>Shadow shortening is unavoidable.  So what's your solution? <

Depending on the design you might be able to fit two "false nodi" either
side of where the true nodus position is. That way "Joe Public" simply
judges the mid point - rather in the same way as he does when telling the
time by judging the  centre of the shadow cast by a cylindrical gnomon. 

There is a 28 metre diameter Millennium dial in Gosport  (UK) that uses a
double cone in this way (it's intended to be redolent of Einstein's cone
diagram) as a nodus. You can see a picture (well, sort of!) at
http://www.sundials.co.uk/newdials.htm. There are several dials there, you
will need to scroll down to find the dial called 'The Millennium Timespace
at Gosport'.

Patrick

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