Interesting work by Mike Davis, potentially usable by interested Italian enthusiasts
The escalation towards the amateur construction of ever more powerful Newtonian Dobsonian reflector telescopes (thanks to parabolic mirror lenses of ever larger diameter trying to contain their weight) it collides head-on with some technical problems that grow exponentially with respect to the benefits provided.
In fact, it is noted that:
- The benefit given by the need to build large diameter mirrors, and possibly lightened type to contain costs and weight of the telescope, collides with increase the height from the ground where the eyepiece will be located. Height which is determined by the focal length, however important, even if contained in only three or four units, multiple of the diameter of the mirror, with the risk of having to reach the eyepiece using long and light stairs of dubious safety due to their considerable size.
- The benefit of a large mirror of short focal length, collides however, always and in any case with a common, very difficult parabolization process of its reflecting surface, due to the quadratic growth gradient of the parabolic slope of the curvature, gradually from the depth of the arrow to the mirror center, it rises up to the edge of the blank surface. It is therefore always a process that can only be carried out with tools with a small fractional diameter compared to that of the mirror, all of which working locally, creating discontinuities of curvature with respect to the reference parabola that are difficult to connect without exceeding the tolerance of qualitative acceptability of 68,75 nanometers high., difference between peak and valley on the glass, of the maximum roughness of the surface, in deviation from the theoretical parable taken as a constructive reference, which is the "entry level" limit of a "diffraction limited" mirror given by the reflection quality of a Lambda / 4 light wave of green light.
- The benefit of a large mirror of short focal length, collides however, with a very heavy conventional processing of roughing and initial excavation with abrasives of a deep bowl "arrow", or spherical cap, inside the glass blank disc whose thickness must be able to contain it, finalizing the parabolic mirror into a flat concave disc of asymmetrical thickness with a thinner center than the edge.
The maximum facilitation bypassing most of the difficulties expressed in these three points, it would certainly come from the creation of a blank of raw glass, in a rotary melting furnace, to obtain with its cooling in rotation, a parabolic surface automatically generated by the centrifugal force acting on the mass of the real melt. In fact, it is the method used to produce the largest professional telescopes today,. But a rotary kiln that reaches the temperature of over a thousand degrees necessary for the melting of the glass, it is certainly not an amateurish method.
There would therefore remain the possibility of greatly alleviating the problems at least of the points 1 e 3, curving a flat glass plate, to generate a blank in the shape of a meniscus, in a softening oven around 800 ° C, causing it to collapse onto a convex refractory base with parabolic curvature, thus making the glass blank assume the complementary concave parabolic surface.
A blank to meniscus, contrary to a conventional blank, it has the advantage of not having to be excavated, and have a single and uniform thickness, potentially thinner and lighter than that of a traditional blank. And therefore the residual processing would in any case only be smoothing. polishing and parabolization of what will be the reflecting surface, which as raw glass is already potentially close to the definitive parabolic shape. In any case, it is much closer than any other meniscus blank made by collapsing on a mold generated in a different way from that of spin casting.
A disadvantage of the meniscus compared to a flat concave mirror, instead it is given by the need to support it in its rear curvature in order to adapt its support, both for a correct and firm contrast to the pressures and the working process, especially that manual involves. And both for a correct support in his cell, so as not to deform while it is in place in the telescope, in the various structures that it will assume in its aim. And on the study of this attitude an interesting work can be found here: http://strock.pi.r2.3.14159.free.fr/Ast/Art/Menisque.html
That said, the initial action to be taken in that direction is to prepare the convex shape in refractory material, on which to later collapse a flat glass in the oven at around 800 ° C, transforming it into the desired meniscus.
Convex shape that comes from a casting, for example in refractory gypsum for glass works, inside a concave mold which in turn can be made in different ways.
Among these different ways of realization, the most convincing, that of the centrifugal casting at room temperature of epoxy resin of a concave mold, whose rotation speed automatically determines the desired hard parabolic surface.
About this, the procedure proposed by Mike Davis in the following You Tube video is very interesting, what comment in this text, to eliminate the difficulties of understanding the soundtrack in English:
The centrifugal casting in Mike's work is seen performed over a rotating disc of plywood with a containment rim, using a clear epoxy resin, choice of a grade having a long cure time, to avoid the major deformations potentially coming from a fast polymerization that is always very exothermic.. In the video, the work takes place outdoors, where the “turntable” motor is installed on a well-leveled platform with three adjustable feet.
Mike says that the novelty of this work is the precise electronic regulation of the rotation speed in revolutions per minute of the "turntable" motor., with the aim of obtaining the parabolic curve of a telescope diameter 406 F3.5.
Rotation value that Mike does not declare, but claims to have found experimentally (however the speed can be approximated by counting the revolutions in the movie).
(At the end of this article, however, I have included an example note for calculating the precise rotation speed to obtain a parabolic surface according to the desired focal length.).
The outside diameter of the wooden board is approx 7 cm greater than that of the mirror diameter 406cm, due to the presence of the step necessary to house the anti-draft rubber strap, which acts as a containment dam for the epoxy casting.
Minute 2,27 of the movie:
gluing resin, the centrifugal force of the rotation automatically arranges it in the form of a concave parabola from the center to the edge, going to find the stable equilibrium determined on Earth solely by gravity and the specific speed of rotation.
The attention paid to this work that took place outdoors, was to cover the rotating casting of the resin, to avoid that on its surface of honeyy consistency, wind-borne debris and pollen were deposited.
In a previous event Mike had poured the casting by moving radially, then helping with a spatula to spread the resin covering the surface. While in this video he instead made the casting in the center, leaving the task of making the casting reach the edge to the centrifugal force.
Another disturbance to the quality of the smooth surface of the resin casting, is given by the presence in the mass of the casting of air bubbles incorporated in the manual resin-catalyst mixing operation, which must be done with insistent continuity over a period of a few minutes, albeit not excessively vigorously to limit the incorporation of air.
These air bubbles rise very slowly in the honeyed density of the casting, and solidifying to the hair of it would ruin its smooth gloss.
Mike sees them rising in transparency after about a quarter of an hour from the start of the casting.
So they are worth keeping an eye on, speeding up their emergence and disappearance as Mike is seen doing locally, with wide and fast passes of the flame of a gas welding torch, which is evidently capable with localized heat, to instantly zero the viscosity by making them explode on the surface, without changing the general trend of polymerization too much.
Minute 6,00:
Mike in observing the casting in rotation, he still notes the presence of an area at the edge, in the shape of a half moon in which the resin has not yet arrived. He could push it with the spatula, but decides to give the resin more time to expand, and always goes to cover the turntable with the board to avoid falls carried by the wind.
Minute 6,42:
Check it out, and notice that there is still a "dot" at the edge where the resin has not reached, while as far as the elimination of bubbles is concerned, he believes he will wait a little longer 10 minutes (he probably still notices them too deeply).
(NOTE: This observation of the slowness of expansion of the casting up to the edge risking in fact some astigmatism of the reflecting surface, would recommend the precaution of not taking too long to "help" the resin to "wet" even minimally the entire surface, without our help heaping her on the edge. This is to leave the specific task thus facilitated to the centrifugal force, to uniform the thickness of the resin in parabolic form, before the polymerization time prevents it with a significant increase in viscosity on the way to drying the resin).
At the minute 7,17, spent 15 minutes from the start of casting, Mike decides to tackle the elimination of bubbles still on the surface under the surface tension of the resin, making them emerge and disappear "magically" with the already mentioned “torched” of the gas gun.
Mike checks and exclaims that it seems impossible to him to have them all with a single click of the gas pistol, noting that this will probably be the best surface he has ever obtained.
It will still take a few hours of time accompanied by the rotation, to be able to stop it only when perfect polymerization is obtained.
Minute 8,41 of the movie:
Is’ the time in which the drying of the epoxy resin appears to have finished, since the resin-catalyst mixing spatula remained hard glued to the plastic resin mixing container; But in fact mold rotation stopped, the parabolic surface is still sticky. Mike then decides to cover the casting and wait for the next day.
Minute 9,15:
There are some bubbles left on the surface that Mike missed, which, however, does not consider them worrying.
Mike still awaits the completion of the casting drying for an additional next day.
Minute 9,39:
The next day Mike finds the resin casting surface hard as stone and no longer sticky.
Then measure the parabolic arrow with a metal crosspiece equipped with a centesimal comparator, even if it is only 13.75 "long (349mm) and not the 406mm of the useful diameter of the mold. Rotating the crossbar on the surface, actually finds a few hundredths of mm of slight astigmatism, which, however, he fears coming from the response in contraction of the surface of the plywood bottom.
However Mike thinks that all the current work can fall within the tolerance of a 406mm diameter mirror with a focal ratio of F3.75 , therefore with a parabola arrow a little shallower than the focal ratio F3.5 that was his goal.
Mike thinks this slight curvature defect may be due to a small error in his set turntable rotation speed, set just a little slower than necessary to fulfill the desire for parabolic curvature with focal ratio F3.5.
He therefore concludes that substantially the detected values are very close to the desired one, and therefore would not justify the repetition of the centrifugal casting experiment, the error being completely correctable with a minimum of additional correction work on the meniscus blank that will be obtained, However, this correction is always necessary for polishing and parabolization tending to perfection.
Note on calculating the speed of rotation in revolutions per minute (RPM) to obtain a parabolic cast of desired focal length expressed in meters (Lfm)
The formula to be applied is obtained from the following relation:
g = 2 * Lf *w2
Where:
g = acceleration of earth's gravity expressed in meters per second squared = 9,81 (m*sec2)
w = pulsation of the rotation speed, expressed in radians per second
Lf = focal length also expressed in meters
Then 9,81 = 2* Lf *w2 simplifying with a division by 2 of both members becomes 4,905 = Lf *w2
than leading to the left w becomes w = root of (4,905 / Lf)
Now inserting the focal length Lf of the movie mirror into the formula, which has a diameter of 406mm or 0.406m, with F3.5 focal ratio, you get the focal length Lf = (0,406*3,5)= 1,421 meters
So the pulsation will be w = Root of (4,905/ 1,421) = root of (3,451) = 1,8579 radians per second
To now convert the pulse of 1,8579 radians per second, in revolutions per minute, we know that they are in a corner 6,28 radians; Hence the angular velocity of 1 radian per second corresponds to (60/6,28) = 9,55414 revolutions per minute, or rpm.
therefore 1,8579 * 9,55414 = 17,75 rpm
In conclusion, to generate, according to that formula, a parabolic surface with a diameter of 406mm with a focal ratio of F3.5, with a centrifugal “spin casting” of epoxy resin, it is necessary to rotate the mold until completely dry, at a rate of 17,75 rpm
End note