Dear Allan, John, Frank et al I've just read Allan's article. I highly recommend it. He performed an experiment in which volunteers consistently estimated the shadow edge at around 8mm from the dark edge of a 68mm penumbra, giving the figure John quotes of 12% of the sun's diameter uncovered. That's 38% of the sun's diameter from the geometrical centre of the penumbra.
For completeness, two other factors that affect reading a sundial should perhaps be considered. These are the different apparent size of the sun from perihelion (32.53 arc minutes in January) to aphelion (31.46 arc minutes in July) and the fact that the sun appears to move faster along the 360 degree great circle that is the equinoctial path than the smaller (330 degree) circles that are its solstice paths. So, in January it crosses its own diameter in around 142 seconds, in April/September in around 128 seconds, in July around 137 seconds. 38% of each of these gives the error in reading a sundial (unless it has been pre-distorted as discussed earlier), as 54, 49 and 52 seconds respectively. On average, that's about 50 seconds. Which is back where I started, but at least we've got Allan's experiments to justify it now. I'm convinced that pre-distortion is a good idea, and will be incorporating it the next time I make a sundial with a edged, as opposed to a cylindrical style. Best wishes Chris ----- Original Message ----- From: JOHN DAVIS To: Chris Lusby Taylor ; Frank King Cc: [email protected] Sent: Sunday, February 17, 2008 8:46 PM Subject: Re: Monumental Sundial; 14 missing seconds Dear Frank, Chris and the List, An experiment to determine the position of the shadow edge was reported by Allan Mills in his article "Sunlight and Shadows - or, what's the point of big sundials?", British Sundial Society Bulletin 96(1) pp.22-27 (February 1996). Allan's key result for the question now under consideration is: "the perceived edge of the 'optimum shadow' corresponded to a point where just a little of the sun remained uncovered. ...... but correspond to about 12% of the Sun's diameter being uncovered." Allan's paper considers the circular shape of the light source, the effects of limb darkening and background illumination, and the non-linear response of the eye. I haven't tried the calculation to convert the 12% into a time offset. Regards, John -------------------------------------------------- Chris Lusby Taylor <[EMAIL PROTECTED]> wrote: Dear Frank, Try as I might, I can find no published information on where people judge the edge of a shadow to be. It would certainly be an interesting experiment. As John Davis observed, the human eye is very non-linear. Experience with photography seems to suggest that, like the ear, it is logarithmic. I imagine one's judgement of a shadow would to some extent depend on how clear the sky was and might well vary from person to person. For instance, someone well experienced with the phenomenon might have trained themselves to judge the 50% point more accurately. My own informal experiments with a shadow sharpener suggest that I tend to judge the edge at about 10% of full illumination, which corresponds to about 70% of the 64 seconds passed, or 45 seconds, but it may depend on a lot of factors including the colour and optical qualities of the surface - white matt paper v polished brass, for instance. One point you make that I don't understand is that you expect different results going from dark-to-light than light-to-dark. Why should that be? Shadows move so slowly that I'd imagine one would err towards the darker side consistently regardless of whether the dark area is shrinking or growing. Regards Chris
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