I do some of my best thinking in the shower. Some people sing. Others are still sleeping. Being a morning person and morning shower-er, I most often use my shower time to intellectually explore various and sundry topics. [My wife is fond of saying I always think about cosmology, origins-of-the-universe, black holes, Relativity, and other such spaceborne, far-out concepts, but my shower-thought repertoire is more varied than that.] One such topic is the very process of getting the perfect temperature for the shower water: when the shower starts to cool, which is better, turning the hot up or the cold down? When you're in the shower, and the temperature just isn't quite right, turning which knob is more effective?

Much depends upon the relative positions of hot and cold in the beginning (prior to the hypothetical adjustment). In my experience, hot is more "on" than cold. This means any movement of the hot knob will make less of a difference. For example, if the hot knob is turned on by two, full turns while the cold knob is turned on by only one turn, then subsequent movement of the hot knob will be half as effective. A quarter turn of the hot is a ratio of 0.25/2 (quarter-turn relative to two full turns). A quarter turn of the cold knob is a ratio of 0.25/1, which is twice as big in net effect. This means turning the cold knob down would be more effective than turning the hot knob up, given the same degree of adjustment per knob.

If the ratio between the knobs is reversed, then the conclusion would be reversed as well. If more cold is in use than hot, then adjustment of the hot knob would have more effect. And as these adjustments occur, it's possible for this knob-to-knob ratio to reverse in significance. If it's too hot because the hot knob is turned on more than the cold, then there's a point at which turning the hot knob down will cause it to become the knob less turned on; this makes the cold knob adjustments more significant again.

There are other variables to consider, though. The water heater comes into play. If the hot valve is opened widely enough, the drain on the hot water heater could be significant relative to its total volume during the course of a single shower. The average temperature of the water heater's contents will drop as hot water is drained and replaced with cold. However, if the water usage is lower than the rate at which the newly added cold water can be reheated, then this factor can be overlooked. If the hot water is being used faster than the replacing cold can be heated by the water heater, then the average temperature of the hot water will tend to drop over time.

Also the setting on the hot water heater will affect the knob's proportionate on-ness. If the water heater is turned all the way up (be careful of scalding!), then less hot water, relative to cold, is needed to reach the ideal temperature. If the water heater's setting is lower (saving energy in the long run), then more hot water will be needed relative to cold water to reach the desired temperature.

This does not take into account the location at which cold water enters the water heater and from whence it is extracted. If extracted near the heating element (electric or gas flame) and replenished far away from this heating source, heat recovery becomes somewhat less significant again--until the ratio of hot to cold water reverses in the water heater, of course. Many water heaters, though, have their intake and outflow more or less in the same place.

One other variable not yet accounted for is the type of valves used for the hot and cold water knobs. If it's a simple piston/washer type, then the volume of water can be reasonably characterized by a cyclinder, making the change in volume flow vary geometrically (linearly) as the valve is opened. If the valve is a ball valve (not too common in my experience), though, the change in volume flow will vary not geometrically but following a sinusoidal curve. This means, the significance of adjusting a knob will vary not only proportionately to the other knob but nonlinearly.

Still another factor in the knobs is "slop". If the knob and valve are not physically bound without any sloppy movement, then knob movement will effect corresponding valve movement. However, if the knob is at all loose, the following valve movement may be delayed or dampened. This looseness may occur at the outer knob itself, of course, but it may also occur between the knob's shaft and the valve, depending upon linkages. An odd effect of loosely coupled knobs and valves is a reverse effect in temperature. Turning the hot knob up more can yield less hot water, if the adjustment is very small. When the adjustment becomes large enough, the valve will "catch" with the knob and beginning turning in the appropriate direction. This reverse turn is due not only to knob slop but often to water pressure itself, too, pushing or pulling on the valve in undesired ways. Much more significant, though, is knob rotation direction reversal. Knob slob can be frustrating when attempting to make small temperature adjustments in this way. As you adjust a single knob back and forth, the slop is significant (relative to small knob movements) and so the knob can appear to have no effect or a reverse effect. A good rule of thumb is to then adjust each knob in only one direction. If you tend to adjust the hot knob up, then only ever adjust it up. To get bidirectional temperature adjustment, though, the cold knob would also need to only be adjusted upward. Keep in mind the overall volume of water will be affected by these unidirectional adjustments, though, further affecting their effect.

While achieving and maintaining just the right temperature for your shower can be mathematically determined, were all variables known, it's generally too complicated for most bathers to do so in their heads in the early morning, making shower temperature a bit of an art form after all. Now in the spirit of openness, I don't often think of these things; in fact, to my recollection, I've only explored this topic once--I hate to rehash old ideas in my valuable shower time--but I thought it was high time to share my thoughts on such an important topic.