Experimenting With 2-D Parabolic Reflectors

I learned so much from my last question, I thought I'd give this a
spin here:

Is there a practical, minimally-technical way to come up with a
physical template for the proper curvature of a two-dimensional
parabolic reflector to amp-up and directionally focus a vertical
omnidirectional antenna? I've seen raw formulae, but they've lost
me (I was an Art major). I've spent a few days searching on the
web and haven't come up with anything like this except for very
small examples:

http://www.freeantennas.com/projects...ate/index.html

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'd also be interested in the relative merits of centered and
offset reflectors in this sort of application.

Again, this is more by way of education than anything else, but I
do intend to make some experimental examples and see how they
perform using signal-strength recording programs.

Many thanks for any assistance!

Always Thinkin' <(E-Mail Removed)> wrote:
> http://www.freeantennas.com/projects...ate/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" <(E-Mail Removed)>

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" <(E-Mail Removed)>

The "changing length" string shockwave
http://www.exploremath.com/activitie...m?ActivityID=8

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



Supplied by "Clive" <(E-Mail Removed)>
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/t...t/didac_e.html



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

Always Thinkin' <(E-Mail Removed)> hath wroth:

>I learned so much from my last question, I thought I'd give this a
>spin here:

I'm partical to "Learn by Destroying". If you have broken and fixed
something, you don't understand it.

>Is there a practical, minimally-technical way to come up with a
>physical template for the proper curvature of a two-dimensional
>parabolic reflector to amp-up and directionally focus a vertical
>omnidirectional antenna?

Sure. I do it all the time. It's borrowed from wood aircraft and
wood boat construction. Make a template with the proper curve using a
sheet of thin 1/4" plywood. Draw the parabolic shape on the plywood
and cut it to shape with a jig saw. I was building some rather large
(8ft dia) sheet metal parabolic reflectors for weather satellite
dishes this way. However, instead of using the plywood for a
template, I was using it as part of the dish structure. I attached
aluminum flashing to the plywood with a staple gun or tack hammer.
I'll see if I can find some photos.

However, permit me to offer a clue. There's not much difference in
gain with small reflectors of the same size between a parabolic dish,
flat plate, or corner reflector. For example:

Flat plate (8.3dBi):

http://802.11junk.com/jeffl/antennas...tor/index.html
Parabolic Dish (7.7dBi):
http://802.11junk.com/jeffl/antennas...h08/index.html

The flat plate reflector has 0.5dB more gain than the equivalent size
dish. However, don't assume that this works for all sizes of dish and
flat plates. The difference is bigger for larger diameter antennas.

Also, I should do a similar corner reflector for comparison, but not
tonite.

>I've seen raw formulae, but they've lost
>me (I was an Art major). I've spent a few days searching on the
>web and haven't come up with anything like this except for very
>small examples:
>
>http://www.freeantennas.com/projects...ate/index.html

See:
| http://www.nodomainname.co.uk/parabolic/parabolic.htm
for some construction details.

You can draw a parabola with two thumb tacks, carpenters square,
string, and a pencil.
| http://www.sciences.univ-nantes.fr/p...ra_string.html
| http://home.germany.net/100-441770/amsi-model.html

>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 can't guess if this size antenna is suitable for your unspecified
purpose. The design and construction of the dish is usually not a
problem. At best, just buy a commercial dish or adapt something from
a DBS pizza dish. The problem is designing the feed. Too wide a
pattern and you have overspray. Too narrow a feed pattern, and you
don't illuminate the entire dish resulting in gain loss. It's not
easy.

>I'd also be interested in the relative merits of centered and
>offset reflectors in this sort of application.

Here's your homework for the next few days:
http://www.w1ghz.org/antbook/contents.htm
There's a chapter of offset feeds. Basically the advantage of offset
feeds is that the feed itself does not block the signal. Also, the
mount is out of the pattern. It's not horribly important for large
diameter antennas, but is critical for small dishes. One thing for
sure... calculating and building your own offset dish is a
mathematical mess. I wouldn't even try.

>Again, this is more by way of education than anything else, but I
>do intend to make some experimental examples and see how they
>perform using signal-strength recording programs.

Suggestion: Build or buy a directional reference antenna with a known
gain. Spend some time learning how well it works at different
frequencies (channels), and at different heights above the ground.
Then, do you gain measurements using this reference antenna as a
standard. If something changes in the test setup, it will change for
both the reference and test antennas, and will be obvious.

--
Jeff Liebermann (E-Mail Removed)
150 Felker St #D http://www.LearnByDestroying.com
Santa Cruz CA 95060 http://802.11junk.com
Skype: JeffLiebermann AE6KS 831-336-2558

Jeff Liebermann <j...@comix.santa-cruz.ca.us> writes:

>I'm partical to "Learn by Destroying". If you have broken and
fixed
>something, you don't understand it.

[...]

>Here's your homework for the next few days:

Hey, guys!

Thanks for these tips, but as soon as I posted this, a rolling
rash of unrelated but _really_ terrible stuff started happening to
several of my close friends here, and I've been busy with
funerals, lawyers, cops and hysterically bereaved and distraught
people. I haven't have the presence of mind to attend to more
pleasant stuff like antenna design.

I'll get back to you on this maybe next week and we can have some
fun with it! I'll be ready for some diversion, believe me!

Thanks!