Is this a parabola?

That is a link to your personal private copy.

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Regards, 
Martin Brown

Had some problems getting the link to copy, found the solution!

On Nov 14, 2019, Martin Brown wrote (in article ):

It works with molten glass as well:

.

(Want To Make A Giant Telescope Mirror? Here's How, January 26, 201212:01 AM ET, NPR)

Joe Gwinn

Wow. That article is from 2012 and they expected the mirror to be in use in 2020... so practically any day now.

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  Rick C. 

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The schedule has slipped a bit commissioning expected to begin in 2029.

-- Regards, Martin Brown

More than a bit I guess. At least it's not holding up a satellite launch.

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  Rick C. 

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Actually it's good enough. It is a means of carrying large diameter mirrors into space without using up valuable cargo space. They use this same Mylar film. It is deployed in space with pressurized gas to maintain its form.

[snip]

I belive this is correct. The surface is defined by the tension produced by the pressure vector. Which is normal to the surface and points toward an imaginary center point. A parabola can be produced using the spinning Mercury trick because the surface is defined by the combination of a (constant) downward gravity vector and the radial centrifugal force, which is proportional to the distance from the spin axis squared.

For a sphere, at the 90 degree point, the vector points laterally. For a spinning liquid, there is always a downward component (due to gravity) combined with an increasing outward vector. Hence, you never reach "the side" of the curve where it turn in again.

--
Paul Hovnanian     mailto:Paul@Hovnanian.com 
------------------------------------------------------------------ 
Human beings were created by water to transport it uphill.

by

h

I don't think it is either a parabola or a sphere. It is something else. The issue of the stretching of the plastic is not so simple I think. As so meone pointed out while the stretching near the center is even in all direc tions, near the perimeter the stretching is only along the radius of the ci rcle, not around the perimeter. So this should produce a more cylindrical curve fading into a spherical curve at the center. I think this will be mo re similar to a paraboloid and less similar to a sphere.

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  Rick C. 

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I guess at this point is, If the shape is not a parabola, does it reflect as much of the energy to a point, as a parabola. Looking at the area highlighted by the smoke it sure seems that no energy is missing the focus point. I wonder if this can be done with a vacuum, with a sealed container on the back side. Then, you would have no need to cover the back side.

Mikek

More questions, I'm wondering how it would work if I put a sealed chamber on the rear and drew a vacuum to make the shape. I don't know how the PSI on the outside would compare to the inches of Mercury on the inside, but I'm curious. Also, will aluminized Mylar hold a vacuum? It does better than rubber with helium as far as molecules leaking through . And more important, is the shape actually a parabola, as a telescope would have. I'm wondering if using a vacuum could be an easy way to make a 6ft telescope mirror.

Mikek

The caveat that the outer rim will not be stretch circumferentially and hence not the same shape as the centre might be minimised by only using the centre portion. May be there is even a way of clamping the centre portion after it has been tensioned. Then the annulus could be discarded by a bit of clever juggling of vacuum vessels. Alternatively, clamp the rim with a device that can pre-stretch before pressure differential is applied...

Mike.

ed by

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a e

e. The issue of the stretching of the plastic is not so simple I think. A s someone pointed out while the stretching near the center is even in all d irections, near the perimeter the stretching is only along the radius of th e circle, not around the perimeter. So this should produce a more cylindri cal curve fading into a spherical curve at the center. I think this will b e more similar to a paraboloid and less similar to a sphere.

You need to be a bit more practical. Only a theoretical parabola will refl ect energy to a point. A point, having an infinitely small size will recei ve zero energy from any real parabolic surface due to irregularities. Sinc e the finite amount of energy will be spread over a finite amount of space any point may have a finite energy density, but the total energy will be ze ro due to the zero size.

So, to measure what you are trying to measure you will need to define the s ize of the region you want the energy to be targeted. Then you can compare the relative energy (or more practical, the power) received in that area, or maybe even a volume. If the dispersion of the non-parabolic shape keeps all the light beams in this area/volume, it will provide the same power to your receiver as a parabolic shape.

Think of a car self driving. It doesn't need to stay perfectly in the cent er of the lane. It does need to stay within some portion of the lane. Onl y if it strays from that region is it a problem.

If your focus point is not a point, but a size some two or so inches across , then yes. This reflector looks pretty good. Also consider that the fold ridges were never completely removed. They are reflecting light well away from the focus, but they are some tiny percentage of the total. Otherwise it looks like a good focus.

It would need to be covered all the time with a container strong enough to maintain the vacuum. Potentially a vacuum could be pulled on a solid sheet of plastic, then heated enough to let it form the shape, then allowed to c ool. But it would be hard to heat it evenly enough to not distort the shap e.

--

  Rick C. 

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ed by

an

hich

a e

e. The issue of the stretching of the plastic is not so simple I think. A s someone pointed out while the stretching near the center is even in all d irections, near the perimeter the stretching is only along the radius of th e circle, not around the perimeter. So this should produce a more cylindri cal curve fading into a spherical curve at the center. I think this will b e more similar to a paraboloid and less similar to a sphere.

I think there are a lot of potential problems. The film would need to be r ather perfectly positioned and evenly clamped to not distort the shape. On ce you pull the vacuum any temperature variations would cause the focal len gth to change.

It would be interesting if the guy in the video took some photos of images of stars using his mirror. That would give you a great indication of the a ccuracy of the shape. Or to put a piece of paper at the focal point and sh ine a laser pointer at the mirror to see how the spot moves on the paper as you move the laser pointer.

--

  Rick C. 

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I meant, never mind you can probably figure out what I meant.

It can. I don't know if it was on instructables.com or a random YouTube video suggestion, but I saw (and tried) this with some mylar "fancy wrapping paper", a plastic (round) sweets container.

Film glued around the edge and then strapped in place to dry, a small diameter tube (like a biro-pen refill) into the container, and a plug of Blu-Tack to reseal it :)

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--------------------------------------+------------------------------------ 
Mike Brown: mjb[-at-]signal11.org.uk  |    http://www.signal11.org.uk

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lse. The issue of the stretching of the plastic is not so simple I think. As someone pointed out while the stretching near the center is even in all directions, near the perimeter the stretching is only along the radius of the circle, not around the perimeter. So this should produce a more cylind rical curve fading into a spherical curve at the center. I think this will be more similar to a paraboloid and less similar to a sphere.

reflect energy to a point. A point, having an infinitely small size will r eceive zero energy from any real parabolic surface due to irregularities. Since the finite amount of energy will be spread over a finite amount of sp ace any point may have a finite energy density, but the total energy will b e zero due to the zero size.

he size of the region you want the energy to be targeted. Then you can com pare the relative energy (or more practical, the power) received in that ar ea, or maybe even a volume. If the dispersion of the non-parabolic shape k eeps all the light beams in this area/volume, it will provide the same powe r to your receiver as a parabolic shape.

center of the lane. It does need to stay within some portion of the lane. Only if it strays from that region is it a problem.

ross, then yes. This reflector looks pretty good. Also consider that the fold ridges were never completely removed. They are reflecting light well away from the focus, but they are some tiny percentage of the total. Other wise it looks like a good focus.

on

to maintain the vacuum. Potentially a vacuum could be pulled on a solid s heet of plastic, then heated enough to let it form the shape, then allowed to cool. But it would be hard to heat it evenly enough to not distort the shape.

No, actually, your post seemed to indicate some lack of understanding, so t hat's why I asked the questions and posted the info. If you actually under stood what was going on I would not have expected you to have asked the que stion.

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  Rick C. 

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No. Only a perfect parabola has that property (by construction).

It is but not by all that much. The caustic curve you see in the smoke represents the pattern that the converging light rays make.

A vacuum cleaner or more reliable pump applied to the back would suck it in and make the surface concave. You could probably suck hard enough by mouth to make it take the right shape provided that you had a valve.

The shallower the depression and longer the focal length the closer an approximation to being a parabola the sphere becomes and for anything past f8 you can ignore pretty much spherical aberration for all but the most demanding diffraction limited optics.

That mirror looked to be roughly f2 that is focal length about twice the diameter. You can work out where a parallel ray incident at a distance r from the optic axis will focus if the radius of curvature is R.

The incident ray makes angle A with the normal st sin(A) = r/R The reflected ray makes angle A with the normal too.

So you have an isosceles triangle with side R and two angles A. The length of the unknown side is therefore R/(2cos(A)) = R/2

And the focus of the ray is R - R/2/sqrt(1-(r/R)^2)

~ R/2 - r^2/R + O(r^4)

or more accurately using a slightly better approximation

~ R/2 - R.r^2/(R^2-3r^2) (subject to typos and algebra slips)

There is a sliver of mirror 2pi.r.cos(A) illuminating that on axis focus point. The optimum focus moves towards the mirror as its focal ratio becomes shorter. Much is disguised by the sun being 0.01 radians across.

Two rays that that are tirvial to raytrace are.

Almost paraxial when the focal length is R/2

The ray hits mirror where it is at pi/4 to the incoming ray. when r = R/sqrt(2) and focal length is R(1 -1/sqrt(2))

The optimum energy concentration will be roughly when the cone for the close paraxial rays diameter and the divergent cone of the rays from the outer part of the mirror that have passed through focus are about equal. The hottest spot will be between there and the closest focus.

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Regards, 
Martin Brown

You can get rolls of aluminized Mylar from Amazon and most greenhouse supply places, usually in 47-50" wide by 25 or 50' long rolls. Stays nice and flat as you unroll it so no issues with the folds from a space blanket. Thicknesses from 1 mil up to about 7 mils so choose your stiffness. A random search result at Amazon gave a price of under $8 for a 2 mil x 50" x

25' roll from one vendor so a much better starting point than the space blankets.

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Regards, 
Carl Ijames