I'm imagining heating some water pipes using heating coils similar to these. Under various conditions, would I need to apply almost continuous lengths of heating coil to the entire length of pipe? Or could I leave "gaps" along the pipe, allowing some sections to be heated by adjacent sections? What other major factors would affect this?
I've used them. I've never been happy with them. If you do use them you need to follow these rules:
If you wrap them you must have the wraps evenly spaced. You can't have 3 turns per foot at one end of the pipe and 6 turns per foot at the other end.
The temperature sensor (disk on the orange blob) must be pressed tightly against the pipe.
The full length of the pipe must be covered. You can't have 4" uncovered at one end. This can be a problem if the pipe comes out of the ground. In this case, dig out 6-10 inches, include that in the tape, and rebury.
You MUST NOT cross the tape over itself.
tape the heat wrap firmly in position. Even a small air gap between the tape and the pipe is double plus ungood.
Wrap about an inch of flexible foam insulation around it. The foam underlay for laminate works, as does packing foam for separating dishes. Bubble wrap works too. Key here: Uniformity.
Less insulation means that the heat tape runs more.
Insulation will even out small amounts of non-uniformity in wrapping.
Most of the time they haven't lasted more than a year or two. I now regard them as a temporary fix while I figure out how to keep the whole space where the pipes are above freezing.
Addition in response to comment:
Cheap switches in the thermostat result either in the tape sticking in the off position, or sticking in the on position. If the latter, then some spot that is better insulated than the rest, or a place where the turns are closer togehter will overheat and burn out the wire.
If the tape wraps over itself you have a hot spot that melts the insulation and allows wires to touch. Zot. Short circuit. The short usually will destroy enough of the wire that when you reset the breaker all is good.
If the tape is better insulated at one point than where the thermostat is, then on a cold night the thermstat can remain on while the wire gets too hot.
If the tape is NOT in contact with the pipe for several inches, heat is not being removed from that section of the tape. It gets warmer, eventually melts and the wires burn up.
Note that the wiki article https://en.wikipedia.org/wiki/Trace_heating mentions several other designs that are inherently safer and more durable. I suggest that you also gooogle "failure mode heat tape" for other leads.