Re: ATM (no subject)

[andydtg@phoenix.net]

Richard Schwartz wrote:

>I know that when a plane cuts a cylinder at 45 degrees, the resulting
>ellipse has axes in the ration of 1 to sqrt(2).   Is this proportion the
>same if the plane is cutting a cone at 45 degrees?  I think not. 
>Example: the cone apex angle is 45 degrees!  You get a parabola!  So the
>ellipse we really need is probably longer and narrower than the standard
>45 degree ellipse that we are sold because our apex angles are between
>zero (cylinder) and 45 degrees (the above mentioned cone).
>
>The actual shape of a diagonal for coverage of a field of non-zero
>diameter is also not so obvious.  Has anybody analyzed this?

It's still an ellipse, but as you say, *not* the 45 deg case. The
difference in a normal f-ratio/field size is small, probably not
bigger than the mfg errors in the 45 deg secondaries on the
market. I've measured several & none were exactly 45 deg ellipses.

BTW the solution for the exact offset between the center of the ellipse
and the optical axis intersection, given the other parameters of focal
length, field size, and primary-secondary spacing is not trivial &
looks like the solution to a 4th order 'quadratic' equation. I plugged
this into MathCad & it spit out a set of equations that works but
is a page full of algebraic expressions. I managed to stuff it into
a spreadsheet & verified the empirical solution given by drawing
the system in AutoCAD, drawing it is *much* easier.




Andy Saulietis / DTG Alt-Az-Fp Drive Systems
HDPE Worm Gears, Custom designs & Machine work
12617 Harriet Ln
Santa Fe, TX 77510 USA
409-925-8854 Voice/Fax
e-mail: andydtg@phoenix.net