Yikes, you have me spooked now... Tell me if I'm being naive here please:
I simply eyeball a 15º angle where the rode penetrates the surface; I double-check this by visually comparing the base & height of the surface triangle that I can see. If the distance from the stem to where the rode penetrates the surface is >= 4x the height of the chock above the surface, then my scope is a little more 4:1. Of course I do this with some load on the anchor, so it if there is no breeze or current, then I add light reverse throttle.
At the beginning, I did measure rode out on my deck, but then it occurred to me that if I did it by angle, I would never need to measure. 4:1 scope corresponds to about a 15º angle at the anchor. The right triangle formed by the rode and the surface of the water is proportional to the one formed by the rode and the "seabed", so if the one I can see has 4:1 scope, then so does the one that matters.
This all hinges on the idea that the surface of the water is perpendicular to gravity, so if it's really choppy, this wouldn't work very well. But I also wouldn't anchor anywhere that was that choppy if I had any choice.
Other caveats:
- My boat only weighs 2500 lbs
- It's a trimaran, so I can go out near the float bow and asses the surface triangle with effectively no parallax
- I do hard-reverse and watch my water-speed to verify that it's zero (haven't had to anchor in significant current yet)
- I'm definitely a princess in terms of how much protection I required to spend the night
- I usually anchor in 8'-10' of water
- I use a Spade anchor
If I had to do it in rough conditions, I would watch it for a little while, and look for the maximum height surface triangle over the course of a minute or two, and use that for my assessment.
I also basically stopped using anchor watch electronics. My calculus goes like this: "If I don't trust my set enough to go without an alarm, then I don't need an alarm because I'm not going to sleep anyway." I haven't found an alarm yet that doesn't yield false alerts. One alert whether it's false or true means I won't sleep the rest of the night, so anchor-watch means no sleep, and no sleep means anchor somewhere else, or just accept that I'm the anchor-watch. I will sometimes set a pin on my iphone, and occaisionally check that I haven't strayed far from it.