so for academic purposes, how do you calculate where your first decompression stop is based on depth and time?
It's a good question.
Obviously there's the "run the Buhlmann algorithm. The algorithm will be available somewhere on the internets even if it is in Fortran!
The deco curve does have patterns. Your first few stops will be shorter than the later stops. The curve flattens out and typically half your total decompression time will be at 6m/20ft. Typically a dive to 45m/150ft will have 1:1 bottom time to deco time (e.g. 1h on the bottom is 1h of deco). At 60m/200ft this is 1:2 (e.g. 40mins on the bottom and 80mins of deco). 75m/225ft will be 1:3...
Example: 70m dive for 35mins with total 2h20 runtime
(i.e. 35mins on the bottom, 105mins deco = 1:3 ratio)
All of those patterns vary to a certain extent depending on the depth, time and gases used.
Prior to the advent of reliable and easy to use computers -- hat tip to Shearwater and others -- people used a manual mental arithmetic approximation which is generally called "
Ratio Deco". This requires you to average your depth in 5 minute (ish) intervals and remember these numbers. When it comes to the ascent (you have a pre-planned max bottom time!), then you will do some arithmetic which, with practice, gets easier (apparently). GUE (Global Underwater Explorers) use this (or maybe not nowadays?) and definitely UTD (Unified Team Diving) still use and promote their method of doing this (they blather on about this on their podcasts).
Apparently it's really easy: add the numbers, divide by something, halve the depth in ATA, blah blah blah. Probably why they need a team!
Sorry, it's 2023. I look at my computer to tell me what the first stop is and for how long. My second computer will confirm this. And even my third one if diving deeper. If I loose interest then my computer(s) will recalculate the stops.
Computers are good at running algorithms. Humans aren't. Divers definitely aren't as they started off as humans and their IQ halves as soon as they drop in the water. Mine does anyway.
However, for NDL diving, you'll memorise your max bottom time (30mins on 32% at 30m/100ft). You then ascend quickly to the first 3m/10ft increment past half way up (e.g. 15m) and stop for 30 seconds, then slowly ascend by 3m/10ft, stop, ascend... until you reach the surface. This isn't true decompression as such, more a way of slowing the ascent within No Deco Limits. On the other hand, most others just do a 3min stop at 5m/15ft.