How to Flatten a Rock

Ah, the wonders of the Internet.  The other day, without having to leave home, I bought a Chinese rock.  (This, by the way, is pretty well guaranteed to please your UPS driver no end.)

Not, as you might think, some naturally sculptured scholar’s stone, but a nice, flat piece of granite.

Called a surface plate, it’s a shop tool for measuring things.  12 inches by 18 inches by 3 inches thick, it’s flat over its entire surface to less than .0001 inches.

Why so flat, you may ask?

Well, the rule of thumb in the measurement biz is that to measure anything accurately, you need a standard that is at least 10 times more accurate than what you want to measure.  So, if you want to measure things to .001 inches (pretty much shop basic) you need something that is 10 times better than that.

And how, you might ask next, do they measure the surface plate itself?

Not too surprisingly, they, too, use a standard that is 10 times flatter still, and so on.

But hold on, I hear you say, somewhere along the line somebody has to make the first measuring plate.  How do you do that?  That is, how do you make something that will be 10 times better than anything you’ve already made?  If everything in your shop is, by definition, cruder than your target, how can you ever get there?

This a generic problem of the machine age and the solutions are almost always something incredibly simple and incredibly clever.  In the case of surface plates, we owe it all to Sir Joseph Whitworth.

During the early and middle part of the 19th century, Whitworth made the most accurate tools in the world.  Ergo, he ran up against the “how do you make the first standard” problem fairly often.

First, he tried machining a plate as flat as his machines would achieve.  That was clearly not good enough.  It wasn’t smooth enough and it wasn’t flat enough.  Next, he set his most skillful workers to eyeball the surface and lap (i.e., rub with the finest possible abrasive) down any high spots.

Alas, this wasn’t good enough either.  While the human eye and hand is good at spotting small defects and removing them, they don’t do so well at flatness.  He ended up with very smooth, out-of-flat plates.

Back to the drawing board.

His next idea was to take two plates and rub them against each other with lapping compound in between.  That would automatically highlight and grind down any high spots.

Well and good, as far as surface finish goes, but once again, not so good for flatness.  If one plate, say “A,” is convex, then rubbing “B” against it is more likely to simply make “B” a bit concave to match.  The result would be two plates with beautiful finishes, no high spots, and matching curvatures.

Here is where Whitworth had his inspiration.

Instead of working with just two plates, “A” and “B,” he simply added a third, “C.”  Suppose you grind “A” against “B” and get a convex/concave set.  Now grind “C” against both of them.  “C” cannot possibly be made to match both “A” and “B” if either is out of flat.  To put it a bit technically, for a three surface problem, there is only one solution: a flat plane.

By rotating through three sets of plates, lapping them in alternate pairs, Whitworth was able to produce absolutely flat plates.  Three of them.  Then three more.

And that is how surface plates are produced to this very day.

And that is also the answer to our original problem:  how to make the original standards all the others are measured against.  Since there are, by definition, no devices accurate enough to create measure the very best (and no standards to measure them against), you have to come up with a method where the widget you are making becomes self-correcting.

Which means that today I can afford to buy an accurate surface plate for very little money.  I could even afford a super-accurate plate to check it against, since wear and usage will eventually destroy its perfection, but that thought brings back memories.

Once upon a time I worked for a large aerospace company.  It seemed as if every piece of equipment we owned had a little green calibration sticker somewhere on it.  Even things that one would be hard put to figure out how to calibrate still had little green stickers.  And each item with a green sticker had to be retested on a regular basis, and an updated sticker added.

The old saw in the military is, “If it moves, salute it.  If it doesn’t, paint it green.”  Around our place, I often had the feeling that if I didn’t move fairly often, I’d soon have a little green sticker on my butt.  They were everywhere.

Sure enough, all of our granite surface plates had to be re-calibrated regularly.  Given the fact that we had lots of them and a couple of them were on the order of four by eight feet by a foot or so thick, this was not a trivial job.  Still, I used to wonder about the folks who did it.  Good, worthy people, I’m sure, but…

“Well, how did work go today?  What did you do?”

“I calibrated a rock.”

“Oh, honey, I’m so proud!”

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