A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Position-Finding
From: Frank Reed
Date: 2018 Jan 8, 10:59 -0800
So test it out experimentally. While you're on the ground, get out and take a half-dozen sights with no windscreen interfering. Then at the same location, shoot from the cockpit. Alternate back and forth. Do this over a long enough period of time, and you will create your own "dome refraction" table. You may discover that there is no statistically significant correction different from zero. As long as the glass is plane-parallel, there should be no correction.
Also, do you have a marine sextant? Or can you borrow one? Shoot a star-to-star angle --for example, Sirius to Capella. You'll get some angle that varies only slowly with time and location, which you could compare against a computed angle, but that doesn't necessarily matter. You don't need to worry about any sextant or astronomical refraction corrections. What you should look at it is the change in angle as you move around in the cockpit: a foot left, then right, forward, back. You can do this "live". That is, while holding the two stars in apparent contact in the sextant's field of view, move yourself about so that your lines of sight pass through different sections of the windscreen. The stars will change their contact slightly due to this "dome" issue. If it's ony a minute of arc or a few minutes of arc, then that's negligible for air celestial navigation.
Finally, unlike most of the corrections in celestial navigation, the old "dome correction" table was surely a "hack" --a "better than nothing" solution to a tricky problem. There's no need to worry about those old tables. And there's also no hard evidence that they had any real value even when they first published, let alone decades later.