Something Perfect In The World
I’ve been wrestling with how to admit what I’m about to write about. I’ve deleted versions of these introductory words several times. Not only is the subject an objectively simple object — a rectangular flat block of stone — but what is interesting about is seems extremely abstract at first. For me, it’s an object of almost mystical perfection but to a lot of people it will look like a tombstone that hasn’t been engraved yet.
I’m talking about a tool called a surface plate. Since it’s invention in about 1840, this simple device was been critical to the development of practically all modern manufacturing and remains indispensable today but my interest in technology and the the history of technology has very little to do with why I find this device fascinating.
I discovered these things in connection with playing around with machine tools. Let me admit forthrightly that one of the big attractions of machining is the sheer coolness of the gear. Machining has a lot in common with photography that way. Photographers love making photographs of course but they also love the sound and feel of all that silky smooth precision. It’s the same with machining: exquisitely made tools of burnished steel making cuts that are accurate to small fractions of a thousandth of an inch. What’s not to like?
A surface plate has none of that glamor. It’s is just a thick slab of stone (or sometimes cast iron) one side of which is ground and lapped to perfect flatness. Nothing in the world is truly perfect, but these objects come so close that they seem almost mystical. Their perfection approaches the Platonic, a sculptural representation of a Euclidean plane. When you realize just how perfect they are, it’s almost dizzying.
The black granite slab in the picture below that looks like an extra-thick kitchen countertop is a surface plate. I got it used for $80 bucks, which is about a quarter of what it would cost new. It’s thicker than a granite counter top to make it resistant to bending (more below about why you have to worry about solid granite bending) but other than that, the only difference is the degree of flatness on the top surface. And that’s where it gets interesting. It’s hard to describe how precisely flat these things are without coming off like Carl Sagan breathlessly trying to convey to the laity how far away galaxies are.
The precision isn’t just nerdy number-porn, like a fashion lover who counts the number of stitches around each buttonhole; it’s actually the opposite. The essence of engineering is reconciling the crudeness of the physical world with the perfection of mathematical abstractions. The intellectual work this entails can be brutally hard without being particularly interesting and even when it is interesting, a lot of what engineers do is so abstruse as to be inaccessible to non-initiates. But once in a while it comes down to something extremely simple where the numbers bring you face to face with the real nature of the physical world.
Surface plates serve as an almost geometrically perfect reference surface for machinists, tool-and-die makers, and workers in various kinds of laboratories. A measuring device that is set to some particular height or angle can be moved anywhere on the surface without those values being altered. In other words, every square centimeter of the surface is as precisely alike and lined up with every other square centimeter as human ingenuity can make it. There is almost nothing made in a modern factory that doesn’t indirectly require using these simple devices because making the machines or making the machines that made the machines required a surface plate.
The one in the picture is tiny, by the way, weights a mere 230 pounds. In industry or laboratory settings, surface plates as big as a full sheet of plywood and two feet thick would not be unusual and they come bigger than that. A four-by-eight surface plate weighs about 14 tons.
It’s the perfection of the flatness that’s fascinating. They are made in three standard grades, the flatness of which are rigorously defined by Federal law in a document called Specification GGG-P-463c. Grade B (like mine) is for the where machinist work; grade A is for a more controlled environment such as the tool room where fancy machining is done or inspection areas; AA is laboratory grade.
I had to read the spec a few times to be sure I was understanding it correctly. To understand what the spec says, you have to distinguish between the two most important kinds of non-flatness. One is local irregularities of a surface, and the other is the overall geometric non-flatness. Picture a potato chip. If you get super close up, you’ll see that the surface of the potato chip has all sorts of irregular bumps and ripples; this is the first kind of non-flatness. A potato chip as a whole also has a compound curvature, which is an example of the second kind of non-flatness. Even the most perfect physical object is going to have at least some component of both kinds of non-flatness.
So here’s how they officially describe how flat a surface plate is. Imagine that the top surface of a surface plate is contained between two parallel planes with one plane touching the highest spot on the surface and another plane running through the stone and just kissing the lowest spot. These two imaginary planes form a tight boundary around all deviations from perfection. For an AA surface plate of this size, those two imaginary planes can be no more than 35 one-millionths of an inch apart.
That’s a little less than a micron, which is about the size of the smallest bacterium (bacteria range between 1 and 10 microns.) That doesn’t mean there is any actual physical deviation from flatness in the stone itself that is that big — that’s just the depth of the box that would hold both the deepest valley and the tallest peak at the same time.
With an el-cheapo shop-grade B surface plate like mine, the two planes can be up to a slatternly 110 millionths of an inch apart, which means that some middling size bacteria could fit between the two planes but nothing huge like, say, a red blood cell (7 microns) would fit.
I’m trying to think of anything you can actually see and touch in normal life that’s so perfect. Components in a microchip are made to even finer standards but you can’t normally see them. The only thing I can think of are high-quality camera or a telescope lenses, the surfaces of which can be perfect down to the millionths of an inch range.
Machinists fail to be amazed because they know how this kind of perfection is achieved and deal with it routinely. Most non-machinists don’t know enough to be amazed; a centimeter, a millimeter, a micron, what’s the difference? You have to be in the technological Goldilocks zone to be properly awed.
Surface plates have to be checked occasionally for accuracy and lapped back into flatness if they have departed from the standards of their nominal grade. (Lapping is a very fine, controlled grinding process.) Granite is very hard but when you’re talking about millionths of an inch, even a little wear can be significant and the dust in machine-shops can contain tiny amount of silicon carbide, diamond dust, etc., that are hard enough to abrade granite.
When technicians evaluate a stone, the two kinds of flatness are measured separately. Even if every place on the stone is very flat relative to the surrounding surface, the stone as a whole can still be warped, and this is where the difference between the two kinds of flatness matters. Local non-flatness usually represents a genuine flaw, often a place where the surface has been heavily used. Think of the scoop worn into the cutting board at the delicatessen. However, if the stone seems to be locally flat everywhere, but shows an overall non-flatness, it might just represent a transitory change in shape caused by a temperature differential.
The evaporation of solvent or water used to clean a stone can chill the surface causing it to shrink minutely, which temporarily warp it into a slightly concave shape. It’s not that cooling causes a dent to form. What happens is the shrinking surface pulls laterally, warping the whole slab. A sunbeam or even a lamp shining on the surface can have the opposite effect. Uneven temperatures in multiple places can cause a temporary potato chip like deformation. The time of day matters; if it’s been cool all night, as the shop starts to warm up during the work day, a stone may warm more quickly on top where the air is slightly warmer and faster moving than on the underside, closer to the floor. Technicians know to consider this when evaluating the condition of a stone. If a surface plate is known to have once been flat, and still appears to be locally flat but is out of flat across the whole surface, it’s a strong clue that the problem is uneven temperature rather than a genuine departure from flatness. They may want to let the stone quiesce for a few hours and then measure again.
The process of measuring and re-grinding a stone is fascinating. Tom Lipton of the OxTools YouTube machining channel, filmed a pair of technicians giving his surface plates a checkup and performing some corrective lapping. Lipton makes precision tools and equipment for Livermore National labs, so his workroom standards are exacting. The amazing thing is how simple the tools are, particularly the laps used for flattening the stones. It’s not done by some huge machine. It is a manual process in which diamond dust is sprinkled on the surface plate and then a flat metal lapping plate is rubbed systematically over the surface to cut away the high areas. Properly done, this process is self-correcting, The lap and the surface plate tend to flatten each other because each bears down on the diamond dust hardest wherever the high spots on each other come into contact. The word “cutting” makes it sound rougher than it is. We are talking about shaving off millionths of an inch, so the stone removed is only enough to make the water used to lubricate the process a bit milky. The speed with which they bring Lipton’s stones back to immaculate AA perfection is astonishing.
There is a peculiar risk inherent in surface plates. Machinists also use a variety of other tools that also have exquisitely flat surfaces. If you put an object like that down on a perfectly clean surface plate it can glide silently away like an air-hockey puck and go right over the side. I’ve done this myself. The opposite happens too. If a super-flat object sits on a surface place for long enough to squeeze out the thin film of air between them, it may feel stuck to the table as if by a weak magnet.
Do I need such perfection? Me personally? Not really. I’m a tourist in the world of real accuracy because I’m really a carpenter and woodworker who sometimes does some basic machining. Accuracy is a way of looking at the world. While in fine woodworking you often work to finer accuracy than is represented on your measuring tools, it’s significant that woodworker’s measuring tools are typically graduated in 1/32 and 1/64 inch, while machinist tools are graduated in 1/1,000 and 1/10,000 inch.
The surface plate is clearly better that the piece of granite countertop that I used to get by with but my true pleasure in it is more in its almost Platonic perfection; a Euclidean plane sculpted out of 200 pounds of stone.
