From where I am sitting, the earth is flat. The floor that runs the length of the unit my hackerspace sits in is flat, the concrete apron behind it on which we test our Hacky Racers is flat, and a few undulations in terrain notwithstanding, it remains flat as I walk up the road towards Stony Stratford.
Of course, Hackaday hasn’t lost its mind and joined the conspiracy theorists, the earth is definitely spherical as has been known and proved multiple times since antiquity. But my trivial observation made in a damp part of Buckinghamshire still holds; that for a given value of flat which disregards a few lumps and bumps in the ground, my corner of the English city of Milton Keynes is pretty flat. Which leads from a philosophical discussion to an engineering one, if I can reasonably describe a city-sized area on an Earth-sized sphere as flat, how flat does a surface have to be to be considered flat? And from that stems a fascinating story of the evolution of precision machining.
Precision Starts With Something Flat
The history of machine tools stretches back into antiquity, in that simple lathes have been found in the archeological record of several regions of the world. There’s an industry which just about survives using rudimentary lathes pretty close to where I grew up, the chair bodgers in the English Chiltern hills use temporary pole lathes which wrap a rope around the part to be turned and balance it against the springiness of a tree branch to turn traditional wooden chair legs.
But these machines and their more refined descendants, while very good at producing the turned items they do, are not precision tools. The dimensions of the bodger’s chair leg depends on his eye and skill rather than the machine itself, because it lacks the flat bed of a modern machinist’s lathe as a baseline for its tooling. Like the city of Milton Keynes mentioned above, it’s easy to make something that looks pretty flat, but it remains hard to make something which is flat enough to use as a reference from which to machine other things. The method for making a truly flat surface without another to compare it against is thus one of the most significant innovations in the history of engineering, and definitely deserves a look.
Flatness Without Precision Tooling
The problem facing anyone tackling the manufacture of a flat surface is that by using a tool on a piece of material, be it one stone rubbed against another, a plane on a piece of wood, or a file on a piece of metal, the work piece will reflect the imperfections in the tool and in the technique.
Thus it’s not too difficult to make something that looks fairly flat, but the result will not be really flat. Rub two pieces of stone together and they will become smooth for example, but it’s likely that they will tend towards one becoming concave and the other convex. The problem of making a truly flat surface in this way was solved in the 1830s by Joseph Whitworth, he of the Whitworth standard threads, who instead of testing two surfaces against each other, instead used three.
The idea was that having a set of three plates and testing them in pairs against each other in turn, he could eliminate the errors in one affecting the other. By coating the surfaces with engineer’s blue, a dye, he could lap one surface against another leaving the areas in which there was a gap between them as blue. He could thus machine the layers down where the blue dye had been worn away and repeat the process against each of the other plates in turn, until he was left with three perfectly flat surfaces that could be used as standards in his machine tools. It’s by necessity a slow process as you can see in this video, but its beauty is that it can be done without precision tooling.
There probably aren’t many inventions that could be claimed as somewhere at the basis of so many others as can Whitworth’s flat surfaces without being more widely known in their own right. But the precision his technique afforded to every subsequent piece of engineering lives on with us today, and its elegance is in its simplicity. In every engineer lurks a metrologist, and it’s in things like Whitworth’s three plate method that mine finds fulfillment.
Surface plate header image: Rrudzik, CC0.
O, un mármol de ajuste !
Check out this book: https://www.amazon.com/Perfectionists-Precision-Engineers-Created-Modern/dp/0062652559
That is not the whole truth. Woodworking is definitely about precision (try making a four-legged chair that doesn’t rock without precise methods and tools) which is achieved by means of assorted jigs, templates and tools and not an eye. What these machines lack is accuracy. Legs made in one shop won’t fit right off the bat into a seat made in another.
There was an article about this!
https://hackaday.com/2021/03/20/machinists-precision-vs-woodworkers-precision/
I am following a 2-year long furniture making course. As important as all the planing and joinery methods are, the practical side is mostly about making do with your mistakes…
– Oh you chiseled your tenon too thin? Just put some veneer on it to make it thicker again!
– Oh your wood was so warped that planing it to the thickness on the drawing still leaves some defects? Just machine it 1mm thinner and adapt your drawings.
Yup. And that is why most CAD programs are hard to use for “individual” (not necessarily hand-tool) woodworking. They can describe parts’ dimensions but not relationships between them and which are important ones and which are not. At least I haven’t seen one that can.
Woodworking considers precision in the order of mm – which is entirely fair enough as wood is a natural product that will warp, swell, tends to be rather elastic and all that matters is it looks and functions good enough at a human scale. So something that looks flat and feels smooth is ‘flat’ etc.
Machinists tend to be working at the sloppiest end to the nearest 0.1mm, and usually much more precise tolerances than that as all these parts have to reliably and repeatably move past each other on that thin film of oil, or press fit snugly etc. But you can still have the same problem with the fit of parts for machine A not working on B, or in many cases if put it back in any other one of the many ‘identical’ locations on the machine they came from. Which is why you will often see punch marks or even stamped in letters and numbers to ensure parts go back on the same machine in the same place and orientation they were made on old machines. Its only in relatively recent history you can just expect a part made precisely to spec to just work in a machine made somewhere else. But either way the machinist really wants a proper reference surface – even if that part only has to fit to a single location and not be interchangeable with any other machine the degree of precision in play is substantially higher than woodworking and in nearly all cases the location of that feature must stay within a tight tolerance of heaps of other features for the machine to function.
Believe me, you don’t want a half millimeter gaps in your furniture where you don’t need them. You want tight fits. 0.1 mm is what you aim for in terms of precision (and thanks to appropriate method you can achieve it without much effort).
That is exactly what woodworkers do, they make parts tightly fit together with no gaps to form a single piece of furniture but don’t care about interchangeability. At least those in shops, furniture factories are a different story. They relay on repeatability.
That is accuracy and it’s about 100 years old. It became possible to achieve it when accurate gauge blocks (and reference surfaces) became available.
That is entirely correct. Wood is much more forgiving because it moves seasonally anyway. OTOH you need to take it into account to prevent a piece from falling apart.
More importantly, wood is fairly elastic and while you don’t want gappy joints, things like drawboring and clamps can force a close joint into alignment. To some extent everything is rubber, even a concrete floor moves under pressure and can be read with an optical collimator. BTW, the three plate theory is more formally known as the “statistical distribution of errors”. Oxtools did a YouTube on producing three lapping plates using this methodology.
Quite often more time and effort goes into the jig rather than the final product.
In a hobby shop — yes. In a professional one — no, that’s why it’s called professional. Pros engineer their production to make it profitable and they’ve done it this way for centuries.
But that’s what Bob said… the pros who “engineer their production” will take far longer about engineering their production than it takes to make any one single product.
A single piece rather than a batch. Yes, you are right. I didn’t get the gist.
Millions are spent on tooling for products with prices orders of magnitude lesser.
The only way a 4 legged chair won’t rock is if the legs are the same length AND they are sitting on a perfectly flat surface. If you really want something to sit on that won’t rock on a typical unflat floor, use three legs. A three legged stool can sit on any floor without rocking. It has something to do with the geometric idea that three points, not four, define a plane.
The reason a four legged table will sit on a typical floor without rocking is that the table top flexes enough to allow all four feet to touch the floor. OTOH, many pedestal type cafe tables will rock on an uneven floor is because the steel pedestal is too stiff to flex. That’s when you slide a piece of folded paper under one of the feet to stop it from rocking. It’s the same reason why appliances usually have adjustable feet.
This is correct, three points define a plane which is why a three legged stool will never rock. Commonly I would leave chair legs a hair long and then put the finished product on something pretty flat like a table saw. From that surface you lay a small block and mark each leg and take a final cut to level everything up at the end.
>the earth is definitely spherical
Actually, depending on which geodetic system you use, it’s at least an ellipsoid rather than a sphere. :P
… and even that ellipsoid is pretty bumpy/uneven. ;-)
And yet, at the scale of a billiard ball, smoother.
Yes. I have never checked the math on this, but there is a clip of Neil DeGrasse Tyson saying that a scale model of the Earth the size of a billiard ball – including Everest and the Marianas Trench at scale – would be one of the smoothest objects ever manufactured.
Unless I’m making a calculation error, I have to disagree. The earth is about 12.7 Mm(megameter) in diameter. The Mt Everest is 8.8km, the Mariana trench is 11km deep. Scaled to the 57mm diameter of a billiard ball, the Everest would be 39um high and the Mariana trench 49um. That is about ½ to ⅔ the diametre of a human hair, and definitely something you can feel with your fingers.
New billiard balls generally have bumps and cracks to within 1um, see https://billiards.colostate.edu/faq/ball/smooth/. So a billiard ball is way smoother than the earth.
IIVQ looks correct to me. They say that as you grow older you have fewer and fewer heroes and one of mine faded a little bit with this.
https://www.youtube.com/watch?v=hrjWzBY_dLw
Pick better heroes.
He’s a TV presenter.
Had a choice, said: ‘F- science, there’s top shelf hookers and blow over here.’
All he did here was repeat derp once. Is human. Likes stuff/people he agrees with. Doesn’t check all the math.
Better yet. Give up on idea of ‘hero’.
Indeed, spheroid rather than spherical.
Also, Moore Tool published three foundational books for thinking about precision and accuracy in machining.
-Precision Hole Location in 1946, by the company founder.
-Holes, Contours, and Surfaces, 1955
– Foundations of Mechanical Accuracy
https://mooretool.com/about-us/publications/
https://hackaday.com/2023/03/16/laser-and-webcam-team-up-for-micron-resolution-flatness-measurements/
Once you have established a flat reference plane you can also make perfect
right angle plates with a similar process. Moore’s book on Foundations of Mechanical accuracy goes into a lot of detail about the history of metrology as well as practical matters needed to make incredible, war-winning machine tools. One of the principals is that references should be self-checking without need for outside reference. Even as a technical volume it’s an amazing read.
Seconded hard for Foundations Of Mechanical Accuracy by Moore. That book is a phenomenal master reference for anyone serious about understanding things this post is about.
I say this as a professional machinist. The guys at the top of the field all know this text. If you want to know how accuracy is fundamentally generated in machine design, nothing else beats that book. I pray it never goes out of print.
https://archive.org/details/FoundationsOfMechanicalAccuracy
For those curious.
thank you
Good man for linking that. That’s book #1 for restarting society after cataclysm for me, I’d guard it and reestablish industrial precision with it, I consider it that significant.
While I agree its got to be right up there for me it can’t be number 1 unless the cataclysm is a very minor one – like no more shipping in from the cheap labour markets so local precision engineering has to ramp up. Otherwise Bushcraft, pre-industrial farming, basic physics and chemistry etc have to come first – can’t have the population to support precision machining without food or the materials to work in without some other sources first.
Though he’s best known for his machines to mass-produce fasteners, Whitworth is also incredibly important for his work with precision screws, being noted for using similar techniques to make extremely accurate leadscrews.
He then used these leadscrews to make precision lathes to make even more precise leadscrews which in turn mass produced the leadscrews that drove the machines of industrial revolution.
He was really the first guy to produce very accurate machine tools _specifically_ to mass produce very accurate machine tools, and so on.
It’s kind of elephants all the way down, but if you have a mill or lathe near you the odds are really, really, good that the leadscrews can trace their parenthood down through the screws of dozens of machine tools and eventually back to Whitworth’s original master screw, which now quietly resides in a display case of ‘Victorian Science Things’ in the British Museum of Natural History.
http://www.whitworthsociety.org/history.php?page=2:
Wow!
Thanks for the link!
Don’t forget the work of Henry Maudsley in screw cutting and engine lathe development. 2 of his lathes are viewable in the Henry Ford Museum.
I remembered a teacher at my Alma Mater, in one of her classes she said Earth’s mass is constant while the students argued it is variable.
Constant over what time frame and to what precision? It certainly wasn’t constant when some large planetoid slammed into it and threw off matter that formed the moon. It’s not constant anytime meteors slam into it. It’s technically not constant as hydrogen escapes the atmosphere, which happens regularly.
yeah right answer :) and we need to subtract the mass of mad made rockets, satellites, all the robots on Mars and…
Nuclear decay also reduces mass of the earth. Solar winds may sweep way parts of our atmosphere (or do they add mass too?).
The Earth also collects dust, so it’s getting heavier.
would love to know if Earth is actually getting fatter or thinner :)
I think your opening argument is fairly disingenuous. Going to an online calculator shows quickly that at 1.22 Miles (2KM) you would experience a foot (12 inches/ 0.3M) of elevation change on average. I daresay your average surveyor is quickly taught how to account for that.
You can quickly find practical applications of this in bridge towers, such as the Golden Gate Bridge: ” . . . towers are 1410 metres apart, and 155.5 metres high.” “. . .the tops of the two towers are 36 millimetres further apart than at the bases”.
I just get the immediate impression of wide-eyed handwaving when the logic of the introduction does’t work.
That may be a perfectly grammatically correct use of the word “disingenuous”, but it’s not really a fair characterization due to its negative connatations of insincerity. Although it’s clear to most that the author is using rhetoric to lead the reader, nothing she said was technically incorrect.
As far as I am aware there is nothing in this universe that is actually truly flat. Ergo, everything that we label as flat needs some reference or context. For some definition of flat, the earth can indeed be flat(*). For some definitions of flat, so the hackerspace floor, the concrete apron, and the road towards Stony Stratford are also flat. The very first sentence, “From where I am sitting,” gives you context. It’s a personal visual reference. That may be chosen for dramatic effect to support the rhetoric, but it’s not wrong. I can state that my flat-screen television is flat, but I think that everyone would understand from context that I won’t be using my television as a surface plate any time soon, yet compared to an old cathode ray television it is indeed … flat(**).
You might believe that the following appears be more technically correct, but it actually resolves to the same personal visual reference to flatness, and doesn’t have the same impact on the reader:
“From where I am sitting, the earth appears flat. The floor that runs the length of the unit my hackerspace sits in appears flat, the concrete apron behind it on which we test our Hacky Racers appears to be flat, and a few undulations in terrain notwithstanding, it appears to remain flat as I walk up the road towards Stony Stratford.”
The logic worked just fine. The first paragraph might be rhetoric, and perhaps even a little clumsy, but I don’t see any wide-eyed handwaving here.
(**) Notwithstanding any distortions due to mounting or its own mass, my flat-screen television is almost certainly about as flat as the earth is wherever the glass was floated.
(*) The earth at the glass factory where my television’s glass was floated is about as flat as my flat-screen televsion.
Fair points. Even rhetorically I cringe at calling a town flat, much less a city.
XD, apologies to your television, but I’d wager if you layed it with the screen facing vertical you could probably measure a curve greater than the Earth’s surface. Having disassembled many LCD screens the panels are anything but ridgid, and usually quite a bit of ripple can be observed in the panel as it hangs on the wall. As a child our TV was a Trinitron, and was impressively flat in the Y axis, if not the X.
I’m a troglodyte still using a plasma TV. No discernible ripple!
It’s ironic that Jenny introduced the town of High Wycombe and the Chiltern Hills after talking about flat towns though. The Etymology of the name is “High in the Valley of the River Wye”. and the town basically grew around the highest point on the river that would support mills. At one point there were close to 30 mills in that 9 mile stretch of river. On either side of the town the main roads out are steep, rising over 300 ft. The area is anything but flat!
I propose the use of the word
flatt
to indicate a theoretically ultimate perfectly infinitely flat surface.
Any geometric shape is in comparison to a reference plane which in machine tools is normally a reference to local gravity and two points which form a line which is straight by geometric proof. Everything else is geometric proofs for perpendicularity and parallelism.
Oh, so that’s why everytime I run a 10k marathon it feels like I’ve climbed two flights of stairs!
As a long-time member of the Chairboys’ Barmy Army, I wholeheartedly appreciate the video link to the old-time bodgers!
The really interesting thing to me is that flatness is a concept that I don’t think actually exists anywhere but theoretically. A flat object is defined by having a surface of which every point lies exactly within a plane defined by 3 points in space, but any attempt to create one fails. The 3-plate method could work, but only once gravity is removed from the situation, because the plates sag. You’d also need to remove all temperature fluctuation too, as objects expand and contract at different rates at their corners and vertices due to the differences in surface area-to-mass. By using friction to lap them flat though, that becomes difficult. I’d guess that since most materials have a positive coefficient of thermal expansion, that most plates end up slightly concave.
The best chance of creating a truly flat object would be to utilize the 3-plate method on plates with as close to zero thermal co-efficient as possible, (such as some very expensive engineered glasses and ceramics exhibit), in a zero gravity environment (i.e. space). I’m not quite sure how to make them practically useful though, since the plates would still sag once exposed to gravity, and I’m fairly sure that astronauts really don’t want to create fine abrasive dust in their spacecraft.
So whatever we do, we’re stuck with a tolerance grade, where the tolerance defines two parallel planes that each point of the surface will fall between. At the highest grades used as national standard references, plates are kept in tightly conditioned environments with minimal lighting (light means heat), with precautions taken to ensure that both sides of the plate remain isothermic (or it warps). Users wear suits and gloves, minimize their time in the environment, and use tools to handle anything being measured, all in order to prevent heat transfer to the object or plate. They set up the measurement, then leave and wait for everything to stabilize before coming back to measure. At local reference grades, many of those precautions are still applied, but generally to a lesser degree. Inspection grades less so again, although usually still in a conditioned space. Toolroom grades are generally subject to wide environmental changes because of the nature of most workshops.
In the absence of a calibrated surface plate, granite countertop are often the second flattest item in a home. The flattest is often the platter of an old hard disk drive, although its size makes it of limited usefulness (*). A piece of float glass is pretty flat too, the thicker the better.
(*) Way back in the early nineties, an electronics professor did an analysis of then-current HDD mechanics and concluded that the head size and speed across the platter was analogous to the Empire State Building lying on its side, flying across a field at the speed of sound at a height of 5mm and counting every blade of grass along the way. Disk platters are darn flat.
I’ve tried to use household granite countertop material as a flat plate, but even for rough lapping I found it completely worthless, like .01+” variance across a few inches. It only looks flat. Maybe plate glass is better.
Plate glass is maybe a little better, but much thinner and will bend like crazy when measured to such tolerances. Just get a certified flat plate, typically they are either made to bend as little as possible with suitably placed supports or are really thick, so they will just not sag.
I just checked a section of my kitchen countertop using a Rahn 18″x3″x1.5″ granite parallel on a pair of 123 blocks and a dial indicator. In one direction, the total deviation was under 0.0002″ across 18″. In the orthogonal direction, there is a valley of 0.004″ across 18″.
For reference, an in-spec 18″x18″ Grade B surface plate should have a total deviation within 0.0002″, so the countertop meets that in one direction, but is about 20x worse in the other. Support is important with thin materials, and kitchens aren’t installed with meteorology in mind.
I’ve used successfully used that section of countertop to lap a waterblock with fine grit paper before – there was no way I was putting abrasives on my good surface plate. Good lapping techniques minimize the impact of deviations anyway.
I can actually wring the parallel and countertop together in the good direction.
It’s not difficult to get something that has almost no expansion at a particular temperature range. Historically, invar alloy and glasses made to resist thermal shock were pretty low. Later, the materials of lenses and telescope mirrors and things became even better. If you want a different material rather than focusing on that one property, of course you can make up for that by taking great pains not to change the temperature. But the coefficient is pretty good now for e.g. Zerodur used as designed if that’s all you need.
For under $100 you can get small convenient granite plates from reputable manufacture or even cheaper for import ones. Just look for free shipping deals because they are heavy. Anyone interested in that degree of flat could probably justify the financial outlay.
Or do what I did and lurk on Craigslist till a suitable big one comes along- you may be able to score a “if you can move it you can have it” deal. For my roughly 24×36″ plate i found the biggest friend I could to help me and brought an engine hoist. We estimate it weighs 400+ lbs. good times.
Simon Winchester has a wonderful book called:
The Perfectionists: How Precision Engineers Created the Modern World
Your local library should have a copy. A fascinating read. He has a chapter on Whitworth.
Agreed- that is a fantastic read. Highly recommended
For home-lab use, an old platter from a defective harddrive can be utilized as a small precision flat. I keep an old platter from a 10,000 RPM SCSI (5.2″) drive handy when something more accurate than my old Starrett ruler is needed.
I have an old platter from a big hard drive (more than 30cm across) and it is pretty flat too.
I shot all my 5.25 drives.
There was a chance they had Netmare 2 on them.
Couldn’t risk it. Was fun!
Of course, that ammo is like Bitcoin now.
You neglected to mention hand scraping.
I was just looking to see if anyone else caught that.
Whiworth did NOT “machine” the blue away. He scraped it away by hand
The thickness of blue is 2.5 mu.
https://www.practicalmachinist.com/forum/threads/thickness-of-blue.326682/
And in the end, after lapping, Whitworth burnished it, which means smeared and smushed (the peaks of the smallest of the microscopic sharp peak projections).
He was actually a smusher, not a scraper.
That’s actually ok. Doesn’t really matter as long as one follows the algorithm, essentially.
Totally misses the point. If you don’t understand scraping, you probably don’t understand geometric approximation or how to physically reduce and spread/push error. Makes this article a big jumble of words that don’t really explain how flatness is accomplished.
Last Bastion for Blacksmiths’ Art in a CNC World
https://www.engineering.com/story/hand-scraping-the-last-bastion-for-the-blacksmiths-art-in-a-cnc-world
Is this where the term ‘bodge’ comes from? I.e to bodge something together – assemble or manufacture from stuff you have laying round. Was England just full of dudes MacGyvering lathes out of whatever?
Nevermind. Bodge (to make something sloppily) comes from botch. Makes sense really.
Protip: Never use ‘bodge’ in a sexual sense.
Even if you just learned it means ‘make something sloppy’.
Just don’t do it.
Even if some comment on hackaday put the idea in your head.
Push it out of your mind, before it slips out at a bad time. Perhaps muffled.
Ask me how I know.
I’m curious: Did Whitworth ever express a view about the metric system?
Ah yes the three seash ehh i mean stone, technique. It really does work. Used it several times with great results.
Speaking off the flat earth theory. We employ a lot of surveyors. I met one that was a flath earth believer. A surveyor. Went to school to become a surveyor and learned how to do calculations based on the curvature of the earth. He was later fired because he failed a drug test. So there’s that.
Or was he fired because he really failed the curvature test?
Sadly no. He finished school many years before, got send overseas to survey a harbor where they did tests on people entering. He failed. He was a bit of a strange person.
The silicon wafers that computer chips are from are “atomically” flat. If you put two of them together you can “wring” them together. The problem is once they are stuck together you can’t get them apart without breaking at least one and typically both of them.
I kept thinking about this and how one define flat. Like- a molecule of cyclopropane would have the carbon atoms atomically flat. Well, then you start thinking about atomic motion, wave mechanics, the wavelength of an electron etc and the whole thing breaks down eventually anyway.
“atomically” flat is still but only a partial way towards “flatt” –
halfway to infinity is a long way but still not a lot
Heronimious says:
December 7, 2023 at 5:38 am
I propose the use of the word
flatt
to indicate a theoretical infinitely perfect flat surface.
Planar.
Perhaps ‘perfectly planar’. Is redundant.
‘flatt’ is useless in engineering. Only used by the unaware.
Math already has this covered.
Besides which, private word definitions just suck.
Would you ‘#define eh ;’?
Canada.h? No possible complications…
…Why does this remind me of that one scene where Morty experiences “true level”?
we DO Dabble in Precision around these parts…
https://www.ardentheavyindustries.com/straightedge/
Burning Man Project from several years ago that helps one visualize the curvature of the Earth on one of the flattest lakebeds around. :D
Now that is cool! Flat earthers brains will melt upon seeing it I hope, lol
I prefer Tom Lipton’s series on 3 plate lapping
https://youtu.be/rHmsQEAx16o?si=XDpacUGvoK56w2iY
https://youtu.be/-w4R2eAHHiI?si=dA59vD0MXs882Y52
https://youtu.be/Whyw5v7L70c?si=-juoeRzW7v1Z72Mt
https://youtu.be/zwrTGVSxzJI?si=QQXUl-GCjOziLiwq
Seconded- Tom is proper learning at high level. I recommend him and Robin Renzetti’s channels, and Stefan Gotteswinter’s to every person interested in learning more in machining.
I have an optical flat 12.25″ in diameter… The only person who has one bigger I know of is Robin, haha.