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:

2.02 THE NET ASSEMBLY
2.02.01 The net assembly shall consist of the net, its suspension and the supporting posts, including the clamps attaching them to the table.
2.02.02 The 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.
2.02.03 The top of the net, along its whole length, shall be 15.25cm above the playing surface.
2.02.04 The 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.”

 

10 thoughts on “Ounce-Centimeters of Fury

  1. Roughly 15 min of Google research was sufficient to determine that the ITTF is a non-profit organized under Swiss law, and that the actual rules of the game express the length and width of the table in meters, but a number of other dimensions are in centimeters or millimeters. In NO case are the units spelled out, all are expressed only as symbols; however, none include the (required) space between number and symbol, so I guess we don’t really know how they would choose to spell the units. Apparently metric Europeans can misuse the metric system as well as we can. Oh, and the ball is 2.7 g, 40 mm dia. sphere.
    http://www.ittf.com/ittf_handbook/ittf_hb.html

    I think it is obvious that 152.5 mm has already been “rounded” from 152.4 mm (6″) and that the game was originally Customary/Imperial and was metricated by an international body when the popularity of the game expanded. Conversion of other dimensions show rather modest discrepancies to round Customary dimensions. I think metrication of a US or UK game will always entail this.

    You probably wouldn’t like the field events in athletics (track & field) where performance is measured to the lower whole centimeter but expressed in meters to two decimal digits, either.

    It is interesting to me that most sports give only the nominal dimensions of the playing field or surface, no tolerances. As an engineer, that seems deficient to me, but the ruling body of the game is responsible for the rules. (Fields of variable dimensions like soccer give min/max, but football, baseball, basketball, etc only give the nominal.)

  2. Generally, I find that the common metric units of meter, liter, and gram are subdivided into thousandths. Yes, in some countries, for some reason centiliters pop up, but most work, especially in science and medicine, proceeds in “mL,” which led me, as a pharmacist, to favor the use of decimal point-free numbers.

    The U.S. is about to experience (thanks to a marvelous consortium of official agencies such as ISMP and CDC!) a long-overdue metrication of its household and prescription oral liquid medication dosing, such that “milliliter” will soon become a household word (it is even explained on the Drug Facts label panel, i.e., “mL = milliliter.” )

    During my visit to Germany, however, the Rule of 1000 was ignored, and I drank Coca Cola in 0.2 L sizes.

    • “During my visit to Germany, however, the Rule of 1000 was ignored, and I drank Coca Cola in 0.2 L sizes.”

      After the US finally went metric, they will to have learn yet another thing: Significant digits and tolerances. In Germany (and I presume in many other metric countries) the order of magnitude multiplier alse serves as in-band signalling for how preceise the measurement is. Usually its expected to be within a 5% for consumer products, 10% for bulk material and 1% for engineering, of the given value. So getting served 0.2L of a drink means something between 190mL to 210mL will be in the glass.

      I’m fully aware that for metrification its sensible to stick to the rule of 1000s and never to use decimals.

      But it simply doesn’t make sense to measure for example a board of wood in mm without then also specifying under which conditions it was measured (humidity, temperature, how much time went by between the tree was logged and the measurement made) because wood constantly alters its shape; anisotropically even. Saying something is 345mm long implies that it has been determined with at least 0.1mm of tolerance.

      Similarly it doesn’t make sense to measure, say a network cable down to the milimeter. Simply by coiling it up it up, there’s enough strain that the outer edge gets longer by 1mm compared to the inner edge.

      Ordering 1000mm of a cable in Germany means: “I WANT EXACTLY 1000mm CUT TO A PRECISION TO 0.01mm !!!!1!!ELEVEN”.

      In the lab it usually goes: “Hey, do you got a 3m extension cord?” (Doesn’t matter if it’s a few cm longer or shorter). Compare that with (equally often heard) “Hey, could you make me a 43cm delay line please?” (being in a lab that implies a tolerance of 1%, i.e. cut to about 5mm please).

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