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umunna

Member

Registered: 2013-08-10

Posts: 5

Parabola angle

I am trying to make a parabolic satellite dish of 4.7 meter size . Can any one please help with the formula .

Agnishom

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From: Riemann Sphere

Registered: 2011-01-29

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Re: Parabola angle

Post in help me section

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'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

Bob

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Registered: 2010-06-20

Posts: 10,643

Re: Parabola angle

hi umunna

Welcome to the forum.

I'm assuming that measurement is the diameter of the dish.

But many parabolas can be constructed that would have that diameter at a given point.

The graphs below show this.  Both parabolas go through (5,5) so have a radius of 5 units at that point.  But the equations are different.

I seem to remember, from A level physics, that parallel rays hit the reflector and get concentrated at a point called the focus of the parabola.  That would be where you place your receiver.

For a given parabola equation, I can calculate where the focus would be and maybe that's enough for you.  But, before I do, have you got any other constraints.

later edit:  This page might help:

http://en.wikipedia.org/wiki/Satellite_dish

That's a big dish compared with the usual satellite ones! 

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

umunna

Member

Registered: 2013-08-10

Posts: 5

Re: Parabola angle

Hello Bob, thanks for your explanations , I have presently a 4 meter in diameter with the following statistics , dept 65cm , and focal point of 152cm.
If you can assist me with a calculation for the 4.7 meter ( with chart )  that will work very well , I will forever be grateful . Umunna

Bob

Administrator

Registered: 2010-06-20

Posts: 10,643

Re: Parabola angle

OK, thanks for the additional data.  I'm in the middle of some woodwork at the moment and only stopped for a coffee.  I'll work out a formula later today. (My time 11.45 now)

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

umunna

Member

Registered: 2013-08-10

Posts: 5

Re: Parabola angle

Bob , many thanks , I wait for your reply soon . Umunna

MathsIsFun

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Registered: 2005-01-21

Posts: 7,713

Re: Parabola angle

Some info at bottom of this page also: Parabola

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

Bob

Administrator

Registered: 2010-06-20

Posts: 10,643

Re: Parabola angle

Thanks MIF.

umunna:  I've put two diagrams together below.  The first is for the general theory; the second has your values substituted in.

A parabola is a curve with the property that points are the same distance from a fixed line (called the directrix) and a fixed point (called the focus).

In my first diagram, the curve is shown passing through (0,0).  This makes the working easier.  The directrix is the vertical line, x = - a, and the focus is at (a,0). 

note: the origin is 'a' units from both the directrix and the focus.

If (x,y) is any point on the parabola then the two black line distances must be equal.  Sorry they don't look it on my diagram but it's the algebra that counts, not the accuracy of the diagram.  Squaring the two distances to avoid square root signs:

So far I've just worked in two dimensions.  The parabolic reflector for a dish is made by rotating the curve around the x axis in a circle.

For your measurements (make sure you convert cm to m) a = 1.52

My second diagram shows a point with y coordinate 2.  This is because you gave the diameter as 4m so the radius will be 2.

calculating:

which I make 0.65789.  So I've rounded up to 0.658.

For your new dish you will have  y = 2.35.  You can choose an x and hence find a or the other way round.

Good luck with the build.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

umunna

Member

Registered: 2013-08-10

Posts: 5

Re: Parabola angle

Hello Bob , many thanks for all your efforts . My dish is 4.7 meter , focal point is 1.8 meter please help me get the dept of the dish . I will also like if possible to make a curve I can use to make the plate of the dish

Bob

Administrator

Registered: 2010-06-20

Posts: 10,643

Re: Parabola angle

OK.  The centre of the dish is at (0,0).  The x axis runs out towards the focus.  The y axis is at right angles to this.

The equation for points on the dish is

where the focus is at (a,0)

You want a diameter of 4.7 m  That means the radius (distance from the x axis) is 2.35 m

And you want a = 1.8 m

So the depth of the dish will be

To make a card former for  points on the surface of the dish, you need to plot the graph

If you compute y for a set of values of x using this:

you will get the top half of the curve.

You could calculate coordinates using a calculator and plot the graph, or maybe, use a graph plotter.  There are plenty available on the net.

Good luck ... let me know how it goes. 

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

umunna

Member

Registered: 2013-08-10

Posts: 5

Re: Parabola angle

Hello Bob , I think I made a mess of the graph plotting . I not able to plot it correctly . If there is assistance you can give , that will be wonderful .

Umunna

Bob

Administrator

Registered: 2010-06-20

Posts: 10,643

Re: Parabola angle

hi umunna

I 'googled' for a graph plotter.  This one looks good to me:

http://www.graphsketch.com/

My picture shows the graph I got and the settings I used.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob