Is this a parabola?

On Nov 14, 2019, Martin Brown wrote
(in article <qqk2f3$18a1$1@gioia.aioe.org>):

On 14/11/2019 16:45, jlarkin@highlandsniptechnology.com wrote:

On Thu, 14 Nov 2019 10:26:28 -0600, amdx<nojunk@knology.net> wrote:

It looks like a good focus if not long.
But does it follow y=ax^2 as I understand it?

If not a parabola, does it still focus as much energy as a true parabola.
Why would the compressed air automatically make a parabola?

It is the boundary conditions and uniform deforming force of air
pressure that make it form a parabola (of sorts).

I am not convinced it will be an exact parabola but I can't be bothered
to do the integrals. It is forming the 2D equivalent of a catenary.

1D analytic solution would be cosh(ax) ~ 1 - (ax)^2/2! + (ax)^4/4! - ...

My instinct is that the solution for the deformation of a drumskin will
be J0(x) so a bit closer to a parabola than that but not quite perfect

J0(x) ~ 1 - x^2/4 + x^4/64 - ...

It might even be slightly better than that on reflection. You can see in
the smoke that it isn't quite free from spherical abberation.

Another way to make a perfect parabola is spin casting on an old record
turntable ( the Canadian mercury mirror scope works this way). This
generates a perfect parabola when done exactly right - getting the
bearings really smooth is key to useful optics though. And you can only
look at the zenith with it.
It works with molten glass as well:
Click to expand...

..<https://www.npr.org/2012/01/26/145837380/want-to-make-a-giant-telescope-
mirror-heres-how>

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

Joe Gwinn
 
On 11/15/2019 7:56 AM, Martin Brown wrote:
On 15/11/2019 13:48, amdx wrote:
On 11/14/2019 9:18 PM, whit3rd wrote:

If the focal length is long enough, minor deviation from parabolic
doesn't much matter.

Spinning a mass of molten glass (or mercury) under gravity DOES make
a parabola
rather accurately.   You could do this with plaster of paris, a
turntable, and
finish with some aluminum paint.

For those that didn't see the video, here is a screen shot of the focus.
https://www.dropbox.com/preview/Parabola.jpg?role=personal

                                     Mikek

That is a link to your personal private copy.

https://www.dropbox.com/s/6vzijhs5gwmsd3r/Parabola.jpg?dl=0
Click to expand...

Had some problems getting the link to copy, found the solution!
 
On 15/11/2019 13:48, amdx wrote:
On 11/14/2019 9:18 PM, whit3rd wrote:

If the focal length is long enough, minor deviation from parabolic
doesn't much matter.

Spinning a mass of molten glass (or mercury) under gravity DOES make a
parabola
rather accurately.   You could do this with plaster of paris, a
turntable, and
finish with some aluminum paint.

For those that didn't see the video, here is a screen shot of the focus.
https://www.dropbox.com/preview/Parabola.jpg?role=personal

                                    Mikek
Click to expand...

That is a link to your personal private copy.

--
Regards,
Martin Brown
 
On 11/14/2019 9:18 PM, whit3rd wrote:
On Thursday, November 14, 2019 at 8:26:35 AM UTC-8, amdx wrote:
It looks like a good focus if not long.
But does it follow y=ax^2 as I understand it?

Probably not, for two reasons: first, Mylar is rolled out in production, it
is NOT a homogeneous material (like a cast plastic is) but has been
pre-stretched in one (or more) direction.

Second, the elastic properties as it stretches will make the center of the sheet stiffen
(because the disc is, to first order, not stretched at all at the outer radius) in the
usual work-hardening way (assuming, of course, inelastic deformation).

If the focal length is long enough, minor deviation from parabolic doesn't much matter.

Spinning a mass of molten glass (or mercury) under gravity DOES make a parabola
rather accurately. You could do this with plaster of paris, a turntable, and
finish with some aluminum paint.
Click to expand...

For those that didn't see the video, here is a screen shot of the focus.
> https://www.dropbox.com/preview/Parabola.jpg?role=personal

Mikek
 
On Friday, November 15, 2019 at 9:39:26 AM UTC-5, Joseph Gwinn wrote:
On Nov 14, 2019, Martin Brown wrote
(in article <qqk2f3$18a1$1@gioia.aioe.org>):

On 14/11/2019 16:45, jlarkin@highlandsniptechnology.com wrote:

On Thu, 14 Nov 2019 10:26:28 -0600, amdx<nojunk@knology.net> wrote:

It looks like a good focus if not long.
But does it follow y=ax^2 as I understand it?

If not a parabola, does it still focus as much energy as a true parabola.
Why would the compressed air automatically make a parabola?

It is the boundary conditions and uniform deforming force of air
pressure that make it form a parabola (of sorts).

I am not convinced it will be an exact parabola but I can't be bothered
to do the integrals. It is forming the 2D equivalent of a catenary.

1D analytic solution would be cosh(ax) ~ 1 - (ax)^2/2! + (ax)^4/4! - ...

My instinct is that the solution for the deformation of a drumskin will
be J0(x) so a bit closer to a parabola than that but not quite perfect

J0(x) ~ 1 - x^2/4 + x^4/64 - ...

It might even be slightly better than that on reflection. You can see in
the smoke that it isn't quite free from spherical abberation.

Another way to make a perfect parabola is spin casting on an old record
turntable ( the Canadian mercury mirror scope works this way). This
generates a perfect parabola when done exactly right - getting the
bearings really smooth is key to useful optics though. And you can only
look at the zenith with it.
It works with molten glass as well:

.<https://www.npr.org/2012/01/26/145837380/want-to-make-a-giant-telescope-
mirror-heres-how

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

Joe Gwinn
Click to expand...

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

--

Rick C.

- Get 1,000 miles of free Supercharging
- Tesla referral code - https://ts.la/richard11209
 
On Friday, November 15, 2019 at 10:52:11 AM UTC-5, Martin Brown wrote:
On 15/11/2019 15:40, Rick C wrote:
On Friday, November 15, 2019 at 9:39:26 AM UTC-5, Joseph Gwinn wrote:
On Nov 14, 2019, Martin Brown wrote

Another way to make a perfect parabola is spin casting on an old record
turntable ( the Canadian mercury mirror scope works this way). This
generates a perfect parabola when done exactly right - getting the
bearings really smooth is key to useful optics though. And you can only
look at the zenith with it.
It works with molten glass as well:

.<https://www.npr.org/2012/01/26/145837380/want-to-make-a-giant-telescope-
mirror-heres-how

(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.

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

https://www.gmto.org/overview/
--
Regards,
Martin Brown
Click to expand...

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

--

Rick C.

+ Get 1,000 miles of free Supercharging
+ Tesla referral code - https://ts.la/richard11209
 
On 15/11/2019 15:40, Rick C wrote:
On Friday, November 15, 2019 at 9:39:26 AM UTC-5, Joseph Gwinn wrote:
On Nov 14, 2019, Martin Brown wrote

Another way to make a perfect parabola is spin casting on an old record
turntable ( the Canadian mercury mirror scope works this way). This
generates a perfect parabola when done exactly right - getting the
bearings really smooth is key to useful optics though. And you can only
look at the zenith with it.
It works with molten glass as well:

.<https://www.npr.org/2012/01/26/145837380/want-to-make-a-giant-telescope-
mirror-heres-how

(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.
Click to expand...

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

https://www.gmto.org/overview/
--
Regards,
Martin Brown
 
On Thursday, November 14, 2019 at 10:18:05 PM UTC-5, whit3rd wrote:
On Thursday, November 14, 2019 at 8:26:35 AM UTC-8, amdx wrote:
It looks like a good focus if not long.
But does it follow y=ax^2 as I understand it?

Probably not, for two reasons: first, Mylar is rolled out in production, it
is NOT a homogeneous material (like a cast plastic is) but has been
pre-stretched in one (or more) direction.

Second, the elastic properties as it stretches will make the center of the sheet stiffen
(because the disc is, to first order, not stretched at all at the outer radius) in the
usual work-hardening way (assuming, of course, inelastic deformation).
Click to expand...

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.


If the focal length is long enough, minor deviation from parabolic doesn't much matter.

Spinning a mass of molten glass (or mercury) under gravity DOES make a parabola
rather accurately. You could do this with plaster of paris, a turntable, and
finish with some aluminum paint.
Click to expand...
 
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