A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Frank Reed
Date: 2022 Dec 1, 08:23 -0800
You can drop a rock, too!
If you drop a small dense object (a rock, a bolt, your laser rangefinder... anything negligibly affected by air resistance), the fall time is directly proportional to the dip. If you observe the fall time in seconds, you can get the dip in minutes of arc by multiplying by 3.89:
dip (m.o.a.) = 3.89 · fall_time (seconds).
To get the dip to the nearest tenth of a minute of arc (which is really overkill, but anyway...), you'll need the fall time to the nearest 0.025 seconds. That's impossible with eyes and a watch. But if you have a standard smartphone in your pocket, you can video the fall and get the required accuracy. It's important to release the falling object without any upward motion. If you toss it out in front of you, you may get a little lofting which can significantly throw off the timing.
But let's be serious here. If Jeremy is asking his young crew members to figure their height of eye to a fraction of a foot (taking back a few inches from individual height?), then this is more of a rite of passage into the world of celestial than anything else. Dip values from height of eye are only estimates.
Could we measure dip with ordinary sextant sights? In twilight there are often options to measure dip without a lot of calculation during a round of sights (especially if you have eager crew / extra hands). Shoot "beamy" stars, port and starboard. If they are nearly perpendicular to the vessel track, there will be no correction for vessel motion. For example, tonight in early twilight if my course happens to be nearly east or west, I might shoot three shots each of Saturn (in the South) and Polaris (in the North, I'm assuming a northern hemisphere observer, of course). For good measure I might alternate back and forth between them. If I assume zero dip, then the average of the intercepts, left and right, will yield the dip directly.
Of course I can also measure dip with a bunch of sights in a standard fix. Technically, if I have at least three sights, I can treat dip as an unknown. I would prefer five or six sights though, and that's not all that hard to do. We select a dip value that produces the tightest plot of LOPs around the fix. Or imagine shooting eight sights more or less evenly-spaced in azimuth. You plot them and in the vicinty of your fix, you see an "octagon" of LOP segments with a radius of 6.5 minutes of arc (all towards). If you subtract 6.5' from each sight, that octagon would collapse. So that's your observed dip. Height of eye? Irrelevant!