Dear Frank,
 
Yes, the width of the shadow of a round rod polos with 0.5" in diameter is not always the same. I realized this not before 2009 when I was already engaged in sundials for at least 25 years!
 
The figure shows the width w without penumbra on a horizontal dial as function of the hour angle t for the latitudes 0°, 15°,...,75°,90°.
 
Best wishes
Rolf Wieland
 
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