NavList:

I glanced at lunch, and as a relative newcomer of a couple of years to CNAV, I had a few thoughts.

First:  short methods to me (speaking in manual solution vs computer terms), implies a couple of extra things more than fewest steps:

Logical and easy to follow (even when cold tired and wet)

Codified with simple lookups, and minimal rules and decison making.

Arithmatic that is easily done by anyone with very basic math skills with minimal risk of error. (simple adds and subtracts and minimal goofy interpolation)

Reasonably quick....but  I'm a water guy, so an extra minute or two is not my bug.  As long as it is not adding error prone minutes.  I would guess that the air guys necessarily put more criteria on calculation speed,  as they are moving a lot faster than I  do.

So with that said:

I was first led to believe that early celestial navigation was once a mathamatical horror of logarithms and rules, and at one time I guess it was.....but Frank's 19th century course convinced me that once it was codified into a procedure and efficient reference tables, it was within reach of ordinary and occasionally dense men like me (actually I am a bit A.D.D.), . The key is the codified structure and references. I left the course thinking:  "I could do this"; at sea; and find my way around.

I first learned using the much worshipped St Hilaire method by myself on HO229 and HO249, something which I found a bit of a bother frankly. My first problems I worked I always seemed to be making dumb mistakes from tables or plotting.  In truth, dumb forgetful mistakes seemed to be a specialty of mine. I was of course just learning cold turkey...but....it was intimidating thinking knowing I was doing it at a clean dry desk vs at sea. Ultimately I asked enough questions and got fairly comfortable.  I also have since learned that St. Hilaire is a really ok flavor, but there are others I personally like better.  

In my wandering around I picked up some of the other used volumes of 211 & 214,  then got a hold of self contained celestial with HO208 (John Letcher) plus a 1930's copy of the original tables.  I opened up 211 and it just looked more intimidating than my tired mind wanted to deal with that night.....so instead I worked problems with no calculator following John Letcher's 208 cookbook perfectly.  The rules were simple, and my results excellent.  I got correct answers right  out of the gate on a known sight....and repeated this shocking result twice more that evening.

The key was it was simple and non threatening, and that John Letcher knows how to write an explanation.  Thats the hugest help.  He codified the approach to the point I think your average 12 year old (about my mental age sometimes) could give you a right answer.  That's a winner.  I would happily take that book to sea in my sextant box as a backup plan on Ole Mr. GPS.

So if we speak of hand solution methods without a calculator.....yup..I think a lot depnds on the particular flavor, the guy who explains it,  and your own orientation.  I learned even longhand Lunars could be done and were not so intimidating as I was led to believe.....once the more complete tables and cookbook was around..so I think sometimes a shortcut might actually be "the longest distance between two points".

On th eother hand, before the developments during the 1800's of the more advanced  tables....ughhhh...sitting on an old East Indiaman doing longhand lunars with logarithms...just shoot me....