Hmm...let's straighten a few thing out here:
Absolutely! If I've misinterpreted things please set me straight!
1) The CFZ is determined only by the focal ratio of the system and it does not vary with temperature. (For anyone tempted to nit-pik, the F/# does vary by a small amount as the spacing changes but this is a higher order effect that is insignificant for the purpose of this discussion.) There are different ways to define the CFZ (called the depth of focus in optics) but it's close enough to use 2.5 (F/#)^2 (in microns), which is about 291 microns for a F/10.8 system.
As understand things, the CFZ is set by the distance between the primary and the secondary plus or minus a value dependent upon the airy disk diameter at a specific seeing; you had a very nice picture in the May thread [https://www.cloudyni...p/#entry8496954] that showed that, as well as formula to compute the change in that distance as a function of change in temperature [https://www.cloudyni...p/#entry8497752] ... which implies that it does vary by temperature as the tube expands or contracts and changes the distance between primary and secondary. There was also a graph by Dickerson on a Meade in thread a few months prior that showed the change in CFZ also as a function of temperature as well as a discussion by Frank in 2016, by Jerry Lodriguess earlier in an essay on his website and even by Jon Rista about the importance of the CFZ and how it relates to temperature ... did I err?
Yes, you are confusing the thermal sensitivity values that I posted for various telescopes with the depth of focus. The depth of focus does not vary with temperature and depends only on the F/#. The thermal sensitive shows how much of a change in temperature is required to move the focus position by 1/2 the CFZ for any given telescope. The CFZ is not changing; it's the focus point that changes with temperature.
Got it ... so when the temperature changes the length of the tube it doesn't change the CFZ (which is a function of the optics), it changes where that CFZ is physically located ... thanks for helping me to understand that! (Remember the 50% rule, that was the 25% that I misinterpreted) ... given that, your formula is good for calculating the change in CFZ physical location, yes?
2) Your 75 micron length change for a 0.59m long aluminum tube undergoing a 10C temperature change isn't right. Can you explain in more detail how you arrived at that number? Was this for a tube in equilibrium? Were you heating only part of it? A 0.59m long aluminum tube in equilibrium will change length by 13.92 microns per degree C. So if you induce a uniform temperature change of +10C, the tube will grow by 139.2 microns.
Recall that in my experiment I'm only heating the end of the tube (para 4) and only applied the point heat until the glass next to the heat source hit the target temperature (para 5), *not* until the tube hit equilibrium; that was the whole point of the experiment, to find out how much of the tube would "heat up" before the glass hit the target temperature. That's why I asked about the composition of the tube, to see what the anticipated thermal conduction of it would be ...
OK, but I'm not sure what that tells you. If all you care about is getting the temperature of the inside of the glass to a particular temperature, the temperature distribution over the tube will depend on the ambient air temperature. That's all ok but what does it mean? Finally, I still don't understand how you came up with the 75 micron number.
Cool, maybe (hopefully) there's a flaw in my methodology that you can help with! Basically we know the rate of thermal expansion/ contraction for aluminum, and since it's a tube we can calculate that pretty easily (and you did that in May). Since you told me the tube is all aluminum (homogeneous) then we know that assuming the temperature change is the same for all sections of the tube then each section will move by a proportional amount; if the length of the tube is 1000cm and the formula says it will expand 1cm per 10C then we can infer that every 10cm of tube will expand 10mm per 10C, or 1mm per 1C. That's assuming a perfectly even temperature change across all sections with no loss of heat to the system.
Now let's change the experiment a bit and apply heat only to one 10cm section, and suppose that each section warms at a rate of 1C per minute ... so, at one minute the section being heated has warmed 1C, all of the other sections are unaffected ... at two minutes the heated section is up to 2C, the one next to it is at 1C, all the rest are unaffected ... after 5 minutes the progression of warming is 5C, 4C, 3C, 2C and 1C with the other five sections unaffected. Let's take our measurements at this point, at 5 minutes ... the section that has heated by 5C will have expanded (1mm per 1C times 5C) 5mm, the section next to it will be at (1mm per 1C times 4C) 4mm, etc. for a total aggregate movement of the tube after 5min of point heating of 5+4+3+2+1 = 15mm
I don't have any equipment capable of measuring micron distances, but I *do* have high precision thermocouples (+/- .01C)... so as I described I segmented the tube into five equal 4" sections (starting about an inch away from the mirror cell and the corrector cell) and placed thermocouples that were bedded into the tube material and insulated from both ambient air as well as radiative cooling at equal distances around the tube (12, 3, 6 and 9 o'clock). I also used either an angle grinder or a dremel to bed thermocouples into the mirror cell/ corrector material about an inch away from the junction between it and the tube, as described.
For the experiment as described I acclimated the tube to room temperature 20C, placed the tube in a nose up orientation and applied a heat source to the corrector plate section at positions 3 and 9 o'clock capable of heating the corrector plate section by .15-.2C per minute and recorded all of the thermocouple readings every 30sec. As expected from thermal conduction the corrector cell section warmed up first at 3 and 9 o'clock where it was being warmed, soon after the first tube section warmed at 3 and 9 o'clock and the corrector section 12 and 6 o'clock warmed, etc. and the glass also began to warm by a much smaller degree.
At the same time I monitored the interior skin temperature of the corrector plate at four locations around the secondary holder as described to ensure I was reading glass skin temperatures and not ambient air temperatures. The experiment ended when the plate temperature next to the secondary holder reached the target 10C above ambient temperature, at which point I had temperature readings for all five 4" tube sections, the corrector cell section and the mirror cell section. All section readings (12, 3, 6 and 9 o'clock) were summed and divided by four to get an average temperature (you stated that tube expansion is unconstrained, which means even if the 6 o'clock section is warmer than the 9 o'clock section it will be constrained by the cooler 9 o'clock section and the net expansion would be the sum of the two sections divided by two). This gave me temperature differential between the six physical sections of tube.
Once I had those differentials I simply applied your formula to compute the expansion movement of that section and summed them; the result was 74.98mm, rounded up to 75mm (so, that's where I got the number). It was interesting for me to note that the warming was only detectable down to the 4th section, or slightly midway down the tube, at the end of the experiment
3) The change in focus for a 75 micron change in length of the tube is huge! For any Cassegrain type configuration, the shift in focus will be approximately equal to the length change of the tube times the square of the optical magnification. A C14 has an optical magnification of roughly 5 so the change in focus due to a spacing change of 75 microns will be about 1.875 mm or 6.4 times the CFZ. That's not a small focus shift.
Hmm ... from the Dickerson graph [https://www.cloudyni...-3#entry8985035] I show a CFZ "spread" of 345 microns using a Meade 10, from threads that Frank and Jon had over the years like this [https://www.cloudyni...s/#entry7206543] discussing vCurves it also appeared that the CFZ had a "spread" of about 300 microns for the C14 ... so what would you consider the CFZ "spread" to be for a non-edge C14?
The depth of focus (CFZ) in microns is roughly 2.5 times the focal ratio squared. So take the focal ratio, square it and multiply by 2.5. For a F/10.8 system, the CFZ = 291 microns. However, the change in focus for a C14 with a 0.59 m long aluminum tube that grows (or shrinks) by 75 microns will be roughly 1.875 mm. That's 6.4x the CFZ! At that level the telescope will be severely out of focus!
Hmm ... OK, great to know that! That means that the maximum allowable expansion for the tube to remain in the CFZ would be (291microns / 25 = 11) microns, yes?
4) The amount of change in length of the tube depends only on the temperature change--not on its thermal mass. The thermal mass (or heat capacity) is related to the specific heat, which is how much energy is required to induce a 1C change per mass of the material. Aluminum and glass have very similar specific heat values (0.90 vs 0.84 J/g-K) and since there is a lot more glass (by mass) in the system that's where most of the heat is stored. I think that what you may be referring to is the the thermal diffusivity of the material, which relates to the heat transfer rate through a unit thickness and unit area of material per degree C of temperature difference. It is a measure of how well a material conducts heat. Aluminum is a very good heat conductor (with a thermal conductivity of 237 W/m-K it's not quite half that of copper) so it will change temperature relatively quickly as the ambient temperature changes. On the other hand, glass has a thermal conductivity of only 0.78 W/m-K so it will take a long time to change temperature--as we all know.
Yep, I think I'm using the wrong terminology but we're describing the same effect ... different materials conduct heat at different rates (thats why copper is a good heatsink material and not glass block) ... what I was referring to as the "thermal mass" should have been more properly described as "more of it" ... a 2 ton block of copper will heat up a lot slower than a 6" cube of glass simply because there's more of it to heat up ... so basically what I was interesting find out was how much of the aluminum tube would heat up by the time that the glass plate hit it's target temperature (answer: not too much) and if that increase would be uniform (answer: it's not) ...
Ah, ok. That's not really right. You should adjust the amount of heat so that the glass stays at the target temperature for, say 30-40 minutes--and then measure the tube temperatures. Aluminum is a good conductor but you want to make this measurement in equilibrium so that you aren't recording transient values. BTW, in my view, this is not a good way to operate a telescope but I'll address that issue later. Right now, I'm just trying to help you to make a valid measurement and to help you to better understand your results.
Hmm ... once the glass got to the target temperature it would start to reach equilibrium with the aluminum tube, so essentially I would be warming the entire OTA up to the target temperature over time but that wasn't the experiment: I wanted to see how much the tube would be calculated to expand once the glass got to the target temperature ... I'll be repeating the experiment another few times to verify the results, then start doing the experiment with the OTA having a lower starting temperature and see what changes ...
And yes, I know that this isn't a good way to operate a telescope because this will cause thermals but remember my end goals ... if I can't stop dew and frost from collecting on the corrector (or even worse, inside the OTA) then no amount of focus adjustments will make any difference, if I can't get the focus shifts under control for my 20min window then getting the thermals controlled won't make any difference ... one step at a time ...
As always, great feedback and suggestions!