You first want to consider that tapes will travel on different paths through different machines. From this we go into forced-guidance tape paths versus precision guidance ones.
This is a fun FAQ that people ask MRL.
The answer is given in a technical paper by J. G. McKnight that explains the method. If you're a physicist, you could find the method rather elegant, as it reverts to first principles.
I glean from your question that you might want a way to set the repro azimuth (ORA) just once, and then leave it alone?
You cannot do that, because each tape will most probably have its own ORA in any machine.
(No one has yet brought up the matter of accurate tape width, and of tape slitting. The variable that this introduces into the subject of guidance is huge.)
A question that I like to ask of training class participants (here I mean training tailored for tape professionals from the recording industry) is to ask them to explain the difference between forced-guidance and precision (non-forced) guidance transports and headblocks.
Or, ask them what is the major difference between the Ampex ATR-102 and the Studer A80 headblocks?
Very, very few will correctly answer this, before sitting through the day's training and actually observing what is going on with tape guidance and azimuth.
If by this you meant without alignment tones, then that's another FAQ, and an excellent one that I believe the OP here asked me sometime in the past year. Let's leave it hanging for now.
The Nakamichi Dragon cassette deck, first manufactured in 1982, recognized that correct azimuth would vary for each tape played, and employed a motorized azimuth correction system that automatically set the correct azimuth for the tape being played. It did so by splitting the playback head gaps for the right channel; the playback signals from these electrically-isolated gaps were sent to electronics that could detect whether there was the slightest time misalignment in the signals coming from the two gaps. If a misalignment was detected, a motorized servo circuit adjusted the playback head azimuth until no time alignment error could be detected. This was all done automatically every time a tape was played (and obviously was done for different sides of the same cassette). I always wondered why Studer or Ampex did not incorporate such a system in their TOL mastering decks. Perhaps one consideration was that the Nakamichi system was complex and required regular service; having the reproduce head attached to a motorized platform also may not have been acceptable for RTR mastering machines seeing heavy use in a studio environment - you would presumably want those heads "locked down" on as stable a platform as possible. And perhaps there was an understanding that in the studio world, tapes would all have alignment tones recorded, which could then be used to adjust azimuth for that tape on the reproducer - so no need for an automated system when the studio tech would take care of it manufally. But the Nak's system did not rely on alignment tones, and therefore could squeeze out the very best performance from any recorded cassette, including commercial dupes of dubious quality. That all this was done in the cassette format 40 years ago is pretty amazing, IMHO.
OK, I always check alignment tones on the distribution and "safety" (I won't get into an argument today about this, save to say that the provenance of all my tapes varies, but they almost all sound great) tapes, which I buy, and always put alignment tones on my own tape dupes.
In that case, you adjust channel 1 for peak and mark the mechanical position of the adjustment screw. Then peak channel 2 and mark it's mechanical position. Then set the azimuth screw mid way between the two marks.
Well, sure they are. You would not align a machine for broadcast or duplication with a calibration tape without regard to output level and say that is has been lined up. Otherwise, your levels could be all over the place. I think what Bruce B. is saying is that if you are taking the time to perform a full alignment, you would first naturally calibrate the deck's meters externally to ensure that the levels indicated on the deck with the alignment tape reflected the correct head/eq/level alignment, and not other variables such as VU or line amp sensitivity.
I have to disagree on the correct method for azimuth. In my opinion there is only one reliable method for any recorder with more than 1 track. That is to use a dual trace oscilloscope in the normal mode, and display two channels, one on each trace. Then adjust azimuth so that the two waveforms line up. Using level alone only works on a mono machine. The level method can result in the phase performance being compromised. Note that in record mode, the record head azimuth if done in selsync, and the azimuth if recording through the machine and replaying, can be different, as the level of bias on each channel can affect where on the recording head the recording process takes place. Also note that reproduce eq will affect azimuth setting. Thats why the process of alignment should be repeated until all factors line up correctly, azimuth, 1 K level, and high frequency level. On a multitrack machine, there can be errors in the way the head is manufactured, so azimuth should be checked on multiple tracks. Just using track 1 and track 24 on a 24 track is not sufficient.