On 15/08/2011 3:52 PM, karon wrote:
<snip> the smaller [sundials] are, by definition,
the less precise they can be.<snip>
This statement got me wondering how small can a sundial be, before
hitting the limits of our visual acuity. Here's my thinking:
Shadow blur imposes a limit of about 2 minutes of time, because the
sun's diameter is half a minute of arc. 2 minutes of time = 1/720 part
of a day. The human eye can resolve about 0.00349 inches (about 0.09 mm)
at 12 inches (30 cm). This figure comes from
http://www.ndt-ed.org/EducationResources/CommunityCollege/PenetrantTest/Introduction/visualacuity.htm.
Of course, it is not really the correct value to use because (i) most
users don't have perfect eyesight (ii) a dial face almost certainly does
not provide the same viewing qualities as the printed monochrome grid
used for testing human eyesight. But it's all I've got so I'll use it
anyway. I conclude that a horizontal dial with circumference of 720 x
0.00349 inches should be resolvable to 2 minutes of time. Multiply out
and divide by pi to get the equivalent diameter.
The result is just under 0.8 inches diameter = 2 cm.
OK, so there's an inadequate theoretical value; does anyone know the
real, practical lower limit for size of a horizontal dial that still
achieves 2 minute resolution? For instance, how small do portable
horizontal dials get before they lose resolution?
And the converse question: what was the typical range of sizes of
antique portable dials, and how does that range compare to the size
required to achieve the best possible precision? (I think I mean
precision not accuracy, but I may have the two words confused).
Cheers,
Steve
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