Posted above are very good explanations of both profile power and profile drag, induced power and induced drag. They are flawless, good accepted answers if someone has an exam to pass and holding onto them will do no harm all the way through a career so don't anybody get confused or ruffled as a result of what I have to say here, please!
Both standard and accepted explanations bother me. If you give power and drag a lot of thought many 'holes' appear in the reasoning. I believe that this can be put down to one major factor - That much fixed wing theory was 'borrowed' many years ago and superimposed onto the Helicopter. It is not suitable, although similar in some ways. Its use may be perpetuated because no significant study or research has been published (to my knowledge, although I'd really like to read Ray Prouty on it).
Fixed wing power and drag must be a great deal simpler, they only (the explanations) have to deal with two or more Aerofoils moving through the air at almost identical V2 values (unless turning or sideslipping) so drag (and therefore power) must be much the same for both, unlike a main rotor. They also have no TR to consider, just for instance.
A good case in point is the TR. Pick up one book and its included in profile, in another it is with induced, others side-step its inclusion completely, maybe because their Authors just don't know where to put it and have not the time or resources to re-evaluate the whole thing.
Let's take the power used to drive the TR for an example, give it a little fresh thought as it has been mentioned. Some may think it belongs with induced because you must have anti-torque to induce a flow on a conventional layout Heli.(not directly of course, but to sustain directional flight) It seems reasonable at outset but the idea collapses quickly.
The TR's power requirement and the resulting drag does not belong under a parasite heading either, as that deals with power and drag values associated with an increase in speed alone. Indeed, as has been said, TR power and drag are inversely proportional to both parasite power and drag due to several factors (not least TR translational lift and the 'offloading' afforded by the vertical stabiliser etc.).
So, it might get thrown in with profile, also incorrect as 212 has said. It does not appear to belong under any of these traditional headings and may well need one of its own, an 'Anti torque power/drag' heading.
Shy T's explanation recognises this in using a fourth denomination, 'installation' and I believe this is a path to proper definition of various types of power and drag when applied to the Helicopter.
As for engine ancilliaries, it seems reasonable to only consider shaft horsepower produced by the engine, and thus the ancilliary power used and drag resulting can be ignored - Can't it?
Well, no, it can't.
Consider the alternator's use of engine horsepower and the drag produced - If you make a high demand for electrical power they both rise sharply as a result, at any speed you like from zero to VNE. Putting this under a heading of 'installation' or 'ancilliaries' which is assumed to be the same across the speed range (a flat line across the graph) cannot be accurate (it is not suggested that Shy T has done this).
It seems there really should be at least three main groups of ancilliary power/drag, ie. alternator/generator, anti torque devices and the remainder of ancilliaries that use roughly constant power and cause constant drag (although not all of them actually do).
Moving on, the MR might need separate power and drag definitions in respect of the advancing and retreating blade because they do not increase and decrease proportionally with an increase in speed.Drag increases for the advancing blade at a different (greater) rate to the reduction of drag on the retreating blade as speed increases.
Just in my opinion, the whole subject of power and drag for Helicopters needs to be stripped right down and started again from scratch.
Are there any Universities or research establishments out there interested in doing that?
SPS
(No animals were harmed during the writing of this post).