What is the purpose of a written plan?
In the beginning, the written plan is to ensure the novice student understands the planning process. It enables the instructor and students to prove their workings and that they’ve considered all factors (depth(s), gases, decompression algorithm, decompression settings/gradient factors, SAC, gas volumes…). It is also an excellent teaching tool to prove the student can plan a dive and dive the plan.
After a few dives, the planning process is understood. The inexperienced diver has proved the planning process and can move on to using practical techniques and away from the time-consuming manual training techniques; think using a calculator for long division, rather than writing it down.
Also, after a few decompression dives, you will have learned the "pattern" of a dive: how much and what types of gas you need, how much you use, how long you can stay at depth, redundancy, typical decompression stop times, how you feel after the dive…
Then as you’ve done hundreds of decompression dives, you know how much you rely upon your computers. If doing a decompression dive with more than a few minutes of decompression you are utterly reliant upon a dive computer. OR you need a depth gauge AND timer, in other words you need another computer.
In summary, with increasing experience writing the plan on a slate/wetnotes is a pointless exercise as you need a computer to run the timings anyway. A pre-written slate usurps the core purpose of a computer — to accurately monitor your personal depth and time and accurately calculate your specific decompression requirements -- how can you possibly know in advance what the bottom profile is, what the scars look like, what part of the wreck you're diving around?
Slate planning is good for learning. Slates are impractical and inaccurate for actually running a dive where computers provide superior accuracy, reliability and utility.
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As an aside, was diving a ~60m/200ft wreck the other day and jumped in with another diver. We ran around on the wreck until the computer's TTS said 90 minutes (at about 40 mins runtime) and began the ascent together up the lazy shot line. We stuck together during the deeper stops, me waiting for his stop to clear and ascending to the next 3m/10ft stop. Once up to the 6m/20ft trapeze there were another 4 divers on/around the bar. I was diving with three computers (Nerd, Petrel and Perdix). The other guy diving with one computer and a bottom timer (and had the ratio deco training to manually calculate the stops) — the first time I’ve seen a bottom timer in many years. Most others had at least two computers. Not a single planning slate in use by anyone.