help parabolic reflectors
Robert Macy
JL>: hi there everyone!!
JL>: is there a way simple and easy way to construct a parabo
JL>: reflectors(dish).i have not bought the downconverter yet
JL>: and also the amplifier to receive this signal.
JL>: can anyone please give me the ful and simple way and
JL>: formulas to contruct the parabolic dish and also recomma
JL>: a good book in the construction of a parabolic dish.
JL>: thanking you in advance.
I assume you're trying to make a parabolic reflector for receiving 4 GHz
coming down from the satellites, yes?
It is extremely easy to make a spherical reflector, just use a string at
some equi distance from your focal point and voila! a spherical
relector. But as you know, a spherical reflector is lousy as you get
out towards its edges. But, how lousy?
Ok, here's a tutorial: first of all you want as much energy as possible
to get into your LNA horn receiver. That means you must have a "low"
angle of incidence into its face. In other words, energy going into the
horn should impinge straight into its face.
That means the reflector should be at least as far away as the "radius"
of the reflector.
Or, given a 12 foot diameter (a nice low noise antenna size) you will
need to mount the horn at, maybe 10-12 feet away from the reflector
surface.
Now, a spherical reflector closely approximates a parabolic reflector up
to a certain point.
Here are the equations for a curve facing upwards:
Parabolic reflector: (cross section along the axis)
y = x*x/4/r where r is the focal length
Spherical reflector:
y = r - sqrt(r*r - x*x) where x < r obviously
If you plot those two functions given r=12 ft, you will get two distinct
curves. Do you have Computer Calculus 4? It's available on most BBS's
as shareware, or freeware. It's easy to use and will show you where the
two functions start to diverge "destructively". If not, log onto The
Engineers' Club at 408 265 3353, leave me a msg, ok?
At 4GHz signals must reflect to the horn within an 1/8 of a wavelength
or they will "destroy" other signals coming in. The wavelength of 4GHz
is about 7.5 cm, so errors in your reflector greater than .9 cm will
start to cause problems. That's about .3 inches. Ain't it great that
you don't need to be accurate?
In other words, if you made a parabolic reflector that had errors less
than 0.1 inch, you'd have a great antenna!
Now, plot the function of the two reflectors. You'll see that the
spherical reflector curves up faster than the parabolic, almost twice as
fast. So you can use the string method, but divide the distance to flat
by one half. A bit tricky, but remember you have a margin of 0.1 inches
with no problems.
Ok, now in English, take a string with a fixed length. The point of
rotation is the focal point (where you put your LNA horn), divide the
distance to flat from the end of your string by 1/2, and you have a
fairly decent parabolic reflector.
Sorry, I don't know an easier way to make a parabolic other than the
classic way of saying, make all incoming waves reflect to the focal.
- Robert -
PS You'll *definitely* be ok out to a five foot radius using this
methond. If you got more questions, fire away.
* OLX 2.1 TD * Everywhere is walking distance, if you have the time.
Robert Macy
RSW>guarantee it!! Try it empirically with cardboard! I did sit down and prove
RSW>it for a school project once and I have looked at it recently. I would not
RSW>have guessed it worked out so easily and practically stood up and proved
RSW>itself! You know, those great proofs that look horrific, and then
RSW>everything falls out leaving a simple elegant term? It is like that!
RSW>This surface will act as a perfect concentrator, whether for sound, light,
RSW>radio waves, or even tennis balls if it's strong enough. Enjoy!
RSW>-Steve Walz rst...@armory.com
HELP!!!!!!!!!
I didn't understand any of this.....I know it's my fault. But I feel
awfully stupid, here.
If you got an easy way to graphically make a parabola, you have my vote.
But how do you apply this to building a reflector that's 12 foot in
diameter?
Tell me how to make lattices and supports and adjustable beams to tack
on my 1/4 inch reflector mesh. Then you got my attention.
- Robert -
* OLX 2.1 TD * Interesting history is awful living.
Richard Steven Walz
Robert Macy <rober...@engineer.uu.holonet.net> wrote:
>RSW>guarantee it!! Try it empirically with cardboard! I did sit down and prove
>RSW>it for a school project once and I have looked at it recently. I would not
>RSW>have guessed it worked out so easily and practically stood up and proved
>RSW>itself! You know, those great proofs that look horrific, and then
>RSW>everything falls out leaving a simple elegant term? It is like that!
>
>RSW>This surface will act as a perfect concentrator, whether for sound, light,
>RSW>radio waves, or even tennis balls if it's strong enough. Enjoy!
>RSW>-Steve Walz rst...@armory.com
>
>HELP!!!!!!!!!
>
>I didn't understand any of this.....I know it's my fault. But I feel
>awfully stupid, here.
When you get tired enough of feeling stupid, I suppose you'll learn the
math! It's old first year algebra! Never thought you'd need THAT now did
you!?:) Yeah, I know that knowing how to plug in equations is easier than
this sort of derivation I posted, and by rights it should be a precalculus
homework problem for review, but it's just not that hard! I hope you kept
that derivation of mine, because you might like to have it about an hour
after you hit your old algebra book!
>If you got an easy way to graphically make a parabola, you have my vote.
>But how do you apply this to building a reflector that's 12 foot in
>diameter?
--------------------------------
Wowie, much bigger and you can pick up Voyager or Galileo!
-Steve
>Tell me how to make lattices and supports and adjustable beams to tack
>on my 1/4 inch reflector mesh. Then you got my attention.
> - Robert -
---------------------------------
The Parabolic Dish: How?
Have you EVER GRAPHED anything, on graph paper? If not simply obtain:
1) the most simple algebra book.
2) read it through where it talks about graphing functions in x and y.
3) a parabola facing upwards is y = x*x/4f, where f is the focal distance
you will need to place your receiver in feet, cm's, inches, or whatever
as long as you use the same unit for everything related to creating the
shape you need. YOU decide the focus you need, and IT affects how
steeply curved your parabola is!!! Longer focus, shallower mirror.
4) Graph the function from the negative diameter/2 you need, to the positive
diameter/2 you need, in values of x.
5) Obtain the resulting values for y. They are your heights at every radius,
(which is diameter/2 ), above being absolutely flat!
6) Do it on shelf paper so you can get the scale right full size.
7) Place on a piece of plywood and make a bunch of curves that shape in
parallel to each other and about 4 inches wide or more apart.
8) If you make them the full diameter, then you can make an interslotted
deck of symmetrically curved slats which will intermesh like pieces of
divider carboard on edge in a corrugated box of bottles or glassware!
9) Cut off the ends vertically as needed to fit the diameter of your dish
at each edge and make the slots for intermeshing downward for the
"North-South group" of slats, (say, as you have it laid out in your back
yard), and upward slots for the other "East-West" group of slats, so
that the slots go only halfway through the width vertically!
10)Assemble the slats in a rectangluar intermesh by sliding the "N-S group"
down into the upward facing slots of the "E-W group" which lay at right
angles to the other group standing on edge, like rockers from a big
rocking chair. You may wish to assemble this first and then you'll see
what I mean about cutting off the ends vertically inside the diameter!
If you DON'T cut off the corners it will still work fine, but it will
look like you bent the world's biggest square plywood spice rack into a
parabolic dish!!!:-)
11)Rigidify this assembly with wood blocks at intersections of the plywood
held with screws through the plywood into the blocks, and you will have
a parabolic dish! The metal mesh, or even plain paper and aluminum foil
work beautifully to concentrate either sunlight to do some light
welding, or else to bring in satellite signals, OR you have your very own
radio-telescope! You can cook weenies on it as well, but they burn fast
with a 6 foot dish, so don't put them right IN the focal point, but a
bit inward or outward! A twelve foot dish CAN weld with aluminum
foil!!! And you'll have to use maybe six or eight inch wide slats of
plywood for that size! The denser the mesh of slats the stronger and
more conforming parabolically the better, but the heavier it will be.
I have seen bright folks make them out of steel rod welded into a frame
member like an aircraft strut fuselage assembly, with triangle trussing.
Should I try to draw a circle with a rectangular (square) intermesh of
cells from above in ASCII or shouldn't I?
Nawh, if you would really and truly want me to design all of it for
you, tell me your diameter and focal length and send me $50 to make the
patterns!! Oh, you COULD also use a radial spoke arrangement, but the one
I use here is stronger. Liberal use of glue with the wood blocks,
(hardwood), and screws, is recommended! Mount it on an alt-azimuthal
mount with sturdy metal or plumbing pipe assembly (the kind like on
little cheap telescopes, you know, up and down and right and left around?)
and you have got it. So there! And remember to put a long pipe on it
and counterweight its weight with slidable concrete weights in coffee
cans, or such. The counterweight pipe is to pass right through the axis
of symmetry of the parabola, (the line you could rotate it around like
an umbrella, and have it still look the same from any angle).
P.S., if anyone doubts that one can be so cavalier with using the same
curve throughout the design, I can supply them with a proof that it will
work. It is elegant, and I first derived it myself and then have seen it in
a couple solar energy books! One simply uses less of the curve, and in
ANY direction at any radius across the dish, as long as it is a symmetrical
piece of the same curve about the apex, or point of the parabolic shape.
-Steve Walz rst...@armory.com
John Lundgren
'Scuse my ignorance.
--
Robert Macy
RSW>Robert Macy <rober...@engineer.uu.holonet.net> wrote:
RSW>>But how do you apply this to building a reflector that's 12 foot in
RSW>>diameter?
RSW>The Parabolic Dish: How?
RSW>4) Graph the function from the negative diameter/2 you need, to the positiv
RSW> diameter/2 you need, in values of x.
RSW>5) Obtain the resulting values for y. They are your heights at every radius
RSW> (which is diameter/2 ), above being absolutely flat!
RSW>7) Place on a piece of plywood and make a bunch of curves that shape in
RSW> parallel to each other and about 4 inches wide or more apart.
RSW>8) If you make them the full diameter, then you can make an interslotted
RSW> deck of symmetrically curved slats which will intermesh like pieces of
RSW> divider carboard on edge in a corrugated box of bottles or glassware!
RSW>9) Cut off the ends vertically as needed to fit the diameter of your dish
RSW> at each edge and make the slots for intermeshing downward for the
RSW> "North-South group" of slats, (say, as you have it laid out in your back
RSW> yard), and upward slots for the other "East-West" group of slats, so
RSW> that the slots go only halfway through the width vertically!
RSW>10)Assemble the slats in a rectangluar intermesh by sliding the "N-S group"
RSW> down into the upward facing slots of the "E-W group" which lay at right
RSW> angles to the other group standing on edge, like rockers from a big
RSW> rocking chair. You may wish to assemble this first and then you'll see
RSW> what I mean about cutting off the ends vertically inside the diameter!
RSW> If you DON'T cut off the corners it will still work fine, but it will
RSW> look like you bent the world's biggest square plywood spice rack into a
RSW> parabolic dish!!!:-)
RSW>P.S., if anyone doubts that one can be so cavalier with using the same
RSW>curve throughout the design, I can supply them with a proof that it will
RSW>work. It is elegant, and I first derived it myself and then have seen it in
RSW>a couple solar energy books! One simply uses less of the curve, and in
RSW>ANY direction at any radius across the dish, as long as it is a symmetrical
RSW>piece of the same curve about the apex, or point of the parabolic shape.
It took a little while for this image to soak in, but....
WOW! What a simple way to make a dish! Just "egg carton" the same
curve. At first I thought that a plane parallel with the center of the
paraboloid would have a narrower ratio. but it doesn't. just the same
curve with the focus moved up.
Now that is an elegant solution for constructing. Just add one more
thing, though. Given the frequency of the satellite's transmitter and
your desired focal length, it is easy to calculate the maximum allowable
divergence from a perfect paraboloid caused by the straight lines
between slats and determine the maximum interslat spacing.
Did you do that, too?
- Robert -
* OLX 2.1 TD * Sometimes the answer to your prayer is "no".
Robert Bailey
forms the shape of a parabola.
******************************************************************************
* I DEMAND THAT I AM BROOMFONDLE!
******************************************************************************
Richard Steven Walz
John Lundgren <jlun...@news.kn.PacBell.COM> wrote:
>Could you define distance to flat?
>
>'Scuse my ignorance.
If you're responding to my longwindedness on this subject, the distance to
"flat" is the elevation of a specific ring of the rotated paraboloid above
a plane that its apex sits on, above that plane.
-Steve Walz rst...@armory.com
David Alan Forsyth
>Subject: Re: Re: help parabolic reflectors
>From: eug...@cnet577.cts.com (Robert Bailey)
>Date: Sun, 10 Jul 94 23:24:33 PST
No it doesn't, that shape has some other name and also is defined by a
simple mathemetic function but I cannot remember now cos I did it in first
year math in 1987, since when I have slept and forgotten (-:
To construct a parabola you can draw two lines at some angle to each other,
say 90 degrees. Now measure equal spaces along each one starting at the
place that they cross. Number those tics from the cross point. Say you have
them numbered 1 to 10.
Now join #10 on one to #1 on the other
#9 to #2
etc
the curve delineated but the joining lines outline a parabola. This looks
like one of those strings-between-nails-on-a-plank artworks.
I prefer to define specific endpoints and y intercept on a cartesian plane
and using some linear multiple equation math calculate the equation for the
desired curve. Now you can generate the curve to any accuracy you desire
with a calculator (PC+BASIC=OK) and measuring device. I'm not good at this
math but get it done eventually <-:
Any questions and I'll delve into storage for my math text book <-:
David Forsyth da...@iwr.ru.ac.za
Institute for Water Research Rhodes Unversity South Africa
----------------------------------------------------------------------
An end user, when asked to respond with a 'Y' or an 'N', invariably
presses '8'.
Karen Hooten
Richard Steven Walz
I certainly don't know off the top of my head, the satellite freq's, but
it's gotta be a lot bigger than the inaccuracy of any dish with a square
support mesh size of say, 8" by 8"! It at least apporximates a sphere, and
that IS what they use commercially! I was just being all purpose. You could
snug up the surface from the bottom with "squares" of mylar or place a
radila form over each part of the surface and pull the segments taut. That
should get you better than 1/10th wave!
-Steve Walz rst...@armory.com
P.S, thanks for the accolades!
Eric de Paauw
>A string held at two points and allowed to sag under the weight of gravity
>forms the shape of a parabola.
No it doesn't. It forms a hyperbolic cosine or somesuch, but not a parabola.
Eric
Paul Kennedy
Are you sure? Seems like back in my rusty memory this actually forms a COSH
curve. When I get 5mins I'll try to excercise the grey cells and check, unless
someone toasts me before that.
+-------------------------------------------------------------------------+
| Dr Paul Kennedy - Paul.z.h.k....@zhflur.ubs.ubs.ch ? |
| Union Bank of Switzerland, ~~~ |
| Bahnhofstrasse 45, 8021 Zurich, Switzerland ( . . ) |
+------------------------------------------------------------ooO-(_)-Ooo--+
Michael Covington
>forms the shape of a parabola.
No, it forms a catenary -- isn't that different from a parabola?
>******************************************************************************
>* I DEMAND THAT I AM BROOMFONDLE!
>******************************************************************************
Huh?
--
< Michael A. Covington, Assc Rsch Scientist, Artificial Intelligence Center >
< The University of Georgia, Athens, GA 30602-7415 USA mcov...@ai.uga.edu >
< Unless specifically indicated, I am not speaking for the University. > <><
For information about any U.Ga. graduate program, email gra...@uga.cc.uga.edu.
Paul Kennedy
>In article <94070906...@engineers.com>,
>Robert Macy <rober...@engineers.com> wrote:
>>
>>RSW>Robert Macy <rober...@engineer.uu.holonet.net> wrote:
>>
[ stuff deleted ]
>>Now that is an elegant solution for constructing. Just add one more
>>thing, though. Given the frequency of the satellite's transmitter and
>>your desired focal length, it is easy to calculate the maximum allowable
>>divergence from a perfect paraboloid caused by the straight lines
>>between slats and determine the maximum interslat spacing.
>>
>>Did you do that, too?
>> - Robert -
>------------------------------------------------
>I certainly don't know off the top of my head, the satellite freq's, but
>it's gotta be a lot bigger than the inaccuracy of any dish with a square
>support mesh size of say, 8" by 8"! It at least apporximates a sphere, and
>that IS what they use commercially! I was just being all purpose. You could
>snug up the surface from the bottom with "squares" of mylar or place a
>radila form over each part of the surface and pull the segments taut. That
>should get you better than 1/10th wave!
>-Steve Walz rst...@armory.com
>P.S, thanks for the accolades!
>
I seem to remember most satellites operate around the 12GHz band, or a
wavelength of about 2.5cm / 1.0 inches. If my memory serves me right,
then you probably could get to this accuracy with the above scheme, but
you're going to have to take a bit of care to get to 1/10th wavelength.
Lance Bresee
>In article 0r...@cnet577.cts.com, eug...@cnet577.cts.com (Robert Bailey) writes:
>>A string held at two points and allowed to sag under the weight of gravity
>>forms the shape of a parabola.
>>* I DEMAND THAT I AM BROOMFONDLE!
>>******************************************************************************
>
>curve. When I get 5mins I'll try to excercise the grey cells and check, unless
>someone toasts me before that.
>
I tried to remember the definition of the parabola myself to
post it...and couldn't for certain. I haven't got my reference
books handy, but here goes the old college try:
The parabola is the set of all points such that the distance
from the point to a fixed point, added to the distance from the
point to a fixed line, is constant.
Then, the parabola is the set of all points a such that
the length of La and the length of af satisfy
La + af = F where L is a fixed line, f is the focus, and
F is the focal length. L passes through the parabola at
one point x and is perpendicular to ax.
In the conic, the definition is the same, save that line L
becomes plane P.
To draw a cross-section of the parabola with a string, thake a string
that is as long as your desired focal length. Attach one end to a
line, and attach the other end to the focus. move the end which is
attached to the line a small distance, and then pull the string tight
at a third point so that the string is perpendicular to the line, and
mark that point. Proceed until you have many points, and connect them.
To make a parabolic dish, make many parabolas as above and connect them
as radi about a circle on a flat surface. Triangular sections can then
be attached to these ribs to make a reasonable aproximation of a
parabolic dish.
I am not an optician, but the optical guys here suggest to me
that it is quite impossible to make a perfect parabola, but that
with our cnc mill they are able to get very close.
There may well be other methods of making a parabolic conic, which
may in fact be simpler and easier to implement, and more accurate
as well. I may even have mis-remembered the definition of the
parabola...I do recal a conic defined as all points equidistant
from a fixed point and a line, but as I said, I do not have my
reference books handy and I just don't remember as well as I
should.
.
Bruce J. Bell
>A string held at two points and allowed to sag under the weight of gravity
>forms the shape of a parabola.
No, it isn't, it's a hyperbolic cosine -- (exp(x)+exp(-x))/2
proof:
consider a small section of cable:
variables: force vector T, components Tx, Ty
force vector G, components 0, -g
coordinates x, y
distance along cable L
cable density rho
tension vector T(x+dx)= T(L+dL)
dx
----------------/
| /
| /
| /
| /
| /
| /
dy | /
| / dL
| /
| / gravity force G * rho * dL
| / |
| / |
| / v
| /
|/
tension vector
-T(x)= -T(L)
vector force balance:
T(L+dL) - T(L) + G rho dL = 0
---> dT/dL + G rho = 0
components:
x: d(Tx)/dL = 0
---> Tx is constant tx
y: d(Ty)/dL = g rho
---> Ty(L) = g rho L
coordinates:
x: dx/dL = Tx/|T|
y: dy/dL = Ty/|T|
---> dy/dx = Ty/Tx = (g rho/tx) L
[ let (g rho/tx) = 1/K, with K having dimensions of length ]
---> dy/dx = L/K
L: dL = sqrt(dx^2 + dy^2)
---> dL/dx = sqrt( 1 + (dy/dx)^2 )
---> (dL/dx)^2 = 1 + (dy/dx)^2 = 1 + (L/K)^2
little hyperbolic trig reminder:
sinh(x)== (exp(x)-exp(-x))/2
cosh(x)== (exp(x)+exp(-x))/2
sinh'(x) = cosh(x), cosh'(x)= sinh(x)
cosh^2(x) = 1 + sinh^2(x)
so, L = K sinh(x/K) solves the equation:
(dL/dx)^2 = K^2 cosh^2(x/K)/K^2 = cosh^2(x/K)
1 + (L/K)^2 = 1 + (K sinh(x/K) /K)^2 = 1 + sinh^2(x/K) = cosh^2(x/K)
*** final solution ***
dy/dx = L/K = sinh(x/K)
---> y(x)= K cosh(x/K) QED
(where K= tx/(g rho)
Whee, that was fun...
Bruce
--
From pages in a book and pictures on a screen
We make ourselves like clay from someone else's dream
Mike McCarty
Michael Covington <mcov...@aisun1.ai.uga.edu> wrote:
)In article <eugen...@cnet577.cts.com> eug...@cnet577.cts.com (Robert Bailey) writes:
)>A string held at two points and allowed to sag under the weight of gravity
)>forms the shape of a parabola.
)
)No, it forms a catenary -- isn't that different from a parabola?
Yes, it is different. It is the shape taken by a flexible cable which is
uniformly loaded along its length. Telephone cables are examples.
The parablola is the shape taken by a flexible cable which is uniformly
loaded along the x axis. Suppport cables for suspension bridges (such as
the Golden Gate bridge in San Francisco) are examples.
Mike
----
char *p="char *p=%c%s%c;main(){printf(p,34,p,34);}";main(){printf(p,34,p,34);}
Clifton T. Sharp
>forms the shape of a parabola.
No, it has the shape of a catenary.
--
Optimists say, "The glass is half full."
Cliff Sharp Pessimists say, "It's half empty."
WA9PDM We realists say, "Before I decide,
cli...@indep1.chi.il.us tell me what's in the glass."
Richard Steven Walz
A hanging flexible uniform string rope or chain makes a catenary.
And the string thingy is just an approximation of a hyperbola!!! And not a
very useful one for a 12' diameter! This would work WORSE than a simple
circular shape!
-Steve Walz rst...@armory.com
Richard Steven Walz
Paul Kennedy <zh...@zh014.ubs.ubs.ch> wrote:
>In article 0r...@cnet577.cts.com, eug...@cnet577.cts.com (Robert Bailey) writes:
>>A string held at two points and allowed to sag under the weight of gravity
>>forms the shape of a parabola.
>>******************************************************************************
>>* I DEMAND THAT I AM BROOMFONDLE!
>>******************************************************************************
>
>Are you sure? Seems like back in my rusty memory this actually forms a COSH
>curve. When I get 5mins I'll try to excercise the grey cells and check, unless
>someone toasts me before that.
Try a catenary, Dr. Paul.
-Steve Walz
Paul Kennedy
>eug...@cnet577.cts.com (Robert Bailey) writes:
>
>>A string held at two points and allowed to sag under the weight of gravity
>>forms the shape of a parabola.
>
>
> proof:
[ proof deleted ]
>Bruce
>--
In article 2...@armory.com, rst...@armory.com (Richard Steven Walz) writes:
> In article <1994Jul11.1...@zh014.ubs.ubs.ch>,
> Paul Kennedy <zh...@zh014.ubs.ubs.ch> wrote:
> > In article 0r...@cnet577.cts.com, eug...@cnet577.cts.com (Robert Bailey) writes:
> > > A string held at two points and allowed to sag under the weight
> > > of gravity forms the shape of a parabola.
> >
> > Are you sure? Seems like back in my rusty memory this actually forms
> > a COSH curve. When I get 5mins I'll try to excercise the grey cells
> > and check, unless someone toasts me before that.
> > Dr Paul Kennedy - Paul.z.h.k....@zhflur.ubs.ubs.ch
> ---------------------------
> Try a catenary, Dr. Paul.
> -Steve Walz
>
Ok, so what's a catenary, and if it's different from a cosh() then where's
the hole in the proof posted by Bruce (br...@frappe.ugcs.caltech.edu).
I had a shot at the same proof and arrived at the same result via a
slightly different route.
Genuinely curious.
+-------------------------------------------------------------------------+
| Dr Paul Kennedy - Paul.z.h.k....@zhflur.ubs.ubs.ch ? |
Bruce J. Bell
[...]
>In article 2...@armory.com, rst...@armory.com (Richard Steven Walz) writes:
>> In article <1994Jul11.1...@zh014.ubs.ubs.ch>,
>> Paul Kennedy <zh...@zh014.ubs.ubs.ch> wrote:
>> > In article 0r...@cnet577.cts.com, eug...@cnet577.cts.com (Robert Bailey) writes:
>> > > A string held at two points and allowed to sag under the weight
>> > > of gravity forms the shape of a parabola.
>> >
>> > Are you sure? Seems like back in my rusty memory this actually forms
>> > a COSH curve. When I get 5mins I'll try to excercise the grey cells
>> > and check, unless someone toasts me before that.
>> > Dr Paul Kennedy - Paul.z.h.k....@zhflur.ubs.ubs.ch
>> ---------------------------
>> Try a catenary, Dr. Paul.
>> -Steve Walz
>>
>Ok, so what's a catenary, and if it's different from a cosh() then where's
>the hole in the proof posted by Bruce (br...@frappe.ugcs.caltech.edu).
>I had a shot at the same proof and arrived at the same result via a
>slightly different route.
Hmm, let's see--
Webster sez:
>cat-e-nary \'kat-e-,ner-e^-, esp Brit ke-'te^--ne-re^-\ -nar-ies
>[NL catenaria, fr. L, fem. of catenarius of a chain, fr. catena]
>(1788)
>1: the curve assumed by a cord of uniform density and cross section
> that is perfectly flexible but not capable of being stretched and
> that hangs freely from two fixed points
>2: something in the form of a catenary
>-- catenary adj
So the solution is a catenary, by definition :-)
(I still suspect it's also a cosh, though...)
Bruce
PS: my favorite ending to this problem is the following poem (whose source
I don't remember:
"Therefore, no force, however great,
can pull a cord, however fine,
into a horizontal line
that shall be absolutely straight."
Paul Kennedy
>zh...@zh014.ubs.ubs.ch (Paul Kennedy) writes:
>
>[...]
>
>>In article 2...@armory.com, rst...@armory.com (Richard Steven Walz) writes:
>>> Try a catenary, Dr. Paul.
>>> -Steve Walz
>>>
>
>>Ok, so what's a catenary, and if it's different from a cosh() then where's
>>the hole in the proof posted by Bruce (br...@frappe.ugcs.caltech.edu).
>
>Webster sez:
>
>>cat-e-nary \'kat-e-,ner-e^-, esp Brit ke-'te^--ne-re^-\ -nar-ies
>>[NL catenaria, fr. L, fem. of catenarius of a chain, fr. catena]
>>(1788)
>>1: the curve assumed by a cord of uniform density and cross section
>> that is perfectly flexible but not capable of being stretched and
>> that hangs freely from two fixed points
>>2: something in the form of a catenary
>>-- catenary adj
>
>So the solution is a catenary, by definition :-)
>(I still suspect it's also a cosh, though...)
Right, now I see. The shape of the curve formed by a rope suspended at
it's ends is a catenary, where "catenary" is defined as that shape
which is assumed by a rope that is suspended from its ends.
And there's me saying dumb things like "it's a cosh()"; duh... boy do I
feel stupid now that I've had the right answer pointed out to me :-)
Robert Macy
RSW>I certainly don't know off the top of my head, the satellite freq's, but
RSW>it's gotta be a lot bigger than the inaccuracy of any dish with a square
RSW>support mesh size of say, 8" by 8"! It at least apporximates a sphere, and
RSW>that IS what they use commercially! I was just being all purpose. You could
RSW>snug up the surface from the bottom with "squares" of mylar or place a
RSW>radila form over each part of the surface and pull the segments taut. That
RSW>should get you better than 1/10th wave!
RSW>-Steve Walz rst...@armory.com
RSW>P.S, thanks for the accolades!
You're welcome.
Not sure, but I think the satellite's run around 4 GHz.
1/10th wavelength would then be 3/4 cm. or about 1/3 inch.
And even though this could be done precisely using y=f(x) compared to
y(i)=f(id) where i has integer values and d is the slat separation.
I think I'll do it graphically: Assume the worst error occurs at the
sharpest curve (possibly wrong) which occurs at the origin.
Assume a 12 ft diam dish with a 4 ft focus then y = x*x/4/4
If the slats were placed 8 inches apart it would take 9 plus the center
one on each side. The curve would be x*x/192 for x in inches
y (for x=0) = 0
y (for x=8) = 0.333 inches
For a straight line the max error wouuld be half that, or .17 inches,
not bad.
- Robert -
* OLX 2.1 TD * They gave him a transfusion in vain.
Robert Macy
PK>>that IS what they use commercially! I was just being all purpose. You could
PK>>snug up the surface from the bottom with "squares" of mylar or place a
PK>>radila form over each part of the surface and pull the segments taut. That
PK>>should get you better than 1/10th wave!
PK>>-Steve Walz rst...@armory.com
PK>>P.S, thanks for the accolades!
PK>>
PK>I seem to remember most satellites operate around the 12GHz band, or a
PK>wavelength of about 2.5cm / 1.0 inches. If my memory serves me right,
PK>then you probably could get to this accuracy with the above scheme, but
PK>you're going to have to take a bit of care to get to 1/10th wavelength.
Sorry to work from memory and not be able to check, but I remember 4 GHz
for the old Satcom satellites, and at that frequency you need 10 to 12
ft to get a good aperture.
I remember that the Japanese launched some satellites that used 12GHz
which allowed the receivers to go down to 3ft in diameter for the same
gain.
Parbly some microwave guy will jump in here and embarrass me.
- Robert -
* OLX 2.1 TD * An intellectual is someone whose mind watches itself.
Robert Macy
BJB>>A string held at two points and allowed to sag under the weight of gravity
BJB>>forms the shape of a parabola.
BJB>No, it isn't, it's a hyperbolic cosine -- (exp(x)+exp(-x))/2
text deleted
BJB>*** final solution ***
BJB> dy/dx = L/K = sinh(x/K)
BJB>---> y(x)= K cosh(x/K) QED
BJB>(where K= tx/(g rho)
BJB>Whee, that was fun...
That did look fun, but my physics book always said it was a catenary
curve. Is that the same shape?
- Robert -
* OLX 2.1 TD * You don't have to explain something you never said.
Christopher J Burian
y = (tension / unit_load) * (cosh(x * unit_load / tension) - 1)
So everybody's right!
Chris
Robert Bailey
********************************************
* A whale is not a fish. It is an insect. *
********************************************
Chris Abbott
No this goesent, especially since gravity along the string is not constant
in the real world.
--
God Bless,
Chris Abbott
=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
C.M. Hicks
>> A string held at two points and allowed to sag under the weight of gravity
>> forms the shape of a parabola.
>> ******************************************************************************
>> * I DEMAND THAT I AM BROOMFONDLE!
>> ******************************************************************************
>No this goesent, especially since gravity along the string is not constant
>in the real world.
Variations in gravity aside, the actual shape is a hyperbolic function.
However, for the shallow curves used for typical reflectors the errors
are small and I suspect that a hanging chain or flexible cord would
be an acceptable pattern.
Christopher
--
=====================================================
Christopher Hicks http://www.eng.cam.ac.uk/~cmh
c...@eng.cam.ac.uk Voice: (+44) 223 332767
=====================================================
Donald J. Miller
Consider a plane surface *A*, the focus *B*, and a string with segment
*C* ALWAYS perpendicular to surface *A*:
*A*-------------------------------------------------------------------
:
:
*B* :
. :
. : *C*
. :
. :
. :
. :
. :
. :
. :
. *P*
As long as the string has a constant length, is kept under tension, and
chord *C* is perpendicular to *A*, The locus of points *P* lies on a
parabola. If one end of a string is tied to the focus, the other constrained
to move about on plane *A*, *C* kept perpendicular to *A*, then the bend
point in the string will move about on a parabola.
Happy trails,
--
-------------------------------------------------
Don Miller Electronic System Products
dmi...@crl.com
-------------------------------------------------
Robert Macy
PK>Ok, so what's a catenary, and if it's different from a cosh() then where's
PK>the hole in the proof posted by Bruce (br...@frappe.ugcs.caltech.edu).
PK>I had a shot at the same proof and arrived at the same result via a
PK>slightly different route.
From ITT Reference Handbook for Radio Engineers, 6th edition, 2nd
printing, 1977, pg 48-18:
Catenary curve:
H = W * L*L /8 /S
S = W * L*L /8 /H = sqrt[ (Lc - L) * 3 * L /8 ]
or Lc = L + 8 * S*S /3 /L
where L=length of span in feet, Lc=length of cable in feet, S=sag of
cable at center of span in feet, H=tension in cable at center of span in
pounds=horizontal component of the tension at any point, and W=weight of
cable in pounds per lineal foot.
Intermediate points at a distance x from the center of the span:
Sx = S * ( 1 - 4 * X*X /L /L )
Does look like a parabola.
- Robert -
* OLX 2.1 TD * 10.0 times 0.1 is hardly ever 1.0
Subas
the feedhorn came with a sclar ring that is bolt to the mounting bracket
of the dish at the focal point of the dish and the feedhorn is then inserted
into the sclar ring.i would like to know what is the pupose of the sclar ring
and the method of aligning the satelite dish.my country latitude and longtude
are N 03 deg 07.8 min and E 101 deg 33.1 min.there were no manuals on the
feedhorn and this is the first time i am installing the dish.
thanking you in advance.
yours trully
subas
su...@intnet.pc.my
David Alan Forsyth
>From: rst...@armory.com (Richard Steven Walz)
>Subject: Re: Re: help parabolic reflectors
That's ok Steve, I don't smoke, drink or do drugs and never have... however
I DO have long hair and play a guitar (-:
I'm a programmer not a mathematician (math and I are definitely not friends)
and I don't remember things I don't like. While at school (circa 1983) a
friend made a 'parabolic' fiberglass dish using this method. It was about
80cm diameter and used for a microphone reflector - it did work very well
indeed even if it was +-hyperbolic, you could hear some amazing stuff with
it. But then I used a 4" folded-horn car alarm speaker with a mike in the
drivers place and also heard amazing stuff.... maybe not conclusive.
>
>A hanging flexible uniform string rope or chain makes a catenary.
>
>And the string thingy is just an approximation of a hyperbola!!! And not a
>very useful one for a 12' diameter! This would work WORSE than a simple
>circular shape!
>-Steve Walz rst...@armory.com
I stand humbly corrected and blame it all on the bloke at school who always
disrupted math class so that little math got done and I fell behind (-:
However, the formula method will work -
I've seen a dish made by cutting (say six) planks to the parabolic curve
desired along one edge (shallow dish this) and then joining them at the
centre at (sixty) degrees and bridging the spaces with wedges of netting
wire. Ends up looking like a potplant stand made of planks on edge. Not
very accurrate focus I spoze but it worked for satelite TV as I recall. It
did have more segments though I can't rem exactly, maybe ten or twelve.
Cheers
David Forsyth da...@iwr.ru.ac.za
Institute for Water Research Rhodes Unversity South Africa
David Alan Forsyth
>From: br...@gluttony.ugcs.caltech.edu (Bruce J. Bell)
>Subject: Re: help parabolic reflectors
>Date: 12 Jul 1994 09:22:53 GMT
[much overt deletion by the Finger Trouble Brigade (thems wot corzez spelin
ehruz]
>Bruce
>
>PS: my favorite ending to this problem is the following poem (whose source
> I don't remember:
>
>"Therefore, no force, however great,
> can pull a cord, however fine,
> into a horizontal line
> that shall be absolutely straight."
Tell that to my fishing line just before it breaks (-:
Or my guitar's strings just before they break ((-;
Richard Steven Walz
Well, yes, a catenary is a function based on cosh(x) such that it defines a
line which connects two points in such a manner that when their curve
segment is rotated about one of them, it subtends a surface of minimum
area, and it comes out to be something of the form
catenary(x) = d cosh [(x - c)/d], where c and d are constants to make that
true for the two points. It also works out to be the curve of least strain
for a hanging flexible cord suspended from two points with isotropic bulk
modulus. Such as a hanging chain. Interestingly enough, it works out to be
worse than a circle for approximation of a parabola! I'm glad we seem then
to agree, I would have guessed it from Hamiltonians though, now that I
think about it. Comes right from Euler.
-Steve Walz rst...@armory.com
Richard Steven Walz
You shouldn't, Dr. Paul. A catenary IS a cosh function of specific
curvature constants to intersect two points from which a chain would hang
in that curve!!!
-Steve Walz rst...@armory.com
Richard Steven Walz
Yes, the error could be greatest at the apex, or center. Out farther it
would be less problematic. And remember that the inner four 8" squares are
probably shaded by the receiver head!!!
-Steve Walz rst...@armory.com
Richard Steven Walz
>BJB>>forms the shape of a parabola.
>
>BJB>No, it isn't, it's a hyperbolic cosine -- (exp(x)+exp(-x))/2
>
>text deleted
>
>BJB>*** final solution ***
>BJB> dy/dx = L/K = sinh(x/K)
>BJB>---> y(x)= K cosh(x/K) QED
>BJB>(where K= tx/(g rho)
>
>BJB>Whee, that was fun...
>
>That did look fun, but my physics book always said it was a catenary
>curve. Is that the same shape?
> - Robert -
Yes, but they often include an x displacement difference for completeness,
vis: y(x) = K cosh [(x-c)/K]
And YES, that IS a catenary! And it's a WORSE approximation of a parabola
than a circle is!!! And a parabola does the best job of focusing parallel
rays.
-Steve Walz rst...@armory.com
Paul Kennedy
>In article <1994Jul12.1...@zh014.ubs.ubs.ch>,
>Paul Kennedy <zh...@zh014.ubs.ubs.ch> wrote:
>> [ tons of quotes deleted ]
>>Right, now I see. The shape of the curve formed by a rope suspended at
>>it's ends is a catenary, where "catenary" is defined as that shape
>>which is assumed by a rope that is suspended from its ends.
>>
>>And there's me saying dumb things like "it's a cosh()"; duh... boy do I
>>feel stupid now that I've had the right answer pointed out to me :-)
^^^
SMILEY
>>| Dr Paul Kennedy - Paul.z.h.k....@zhflur.ubs.ubs.ch ? |
>--------------------------------
>You shouldn't, Dr. Paul. A catenary IS a cosh function of specific
>curvature constants to intersect two points from which a chain would hang
>in that curve!!!
>-Steve Walz rst...@armory.com
>
Still having a bit of trouble with the humour thing Steve?
+-------------------------------------------------------------------------+
| Dr Paul Kennedy - Paul.z.h.k....@zhflur.ubs.ubs.ch ? |
Richard Steven Walz
Paul Kennedy <zh...@zh014.ubs.ubs.ch> wrote:
>In article 6...@armory.com, rst...@armory.com (Richard Steven Walz) writes:
>>In article <1994Jul12.1...@zh014.ubs.ubs.ch>,
>>Paul Kennedy <zh...@zh014.ubs.ubs.ch> wrote:
>
>>> [ tons of quotes deleted ]
>
>>>Right, now I see. The shape of the curve formed by a rope suspended at
>>>it's ends is a catenary, where "catenary" is defined as that shape
>>>which is assumed by a rope that is suspended from its ends.
>>>
>>>And there's me saying dumb things like "it's a cosh()"; duh... boy do I
>>>feel stupid now that I've had the right answer pointed out to me :-)
> ^^^
> SMILEY
>
>>>| Dr Paul Kennedy - Paul.z.h.k....@zhflur.ubs.ubs.ch ? |
>>--------------------------------
>>You shouldn't, Dr. Paul. A catenary IS a cosh function of specific
>>curvature constants to intersect two points from which a chain would hang
>>in that curve!!!
>>-Steve Walz rst...@armory.com
>>
>
>Still having a bit of trouble with the humour thing Steve?
>| Dr Paul Kennedy - Paul.z.h.k....@zhflur.ubs.ubs.ch ? |
(Sigh!) Just not used to humorous mathematicians, Paul. {[ ;->]}
-Steve
John Lundgren
Paul Kennedy (zh...@zh014.ubs.ubs.ch) wrote:
: [ proof deleted ]
: >Bruce
: >--
: Genuinely curious.
Why has it lamely slipped by in all these posts that the dish at Arecibo,
Puerto Rico is just a bunch of cables strung from the edges of a
depression in the mountains...
I think they use some kind of weight arrangement to help it conform more
to a parabola. And the steerable feed horn assembly is made to
compensate somewhat. The dish was fairly low frequency, something in UHF
or L band. But later they put plates over the surface to reflect shorter
wavelengths.
It seems strange to me that with a cost of half billion dollars, the
company that built the Hubble Telescope mirror (I think it was Perkin
Elmer, correct me if I'm wrong) would have been able to get the thing
shaped into a parabola. And an accurate one at that.
Many of the big satellite dishes at the head ends of the cable TV
companies have the dish chopped off at the top and the bottom, so that it
looks like an old round edged TV set.
I think that half the parabolas in the world were at the O.J. Simpson
house and the courthouse!!! What a waste.
--
James Scott
I seem to remember that if you keep the diameter of the dish small
with respect to the "center of curvature" you can use the inside of
a sphere as a good reflector. It is a lot easier to make a sphere
than a parabola and Optic systems actually use sphereical lenses
and mirrors. The focal length is 1/2 the "center of curvature" and
the diameter of the reflector should be small like 1/10 of the
"center of curvature".
This information may not work well with satelite dishes where most
people want conpact antennas. But it is an easy way to approximate
a parabola.
AGAIN: This only works if the reflecting area is only a small
part of the sphere section.
Thats All,
James
P.S. BEST WAY TO REACH ME: ja...@sdicad1.sps.mot.com
-----------------------------------------------------------
this is one lousy sig.
-----------------------------------------------------------
Syed Zaeem Hosain
>
>BJB>>A string held at two points and allowed to sag under the weight of gravity
>BJB>>forms the shape of a parabola.
>
>BJB>No, it isn't, it's a hyperbolic cosine -- (exp(x)+exp(-x))/2
[fun stuff deleted]
>That did look fun, but my physics book always said it was a catenary
>curve. Is that the same shape?
Yes. A catenary == hyperbolic cosine == cosh.
Z
--
-------------------------------------------------------------------------
| Syed Zaeem Hosain P. O. Box 610097 (408) 441-7021 |
| Z Consulting Group San Jose, CA 95161 s...@zcon.com |
-------------------------------------------------------------------------
Peter Cupit
idea of mine.
I asked about and was told that a sphere is pretty close to a parabola as
long as the focal length is long. Does anyone have figures on this, my
maths isn't good enough for me to work it out.
A spherical shape is a lot easier to make:
Idea 1: Make some sort of wooden frame in the shape of a pyramid with an
arm pivoted at the apex. The end of the arm would then trace out a shallow
portion of a shere. Underneath the frame some sort of mould (of cement
maybe) could be build using the arm to shape it. Then a fibreglass dish
could be made in the mould. It could be pretty rough since some sort of
motor with a polishing disk could be attached to the arm to put a good
surface on the disk. I also thought of putting a disk of metal on the
finished mould and heating it till it was soft and then dumping a great
load of sand on it. Then polishing/smoothing afterwards.
Idea 2: Using the motor an back axel of a wrecked car to make a large metal
spinning lathe. There would be an arm constrained to move in a circle used
to shape the former.
Idea 3: Find out if any car windscreens are exact spherical shapes (my
sisters Gemini windscreen appears to be but its hard to measure, I have
often noticed a failry good magnified image of passengers in a car
windscreen so I have hope). Windscreens are probably available cheap from
wreckers. Anyway, the glass could be silvered at a mirror repair place or
the convex surface could be covered with that plastic that is used to
block glare on windows and is reflective on one side. Easy.
Does any of this sound ok? It all depends on how close a sphere is to a
parabola, ie at what focal lenght does the difference not matter much.
Just some ideas,
Peter Cupit.
--
Peter David Cupit.
qp...@werple.apana.org.au
Richard Steven Walz
John Lundgren <jlun...@news.kn.PacBell.COM> wrote:
>
>Paul Kennedy (zh...@zh014.ubs.ubs.ch) wrote:
>Puerto Rico is just a bunch of cables strung from the edges of a
>depression in the mountains...
>
>I think they use some kind of weight arrangement to help it conform more
>to a parabola. And the steerable feed horn assembly is made to
>compensate somewhat. The dish was fairly low frequency, something in UHF
>or L band. But later they put plates over the surface to reflect shorter
>wavelengths.
>
>It seems strange to me that with a cost of half billion dollars, the
>company that built the Hubble Telescope mirror (I think it was Perkin
>Elmer, correct me if I'm wrong) would have been able to get the thing
>shaped into a parabola. And an accurate one at that.
>
>Many of the big satellite dishes at the head ends of the cable TV
>companies have the dish chopped off at the top and the bottom, so that it
>looks like an old round edged TV set.
>
>I think that half the parabolas in the world were at the O.J. Simpson
>house and the courthouse!!! What a waste.
Hubble was a parabola, just the wrong focal length! 1.4 mill to fix on
earth, 1.6 bill in orbit! They should be fined till it's paid off!
What's truly sick was that the money for NASA to test it was cut from the
Hubble Budget!!! They didn't think it needed a test if the vendor thought
it was right!!!:) This kind of shit shouldn't be laid at NASA's door. It
should be hauled in in big buckets and shoveled onto congresspuds and
senators! And the reason for the first pad fire that killed the Apollo
astronauts was failure to wish to reinforce the Apollo capsule to take full
sealevel pressure in space, so they tried to get off with high oxy and low
pressure, which caused the fire, which they had not allocated the funds for
an easily opened emergency hatch!
And the whittling away of the shuttle budget and the increasing of the
expectations of the Challenger were what drove the vendors to sign off on
it again, and they all died at 45,000 feet. (maybe not till they hit the
water, thanks!)
All the garbage that NASA's had to put up with at about 1 to 2% of the
national budget at it's heyday has been from non-scientists screwing around
with its budget!! Fuck managers!! Maybe the Japanese could teach our
executives how to commit sepucu, one senator and one manager for each
astronaut!!! Let's make the game more fair!
-Steve Walz rst...@armory.com
Richard Steven Walz
The focal direction is changed by the receiver assembly, but the parabola
has to be that much more accurate to make that arrangement work for radio
telescopy. They use a continuous weight change along the cables to attain
parabolicity, it was in an old National Geographic.
-Steve Walz rst...@armory.com
Tom Randolph
In article <306o1h$f...@ohlone.kn.PacBell.COM>, jlun...@news.kn.PacBell.COM (John Lundgren) writes...
>Why has it lamely slipped by in all these posts that the dish at Arecibo,
>Puerto Rico is just a bunch of cables strung from the edges of a
>depression in the mountains...
>
>I think they use some kind of weight arrangement to help it conform more
>to a parabola. And the steerable feed horn assembly is made to
>compensate somewhat. The dish was fairly low frequency, something in UHF
>or L band. But later they put plates over the surface to reflect shorter
>wavelengths.
Nope.
The Arecibo dish is spherical. If it were parabolic, it would indeed give the
astronomers a nicely focused image - of exactly one point, straight up. Being
spherical, they can aim the feed in whatever direction and get an image,
somewhat fuzzy, of the appropriate area of the sky.
For the uninformed... Arecibo is the world's largest radio telescope, a 1000
foot diameter dish. It is a simple, non-steerable dish resting in a natural
bowl in the hills of Puerto Rico, pointed more or less straight up, and aimed
as above.
-Tom R. N1OOQ rand...@est.enet.dec.com
Jarek Lis
: I have been thinking about making a parabolic dish for use in a solar energy
: idea of mine.
: Idea 1: Make some sort of wooden frame in the shape of a pyramid with an
: arm pivoted at the apex. The end of the arm would then trace out a shallow
: portion of a shere. Underneath the frame some sort of mould (of cement
: maybe) could be build using the arm to shape it. Then a fibreglass dish
: could be made in the mould. It could be pretty rough since some sort of
: motor with a polishing disk could be attached to the arm to put a good
: surface on the disk. I also thought of putting a disk of metal on the
: finished mould and heating it till it was soft and then dumping a great
: load of sand on it. Then polishing/smoothing afterwards.
With this system you can made parabola. Few minutes with ruler and calculator
give you parabola line on the arm. Some cutting, and you have parabola arm.
And to say the true, cutting the parabola line is the easiest with this setup.
Idea 4:
get big beach ball, smear half of it with epoxy.
If this is just for solar energy - buy many small flat mirrors and mount
(glue or cement) them on parabolical construction.
John Lundgren
during the summer. He brought some surplus stuff home, and one of them
was a sperical 36 in. polished aluminum dish, with a focal length of 18
in, or f: .5. WOW! On a sunny day, that thing could slice a soup can in
two instantly, and a two-by-four just erupted in flame at the focal point.
It was awesome, but the little girl from next door walked in front of it
and it burned through her pants, OUCH. So even though it was spherical,
it did a respectable job of focusing the light. Way too hot for a weenie
roast!
--
=====================================================================
| John Lundgren - Elec Tech - Info Tech Svcs | Standard |
| Rancho Santiago Community College District | disclaim- |
| 17th St. at Bristol \ Santa Ana, CA 92706 | ers apply.|
| jlun...@pop.rancho.cc.ca.us\jlu...@eis.calstate.edu | |
=====================================================================
Richard Steven Walz
James Scott <Ja...@sdascpc.sps.mot.com> wrote:
>Hello All,
>I seem to remember that if you keep the diameter of the dish small
>with respect to the "center of curvature" you can use the inside of
>a sphere as a good reflector. It is a lot easier to make a sphere
>than a parabola and Optic systems actually use sphereical lenses
>and mirrors. The focal length is 1/2 the "center of curvature" and
>the diameter of the reflector should be small like 1/10 of the
>"center of curvature".
>This information may not work well with satelite dishes where most
>people want conpact antennas. But it is an easy way to approximate
>a parabola.
>
>AGAIN: This only works if the reflecting area is only a small
>part of the sphere section.
>Thats All,
>James
>P.S. BEST WAY TO REACH ME: ja...@sdicad1.sps.mot.com
---------------------------------
diameter. A microwave dish is NOT something like that, as most people would
like to be able to mount a minimal focal support for their receiver on the
dish itself, without having to put it on a massive base! So actually, to
get the cleanest reception, you need a parabola, or at least something
damned close to a 10th or 20th of a wave, which are in the range of a
couple cm's wavelength, so that accuracy is a couple millimeters at the
outer, LARGER area of the dish! If you built a very shallow dish like a
cheap Newtonian reflecting telescope mirror which is long enough focus to
be spherical, then your receiver head might have to be 50 or 100 feet in
the air and be maintained there in focus!!! One hell of a long pole and 3
high tension cables which you might have to keep fiddling with to stay
focused, and no good way to figure out where the signal went when the wind
comes up and it all BENDS!!:) I haven't done the math for the difference
for spherical versus parabolic, but the equation of a circle-half concave
up would be y = R - sqrt ( R^2 - x^2) and a parabola y = x^2/4*f. But you
can simply use their difference equation as an estimator of the accuracy of
some spherical segment at a given radius from the center, (NOT the R radius
of the circle. And the R, radius of the the circle, is NOT the focus which
yields best results either, as you will wish to use a circle that is in
error negatively in height close in to the center and positively in error
farther out from the center, but weighted for the rings of area so that the
greatest area is in the closest phase to the theoretically perfect phase of
a true paraboloid surface, and so that the difference in phase is a minumum.
You can write up a program to simply iterate through the possible circle
radii for the one which has this feature of the lowest difference in Area
times Phase taken over the whole dish. Then you can decide whether this is
what you want or not. The figure of merit for each spherical radius will be
least at the one you'd want to use that way. But I still maintain that a
paraboloid which isn't going to be perfect anyway will be superior to the
spherical reflector, because construction defects for a surface will plague
both enough to improve your signal quality with the paraboloid.
-Steve Walz rst...@armory.com
Richard Steven Walz
>qp...@werple.apana.org.au
-------------------------------------------------------
For solar applications it does not matter much. The focal length would be
where you find it! About two radii of the spherical surface's curvature.
If you had wanted a VERY tight point of very hot light, then use a
parabola, however, but I don't know whether you want to cook weenies or
weld/braze metals or cook ceramics! Phase is not important like it is for
satellites, so feel free to use a circular form. I recommend you use an
earthen mold with a tripod and a test plumb. Then lay in sheet plastic.
Then lay in screen wire and sew it at points with cheap tempered wire.
Then apply your resin and then fiber cloth and more resin. When it has set,
and hard, then apply resin to the back with the screen wire. It will be
very rigid this way, but substantially less expensive than counting on the
strength of cloth not to deform like a clamshell and fold on you. I have
also heard of making an earthen mold with a convex surface. In that case
you have to cut a wooden gauge and spin it in a central pipe. Once you have
made a nice surface, it can be firmed up for manufacture with ferrocement,
using earth and sand and cement in a high cement slurry, like the famous
ferro-cement/ferro-concrete boat hulls! Then one can even create wire
reinforcement for dishes more easily as it is easier to get to with a
platform or just reach about on the edges and sew down the metal screening
with wire or even with spot welded pieces which have been curved on a form
and laid into place and either soldered or welded. Then one can use
fiberglass or simply apply a mesh of hexagonal sections or go completely
geodesic. In any case, the best mirror to lay on, for my money, if simply
aluminum foil with the shiny side to the light. It is over 97% efficient at
reflection. I think it is best glued on with a simple cement or glue that
will take weather but be easily refinished with more alumimum foil. Try
simple gun adhesives and an eXacto knife or such. Don't overlap any pieces
of foil. There will be some small wrinkles, which you simply glue down and
allow to form and then use the knife to cut them. The surface doesn't need
any sealant, unless you really want to be durable, and then try the
plastic sealant spray to prevent oxidation. It takes very little of it, you
can see it on the surface at an angle. It will make a bit of diffraction
and make a wet reflection. Enough of this for now.
-Steve Walz rst...@armory.com
Richard Steven Walz
Whichever, they still need weights to achieve that. A catenary is "worse"
than a circle in approximating a parabola. AND the amount of tension with
the weights to circularize it was less than to parabolize it. But remember
than the waves it have been receiving have been longer waves than most of
the television, and thus the accuracy is not as needed.
-Steve Walz
rst...@armory.com
Bart Rowlett
ASCII graphics etc but can give a tad of insight.
Assuming the cable has negligible resistance to bending and is only loaded
by it's own weight, the shape of the resulting curve will be a catenary
given by the equation:
y / c = cosh( x / a) where a and c are constants determined by
the weight of the cable per unit length,
the height of the supports, the tension
and the rectangular coordinate system
chosen.
Assuming the above except the cable is loaded with a constant weight
per unit distance in x, not in arclength like the catenary case, then
the resulting curve will be a parabola. This is the case where the
tension in the cable is constant everywhere and is approximated when the
weight of the cable is negligible compared to the load such as a suspension
bridge or a very taught cable where the tension is many times the total
cable weight. This condition is approximatly met at the bottom of a
catenary justifying the common parabolic approximation used in the
design of horizontal transmission line spans. If the transmission line
is going down a steep slope then the much more difficult catenary solutions
may be required.
Fairly subtle changes in the loading can cause the curve to look more
spherical, parabolic, catenary like or something else.
>>
>>Why has it lamely slipped by in all these posts that the dish at Arecibo,
>>Puerto Rico is just a bunch of cables strung from the edges of a
>>depression in the mountains...
>>
>>I think they use some kind of weight arrangement to help it conform more
>>to a parabola. And the steerable feed horn assembly is made to
>>compensate somewhat. The dish was fairly low frequency, something in UHF
>>or L band. But later they put plates over the surface to reflect shorter
>>wavelengths.
It's my understanding the reflector at Arecibo is very close to spherical
so it doesn't have an optical axis. A parabola would be better for looking
at the zenith but they need the ability to look at various declinations
and obviously can't easily steer the entire reflector. Therefore the
reflector is a spherical surface and the resulting spherical abberation
in the image is tolerated.
>>
>>It seems strange to me that with a cost of half billion dollars, the
>>company that built the Hubble Telescope mirror (I think it was Perkin
>>Elmer, correct me if I'm wrong) would have been able to get the thing
>>shaped into a parabola. And an accurate one at that.
The figuring of the Hubble mirror was very accurate but unfortunately the
tooling was setup for a slightly different than parabolic shape.
>>Many of the big satellite dishes at the head ends of the cable TV
>>companies have the dish chopped off at the top and the bottom, so that it
>>looks like an old round edged TV set.
Gain on axis pretty much is proportional to the total area. The shape
and feed determines the sidelobe and main beam shape.
>--------------------------
>Hubble was a parabola, just the wrong focal length! 1.4 mill to fix on
>earth, 1.6 bill in orbit!
No it isn't. The Hubble primary mirror was fabricated with 5 wavelengths of
spherical abberation, that is to say it was somewhere in between a parabola
and sphere, differing at the edges by less then 5 micrometers.
They should be fined till it's paid off!
Who? NASA bought off test procedures and tooling and even supervised the
inspections.
>What's truly sick was that the money for NASA to test it was cut from the
>Hubble Budget!!!
They didn't think it needed a test if the vendor thought >it was right!!!:)
The vendor wanted testing.
This kind of shit shouldn't be laid at NASA's door. It
>should be hauled in in big buckets and shoveled onto congresspuds and
>senators!
Are you suggesting NASA be abolished?
And the reason for the first pad fire that killed the Apollo
>astronauts was failure to wish to reinforce the Apollo capsule to take full
>sealevel pressure in space, so they tried to get off with high oxy and low
>pressure, which caused the fire, which they had not allocated the funds for
>an easily opened emergency hatch!
NASA had been repeatedly warned by the contractors that ground testing at
20 pounds per square inch absolute pressure of pure oxygen was extremely
hazardous and shouldn't be performed. They were also warned the inside
of the spacecraft shouldn't have been wallpapered in the new Velcro the
astronauts had fallen in love with.
The accident was predicted by the contractors several years before it
occurred.
>
>And the whittling away of the shuttle budget and the increasing of the
>expectations of the Challenger were what drove the vendors to sign off on
>it again, and they all died at 45,000 feet. (maybe not till they hit the
>water, thanks!)
The vendor was exonerated by the Packard Commission report. The components
met the design and production specifaction and NASA insisted the launch
occur outside of design conditions.
>
>All the garbage that NASA's had to put up with at about 1 to 2% of the
>national budget at it's heyday has been from non-scientists screwing around
>with its budget!! Fuck managers!!
No major disagreement...
Maybe the Japanese could teach our
>executives how to commit sepucu, one senator and one manager for each
>astronaut!!! Let's make the game more fair!
They would simply spend more money.
bart
Please email flames as I don't reliably read this group.
Mark Zenier
: Sure, BUT, that works for things which are very long focal length to
: diameter. A microwave dish is NOT something like that, as most people would
: like to be able to mount a minimal focal support for their receiver on the
: dish itself, without having to put it on a massive base!
: cheap Newtonian reflecting telescope mirror which is long enough focus to
: be spherical, then your receiver head might have to be 50 or 100 feet in
: the air and be maintained there in focus!!! One hell of a long pole and 3
: high tension cables which you might have to keep fiddling with to stay
: focused, and no good way to figure out where the signal went when the wind
: comes up and it all BENDS!!:)
Back in the early days of TVRO, they used sphericals. I dug out the 20
year old project plans to see how they did is. Turns out a spherical is
good for +/- 20 degrees off axis, so 1) they could get a bunch of satellites
by setting up a bunch of feedhorns on poles (one per satellite) and 2) they
could tilt the reflector off axis with the satellite above the axis and
the foci (sp?) below the axis, so that the poles were at a reasonable height.
Typical sizes were a 14 foot reflector and a 21 foot focal length.
Feedhorns needed a much narrower beamwidth than the normal today.
Mark Zenier mze...@netcom.com mze...@eskimo.com
Richard Steven Walz
John! (exasperation). Move the weenie to a point above or below the focus
and it will work just fine, you can control the radiation density that way!
-Steve Walz rst...@armory.com
Richard Steven Walz
>I'm not going to derive and solve the differential equation here using
>
>Fairly subtle changes in the loading can cause the curve to look more
>spherical, parabolic, catenary like or something else.
Sure.
-RSW
>It's my understanding the reflector at Arecibo is very close to spherical
>so it doesn't have an optical axis. A parabola would be better for looking
>at the zenith but they need the ability to look at various declinations
>and obviously can't easily steer the entire reflector. Therefore the
>reflector is a spherical surface and the resulting spherical abberation
>in the image is tolerated.
--------------------------------
Reflection off a parabola at an angle by parallel rays goes to a focus
which is parabolic. Do the numbers.
-RSW
>>>It seems strange to me that with a cost of half billion dollars, the
>>>company that built the Hubble Telescope mirror (I think it was Perkin
>>>Elmer, correct me if I'm wrong) would have been able to get the thing
>>>shaped into a parabola. And an accurate one at that.
>
>The figuring of the Hubble mirror was very accurate but unfortunately the
>tooling was setup for a slightly different than parabolic shape.
----------------------------
Ok. Whatever, they blew it! The American people should recover costs!
-RSW
>>>Many of the big satellite dishes at the head ends of the cable TV
>>>companies have the dish chopped off at the top and the bottom, so that it
>>>looks like an old round edged TV set.
>Gain on axis pretty much is proportional to the total area. The shape
>and feed determines the sidelobe and main beam shape.
----------------------------------------
If the surface is parabolic, all whittling off the edges is for is for
stowage or clearance, like on ships and network trucks!
-RSW
>>Hubble was a parabola, just the wrong focal length! 1.4 mill to fix on
>>earth, 1.6 bill in orbit!
>
>No it isn't. The Hubble primary mirror was fabricated with 5 wavelengths of
>spherical abberation, that is to say it was somewhere in between a parabola
>and sphere, differing at the edges by less then 5 micrometers.
---------------------------------
Ok. Still, they blew it at the factory!! If they had to eat that, they
would have tested the thing!
-RSW
>They should be fined till it's paid off!
>
>Who? NASA bought off test procedures and tooling and even supervised the
>inspections.
---------------------------------
I had an article that incidated that the factory DID want to test it, and
that NASA's funding for that was cut, specifically for testing Hubble's
mirror!!!! Congress needs this taken out of their pay cut till it's paid
off! Or out of their pension fund or health insurance!
-RSW
>>What's truly sick was that the money for NASA to test it was cut from the
>>Hubble Budget!!!
>
>They didn't think it needed a test if the vendor thought >it was right!!!:)
>The vendor wanted testing.
--------------------------------
Sounds like we agree.
-RSW
>This kind of shit shouldn't be laid at NASA's door. It
>>should be hauled in in big buckets and shoveled onto congresspuds and
>>senators!
>
>Are you suggesting NASA be abolished?
--------------------------------
Heavens no!!! Where would you get an idea like that. I know that NASA
bashing seems to be an American pasttime, but all I think can redeem this
species is manned and unmanned space travel, each where appropriate,
remembering that if you want your children to have values, that they have
to have a future that looks valuable!!! Just making money at a schlep job
doesn't make it!!
-RSW
>And the reason for the first pad fire that killed the Apollo
>>astronauts was failure to wish to reinforce the Apollo capsule to take full
>>sealevel pressure in space, so they tried to get off with high oxy and low
>>pressure, which caused the fire, which they had not allocated the funds for
>>an easily opened emergency hatch!
>
>NASA had been repeatedly warned by the contractors that ground testing at
>20 pounds per square inch absolute pressure of pure oxygen was extremely
>hazardous and shouldn't be performed. They were also warned the inside
>of the spacecraft shouldn't have been wallpapered in the new Velcro the
>astronauts had fallen in love with.
>
>The accident was predicted by the contractors several years before it
>occurred.
---------------------------------
I don't doubt it. It sounded corrosive to me! And I was only 17!
-RSW
>>And the whittling away of the shuttle budget and the increasing of the
>>expectations of the Challenger were what drove the vendors to sign off on
>>it again, and they all died at 45,000 feet. (maybe not till they hit the
>>water, thanks!)
>
>The vendor was exonerated by the Packard Commission report. The components
>met the design and production specifaction and NASA insisted the launch
>occur outside of design conditions.
--------------------------------------
I agree, but the whistle blowers at Morton-Thiokol weren't listened to by
higher ups, and THEY are the ones who signed off on it under NASA and
government pressure! NASA has always been the one pulled both ways by the
whistle blowers and the congress budget committee and the presidency!!
If we let NASA run it and just TELL us what money was needed, since they
can't very well spend it on anything else, we'd probably have decent and
advanced space travel by now!!! We could have pushed the first skylab back
up with an Agena orbital naneuvering unit for pennies a person, and they
wouldn't do it!!! They even had them laying around!!! We could have built
on to that station and even fixed it! We could have had a series of large
scale intrasystem exploratory ships by now, built in orbit!! What idiots
don't realize is that the NASA budget is less than 2% of the national
budget!!! Between military goof-ups and a means test for social security
and medicare, we could have paid for 50 space programs by now!!! But the
rich would rather have us pay them!!!! The rich don't care about the next
generation, as a rule.
-RSW
>>All the garbage that NASA's had to put up with at about 1 to 2% of the
>>national budget at it's heyday has been from non-scientists screwing around
>>with its budget!! Fuck managers!!
>
>No major disagreement...
>
>Maybe the Japanese could teach our
>>executives how to commit sepucu, one senator and one manager for each
>>astronaut!!! Let's make the game more fair!
>
>They would simply spend more money.
>ba...@wb6hqk.ampr.org
>Please email flames as I don't reliably read this group.
---------------------------
They're not flames, but I'll Cc: it to you in the article header. Tell me
if you get this, okay?
-Steve Walz rst...@armory.com