Re: Experimenting With 2-D Parabolic Reflectors

Always Thinkin' <anon@xxxxxxxxxxxxxxx> wrote:
http://www.freeantennas.com/projects/template/index.html

I like those, but they are smallish. You could scale up.
I use the EZ-12 Windsurfer.

I'm thinking something like .5M-.75M across the horns, formed from
a sturdy but controlably flexible material, possibly sheetmetal,
that one could arch and keep in proper, trued configuration in a
support jig/frame.

I've seen formulae that I didn't bother with, since the images at
freeantennas.com were good enough for me.

There is some "string theory", where you could draw your own of any size
desired.


Supplied by "Don Widders" <widders@xxxxxxxxxxxxx>

Draw a line opposite the focus (where you would have the open face of
the reflector) running parallel to the directrix.
According to one definition of a parabola, fP = fd where fP is the
distance from the focus to a point on the parabola and fd is the distance
from the focus to the directrix. The line you drew is parallel to
the directrix, so it's like offsetting the directrix by some distance.
Since the new line is in FRONT of our reflector instead of behind it,
point P will get CLOSER to the line as it gets farther from the focus
(the farther off axis that P is located on the parabola.) Since the new
line is parallel to the directrix, the rate at which the distance from P
to the new line DECREASES is the same as the rate at which the distance
from the directrix increases and also the same rate at which the distance
from the focus to P increases. So the parabola can be expressed in terms
of the new line as fP + fNL = K where fNL is the distance to the new
line from the focus and K is some constant (the length of the string.)
The T-square rides along the new line that represents the opening of
the reflector. When the T-square is brought as far as possible from
the focus, the cursor will be pulled all the way to the 'crotch' of
the T-square (point 'c') so in this case the marker will be at point
c and the string will be a straight line from point c to the focus.
In this extreme case, fNL = 0 and fP = the length of the string.

I didn't want to change the length of the string for every point on the
parabola, so instead of putting the T-square on the directrix, I put it on a
parallel line on the other side of the focus. The directrix is closest to
the parabola at the point of the axis. The new line is FARTHEST from the
parabola at the point of the axis. As the distance from the focus to P
increases, the distance from P to the new line decreases, so now we can use
a string whose length does not change.

Supplied by "Don Widders" <widders@xxxxxxxxxxxxx>

The "changing length" string shockwave
http://www.exploremath.com/activities/Activity_page.cfm?ActivityID=8

Rather large parabola ;-)
http://www.speakeasy.org/~widders/big%20reflector.jpg



Supplied by "Clive" <c.a.m@xxxxxxxxxxxxxxxxxxxxxxxxx>
Initial focal point determination program
http://www.nospagetti.co.uk/dish_design.zip>

Article from Wireless World, with a drawing of the fixed length string
http://www.nospagetti.myby.co.uk/24cm_antenna.zip
http://www.nospagetti.co.uk/24cm_antenna.zip

The "fixed length" string animation
http://www.nospagetti.myby.co.uk/piece_of_string.zip

The mercury mirror telescope
http://vela.astro.ulg.ac.be/themes/telins/lmt/didac_e.html



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Clarence A Dold - Hidden Valley Lake, CA, USA GPS: 38.8,-122.5
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