On Mon, 21 Mar 2005 16:49:13 GMT, in rec.radio.amateur.antenna you
wrote:
Those I've found all give templates for a parabola, but without any
explanation as to why they have chosen that *particular* parabola, or
the formula used to draw it.

Hi Nigel,

All parabolas have the same formula, simply different constants
(size). If you want more gain, build a larger parabola. There is
some diminishing return because your actual antenna is not getting
larger, and a lot of the gain from the ends would be reflecting into
unoccupied space.

I would offer one caution. The "template" offered appears to have a
geometrical distortion from being stored for printing vs. stored for
viewing (it appears to be squashed from either side, as viewed at the
page).

As for a formula, that would be far more complex than construction
instructions:
1. Obtain a large sheet of graph paper;
2. Along its longest edge, rule a line;
3. In the middle of this line, extend a perpendicular line;
4. Along that perpendicular mark a focus point (5 inches would do);
5. Along that perpendicular, halfway between the line in 2. and the
focus in 4. mark one point of the parabolic surface;

This defines the hallmark characteristic of a parabolic surface, ALL
points lie equidistant from a perpendicular line from 2. and from
point 4. Your graph paper should provide a lot of perpendiculars from
line 2. to use as guides. This will be cut-and-try until you get the
hang of it:

A. Select one perpendicular graph line and mark a point out X inches;
B. Using a compass, measure from focus point 4. X inches;
C. If the compass can touch the mark A. you made a lucky guess;
D. Mark this A. as another point along the parabolic surface.

However, luck is not always with us, and the compass either overshoots
A. or undershoots it. Move A. and adjust the compass equally until
they both match. Repeat A through B along other perpendicular lines
and eventually you will have a rough trace of a parabolic surface.
Connect the dots and smooth the line.

73's
Richard Clark, KB7QHC