An alarming article about studies of bird deaths due to bright city lighting. A couple of quotes:
Every 11 September at dusk, in memory of the 2001 attacks, New York City mounts the Tribute in Light, an art installation in lower Manhattan. And every year, as twin towers of light bloom skyward, they attract thousands of migrating birds, sucking in warblers, seabirds, and thrushes—along with predators such as peregrine falcons eager to take advantage of the confusion. On each anniversary, bird conservationists wait below, counting and listening to disoriented chirps. If the observers report too many birds circling aimlessly in the beams, organizers flip off the lights.
In recent years, on-site observers have also used a complementary tool to quantify the orbiting birds: weather radar, which bounces off birds as well as raindrops. In 2017, a group led by Cornell University ornithologist Andrew Farnsworth found that during seven previous anniversaries, the once-a-year installation had attracted a total of about 1.1 million birds. Within 20 minutes of lighting up, up to 16,000 birds crammed themselves into a half-kilometer radius. But when the lights flicked off, the dense clouds of birds on the radar screen dissipated just as fast, a finding later confirmed by on-site thermal cameras.’
Later, discussing a single building, the author found that a
‘key factor was how many of the convention center’s windows had been illuminated. Each individual bright window left more dead birds for volunteers to find the next day. The correlation suggests halving the number of lit window bays would halve the number of bird strikes, the team estimated, saving thousands of birds at this one three-story building. “It really does seem that each window makes a difference,” van Doren says.’
We are still trying to get our venerable, university-grade Ealing mount to work properly with its new OnStep motor drive system. We thought we had – at long last – everything set up perfectly and running correctly with the various components wired up properly but not yet pushed into place in the interior cavities of our mount. All seemed to be working well until we pushed the last components and wires inside, and then closed the hatches.
Then things stopped working.
We soon figured out that the force we had to use when moving all those items inside the mount had broken some of the leads. We found those broken leads and replaced them with shorter ones.
When we started it up again, we discovered that the mount would not ‘track’ to the west in right ascension — something that the software and hardware are programmed to do as soon as the system is turned on. In fact, I couldn’t slew it to the west either. Eastwards was no problem. Also, we could only slew southwards, not northwards.
We didn’t know what to do, so I emailed a followup question to the wonderful folks at the OnStep wiki. Several folks thought we had a balance issue or a limit switch issue, but I went up today to check on the balance — and concluded that’s not the problem. We have no limit switches yet either in hardware or in software. So that’s not it, either.
Wondering if we had somehow screwed up the MaxESP3 board that is the heart of the OnStep system, I unplugged the board (and all of its sub-boards, as a unit) we had been using last weekend, and plugged in a duplicate board, built by Ken Hunter and ‘flashed’ by him with the same Config.H file as the other one.
Listen to the screeching!
Another suggestion is that we may be creating ground loops by not connecting our wiring properly. I don’t know. I wish I had taken some electronics classes during my time in college. It would have come in handy here!
I’ve got the new stepper motors, and their drivers, and their power supplies, working away just fine on my desk, and I’m pretty excited and confident that we will have enough power and precision to drive and slew the Ealing properly!
These steppers are very strong: I am completely unable to stop the motors with my hands (bare or gloved) either when they are just tracking or when they are slewing at full speed or guiding at low speed, even with a fairly large fixture on the end of the shaft.
Without Ken Hunter’s expertise, there is no way I could have figured out how to get these particular steppers wired so that they would run, especially since they require those special, large, green and black drivers that you see in the photo above, which are about the size of the palm of your hand. Ken deserves a real round of applause, and more. (I have found that his advice on the OnStep wiki message board is much more accurate and friendlier than the advice of many others there.) In addition, he also repaired two boards that had been incorrectly soldered and assembled by someone else and which I and Alan Tarica purchased from that person, separately.
Before Ken’s intervention, the boards didn’t work. He found a number of assembly and soldering errors, and not only fixed them, but he also ‘flashed’ them with the latest OnStep software versions. At no cost! Now, they work very well.
I want to thank Prasad Agrahar again for his original inspiration and follow-through, and also Alan Tarica for his enthusiastic and knowledgeable assistance and advice (which I don’t always follow).
What’s more, as far as I can tell, this arrangement with super-duper steppers and drivers is unique in OnStep. Something like it clearly exists in some form in the professional or amateur CNC world, which is why we can purchase these insanely complex drivers for less than $9 apiece and the steppers for just $37 each, but to my knowledge nobody in the OnStep world has done this particular arrangement.
The old NEMA-23 steppers and these new ones have the exact same ‘form factor’ except that one can use larger bolts to fasten the new ones to the L-shaped brackets I already have installed.
The attached schematic diagram is a first draft of how the connections on the mount itself will be made. The wiring job is going to have a lot of parts, and lots of connections!
At the observatory, we won’t have those old military-grade, 14-connector cables any more, nor that very heavy old hand paddle whose cable we all used to trip over. Instead, I ordered 10 feet of 14-gauge, 4-conductor shielded, stranded cable that is highly rated for both high and low temperatures, in order to connect the DEC drive to the rest of the scope. It will need new strain-relief grommets. So will several other wires. I can re-use most of the existing holes in the cover plates for this mount, and will seal the rest of them to keep out insects. Wiring all of those new connections will take a while!
We will have a local wireless connection (with a small external antenna, like on a router, to make sure there is a good wireless signal), and a small (2x3x5 cm) dedicated basic weather monitor (very basic: just humidity, temp, etc) attached somewhere on the mount*. There will also be an emergency ‘Kill’ switch to allow one to stop the drive immediately if needed.
You can control the scope with a Smart Hand Controller that will be attached via a flexible ethernet-type cable, or, if you prefer, with an inexpensive Android cell phone or tablet that has the proper software installed. (We will leave a tablet up there, with its charging cord.) One won’t need to unclamp, slew, and re-clamp the RA and DEC axes any more in order to acquire a target. We will see how good the pointing accuracy and tracking are, once it’s all up and running.
Since we are using much stronger stepper motors than the ones had been suggested to me and that I had purchased earlier, and they needed a lot more current, we needed different drivers. As a result, most of the connections I had previously fabricated won’t be of much use for us anymore. Perhaps I can give them away to somebody else who is attempting an OnStep conversion on a telescope mount that weighs much less than this one.
Here is a little video of these things in action:
And here is my first draft of the schematics showing how these things all connect inside the scope as well as how we will connect them to the body of the mount itself. It’s crude, but I think it will be useful.
A 3-minute video of the results of our first-time installation of something called an OnStep conversion. We are replacing the telescope drive of a venerable but beautifully machined telescope mount, located at a small group-owned observatory called Hopewell, atop a ridge called Bull Run Mountain*.
Sorry, it’s not the greatest or clearest video. Also, I mistakenly state at about 0:25 in the video that the right ascension axis was turning at 12 RPM, but it’s not: I should have said 5 RPM, or one revolution in 12 seconds.
You can hear some stuttering of one of the motors. You are right, that is not a good sound. We were able to get it to stop and start making that noise and motion by adjusting the precise positioning of some of the gears. It will take some time and experimentation to get that perfect.
Later on (not captured in this video), when I was trying to slew in the declination axis at the highest speed possible, the stepper motor once again screamed and halted. I’m hopeful that all of those problems can be fixed by doing one or more of these things:
1) adjusting the fit of all those gears;
(2) changing certain parameters of microstepping and current to the stepper motors in software; and/or
(3) increasing the voltage to the board from 18 VDC to 24 VDC.
I’ll need to test things out on my desk at home, using the same OnStep board, but without the gears and timing belt. (That stuff was a royal PITA to remove screw back into place, and none of us have any desire to take them back out again!) I have some identical extra stepper motors that I can test out, with gloved hands, to see if it is possible to stop the motors from turning. Right now, I still don’t think they are putting out the amount of torque needed.
*Yes, that famous Bull Run of Civil War fame is not far away. However, our observatory is named after a different geological feature, namely the Hopewell Gap that cuts through the hard rock of Bull Run Mountain right about where where the creek called Little Bull Run begins.
If you are reading this, you probably know that serious amateur, and all professional, astronomical telescopes (except for Dobs) are generally driven by ‘clock drives’ so that the object one is viewing or photographing stays properly centered as the earth rotates imperceptibly beneath us. The original Ealing motor drive at Hopewell, while turning excellent Ed Byers gears, had been an intermittent problem ever since it was delivered to the University of Marylandabout 50 years ago. It was in fact not operational when they sold it to us for a pittance about 30 years ago. (If you go to the University of Maryland Observatory site I linked to, the scope we have now is the one in the center of the 1970s – era photo labeled ‘Figure 4’.)
Bob Bolster, one of the founding members of Hopewell observatory, disassembled the drive, modified it considerably, and got it working again, several years before I joined the group. The scope worked, off and on, with a very complex clutch system for ‘fast’ and ‘slow’ movement of the scope, for most of the rest of the last 25 or so years, except for occasional motor burnouts and clutch replacements. Also unfortunately, the optics on the original 12″ Ritchey-Chretien telescope, were not very good, so we removed them, had them in an attic for many years, re-tested them, and finally sold the glass and the holders, for a pittance, to someone in Italy who wanted to try to re-figure them.
This was originally a ‘push-to’ telescope, meaning that one loosened up two Byers clutches (one for each axis), located the desired target in the sky, tightened the two clutches, did some fine tuning with an electric hand paddle to center the target more precisely, and then allowed the telescope drive to then keep the object in the center of the eyepiece or camera field of view as long as one wanted. It originally came with metal setting circles (basically, finely-made protractors that showed where the scope is pointing vis-a-vis the polar and declination axes), which made finding targets possible, though not trivial!
About 15 years ago, Bolster (with some help from me) installed Digital Setting Circles, which used a rotary encoder on each axis, along with a small hand-held computer and screen display, to allow one to select a given target; the DSC hand paddle’s display then would indicate how far one should rotate the scope along those axes to find the desired celestial object; when it was in the field of your widest eyepiece, one used the hand paddle to center it more precisely.
Converting this scope to an OnStep drive will, I hope, make this a Go-To scope in which one can command the telescope to aim at whatever target one desires.
Unfortunately, right now, the fastest it seems to rotate in Declination, with no load whatsoever (all scopes have been removed, so no balance or inertia problems) is about one degree per second. So doing a 180-degree turn in a North-South direction would take a full three minutes. A 30-degree turn would take 30 seconds. Can we make this a bit faster? I hope so.
I wasn’t able to really slew in right ascension (East-West) because the counterweight box, even though empty, seems to require too much torque to rotate right now.
Bolster passed away a few years ago, and this summer, the moment I had been dreading finally arrived: the drive on the Ealing died again, and his amazing skills and tenacity in fixing such problems was gone with him. What’s more, in his final years, his incurable, chronic idiopathic neuropathy made it literally impossible for him to speak, and even typing email responses to the rest of us took a very long time. So most of his wealth of knowledge and experience died with him.
As indicated in my earlier posts (here, here, here, and here), with help from others, I was able to take the two motor setups for the two axes out from the mount and get them working again on my workbench in their original format. I was even able to order and install material for the clutches. However, I discovered that one needed to adjust the clutches very, very precisely, or else they wouldn’t work at all.
I couldn’t figure out how to do that.
And nobody else who belongs to our observatory volunteered to help out, except for removing the scopes and drives from their former positions inside the mount.
So I decided to convert to a totally different type of telescope drive, one inspired by the Arduino boards and 3-D printers. A group of really smart and resourceful hobbyists (engineers?) designed a system around the Arduino environment that uses inexpensive off-the-shelf printed circuits and complex sub-boards and components, used originally mostly in the 3-D printers that have become so popular, to drive at telescope just the way astronomers want them to be driven.
Apparently, there have been many, many OnStep successes, but what we are doing may be the largest and most massive mount to date that has done such a conversion.
I was warned that the entire process would take some months. Those warnings were correct. But that’s OK. I’m retired, I have time, and I have access to tools and people who are interested in helping. What’s more, I have learned a whole lot about modern electronics, and my soldering skills are much better than they ever were.
I’d again like to thank Alan Tarica (who’s physically helped a **tremendous** amount), Prasad Agrahar (who first showed me the OnStep conversions he had done on a much smaller equatorial mount), Howard Dutton (who first conceived and implemented OnStep), Ken Hunter (who made and **donated** to us a complete, functional OnStep board together with all sorts of accessories and walked me by phone and video through many of my fumbling first steps), Khalid Bahayeldin, George Cushing, and many others.
I have made a lot of progress over this winter break in converting the 50-year-old Ealing telescope mount at the Hopewell Observatory, as you can see in this video.
We are swapping out an electro-mechanical “dumb” drive that failed, in favor of a modern, solid-state one built in the Arduino environment. If it all works out as planned, this mount will be able to slew to any target and keep the target steady enough for astrophotograpy. I hope.
With a project like this, with delicate electronics that can easily get fried, I believe that having spare parts on hand is a good idea. The main board is pretty cheap: under $100, completely assembled, and the motors were about $30 each. We have spare stepper motors, spare stepper drivers, and a total of three main MaxESP OnStep boards.
Except that two of them (the ones we purchased from George C) don’t work at all, and I don’t know why. The one that Ken Hunter built and **donated** to us works just fine, after I did the required tweaking of various settings inside the Smart Hand Controller or SHC and inside a CONFIG.H file in the Arduino programming environment. And added the gears and belt.
I see almost no serious differences between George’s boards and Ken’s board. I am confident the problem is not my wiring or soldering, and it’s not the fact that George’s boards have RJ45 jacks, but what it is, I have no idea.
This is my second build of the connections between the stepper motor and the worm gear.
Without the help of Ken H, Howard Dutton, another Ken, Alan Tarica, Prasad Agrahar, and Khaled Bahayeldin, I never would have gotten this far. I am very appreciative of the amount of work that went into programming all of the many parts of the OnStep project as a whole. However, I found the OnStep Wiki rather confusing for beginners, and I hope to help them make it clearer in the future.
You can probably see that there is a good bit of wobble in the gears that involve the belts. That is probably because I failed to get the gears perfectly flush against the lathe chuck when I was enlarging their central holes from 5 mm to 1/4 inch despite using a dial indicator with a magnetic base to center it. I think I will need to order a new set of gears that have a 1/4″ axle hole already made at the factory. I don’t think I can do any better than I did, and that wasn’t good enough.
The reason for having the gears and belts is something to do with microstepping on the stepper motors that I really don’t understand. OnStep experts told me that the OnStep board, drivers, and steppers simply cannot handle gears that are 1 : 20 : 359. So we added a 3:1 toothed-gear-and-belt system so that the ratios are now 3 : 1 : 20 : 359. That set of ratios seems to make the steppers happy. (These motors have 200 steps per rotation, and are being currently driven at a rate of 1/16 of a step.) They don’t scream and stall any more, but the wobbly gears will probably translate into periodic error that one can see in the eyepiece or on long exposures with some kind of camera.
My next step is to take this entire apparatus up to the Hopewell Observatory itself and see what happens when I install them in the Right Ascension and Declination drives.
Then, we need to repair the electrical supply for the roll-off roof.
Then we have to put the telescopes back onto the mount.
Then, and only then, can we try having a “First Light” with the new motor pushing a very nice Ed Byers drive in an big, old, and very well-built university-grade telescope mount.
I think I have succeeded in getting our OnStep build to work properly. Previously, whenever I asked the drive to slew to an new location, the stepper motors would build up to a certain speed and then stop rotating while they screamed, seemingly in protest. It’s called stalling.
With the help of several of the principal leaders in the OnStep project (Howard Dutton, Ken Hunter, Khalid Bahayeldin) and Alan Tarica and Prasad Agrahar, I think I may have finally got the settings set properly. The final secret was to reduce the slewing speed in the smart hand controller to the lowest setting.
This does make slewing rather slow, however. To go from the location of Jupiter to Capella tonight, which is a pretty long distance across the sky, took nearly eight minutes. Watch the video.
Here is a photo of the inside of the declination axis of the Ealing mount at Hopewell Observatory.
The gears you see were made about 50 years ago by the Ed Byers company, who continue to produce some of the finest gears anywhere. The periodic error on this mount is very, very low, which is a Good Thing, and why we want to keep it and just upgrade the old drive. As you can see in a previous post, the old system had a finicky clutch drive that had caused a lot of problems, but worked very well indeed when it worked properly.
I am working to replace it with a more modern, reliable and user-friendly, namely an OnStep ‘build’.
The friendly and helpful folks at the OnStep project were asking for a picture showing how the existing Byers drive was put together. I hope these four photos help.
In the first photo, notice the greasy worm gear at the bottom left. It was removed from the mount, along with the old motors, and is sitting on my desk (with the old grease cleaned off), directly coupled to the stepper motor, which connects to one of the OnStep boards (in the wood-and-black aluminum box). In the second photo,
The black anodized bracket in the second photo holds the motor and the worm gear rigidly together. The bracket bolts into a place in the mount (not shown). It took a bit of work to get the stepper motor and the worm gear lined up within a couple of thousandths of an inch, but it’s done. Prasad turned me onto those cool little universal joints that permit one to connect items that don’t match perfectly.
20 turns of the worm gear, times 359 teeth on the big gear, means that it takes 7,180 turns of the stepper motor to make one full revolution of this declination axis or of the right ascension axis, which is identically mounted. (Not that you would want to go about spinning your telescope very far on either axis!)
So 19.97 turns of either motor make the scope travel 1 degree (7180 divided by 360).
And since our stepper motors make 200 steps in one revolution of the worm gear, it takes about 3994 motor steps to make the scope turn by that one degree (the last result, times 200).
Or if you are micro-stepping by, say, the rate of one sixteenth of a step, then by my calculations it will take 63,911 microsteps to turn by that degree (the last result, times 16). And that seems to be outside the range of permissible microsteps for these stepper motors, perhaps causing them to scream in protest. (I swear, that’s what it sounds like!)
It appears that Khaled and Prasad might be correct: I might need to add a toothed gears and a belt to this arrangement to reduce that last number (63,911) by some factor. For very little money I just ordered a pair of such things, designed for 3-D printers and other computer-controlled machines. It will have 60 teeth on the motor and 20 teeth on the worm gear, and then the above would instead have only 21,304 microsteps to turn one degree. (No wonder they protest!) Once again I’ll have to disassemble the motor and drive bracket and do a bit of machining. A drill press and a punch will be fine.
The last two photos give some more detail on how the old drive system worked.
A few blog entries ago, I thought I had made great progress in getting the old telescope drives for Hopewell Observatory’s venerable Ealing Mount to work again. Unfortunately, it became clear that one had to adjust the amount of friction in the clutches very, very accurately, and I saw no way to fine tune it.
So I bit the bullet and decided to convert the mount over to an inexpensive system, at least partly DIY, that uses very inexpensive solid-state printed circuit boards and Android phones to control stepper motors that make the telescope point in the directions desired. (Instead of spending many thousands on a Sidereal Technologies rebuild.)
This system is called OnStep and is spearheaded by a number of very generous volunteers: Howard Dutton, who basically invented the system and wrote all the original code, along with Ken Hunter, George Cushing, and Khaled Bahayeldin, and a number of others whose names I don’t recall. It uses off-the-shelf components, chips and sub-boards, that cost very, very little; these are put on one of a slew of different possible 3D-printed circuit boards. There is even a Wiki that could use a bit of editing. It’s got a ton of information but when I was starting out, I found it extremely confusing, and I am not alone. I promised to try to improve it when I get the Ealing telescope working properly.
After getting the software to work, then you arrange the connections to your telescope’s gears, power supply, and communications inside your own mount.
I am immeasurably aided in this conversion effort by Alan Tarica, who is the co-leader of the Washington, DC-area’s Telescope Making, Maintenance, and Modification Workshop (which has been going on for about 80 years) and by Prasad Agrahar, who made a remarkable telescope in our TMMMW several years ago and went on to build his own OnStep conversion of an existing commercial telescope. Prasad’s example showed me that if our old Ealing drive died, we should try OnStep.
Well, the Ealing drive did finally die. (It had presented problems ever since it was first delivered to the University of Maryland Observatory nearly 50 years ago.)
Michael Chesnes and Bill Rohrer of Hopewell helped materially with removing the old components of the scope and with then trying to debug the electrical problem that has now sprang up with our roll-off roof.
Ken Hunter made for us, and debugged, an entire OnStep board and refused to take any money for it. Prasad Agrahar gave us some NEMA17 stepper motors and some wires and likewise refused to let us pay. Prasad drove all the way from Philadelphia to help Alan and me figure this stuff out in person, both at the workshop and out at the observatory. Ken has spent hours, remotely from Yuma AZ, walking me through the various steps in managing the many settings that need to be uploaded and adjusted in order to get things to work. Ken told me he used to run the ATMFREE list-serve, but retired from that after an injury, and he remembered meeting me once at Stellafane. He also very kindly sent us an antenna for the system so that it can run WiFi or BlueTooth more efficiently from inside our massive metal mount.
Alan and I are fairly far along in the conversion, thanks to all this help. I had to learn some of the basics of the Arduino operating environment, which one uses to set all the many, many parameters needed to get the system running. And had to improve my soldering techniques! Fortunately, all the heavy lifting of getting all of the many lines of code working together has been done by Howard, Ken, and the others, so all I had to do was set things up to fit our particular set of choices for the board, the stepper driver, the sub-boards, the gears, and the motors.
Here is our current setup: we have two (now three) MaxESP boards running OnStep version 2.04 (iirc). (Multiple boards because they are cheap and in case one gets fried by a lightning strike or stupidity. It happens!)
They have TMC5160 stepper drivers, connected to two rather beefy NEMA23 stepper motors (200 steps per turn), which I arranged to fit exactly in-line with the worm gear that we will later put back into the mount. We have tweaked the ‘CONFIG.H’ file settings the best we could, and with an enormous amount of help, I think I’ve set the speeds of the stepper motors correctly. The worm gear turns another gear with 20 teeth, which turns another one with 359 teeth. (All made by Byers, and made very, very well.)
(We had NEMA17’s run by the TMC2130 stepper drivers, but we didn’t think they were beefy enough to rotate the very large mount we have, even if we balance it perfectly.)
It’s been a very interesting learning expedition. It’s taken quite a bit of time, but not really very much money. With mass production, the components (screws, capacitors, diodes, resistors, and so on) if purchased in medium quantities, are really very inexpensive.
However, the stepper motors are still not behaving properly. They scream instead of moving, as you can see in this video. I will post the current parameters on the OnStep wiki, where I said. You can see and hear the action in this little video. When I try to slew to any random, dummy target, the steppers will start rotating and also start making a deafening squeal that gets higher in pitch and volume. However, after a little while, both rotors stop turning either completely or almost completely. The smart hand controller pretends that the mount is moving in both axes, but it’s not true.
Right now, I don’t know what is causing this problem.
I had the pleasure of helping lead a field trip for 9th grade Geometry students at School Without Walls SHS that we call ‘Math on the Mall’ assisting with two colleagues from the SWW math faculty.
One of our goals is for the students to see how beautifully and geometrically this city was laid out by Pierre l’Enfant, Andrew Ellicott, and Benjamin Banneker about 230 years ago.
While there are lots of myths written and repeated about Banneker’s actual contribution, the fact is that he was the astronomer, who was responsible for determining due north, exactly, and the exact latitude and longitude of the southern tip of the original 10-mile-square piece of land. With no Internet or SatNav or even a telegraph or steam engine, but with a very nice refractor and highly accurate clock that he was entrusted with, but with no landmarks to measure from, he was able to do so, in 1790.
I was sad to see that exactly none of the students know which way was north – in a city where the numbered streets near the Mall and the rest of DC’s historic downtown were almost all laid out perfectly north-south, and the streets whose names begin with letters or words like ‘Newark’, and the streets along the Mall, are all laid out perfectly east-west. Very few of them had ever seen the Milky Way, though most had heard of Polaris or the North star.
Hopefully they will remember that in the future as they do more navigation on their own in this great city.
I challenged them to try to figure out why the angle of elevation of the North Star is the same as their latitude. Here is a diagram illustrating the problem:
This diagram is intended to help you understand why the North Star’s elevation above your horizon always gives you your latitude (if you live north of the Equator.
The big circle represents the Earth. The center of the earth is at E. The equator is AD.
YOU, the observer, are standing outside on a clear night. You see Polaris in the direction of ray BG. Line HCE is the Earth’s axis, and it also points at Polaris – which is so far away, and seems so tiny, but yet is also so large, that yes, parallel rays BG and CH do, for all practical purposes, point at the same point in the sky. Ray ED starts at the center of the Earth, passes through you at B, and goes on to the zenith (the part of the sky that is directly overhead). The horizon (BF) and the zenith (ray EB) are perpendicular. Also, line HCE (the earth’s axis) is perpendicular to its equator (segment AED).
Using some sort of angle measuring device, if you are out on the National Mall at night, you can very carefully measure the angle of elevation of the North Star above the local horizon, and you should ideally find that angle, FBG, is about 38.9 degrees, but we could also call it X degrees.
Prove (i.e. explain) why your latitude (which is angle AEB) measures the same as angle FBG.
Full disclosure: My daughter graduated from SWW two decades ago, and I taught there as well for a year and for 10 years at a school that is now associated with it: Francis (then JHS now a middle school).
The kids were nice back then, and they still are. I thought the teachers did a great job.
This is a DC public high school that you have to apply to.
Benjamin Banneker was an amazing person. There are a lot of myths that have been attached to his work and accomplishments, which I am guessing might be because those people didn’t actually understand the math and astronomy that he did accomplish. The best book on him is by Silvio Bedini.
‘Math on the Mall’ was originated by Florence Fasanelli, Richard Thorington, and V. Frederick Rickey around 1990. I participated as a math teacher in a couple of those tours led by FF. Later, I wanted to take my students on a similar tour that would include a trip to see a number of the works of the geometer and artist Maurice C. Escher, and couldn’t find my copy of their work, so I made up my own, and added to it using the work of FF, RT, and VFR and suggestions from teachers and students. Later on, the Mathematical Association of America made something similar, which you can find here.
My version was on the website of the Carnegie Institution for Science for a number of years. See page 56 on this link. I need to find someone to cut out some of my excess verbiage and then trot it out to a publisher.
More progress with the 22-inch wide, 4-inch thick mystery glass.
It took four of us old farts- Jim Kaiser, Alan Tarica, Tom Crone, and me – to extract the mirror from its case (which was located under a very heavy Draper-style grinding and polishing machine) roll it onto a little stand we fabricated on a decent gym scale I borrowed from my gym ( http://www.True180.fitness ) and weigh it.
We were very careful when moving that heavy mirror. Nobody got hurt in any way. When putting the mirror back into its sturdy wood carrying box, we used ancient Egyptian technology of little rollers, and it worked like a charm.
The bathroom scale we had used earlier, up at Hopewell was very, very wrong. We found that the weight of the glass was really 212 pounds (about 96 kilograms, or 96,000 grams), not 130 pounds. Its volume was 20,722 cc, so its density is roughly 4.6. Will have to see what types of glass have roughly that density and an index of refraction of about 1.72 to 1.76.
I heard from one veteran telescope maker:
“I’ve been in the Tucson astronomy club for many decades and also in the optics industry there. Most all institutions that had connections to astronomy or optics in the 60s got portions of several semi loads of “glass bank glass”, glasses that at one point in the past were considered strategic materials for certain optical designs/systems. There was a wide variety of materials, but almost all was identified in some way. We’re there any markings ar data scribed in the glass? The largest I saw was about 15”, so yours might be a different source.
“A co-worker of mine has identified several mystery glasses from an accurate determination of density. Seems like you should be able to get better results w/a more accurate scale. Also many glass types made decades ago are obsolete – my friend has some older glass catalogs that might help you determine what it might be with more accurate numbers.”
So these were cast-offs from the Military Industrial Complex, basically: pieces of glass that the military decided it no longer needed for projects that had either been completed or abandoned, and that they didn’t feel like storing any more. So they gave them away to groups like National Capital Astronomers and Hopewell Observatory.
The only markings on the glass are the following: a heavily inscribed (by hand) apparent date of 2-8-56, which probably means either February 8 of 1956 or the 2nd of August 1956. Judging by the handwriting style of the numerals, it was probably Feb. 8 of 1956 (US style). Under that are the numerals 0225, which we have no idea about. In pencil, someone with US-style handwriting wrote what looks like “Low #” in cursive. Again, we have no idea what that means.