The Design of Everyday Rulers

By The Metric Maven

Metric Day Edition

One day my father was helping a relative create a wooden plaque for an extracurricular project. They needed to find the center of a piece of wood, and searched for my father’s centering ruler, but it was nowhere to be found. The relative grabbed a nearby ruler and began to measure the distance, which involved fractions. They began to calculate and confusion began to proliferate. Finally my father said, let’s do it in a way my son would be proud of. My father always carries a high quality tape measure which has inches on one side, but is marked with millimeters on the other (not centimeters).  A quick measurement produced a value of 86 mm which immediately told them that 43 mm was the center.

When he was relating this story to me, my father commented that the centering rulers he owned had inches, picas and other units, but no metric. At first I thought this odd, but I realized that with a mm tape measure, the need for a centering ruler would be essentially eliminated. It also struck me as an example of a tool that one purchases because in the US we use Ye Olde English measures with fractions. Finding the center with millimeters is such a simple calculation, it essentially eliminates the need for a centering ruler (aka center finding ruler). It was yet another example of unnecessary costs involved with using inches and fractions.

When I started trying to use metric at my place of work about a decade ago, I was also required to use inches, so I was stuck with using a dual scale ruler. Below is a scan of the ruler I used for many years:

I had not looked at it in a long time, but I noticed that it has 1/32 inch minimum graduations over the first inch, that is from zero to one inch. After one inch, the minimum graduations shift to 1/16 inch. I looked at another ruler and found it had 1/32 inch graduations on the 0-1 and 11-12 inch sections, but 1/16 in between. I had a hard time understanding how this could be useful. Was this scale to be used only when measuring below 1 inch? If that was the case why have it repeated on the 11-12 inch section of the ruler? When I looked, all three of the different inch rulers I own have the divisions from 0-1 and 11-12 with 32nds and elsewhere 16ths of an inch as the minimum graduation.

I spent some time online looking for an explanation to this 32nd of inch on each end mystery. My six inch rule was consistent in that it only had 32nds from 0-1 inch and had no 11-12 inch section. Why on earth was this done, and it is done very consistently.

One Saturday, when talking with Sven, I pointed out this mystery to him. He took a breath, and then began: “I swear, I once saw a ruler like this.” Sven then drew the ruler on a sheet of paper as an illustration for me. Here is what he drew:

This is a ruler which has only inch marks from zero to five. In other words there are only whole inches from zero to five. From the virtual -1 inch, which is not marked, to zero the graduations are in 32nds. I looked in astonishment and asked: “How on earth would you measure with this?” Sven then explained that you would take whatever object you were going to measure, and line it up with the closest inch so that the other end would dangle between -1 and 0 inches. One would then figure out the fractional overlap and add that to the integer inch value. I was dumbfounded, clearly that would work. It was complicated in comparison to a millimeter only metric ruler because of the choice of halves, quarters, eighths,  sixteenths, and 32nds, but it would work.

This method could be used with a common ruler, but a person would have to remember to subtract 1 from the inch graduation chosen, and then add on the fractional part. This seemed far too complicated for use by the average citizen, but I see no other possible way to readily use the 32nds scale at both ends. Millimeter only rulers will immediately provide an integer value which is precise to within 1/25th of an inch, and with some judgement, 1/50th of an inch. No need to sort out fractions, just read an integer from a “number line.”

I have mentioned Donald A. Norman’s book The Design of Everyday Things in previous essays. He has an idea called affordance. This is the idea that a product should have designed into it clues as to how it should be used. In the case of the dual end 32nds it does not seem to immediately suggest how one might make use of the scale. Sven’s ruler at least gives you a bit of a clue about how to use it from the fact there are no fractional divisions from 0 to 5. My dual scale ruler also has a clue as to which side should be preferred. One can only read the Dual-Rule logo and the text which documents who manufactured it, when using the inch scale. Despite the inch preference, this was the ruler I really could not give up, because when you turned it over, it was the only ruler I had which had a millimeter only scale on it.

Others were all cm/mm rulers. This was my old reliable.

It would not be until Mike Joy sent me 150 mm, 300 mm, and 600 mm  single scale metric millimeter only rulers from Australia that I would finally be able to retire this dual scale ruler. I don’t use it anymore in my engineering work, but for some reason I keep it on my desk, perhaps because it was the only millimeter-only scale I had for many years.

As I have pointed out previously, the Invisible Metric Embargo in the US makes it very hard to obtain mm only rulers and tape measures. For many, many, years my father has carried around a small dual-scale tape measure. This tape measure is the same one used to find the center of the piece of wood related earlier. My father’s tape measure is unusual because the metric side is in millimeters. Unfortunately, his tape measure finally wore out. The scale of the first 100 mm or so was worn off to the point it had become illegible. My father called all the technical suppliers he knows—and he knows a lot of them. He had no luck finding a replacement. The tape measure had been discontinued. My father was becoming desperate. He never did find a new replacement. He had, however, purchased an extra tape measure over twenty years ago with his original order, and serendipitously found it. Here is what the “new” tape looks like:

Dual Scale Tape with millimeters on top (click to enlarge)

This tape measure is truly a metric anachronism in the US. The tape measure lists meters first on its front (3m-10′) and the millimeter scale is on the top, with inches below. This tape measure suggests metric, with millimeters, and de-emphasizes Ye Olde English. Centimeter/millimeter tapes are common, millimeter-only tapes are sighted slightly less often than Bigfoot and Elvis.

It was brought to my attention that there is a place in the US where one can purchase an American-made millimeter only rule. I ordered one, and after it arrived, realized that ruler designers in the US are essentially Mormons making coffee. Here is a photo of the US ruler and an Australian counterpart:

Australian 300 mm rule (top) and American made 300 mm rule (bottom)

I’m sure my readers realize that the Australian rule is very legible, and the US ruler, despite the high contrast, has such uniformly small numbers, that it is very hard to read. The US design appears to have almost zero thought put into it. This is why I end up obtaining rules from Australia.

One day I received an email from Peter Goodyear. In the email he stated he had purchased a dual-scale metric ruler that weekend. It seemed like a joke, and I treated it as such. Peter then wrote back to tell me it was no joke, and sent me a scan of it. I was stunned. Proof that he had not Photoshopped his way to this ruler arrived in the mail a week or two later from Australia. Here is an image of the ruler:

I was absolutely floored when I looked at it. What I realized was that even something seemingly as simple as the design of a ruler actually has a number of options. The millimeter side of this dual-scale ruler has millimeter graduation lengths which become longer as one approaches half-way and then retreat in the same manner as they approach the next whole number millimeter designation. I’m still thinking about if I think this is a good idea or not—I’m leaning toward not. Sven is not impressed, and would leave things as they are implemented on millimeter-only metric rulers, with half marks and the other designations of equal length.

The remarkable side of the ruler Peter sent me is the centimeter side. I’m perhaps deriving a bit of schadenfreude at the dismal treatment the centimeter is given. It’s just seen as a sort of close-enough for no actual work dimension. It only has half centimeter graduations, and no finer. The centimeter side reminded me of part of an aphorism about workmanship I heard in Montana that I will alter slightly: “He’s the kind of guy that would measure to a millimeter, mark it with chalk and cut it with an axe.”  Well, in this case there’s no need, there is a dual scale ruler for that, and he can use the centimeter side.

Pat Naughtin used to say “Don’t dual with dual.”  I could not agree more. Use millimeter only metric rulers, without a dual-scale, metric or Ye Olde English, and life will be good.

As I was revising this essay, I received a 300 mm long, millimeter only, metric ruler from Peter Goodyear. It looked ordinary enough, but when I flipped it over, the backside had a millimeter only centering ruler!  This came as a considerable surprise. After looking for a mm only centering ruler in the U.S. for a long time, one would show up serendipitously from Australia. Here is what it looks like in case you are curious:

Australian metric centering rule

I noted a setback for metrication this year when I came across this set of calipers in a large electronics retailer:

Calipers with a readout for fractional inches

I’ve never seen an electronic calipers with direct fractional readout before. You will note it is the first option listed on the package. It strikes me as equally useful as offering calculators with an option to have an output in Roman Numerals. It does have a mm scale on the slide, and a very legible readout for them.

This is my third metric day essay, and usually I cannot find a millimeter of change in the US, but this year is different. As I stated above, the only metric millimeter only rule I could find in the US, and manufactured in the US is poorly designed and I cannot recommend it. But this year the Japanese company SHINWA is offering mm only metric rules on a US based website, and I have purchased a 150 mm and a 300 mm ruler. They are actually a bit different from all the Australian rules I have. The 50, 100, and 150 mm labels are in red. The 300 mm rule has them at 100, 200 and 300 mm. The front of the 150 mm rule is given below:

Front of Shinwa H-101A 150 mm Ruler — click to enlarge

These rulers are not just imports it appears. The back of the ruler has tables which are clearly aimed at US users:

Back side of Shinwa H-101A 150 mm ruler — click to enlarge

Yes, it has a table of whole inches to millimeters, fractions to decimals, and non-metric tap information. The rulers have no dual rule markings, no centimeters, inches, or barleycorns, just millimeters. The rulers are as high quality of manufacture as any of my Australian rules.

Here’s wishing you the best on Metric Day. I say this with a minute amount of hope that next year I can report that I purchased a satisfactory millimeter only metric tape measure from a US based website. Until then the only option I know about is the slightly less than satisfactory True 32 (blue case) tape measure.

Postscript 2018-11-02

I encountered an image of a ruler that is marked in a manner different than all the options I’ve seen here or in my essay “The American Metric Ruler.”

Here centimeters are shown as a coarse length, and are labeled alphabetically as CM. They are passively discouraged as they do not have divisions. The numerical (Hindu-Arabic) labeling is given only as millimeters, but not labeled alphabetically. The user is assumed to understand the numerical values are millimeters without explanation. This is another example of poor design choice. All the information a user needs, assuming they are completely new to the device, should appear.

Related essays:

Stickin’ it to Yardsticks

The American “Metric Ruler”

America’s Fractional Mind


If you liked this essay and wish to support the work of The Metric Maven, please visit his Patreon Page and contribute. Also purchase his books about the metric system:

The first book is titled: Our Crumbling Invisible Infrastructure. It is a succinct set of essays  that explain why the absence of the metric system in the US is detrimental to our personal heath and our economy. These essays are separately available for free on my website,  but the book has them all in one place in print. The book may be purchased from Amazon here.


The second book is titled The Dimensions of the Cosmos. It takes the metric prefixes from yotta to Yocto and uses each metric prefix to describe a metric world. The book has a considerable number of color images to compliment the prose. It has been receiving good reviews. I think would be a great reference for US science teachers. It has a considerable number of scientific factoids and anecdotes that I believe would be of considerable educational use. It is available from Amazon here.


The third book is called Death By A Thousand Cuts, A Secret History of the Metric System in The United States. This monograph explains how we have been unable to legally deal with weights and measures in the United States from George Washington, to our current day. This book is also available on Amazon here.

Ounce-Centimeters of Fury

By The Metric Maven

Bulldog Edition

My friend Dr. Sunshine is a player of Table Tennis. He has spent a considerable amount of time practicing. The result of all this effort is that he finally cracked a 2000 rating in Ping–er–uh, I mean Table Tennis. The good doctor then had to explain what a 2000 rating means. I then realized that indeed he’s good. My meager understanding does not stop me from offering a less than informed opinion on the subject. I then asserted “I’m sure you’re really good, but you’re no Randy Daytona.” Dr Sunshine then looks puzzled and asks “who?”  After I explain, he offers his patented countenance of disapproval and states: “I hate that movie.”

In order to engage my enthusiasm concerning Table Tennis,  Dr. Sunshine indicates I should like it, as it’s an international game, and is completely defined using the metric system. I had given this little thought until my friend Pierre sent me this image and a link to the rules of Ping Pong.

Don’t buy a cm from this rat.

I took one look at the diagram, and there it was, centimeters. I knew who was to blame here, it had to be an American, a denizen of the United States. No one in Australia, the UK or New Zealand would spell centimeters with an er. This was yet one more example of using centimeters as a pseudo-inch surrogate for Olde English, rather than descriptively using millimeters. I also noticed that the image was a good illustration of how Americans will come up with ad-hoc excuses to use centimeters and then violate them immediately. Do you notice anything interesting about the dimensions?  Let’s change them all over to millimeters as nature intended for a closer look, and then explore the basis for my objections to the original diagram, and also to this new one:

Countries which metricated long ago, have preserved the junk DNA of centimetres as a vestigial inch measure, and seem to believe they must be preserved. The canonical example is human height. In countries which have long been metric, they generally use centimeters. My height is 179 cm in their view. I find 1790 mm more expressive, which has been vociferously rejected by citizens of long time metric countries. They usually say something like: “That’s crazy Metric Maven, you don’t need that kind of precision for a person’s height.” The argument for this continued use of centimeters is what I call The Implied Precision Fallacy. It assumes ahead of time there is a known optimum dimension for each “type” of measurement, and that you choose the unit depending on what is being measured–but not too small, because that’s too precise, and implies you need that much precision when you don’t, and that you are measuring to this precision which you aren’t. This appears to be some strange pseudo argument which relates back to barleycorns, inches, feet, yards, rods, furlongs, miles and leagues. Choose the right one for your measurement needs! In fact choose two units!—and be 5 foot 10 inches tall. It’s a better system because of this choice and not too much precision! Ask David Gallagher.

When I was in Junior high I recall receiving a report card which listed my height as 68.5 inches. My mind halted, and for an instant, it rejected the strange measurement. Why on earth didn’t it say 5′ 8 1/2″? Inches alone had no meaning, but as I later realized, they were simpler to measure and simpler to express. They are one unit, not two, why use two? It was simple cultural inculcation that caused my “lack of feeling” for straight inches. It was because everyone around me used mixed units from the time I was born. I see those who argue that centimeters are for body measurements as suffering from the same Olde English cultural inculcation in a more vestigial form.

The idea of choosing the “right sized” unit is constantly promoted, and implemented in an inconsistent manner when Olde English measures are used. The Olde English “right sized” unit argument is almost universally invoked to justify centimeters when using metric–but ignored in Ye Olde English when convenient. For instance, you are in an airplane, what is your height above the ground? Say it’s 30,000 feet. Why did you not use 5.68 miles? Isn’t that closer to the “right” base unit for unnecessary precision? Feet are just too small of units.  Perhaps 45.45 furlongs?–is that more optimum? 10,000 yards? Should we use miles above a mile and switch to feet below that?–in the cockpit? Inches when near the ground? Does it make sense to “describe” mountains in feet and not yards? Are feet not too precise for practical use?  How about 5 miles 3600 feet instead of 30,000 feet?

The Implied Precision Fallacy is invoked immediately to argue for centimeters when their use is challenged, but “this rule” is constantly ignored in the Olde English non-system of almost uncountable units, that gave rise to the argument in the first place. A proliferation of units was exactly what was wrong with pre-metric measurements. We could measure height in ells—but which length of ell? Flemish? English? Scottish? German?–which is of more proper length for our measurement?

Have you caught the beef I have with the dimensions on the Table Tennis Table? The net height and net overhang are both 15.25 cm, which are also 152.5 mm. So, the height of the net needs to be accurate within 0.5 mm or 500 μm? Is that precision necessary? One would guess it is not as centimeters are chosen. Here is the rule:

2.02THE NET ASSEMBLY
2.02.01The net assembly shall consist of the net, its suspension and the supporting posts, including the clamps attaching them to the table.
2.02.02The net shall be suspended by a cord attached at each end to an upright post 15.25cm high, the outside limits of the post being 15.25cm outside the side line.
2.02.03The top of the net, along its whole length, shall be 15.25cm above the playing surface.
2.02.04The bottom of the net, along its whole length, shall be as close as possible to the playing surface and the ends of the net shall be attached to the supporting posts from top to bottom

Sven wondered how this accuracy could possibly be met as a single cord by itself would form a catenary curve, and even when loaded along its length, like a bridge, would probably form a parabolic type of curve. The regulation height for the entire length of the top of the net to the playing surface is to be 152.5 mm?—and held to a constant 500 μm value? It seems the tension on the net cord would have to be tremendous!  Wow, and there is no tolerance on the height?

Would the entire game of Table Tennis change if the net height were defined to be 153 mm +/- 1 mm? Clearly the powers that be decided that centimeters alone didn’t have enough precision to describe the net height, they needed two places of accuracy,  and no one decided to use millimeters? Powers of 1000 make a nice continuum: mm, m, km. Millimeters work for metric construction in Australia and the UK, very effectively. There is no need for centimeters other than in response to the irrational desires of US cultural folklore, and to obscure meaning. I have no idea how this specified value for the net height is measured to micrometer accuracy. It is very difficult to believe that it is. What is the surface roughness of the table’s playing surface? and how level? and the tolerance of the diameter of the cord holding the net?

The spin of a ping pong ball is truly amazing. Professionals can rotate the balls at 7,000-8,000 RPM.

Table Tennis Balls — 40 mm  (Wikimedia Commons)

In the 2014 season finale of Mythbusters (Season 13 Episode 8), a segment called Killer Ping Pong Ball examines if a ping pong ball (PPB) can obtain a sufficient velocity to be lethal. Adam Savage doubted it could because of the very low mass of said ball. Which they do not define at that point. Adam and Jamie quote the famous equation F = ma, and are interested in maximally accelerating the PPB. The equation which makes a bit more sense to me is the kinetic energy equation which is:

Kinetic Energy = ½ mv2

where m is mass and v is velocity. When metric is used–as only makes sense–it expresses the energy in joules. A joule is about the energy needed to lift a 100 gram apple one meter into the air.

The Mythbusters duo attempt to hit ping pong balls, pitched by a machine, and quote the results in miles per hour, without exception. This once again shows how hard they actually try to use metric in their show, independent of Adam’s protestation otherwise. The fastest speed they achieved was 33.53 meters/second. Despite the Mythbusters statement that mass is of importance, they do not quote the mass of a PPB for quite some time into the segment. The supertechs put together various pneumatic ping pong devices to accelerate ping pong balls down plastic tubes. Pressure is quoted in PSI of course. The next speed developed is 62.59 meters/second.

Finally at the beginning of the second PPB segment Adam states: “We’ve effectively been attempting to weaponize the one-tenth of an ounce ping pong ball and make it lethal.” So the first “mass” quoted, is in a Ye Olde English unit which is worthless for the computation of energy.

My father once pointed out to me that the factors for millimeters to inches is about 25, and grams to avoirdupois ounces is about 28. So when Adam states that a ping pong ball is 1/10th of an ounce it would be about 2.8 grams. Until this country becomes metric, these will be important ratios to know.

The next “milestone” speed they achieve is 202.51 meters/second.

At the beginning of the third PPB segment Adam states: “In our quest to make the innocent 2.7 gram ping pong ball lethal…” so grams finally make an appearance in the program. The next record speed is 348.24 meters/second, which is faster than the speed of sound. The final speed is 491.74 meters per second. That’s almost half of a kilometer in one second. But of course Adam and Jamie have all the speeds in miles per hour. The final speed is near that of a bullet, and the Mythbusters have a considerable amount of experience with shooting bullets.

Adam and Jamie quoted F = ma as the equation of interest, but never compute the acceleration of the PPBs. They do give the speeds and it would be child’s play to use the kinetic energy equation ½ mv2 to illustrate how the amount of energy in a ping pong ball changes with respect to speed:

33.53 m/s      1.52 joules
62.59 m/s      5.28 joules
202.51 m/s     55.36 joules
348.24 m/s     163.72 joules
491.74 m/s     326.44 joules

Strangely, the show’s other segment, which is on creating an ice cannon, does quote the kinetic energy equation, but they do not use it to compute the energy of the projectile in joules. They do point out that the energy of a 22 caliber long rifle cartridge, shot from a pistol, is about 159 joules. The energy of a 9 mm  is 519 joules. The PPB has an energy between that of a 22 and a 9 mm.

Adam and Jamie then use their ping pong cannon to successfully shoot a hole through a ping pong paddle. Their final test uses a pork shoulder to simulate human flesh. The ping pong ball penetrated almost 40 mm into the pork shoulder, about half the length of a woman’s index finger, which is disturbing. The duo decide that this much trauma would not be life threatening, unless some lucky shot hit a person in a perfect manner to kill them. Myth busted, no killer ping pong balls.

Seriously though, congratulations to Dr. Sunshine, on becoming the Huntsman World Senior Games Champion in table tennis—ok—maybe you are better than Randy Daytona. But shame on the metric usage which is implemented to describe the dimensions of a ping pong table. The largest amount of shame is reserved for the less than informative non-metric presentation of the almost lethal ping pong balls by the MetricBusters.

Recently a dress designer I met pointed out that dress patterns are in centimeters. I just replied “they should be in millimeters.” Her instant reply was “we don’t need that much precision.” It is the automatic US response. I looked online for websites which describe how to make dresses. The first web page I checked had this question and answer:

PLEEASE explain point 13 about the size of dart…I AM DESPERATE…..thx for all your info!!!!!

Hi,

For Step 12, do the following:
-Your bust measurement is 106 cm, so you will subtract 88 cm from that amount, resulting in 18 cm.
-You will then add 0.6 cm for each 4 cm bust increment over 88 cm to the starting amount of 7 cm.
-In your case, you would be 0.6 cm x 3 = 1.8 cm. Then, add 1.8 cm to 7 cm to get your dart size, which comes out to 8.8 cm. (If you wanted to overestimate, you can calculate 0.6 cm x 4 = 2.4 cm, then add that to 7 cm for 9.4 cm.)
-Similarly for people whose bust measurement is under 88 cm, you would subtract 0.6 cm for each 4 cm bust increment under 88 cm then add to the starting amount of 7 cm.

Hope this helps!
Jamie

Wow, that’s a lot of decimal points and leading zeros that I have been assured are not required for dress making, as that much precision is not needed. There are decimal points to keep track of with centimeters that would not be needed with millimeters. The use of cm is a cultural, substitute security blanket for an inch, which is not a very optimum choice for ease of use in everyday work. Millimeters allow for simple integer numbers in most routine work. The choice of the millimeter for metric construction in Australia and the UK was based on assessing what worked best for the average Joe and provided the best insight. There is no reason to believe that suddenly when making dresses, or engineering devices as I do in my work, that centimeters are a better choice. They aren’t. My new aphorism is: “Take away an inch and they’ll make it a centimeter.” or better yet “Friends don’t let friends use centimeters.”


If you liked this essay and wish to support the work of The Metric Maven, please visit his Patreon Page and contribute. Also purchase his books about the metric system:

The first book is titled: Our Crumbling Invisible Infrastructure. It is a succinct set of essays  that explain why the absence of the metric system in the US is detrimental to our personal heath and our economy. These essays are separately available for free on my website,  but the book has them all in one place in print. The book may be purchased from Amazon here.


The second book is titled The Dimensions of the Cosmos. It takes the metric prefixes from yotta to Yocto and uses each metric prefix to describe a metric world. The book has a considerable number of color images to compliment the prose. It has been receiving good reviews. I think would be a great reference for US science teachers. It has a considerable number of scientific factoids and anecdotes that I believe would be of considerable educational use. It is available from Amazon here.


The third book is called Death By A Thousand Cuts, A Secret History of the Metric System in The United States. This monograph explains how we have been unable to legally deal with weights and measures in the United States from George Washington, to our current day. This book is also available on Amazon here.