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We always tell students and divers that 700 PSI is the point at which you signal your DM to let them know you are low on air and time to ascend to your 3 minute safety stop. No need for math while trying to maintain buoyancy at the end of a tiring dive after so long out of the water.
... it surprises me that an IDC instructor with a tech background would give that sort of advice. It'll generally work with a few caveats ... like you mustn't be very deep, your air consumption rate is "average" or better, and nothing goes wrong during ascent that requires you to share air with your buddy ... but we're not supposed to be training people on the assumption that nothing will go wrong.
It makes me wonder how often your DM's are required to deal with OOA emergencies, or how often you have students and clients dealing with LOA situations that, by definition, mean they're cutting their safety margins too thin.
I prefer to train my students to understand how much gas they need for a planned dive before getting in the water. Since there aren't any fill stations below the surface, it helps maintain a certain confidence knowing ... because they planned for it ... that they have enough air to complete the dive. I also prefer to train my students how to think while maintaining buoyancy control ... it helps a great deal if something unexpected happens that they have to deal with.
... Bob (Grateful Diver)