Hi Duncan,
Inspired by your remarks, I derived a series of formulae to calculate the obscuration from the chord length but “did it the hard way” i.e. by using just basic trigonometry, in order to get a completely different method from yours. Comparing my result with yours, for the chord length and sun diameter you quote, I found that the two answers are precisely the same. I think we may therefore conclude that your equation is correct (and very much simpler than my deliberately straightforward but multi-step derivation!).
I then applied the formulae to the observations I had made. I was fortunate to be able to take an image within seconds of maximum eclipse at my location, and as it was captured with a camera using a “hyper-zoom” lens the image was much larger than your projected image, enabling me to get a greater precision in the lengths involved. I found that the chord length was 846px and the Sun’s diameter was 1200px, resulting in an obscuration of 17.98%. I also calculated the magnitude using the same lengths, which was 0.2908. These numbers should be compared to the predicted values of 17.96% and 0.2910 given by the eclipse circumstances predictor written by the well-known “computer” Xavier Jubier. Pretty good result, I thought!
And now addressing myself to Nick James, concerning his message about the eclipse video above:-
Hi Nick!
I was quite lucky here in north Suffolk as although I had patchy cloud cover I was able to capture images between the clouds about every 5 mins, and from them assemble not a video as such but rather a “video animation”. This was after quite a lot of processing to get the images consistent of course! It shows the entire eclipse in just 25secs, as per the attachment.