{2},

which yields

c = 2(T_{3}t_{2}-T_{2}t_{3})/(T_{3}t_{2}^{2}– T_{2}t_{3}^{2}).

Substituting the numerical values T_{2} = -6, t_{2} = 18.4, T_{3} = -11, and t_{3} = 41, we get c = 0.01371. The reciprocal of c, the “time constant,” is 72.96 hours, or around 3 days; it is a measure of how long it takes for the pool to cool off.

Substituting the numerical values back into the original exponential equation, we get, from dot 2, T_{0} = – 26.92 and, from dot 3, T_{0} = -25.59, or an average of T_{0} = 26.3°F, as shown in Fig. 1(c).

(A shorter version of this essay was published in IEEE Engineering in Medicine and Biology Magazine, May/Jun 2003.)