But Frank, This little distortion effect must be quite small. For practical purposes, you can call the shadow a circle can't you, even though it's a tiny bit elliptical. Can't you? If the disk is large, this effect becomes almost insignificant doesn't it?
I'm going to do the simple experiment tomorrow if I have time. I also want to test how useful a horizontal disk is in the early morning and late afternoon and I want to try a disk with a central aperture hole. I'll lay a ruler down on my projection board on the shadow's North/South and East/West diameters and I will take photos of my experiment and will let you know my results. This subject is important and deserves more study. John C. ----- Original Message ----- From: "Frank King" <[EMAIL PROTECTED]> To: "john shepherd" <[EMAIL PROTECTED]> Cc: "Sundial List" <[email protected]>; <[EMAIL PROTECTED]> Sent: Tuesday, July 13, 2004 1:00 AM Subject: Re: Turtle Bay Sundial Bridge opens > Hi John, > > At last signs of the truth... > > > Theoretically it's correct that the projection of a circular > > disc on to a flat surface parallel to the disc will be a circle. > > Unfortunately the sun's apparent size results in the disc becoming > > very blurred when you get a couple of hours off of local noon. > > The theory suggesting that a circular disc casts a circular shadow > depends on the sun being a point source of light which is isn't! > > If the model on which the theory is based is refined to take > the angular diameter of the sun into account, you find that > the shadow is generally degraded into an approximate ellipse > whose major axis is less than the diameter of the disc and > whose minor axis is smaller still. > > The actual shape at a given time can be determined by noting > the shape that the image of the sun that would form if the sun > were projected through a pin-hole at the centre of the nodus > (this image really is a true ellipse). > > You then draw the circular shadow that the simple theory > suggests and at each point on the rim you draw this ellipse, > being careful to preserve its orientation. You then get > two envelopes, the inner of which is a fair approximation > to the true shape of the shadow. > > The inverse of this effect occurs with an aperture nodus. > The anti-shadow of a circular hole likewise distorts into > an approximate ellipse but its major axis coincides with > the minor axis of the shadow of the surrounding disc and > vice versa. Of course the anti-shadow is bigger than the > original hole. You have to use the outer envelope. > > Unless a nodus designer understands all this, it is ever so > easy for the anti-shadow from the hole to exceed the size of > the shadow of the surrounding disc. The result is indeed > pretty useless! > > Frank King > Cambridge University > England > > - > -
