Beagle, it's not me that's overcomplicating the method - but you & your snide remarks. You & I both know that all these heading corrections derived by *all* the methods mentioned so far are nothing more than 'good enough' approximations only.
Anyway, to use your 55nm trip & 3 nm off track example & say, 20 nm run (or 22 or 23 or 19 etc.) AND using the table I outlined above.
3 nm off in 20. Straight off that's 9 deg to parallel track (ie 3 x 3 nm).
Another 35 nm to run? Near as dammit 30 nm so that equates to 6 deg (2 x 3 nm).
All up 15 deg heading change. No difficult formula to remember.
Alternatively alter HDG 18 deg & regain track in 20 nm & the same TI it took to get off track. BTW, the table can be easily expanded for other leg lengths eg dist run 120 nm, use half the dist off as TE ie multiply by a half.
An attendant benefit is that the same distances run and to go can serve a double purpose and be used for subsequent GS/ETI checks afte the heading adjustment is done.
Yes, it can have more to it. What if you've run 75 nm? I use my whiz wheel. Unlike some in the UK, using a whiz wheel isn't considered a 'bad thing' elsewhere in the world. And no, it's not difficult or time consuming. It takes a few seconds.
I can see the benefit of your SCA in some circumstances, but certainly not as the be-all-and-end-all-there-is-no-other method. Where do GS/ETI checks get a look in? Or are you presuming the planned GS is accurate? Not much of a problem on short hops since the accumulated error is small but not a good idea on longer sectors.
If you do conduct GS/ETI checks then how do you integrate them with your SCA gyrations? It may not be common in the UK but in Oz many PPLs use a variety of a/c from 90kt C150s to 160 kt A36s or C210s. How many SCAs would you have them remember (alternatively, would you have them only ever fly at a single speed per type?)
As for some other methods:
I dislike pre-drawn drift lines because they're limited to solving a deviance that commences or terminates at the same origin as the drift lines. They fall over if the off track deviance develops at some point along track or worse, if you divert. The flip side is that if you'r adept at judging angles (or have tool for doing so. I used to have a scale rule with one printed on it), drift lines can be quick & efficient.
Proportional nav can also be useful - particularly if the proportions happen to be simple ratios. Bit of a b@stard if the ratios aren't very cooperative.
Other places I've seen had the students plot two positions & derive the actual W/V then apply that to the TAS & TR to obtain HDGs & GSs. Then calculate ETIs. Bit of a major workload enhancer but do-able & can be extremely accurate. To much bu ggerising around for my liking. Interesting to do as an exercise on very long sectors.
Jesus said it best (never thought I'd ever say that. And me a devout atheist
): It's best to have a toolbox of skills that has a variety of tools.