Curiosity got to me today, and I spent the last hour figuring out how to calculate the size of an eyepiece's sweet spot.
http://upload.wikimedia.org/wikipedi...Bicone.svg.png
Turned out rather interesting - the shape of the sweetspot is a biconical volume like the picture below, and depends on a few factors. If anyone knows references, can you link it in?
Sv - sweet spot vertical length (tip to tip distance of the bicone)
Sh - sweet spot diameter (diameter of the fattest cross section)
Svol - sweet spot volume
Pe - exit pupil diameter of the scope/eyepiece system
P - eye pupil diameter
AFOV - apparent field of view
Assumptions:
SAEP - spherical aberration of exit pupil is negligible
The boundary of the sweetspot is defined as the surface on which, if you placed the axis of your pupil there, you still see the entire AFOV, with vignetting no greater than this figure of overlapping circles - one circle is the exit pupil, one circle is the eye pupil.
http://cdn-7.analyzemath.com/Geometr...problems_1.gif
If P > Pe, then:
Sv = P/Tan(AFOV/2)
Sh = P
Svol = πSvSh^2/12
Svol ∝ P^3
So, I measured my pupil to be 6mm fully dilated, which gives me these results:
Sh = 6mm
AFOV 50° - Sv 13mm Svol 0.12mL
AFOV 68° - Sv 9mm Svol 0.085mL
AFOV 82° - Sv 7mm Svol 0.066mL
AFOV 100° - Sv 5mm Svol 0.047mL
If your eye pupil was say, 8mm, then Sh and Sv proportional increase by x1.33, and Svol increase by x2.37
If you were in daylight, and eye pupil was 2mm, assuming P > Pe, then Svol is now x0.037 or 3.7% of before. That explains why eye positioning is much more critical during the day, unless the exit pupil is big, in which case you use Pe instead of P for the above calculations. Pe=6mm will give the Svol as P=6mm.
Eye relief distance of the eyepiece doesn't affect the above values unless its very short, in which case the vertical sweetspot begins inside of the eyepiece.
Spherical aberration of the exit pupil will reduce all of the above values, Sh Sv and Svol. I have not yet figured out how to incorporate it into the calculation, maybe someone else could give it a go?