This is an evolving design. Comments and feedback are welcome.
1. build a telescope suitable for CCD aperture, differential photometry. (NOTE: this is not a scope for visual use, so I do not mind if the location of the focuser/eyepiece/CCD is in an awkward location for the user. However, some of the design ideas here may be useful to folks building visual scopes.)
2. Use easy to obtain, inexpensive materials, and simple construction techniques.
3. Make the entire structure (mount, scope, and **drive system**) stiff, yet lightweight.
Some sources of design ideas and approaches:
A truss is a good starting point for a design approach. It avoids use of cantilevered structures, which are prone to more flexure, and put large twisting loads on the mount. Here is another site that discusses ideas on truss construction.
How should you terminate the truss member? Should you pin it, or clamp it? Pinning means it's free to pivot or rotate. Clamping means it can't pivot or rotate. Does this really make a difference? Yes. See this article on Euler Buckling...the way a truss/column can fail. See this on buckling length (especially the diagram at the bottom of the page)...the way you teminate a truss member has an impact on its stiffness. If you are going to build large telescopes, then this may be worth investigating.
Should a truss be simple, or in stages, as is used with the Keck 10 Meter scopes? A multiple stage truss shortens the critical length of truss members, and keeps most of the additional mass nearer the pivot point of the telescope. Again, as scopes get larger, trusses may have to get more complex...or you may be forced to use materials stiffer than steel or aluminum...composites...are they worth the extra expense?
Fairborn Observatory. (Especially look at the designs of the 32 inch telescopes.) You can make a very compact design if no person needs to be peering through an eyepiece. Similar ideas in use at the Katzman Automatic Imaging Telescope. Note that these are all equatorial designs.
What about alt-azimuth mounts? See Apache Point Observatory's 3.5 meter scope (see figure 3), and the Sloan Digital Sky Survey's 2.5 meter scope (especially look at the azimuth cone...a different approach than the typical dob, which uses a ground board and rocker box...which are often cantilevered structures. The azimuth cone is more in keeping with a truss...all elements in compression or tension.)
Why the emphasis on design goal #3 above? If the large truss structure of the Hobby-Eberly scope has a fundamental vibration frequency faster than 5Hz...why can't smaller, amateur scopes have similar, or better performance? Don't forget to include the drive system in your stiffness analysis...how stiff is one tooth on a worm gear? OK, if you make the worm gear larger, then you get a stiffer drive system, but think of the cost...(think of the periodic error and backlash inherent in worms too).
For the reasons of stiffness, gear errors, backlash, and cost, a roller drive is worth looking into. Some comments by Louis Boyd on friction rollers from the ATM archive. (Talking about telescope stiffness - one of these days I'd like to see amateur telescope making competitions where judges carry around a laptop and acceleromoter...stick the acceleromoter on the scope being judged, gently bump the scope, record acceleration data for several seconds...and use this objective data as part of the rating and evalutaion criteria. The leading astronomy magazines could do this too as part of product reviews of all kinds of scopes, tripods, bincular mounts, etc.) Clive Milne points out that you can purchase a two axis accelerometer board and software for a decent price. It is an off the shelf unit that even comes with software: http://www.analog.com/techSupport/designTools/evaluationBoards/downloads/ADXL202EB-232A_c.pdf
Roller drives can be stiff...but is this guranteed? In other words, you have a stiff mount and tube assembly, but what about the roller bearings in between? Surface area of contact with the driven disk is small, and surface area of contact of bearings to races may be even smaller still. Are there bearing types that are an inherently bad choice? Are there inherently good bearing choices?
What is an acceptable way to connect truss members? Yes, there is welding, brazing, and soldering, but what about epoxy? A truss subjects it's connection points to compression and tension, little twisting is involved. Here are some physical properties of JB Weld. Here is some advice from the ATM archive on how to make good bonds to aluminum. Here are some physical properties of West System epoxy (click on "Product Guide," and then "Typical Physical Properties"), and their chemical surface treatment method (Product Guide - number 860 - Aluminum Etch Kit).
I don't argue that welding is stronger than epoxy...but if you apply truss design well, and use an alt-az mount...your mount will not be bearing significant loads that come close to the yield point of epoxy. (Just don't drop or otherwise shock your mount components.)
This is what I'm currently investigating as a design option for the mount:
A different view (two versions of fork arms are shown):
Another issue. Fork arms - can they be made in a truss fashion, or will a monocoque approach work better? (Another definition of monocoque.) As you can see from the diagrams above I'm initially playing with the idea of monocoque fork arms. (I can't come up with a simple truss to do the same thing, and if you look at the Centurion 18 and WIYN 3.5 meter scope you will again see monocoque fork arms.)
That begs the "JB Weld" question - can epoxy be used to assemble aluminum sheet into a moncoque fork arm?
Refinement of design goals.
This scope is intended to perform CCD photometry for the Center for Backyard Astrophysics. This type of work calls for a long time-series of short exposures in quick succession. We'll use 30 seconds as a starting point for a typical exposure length.
Such a typically short CCD exposure means that an adequate drive system can be described this way: accuracy of a couple arcseconds over 30 seconds duration. Is an autoguider needed for such short exposures? Hopefully not, which would simplify the design and reduce cost and complexity.
How do you ensure the telescope is pointed in the right place? Can a friction roller drive be designed to have zero slippage? Probably not, or at least probably not at the budget level we are working at. One example of encoders in the final stage of the drive train (the telescope axis, or driven ring) is shown here. A long, continuous encoder tape is attached to the driven ring. In this particular case components from Renishaw are used. Note that with a large enough disk, and high enough encoder resolution (such as 1 micron)...encoder counts at the arcsecond level are possible. (And at a cost of about $1,000 per axis, that's really not that expensive...especially compared to other 20 or 21 bit encoder systems.) Using such an encoder system on the final driven disk helps deal with slippage problems in a less-than perfect friction roller drive system.
But do we need arcsecond pointing accuracy in the encoder? Perhaps not for the CCD (short exposure) photometry this telescope will perform. Can we relax encoder performance requirement somewhat? Here is one way that some amateurs currently use encoders - incremental shaft encoders with 2048 counts per revolution from US Digital. If you read each quadrature count, you get 8192 counts per revolution. There are 360 * 60 = 21,600 arcminutes in a full circle. Divide by 8192 and you get 2.6 arcminutes per encoder tick. If your encoder accuracy is 1 or 2 ticks you can get pointing accuracy of 3-5 arcminutes.
Is 3-5 arcminutes good enough pointing? As a cheapskate, I do not want to use a large CCD chip. (Not only CCD expense, a big chip may require a field flattener or other lens elements to allow a fast newtonian optical system to give tight start images in the CCD's corners.) How about a smaller CCD chip? That saves money, and can keep the optical system simple...but pointing accuracy may have to be higher than 3-5 arcminutes. You can gear up the shaft encoders to the telescope by some factor such as 2:1 or 5:1...but now you must contend with gear errors (periodic error, backlash, etc.) in this solution. You may have more counts per revolution of the scope axis, but have you increased encoder accuraccy?
Here is one possible 'hybrid' encoder approach to get better than 3-5 arcminute pointing. Use a large disk, with a linear encoder tape from US Digital. They have tapes with 360 lines per inch. Their longest tape is 34 inches long. 360 * 34 = 12,240 counts, and reading quadrature gets you 48,960 counts per revolution. That gets you about 0.44 arcminute (about 26 arcseconds) per encoder tick. This level of accuracy may be adequate for pointing a small chip CCD, or at least has the chance to give you better encoder accuracy than 2048 (8192) count encoder systems.
Note that this is an encoder system that you fabricate from parts...it's not an off the shelf product. You will need to make your large disk, and than attach the encoder tape. At each step there is the chance to do sloppy work and impart errors in the final encoder scheme.
Should we go to a higher level of encoder accuracy? You can, but above encoder counts of 65,536 (2 raised to the 16th power)...you can no longer use the Micro Guider 5 encoder box from Daivd Lane. This means you would have to build your own encoder box. (Unless someone can point me to an off the shelf encoder box that handles more than 16 bits.)
Can we trust the encoders blindly? Only at your own peril. As covered in the book Telescope Control you should develop a model/map of your encoder errors versus actual telescope position.
The above mount drawings are for an alt-az telescope. Is field rotation a problem? Sometimes. It depends on your exposure length, and in what location of the sky you are imaging. Image rotation in an alt-az telescope is worst along the meridian, and approaches zero at azimuths of east and west. Also, the closer to the zenith, the fast the rate of image rotation. For a moderate latitude (35 degrees) site, imaging along the meridian, only 10 degrees from the zenith, for 30 seconds...the image will roate approximately 1/2 degree. Is this a problem? For small chip CCD's it's less of a problem than for large chip CCD's. For aperture photometry, some smearing of the image can be tolerated (unless the star field is crowded). In this particular application 1/2 degree may be an upper limit of tolerable field rotation. If one is willing to sacrifice the ability to image within 10 degrees of zenith, then image de-rotation may not be called for. This helps keep the overall system design simple and less expensive. (This approach of sacrificing part of your sky coverage to keep cost and complexity down is also used in the Hobby-Eberly telescope.)
What CCD should be used? While not the highest in performance (i.e. low read noise and high quantum efficiency), a kit from Genesis, using the Kodak KAF 0400 seies of CCD's is an affordable option.
What focal length should be used? Using the KAF-0401E CCD chip gives you 9 micron pixels. Assuming seeing of 2 to 2.5 arcseconds (Cloudcroft, New Mexico, elevation 9,500FT), and assuming a sampling of about 1 arcsecond per pixel - you need a focal length of approximately 70 - 75 inches. A 16 inch mirror a focal ratio of approximately f/4.5 will give you the desired sampling. If you use a newtonian optical configuration, an f/4.5 light cone, and a small (approx 5mm x 7mm) chip you will not need corrective optics (field flattener, coma corrector) to keep star images small in the outer corners of the imaging field.
What size will the sky coverage be? Using the above CCD chip and 72 inch focal length...along the short axis you will get about 9 arcminutes of sky coverage. Take into account image rotation over several hours, pointing inaccuracies, and the fact that you can't use the very edge of a CCD chip for aperture photometry...you can consider the central 5 arcminutes 'useable' for this project. Is this too small? My previous CCD photometry used a chip that only covered 5x8 arcminutes of sky, and was less sensitive. When performing photometry on fainter stars, such as magnitude 13-15 ...you will find that they are often spaced close enough together that even in a 5x5 arcminute section of sky you will find nearby comparison and check stars.
Because this is a CCD-only scope, why do we need a traditional focuser and secondary mirror in the upper end? Why not use the approach of the Astroworks Centurion 18? How will we focus the camera? Instead of the challange of making a motorized focus mechanism in the spider/CCD holder...is it possible to move the main mirror instead? Yes. Note - some commercial Schmidt-Cassegrain makers use this approach, but mirror flop is a concern if the design and fabrication are not sound. My initial approach will be to move all three collimation bolts of a mirror cell in synchrony for mirror focusing. If the mirror cell is well designed, minimizing slop and clearance problems, then collimation shift during focusing will, hopefully, not spoil the image quality.
One advantage of main mirror focusing is that the upper ring will be very minimal and light weight...supporting only the CCD and spider. This puts less demand on the truss structure and keeps the center of gravity close to the main mirror, which keeps the angular inertia of the tube assembly low. This can make for a good synergy - light weight, low angular inertia, stiff structure...leads to a scope with a high vibration frequency that can damp out quickly.
We've looked at some design considerations to make the overall telescope structure stiff, but how can we be sure the roller drive system is also stiff? (Just think of the contact area of a small ball bearing in a bearing race...do we need more surface area in the bearings to make a stiff drive? Do we need to think about placement of bearings, and different types of bearings. Absolutely.)
Here are some websites that deal with basic bearing types and related concepts:
http://biz.howstuffworks.com/bearing2.htm - what is thrust load and axial load, anyway?
http://www.dig.bris.ac.uk/hbook/bmenu.htm - good overview on bearing types, operating ranges, and other considerations.
http://www.bradford.ac.uk/research/mbdmst/rotordynamic/bearing/bearing.html - various rolling element bearing types
http://www.textronpt.com/institute/courses/module6.htm - types of rotating shaft bearings
http://www.textronpt.com/institute/courses/module2.htm - not directly related to bearings, but here's an overview of gear types and related concepts. (And you thought gears were simple!)
http://www.textronpt.com/institute/courses/module4.htm - shaft couplings
Go here for an informative discussion, and sample drawings of how to set up bearings for typical telescope applications. (Provided by Tony Owens. Thank you, Tony!)
Wind, truss tubes, and vibration. (And perhaps a bit about string telescopes too).
Earlier analysis by amateur telescope makers have shown that you can use surprisingly thin truss tubes and yet maintain adequate mechanical stiffness to preserve acceptable collimation. That's a good analysis of static forces in a static environment. Now let's step outdoors into the breeze.
Recently Martin Cibulski pointed out that one should pay attention to certain aspects of truss tube design for telescopes. Specifically truss tube resonant frequency, and the frequency of vortex shedding (from the truss tubes) that occurs in moving air. Why is this a big deal? Because if the resonant frequency of a truss tube matches the frequency of vortex shedding...you may get significant, continuous vibration. Yes, but doesn't this only happen in very high winds? Not necessarily. It depends on several factors. Read on.
Ever notice how a flag waves back and forth in a breeze? Check out this description of the Von Karman effect. This vortex behavior happens at all scales of size, from islands to cables in a breeze. This principle is used in vortex meters to accurately measure flow in pipes.
Martin Cibulski pointed out:
The frequency of the air turbulence behind a truss can be calculated. (It is used for flow metering in pipes.) I found the formula on the web:
f = 0.2 * v / D
f: Frequency in Hertz
v: Wind velocity in m/s
D: Truss diameter in m
The formula shows that thinner trusses have higher turbulence frequencies. (inverse linear correlation).
Martin also provided the math for the resonant frequency of a truss tube:
In a book there was a formula for a cylindrical bar (not a pipe) which is held rotatable at both ends (like most trusses are):
f = (D * pi) / (8 * l * l) * sqrt (E / rho)
D = diameter (outer)
l = length
E = elasticity modulus
rho = density
d = inner diameter (for pipes only)
A cylinder's moment of inertia (which goes into the spring constant of the system) is proportional to the fourth power of D. So I added the correction factor (D*D*D*D-d*d*d*d)/(D*D*D*D) to E to subtract the hole in the middle.
The mass of the pipe is proportional to the square of D. So I put a mass correction factor (D*D-d*d)/(D*D) to rho to subtract the inner hole from the bar.
The result after some simplifications was:
f = pi / (8 * l * l) * sqrt ( E / rho ) * sqrt ( (D*D*D*D-d*d*d*d) /(D*D-d*d) )
l,D,d in meters
E in N/m2
rho in kg/m3
l = 1.5 m
D = 20 mm
d = 18 mm (1mm wall)
E = 72e9 N/m2 (aluminum)
rho = 2650 kg/m3 (aluminum)
The frequency came out as 27.44 Hz and seems to be a reasonable figure, but I cannot check this because I don't have pipes to knock on.
Based on the above math for vortex shedding, what wind speed is needed for a 20mm diameter tube to have a vortex shedding frequency of 27 Hz? Only 2.4 meters per second (5.5 miles per hour). Yikes! In this particular case even a light breeze can be bad news for truss tube vibration. What about using carbon fiber tubes instead of aluminum (same diameter as previous example)? Depending on the modulus of elasticity you use for carbon fiber tubes (between 1.0e11 N/m2 and 2.0e11 N/m2)...your truss tube resonant frequency is now 40 - 53 Hz. Whew...that's better...or is it? Perhaps a little bit, but it will only take a breeze of 4-5 meters per second (9-12 miles per hour) to reach the resonant frequency. That's still not very windproof. What if we use aluminum, but increase the diameter of the truss tube to 40mm? Truss tube resonant frequency jumps to 50 Hz (same as for a smaller carbon tube), but because the tube is twice the diameter...it takes twice the wind to reach critical speed...about 10 meters per second (22 miles per hour). That's a more reasonable degree of wind proofing.
Some folks, in the quest to push ultra-light truss tube amateur telescopes to new limits...may make their truss tubes so thin that even light breezes drive the truss tubes at their resonant frequencies. I consider it unwise to design yourself into this regime of truss behavior. This would force you to become very good at building vibration dampers, or wind shields. (In my opinion, simply using somewhat thicker truss tubes will make your telescope design considerably more wind proof.)
Want to 'what if' your next truss design? Here is an Excel spreadsheet I've put together. The green colored cells are user input. Orange are output. You can choose between several common telescope making materials. You will find that aluminum and steel truss tubes give essentially identical behavior. Carbon helps, but are you willing to pay for it?... and do thinner carbon tubes give you the degree of wind proofing you need? (Thicker carbon tubes get even more expensive.) There is one additional thing I realized while reviewing the physical properties of these materials. Steel has 1/2 the thermal coefficient of expansion compared to aluminum. That can be a good thing if you worry about temperature induced focus shift in a non-portable telescope. (Yes, carbon is even better...but I keep thinking of the cost.)
What have the pro's done? For the Sloan Digital Sky Survey's 2.5 meter scope they have built a wind screen that closely surrounds (yet moves with) the telescope. These views are without the wind screen. These are views with the wind screen installed (especially the last image). This observing site is very windy, but I do not look forward to building such a wind screen for my telescope. I'd prefer to just use thicker truss tubes if at all possible.
Martin Cibulski also pointed out that some other folks have wrestled with this problem of vibrating tubes in moving fluids...chimney builders and the oil drilling industry. We can learn from them, and perhaps avoid re-inventing the wheel. In professional circles this problem is often called vortex induced vibration.
http://www.petromin.safan.com/mag/papr02/t60.pdf - Vortex induced vibration - solution involves very smooth surfaces. (More common solution is helical strakes wrapped around the tube.)
http://www.mech.soton.ac.uk/jrc/me207/Notes.3.doc: "The strake is a helical member fixed round the outside of a cylinder. It fixes the vortex separation point at different positions along the cylinder. The vortex shedding then becomes incoherent (different in phase at different positions) along the cylinder, which minimises most of the undesirable effects. Strakes are used in particular near the tips of sheet steel chimneys, which are otherwise prone to vibrations due to vortex shedding. There are standards for the position, number and pitch of the strakes."
http://www.liceng.dk/LIC/Services/VortexSheddingAnalysis/index.shtml - VIV and resonant vibrations in structures
http://www.marktool.com/suppressors.html - VIV suppressors - example of strakes
http://www.marktool.com/vivs.html - VIV suppressors - example of strakes
http://www.2hoffshore.com/papers/docs/pap026.pdf - example test results and graphics showikng typical strake configuration.
At this point I have come to a potential fork in the road. Do I make a truss tube telescope with thicker truss tubes for good wind proofing?...or do I add helical strakes to minimize vortex induced vibration?...or perhaps a combination of both approaches? Before I choose the final path I'll need to do some real-world testing....
What does VIV imply for string telescopes?
Above I showed that you can increase truss tube diameter to minimize potential problems of VIV. Unfortunately string telescopes use (in a matter of speaking) very thin tubes. Very thin tubes generate high vortex shedding frequencies at very low wind speeds. Does this mean that string telescopes are even more vulnerable to this problem, compared to truss tube designs?
Before I jump prematurely to such a dismal conclusion, here are some links on string behavior (frequency versus mass, tension, etc.)
http://www.bikexprt.com/bicycle/pitcheqn.htm - Note that the fundamental frequency of a spoke increases only as the square root of tension. Therefore, every doubling of frequency - one musical octave - raises the tension by a factor of 4. (Does this mean that string telescopes will need very high tensions?)
http://www.falstad.com/loadedstring/ - plucked string applet - kewl!
At this point I need some help. Is the math above correct? Any flaws in the discussion? Have amateurs knocked on truss tubes to compare math versus the real world for resonant frequency? Any amateurs strapped a truss tube to the hood of their vehicle and driven down a road...finding at what speed the truss tube starts to vibrate in resonance with vortex shedding? Any fans of string telescopes strapped a string across the hood of their vehicle and driven down a road...finding at what speed the string starts to vibrate in resonance with vortex shedding?
The Athermal Truss.
Some may find the athermal truss a useful design, especially if you are interested in unattended imaging. An athermal truss has a net zero coefficient of thermal expansion. You can use expensive composite materials, or a mixture of high and low CTE materials. NOTE. Aluminum has almost exactly twice the CTE of steel. This fact can be put to good use at low cost.
http://techreports.larc.nasa.gov/ltrs/PDF/ 2000/aiaa/NASA-aiaa-2000-1409.pdf - See figure 10 (on page 9 of 10) and associated discussion.
http://gpobs.home.mindspring.com/gpobs.htm - see the section on MOTESS. Uses a steel/aluminum athermal truss.
One approach, as shown above, to make an athermal truss is to make all components have zero coeffieicnet of thermal expansion...low expansion glass, carbon fiber tubes (or a combination of steel and aluminum tubes for zero net CTE). This can get expensive, or mechanically complex.
How about this approach? Match, as closely as possible, the CTE of the truss to the glass...and do not be concerned if both have a significant non-zero CTE.
For example, pyrex CTE is about 3.25 e -6 per deg. C.
CTE of aluminum is about 23 e -6 per deg. C. CTE of steel is about 12 e -6 per deg. C.
....but ordinary plate glass has a CTE of about 8.3 e -6 per deg. C.
If you make a truss of steel, and use plate glass...CTE is somewhat well matched.
For example if I make a scope with a 75 inch long steel truss, and use plate glass, and the temperature drops 5 deg. C...focal plane only shifts about 0.0015 inch (that's 1 1/2 thousandths of an inch). That's not too bad for a fairly hefty temperature drop...and you don't need a fancy steel/aluminum truss structure...no temp. compensated focuser. Set the focus in the beginning of your imaging run...forget about refocusing until temp. drops more than 5C...which may take several hours, depending on observing conditions.
This is not a perfect, true athermal truss, but it may be 'good enough' for some applications...at a far lower budget, and far simpler design. (Much of it depends on your design goals...how good is good enough?)
Bob May has collected some thermal expansion information here for easy comparison. Thanks Bob! (Note that his values are for degrees F, not C.)
Does anyone know of other inexpensive glass types with a higher CTE than plate glass? Does anyone know of an inexpensive metal with a lower CTE than steel? (If yes...we could come even closer to an athermal truss.)
Joe Garlitz has proposed another approach at http://www.oregonvos.net/~jgarlitz/thermal.htm that uses geometry and different expansion rates of various materials to achieve an athermal truss.
The Quad-Tripod and X-Brace truss arrangements. (or...truss - variations on a theme)
It may be worth considering various truss arrangements for an amateur telescope. Why? Some may have better stiffness to weight ratio than others. Go here for a more detailed discussion with some graphic examples (*without* structural analysis). Here is some initial structural truss analysis using free software. The results may surprise you.
Here is a generic diagram of the baffling situation I must deal with. The main mirror is gray, the focal plane is a white circle, and the aperture stop is blue-green. In this example the aperture stop is just large enough to allow full illumination (no vignetting) of the desired focal plane size. Note that a baffle disk must be placed just behind the main mirror, extending at least as far as the double arrow line in the diagram. Depending on your focal ratio, unvingetted focal plane size, distance of aperture baffle from focal plane...your main mirror baffle disk can become quite large. If you insist on designing a system that needs a large main mirror baffle, there is a way out of this problem...make the bottom of the truss fuction like a 'mirror box' in the typical Obsession style dobsonian. If you line this mirror box with dark material it can function like a very large baffle disk that would normally be just behind the main mirror.
Main Mirror Cell - sloppy moving parts
The typical amateur mirror cell works well for visual observing. However a close examination of the moving parts shows lots of slop is present. This is not acceptable for an imaging scope that will operate unattended for hours at a time. Especially if main mirror movement/focusing is attempted. Go here for a discussion of the problem.
All feedback is encouraged!
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Last update: 2 Mar 2003