# Stickin’ it to Yardsticks

By The Metric Maven
Bulldog Edition

One of my very first memories of linear measurement, is of my Grandfather’s upholstery shop. He had built all of his wooden  workbenches himself, and embedded wooden yardsticks into them for a convenient measure. Well, they looked like yardsticks, but were actually 54 inches. This was the size of “standard” upholstery cloth he often used.  There were also yardsticks of 36 inches around for  quick measurement. They were ubiquitous in my youth. Why?—because almost every business of one type or another gave them out as free advertising. Below is one from many years ago as an example.

Yardstick (Click to enlarge)

They seem as American as apple pie, but are actually a good example of how much the way we measure is a throwback to the 18th century. Even then they knew better. I explained the problem to a woman one day during a trip, and half-way through my explanation she spouted out “You make the way we measure sound like it’s difficult!”  I wasn’t sure if it was denial mixed with surprise and a hint of exasperation, or the shock of realization. She is no average girl, she has worked on large engineering bids in Korea and London. What’s wrong with our rulers? Let me begin at the beginning. Here is part of a yardstick with typical divisions labeled:

Yardstick with scales labeled

As every American knows from grade school instruction, a yardstick is divided into one inch divisions, half-inch, quarter-inch, and in the case of the yardstick shown, into eighth-inch divisions. Apparently that was close enough for most people, I don’t recall any complaints. The divisions are expressed as fractions, so if you have 1 + 1/2 + 3/4 + 7/8 you cannot add them directly to get 25/8 total. You must find a common denominator for them.

Essentially you have a ruler with 4 scales on it. By a scale I mean graduations you can read and add together directly. For instance if you measure a distance of 1 inch, and then measure 3 inches you can immediately add them together to make 4 inches. This is true for each fraction also, so 5/8  + 7/8 = 12/8 (= 3/2). To designate these scales on a yardstick, the line lengths are all different. Their vertical length is proportional to their horizontal linear graduation size, with 1, 2, 3 inches the longest and 1/8, 2/8, 3/8 the shortest vertical lines.

The Maven has one suggestion that would help make a yardstick much easier to use he-thinks. All of the fractional scales, (i.e 1, 1/2, 1/4 ..) are on top of one another, and share  many equal values. What I mean is  1 inch = 2/2 inch = 4/4 inch = 8/8 inch. So lets just get rid of all the scales except for the integer inches and the 1/8 inch graduations. The yardstick would now look like this:

Yardstick altered so only eighths show.

Now we can measure as precisely as possible with the smallest given graduation, that is, within 1/8 of an inch. The ruler does not have finer graduations, so no matter what you measure, it will be within about 1/8 of an inch. The great part is that now we can add measured values directly. Say we measure 2 3/8 inches and 6 7/8 inches. We can add them easily to get 8 10/8 inches or 9 and 2/8 inches. Now you may want to change it to 9 1/4 inches, but that value is no longer on our scale, so we would leave it in eighths.

The closest we can measure with this ruler is 1/8 inch which is 3.175 mm. If we go to 1/16 inch, that is 1.58 mm, so if we use a millimeter graduated rule we will be just slightly better than 1/25 of an inch. We already start out measuring much more precisely than a common yardstick, just by using millimeter graduations!

What most Americans think of as a metric ruler is shown below. I like showing it, because it’s from a thoughtless anti-metric diatribe, written at the turn of the twentieth century, which was presented before congress—and is wrong.

Centimeter-millimeter Ruler Mislabeled as a Millimeter Scale (click to enlarge)

It is designated to be a millimeter ruler according to the “distinguished” and “scholarly” author of The Metric Fallacy,” but it is not. It is a centimeter rule with millimeter graduations, what a mess! You may be thinking, “but Maven, you already showed us the same thing above is an improvement, isn’t it  better to have a version with centimeters and millimeters?” NO IT IS NOT. Yes this is the type of ruler that is attached to lower edge of inch rulers in the United States as an after-non-thought, and called a metric ruler. It’s clear whoever decided this “design” is a proper set of metric graduations has never actually used the metric system. Other English speaking fully metric nations, like Australia and New Zealand, have learned to eschew centimeters on rulers. Remember! The idea of metric is simplicity, full stop. Properly implemented metric is not harder than the current measurements, it’s much easier, as I will later show.

With this typical American style ruler we would have to measure say 2 cm 5 mm and 5 cm 7 mm to get 8 cm 2 mm. What we have again is two scales, one centimeter and one millimeter. We are forced to use two units, centimeters and millimeters, because of the ruler’s design.This may seem comfortable to a culture which measures people with values like five foot ten inches, but it is still not optimum, and is cumbersome. I would bet that the yardsticks given out in Monticello Iowa, in 1980, were centimeter-millimeter ones. This would probably cause most people there to see no advantage, and ignore the metric side. Here is the ad for yardsticks with metric graduations from the June 25, 1980 Monticello Express:

We will now convert the centimeter/millimeter ruler from 1904, with the magic of computer imaging software, to a true, single scale, millimeter metric ruler:

Correctly designated millimeter ruler — Now just the spelling needs fixing (click to enlarge)

Now this is a simple ruler anyone can use. If you measure 52 mm and 72 mm you can easily add them to get 124 mm. If the free yardsticks offered to Iowans in 1980 had been marked this way, some of the local residents might have immediately realized the advantages of using it. In my view, the mixed graduations of centimeters and millimeters on American rulers have held back metrication considerably. Dual rules, millimeters and inches, also are bad for metrication–but that’s another blog. Don’t use centimeters!—ever! Here is an example of a section from a 300 mm Australian ruler I use in my Engineering work:

Modern metric ruler from Australia (click to enlarge)

I tend not to need a ruler which is more than 600 mm long. It is people in metric countries, who design with fabric, that use full meter sticks with millimeter graduations—Like my grandfather’s larger yard stick. Here is a picture of a person using a meter stick with mm graduations:

Meter Stick with millimeter graduations (click to enlarge)

For the average person, there are only three distance measurement units that are important, millimeters, meters, and kilometers, that’s it. The others, such as micrometers and nanometers, are generally only used by technical professionals.

I spoke with my friend Thern, the Mechanical Engineer, about all of this. He has experience building houses, and said “If we used metric tape measures with only millimeters, people who have been unable to accurately read inch measures for their entire careers, would finally be able to do so accurately, and with way fewer errors when building houses.”

In the Jan-Feb issue of Metric Today in 2005, the story of Professional Engineer Robert Bullard  is detailed. He had the temerity to design a house exclusively in metric–in Florida. He faced multiple layers of metric discrimination trying to get his drawings approved by regulators. The attitude was “you don’t like it–then sue us.”  Bullard was inspired to go metric when he had his first experience with a metric design. The construction design was completed by a draftsman much faster than the US designs with which he had exclusive experience. Overall the entire design was about 20% more efficient

Quoting from the Metric Today article, we see Robert Bullard’s builder, Blake Cougle agreeing with Thern about our current measurement system:

Cougle then turns his critical eye onto U.S. workers, who, he claims, even fail to show mastery of American customary units of measurement. “[U.S. laborers] can’t handle fractions of inches,” he said. “They might use a ruler, but they often end up just counting courses (concrete blocks). You’d be amazed.”

Actually, because I understand how baroque our rulers are in the US, I’m not that amazed.

This is why Australia saves 10%-15% in material costs for building construction every year compared with America. What is a good use for all these old yard sticks?  Perhaps they can be broken up and used to fix tables with unequal legs. Some people already use them to make art. The time has long ago arrived in America to drop by a lumber yard and expect them to hand out wooden meter sticks for advertising—in metric only. Demand millimeter Metersticks not Yardsticks.

If you liked this essay and wish to support the work of The Metric Maven, please visit his Patreon Page.

Related essays:

The American “Metric” Ruler

The Design of Everyday Rulers

America’s Fractional Mind

# Space Case — A NASA Metric Mystery?

By The Metric Maven

Bulldog Edition

The satellite in the photograph is NOT The Mars Climate orbiter. Today: 2012-09-23, is the 13th anniversary of the mission failure of The Mars Climate Orbiter. This major malfunction was due to metric and imperial measurements existing side by  side in the US. The failure is proverbial, every metric advocate knows about it. So let’s talk about something a bit more interesting, a satellite story that is still a bit of a mystery. There may have been an imperial-metric failure connected with it, but the amount of information and explanation about it is so minimal, and obfuscated, it’s hard to know.

This satellite in question has the unfortunate acronym of DART (Demonstration for Autonomous Rendezvous Technology). It was designed to demonstrate that a satellite, without guidance from the ground, could use computer software and sensors to navigate and rendezvous. It was launched on April 15, 2005 (2005-04-15). The mission ended when the DART made a bulls-eye with another satellite known as MUBLCOM. This was not the desired outcome. Unlike a Star Trek episode, they did not rebuild one another and take vengeance on their creators, they just continue to orbit above us.

So what happened? Well, reading the official report is tedious, its prose is opaque, and it took much of Ecuador’s coffee crop to get me through it. I will do my best to translate the main points made by the MIB (Mishap Investigations Board). First, this was a big deal. Any loss of mission over one million dollars is called a “Type A” mishap. “This mishap category requires the most detailed level of investigation.” according to the report. So one would expect a lot of detail, but the technical descriptions seem to be from an altitude of 10,000 meters.

Why so obscure? The report states: “…the DART mishap investigation report was deemed not releasable to the public. The following provides an overview of publicly releasable findings and recommendations regarding the DART mishap.” This restriction was based on International Traffic in Arms Regulations (ITAR).

DART had GPS on-board, and sensors to locate the MUBLCOM satellite. DART’s software alone was supposed to guide the satellite to MUBLCOM. It was to be autonomous technology. NASA was to demonstrate that both the satellites with their on-board GPS alone could get the two satellites close enough for their “close-in” sensors to then operate and take over the rendezvous.

The software was to move DART to a position 3 km behind MUBLCOM, then to within 1 km. This was close enough to test the location sensors. DART apparently was then to move in to closer positions, and following these tests, begin moving away to determine how far the “close in” sensors operated. Then it would place itself in a short-lifetime retirement orbit.

The values of the location and velocity appear to have been incorrect as DART approached MUBLCOM. The collision avoidance system activated, but it was not in time and DART collided with MUBLCOM. It is stated the MUBLCOM satellite was not significantly damaged and again became operational.

DART’s “Premature Retirement” occurred because it had prematurely used up all its fuel.

Ok, so why did it happen? From the report:

Normally, a spacecraft’s software-based navigational system operates by constantly
estimating its position and speed, and comparing these estimates with measurements from its navigational sensors. If the estimate and the measured position are in agreement, then the software can issue the correct commands to the maneuvering thrusters in order to effectively guide the spacecraft along its desired flight path.

The estimated and measured positions reported were so different, that the software would reset itself, and then compute the two values again—reset itself—over and over. The new GPS velocity value was read by the software. The report states it was “introduced back into the software’s calculations of the spacecraft’s estimated position and speed.”

Then prose which almost defy exegesis are offered:

If the measured velocity had been sufficiently accurate, the calculations would have converged and resulted in correct navigational solutions. However, DART’s primary GPS receiver consistently produced a measured velocity that was offset or “biased” about 0.6 meters per second from what it should have been.

This seems to implicate the GPS receiver. But why would it be consistently about 600 mm off? This consistent 600 mm error was enough to cause the software to reset, over and over, and use fuel as it tried to resolve this difference between the distance sensors and the GPS readings. The additional 600 mm introduced into the computation, was too large of an error for the system to accept, if I’m reading this section correctly. The report indicates that if the software had been designed to specification, this introduced error would not have doomed the mission.

Then much later on in the report, after much “explanation,” there is a very curious statement:

Correction of the units conversion error in the simulation math model described earlier led to a lowering of the gains setting to improve the expected proximity operations performance based on mission simulations.

What! What on earth does this mean? CORRECTION OF THE UNITS CONVERSION ERROR! What units conversion error?! Described earlier! There is no other detail in this report on this subject, and it is never mentioned again.

It is not possible to be certain what this means, but one can make some educated guesses. Lets’ suppose that somewhere in the computer code it assumed the distance was in meters. We know that there are 1000 mm in a meter. The second assumption would be that somewhere else in the program, the distance was to be computed in feet. We know that there are 304.8 mm in a foot. This difference?—695.2 mm. The bias difference in the report is “about” 600 mm. I guess it depends what “about” means to NASA.

The UK publication Newscientist stated this about the “mishap”  on June 22, 2009:

Units have also played a role in other spacecraft problems. In 2006, the guidance system on NASA’s DART spacecraft went awry and caused it to ram into a military satellite it was merely meant to dock with.

Before DART’s launch, NASA found that GPS data on its position was mistakenly being read by its computer in feet. Ironically, correcting this to metres in a simulator resulted in an incorrect change to another parameter that was programmed into the spacecraft – a problem that led to the collision.

I’ve always found the DART story curious. Could it be that a second Mars Orbiter type of metric mishap occurred, and was obscured in a report, which claimed that many things went wrong, and you can’t blame just one?—that one being another metric imperial SNAFU. It would be nice to know what this units conversion error was. What was the conversion factor? The cost of the mission was 110 million dollars. Just how much cash are taxpayers willing to lose because we won’t changeover to metric in the US?—if we never know, because the failure reports are opaque, it never cost anything—right. And converting to metric will always be prohibitive.

Epilogue — I contacted NASA Ames, they sent me to NASA Marshall Space Flight Center. My repeated inquiries have been ignored and phone calls and emails not returned. My only question was: “What was the conversion factor?”

Postscript — There was much excitement among some metric advocates when on 2012-05-22 the SpaceX Falcon 9 was launched. The speed and distance downrange were in quoted in meters and kilometers.  An enthusiastic UK based post entitled: US space programme in shock metric conversion jumped the gun and assumed SpaceX was metric.

I called SpaceX  on 2012-05-21 and asked to speak with an Engineer or Project Manager there who could verify if metric was used to build their vehicles or not. I was informed that unless I knew the first and last name of a person working there, I could not speak with anyone. The receptionist gave me her email, with a backhanded promise to look into it.

I sent a follow-up email to their media people, sales people and the receptionist again on 2012-05-24. There were no replies. I called back to the receptionist on 2012-05-31 who informed me again that unless I knew someone, I could not talk to anyone. “It is a matter of security” I was told. I spoke with all the Engineers I know who still work in Aerospace, none knew a contact at SpaceX. On 2012-08-28 I contacted a University Professor who wrote about visiting SpaceX, and asked for his help in contacting SpaceX or determining if they are metric. So far there has been no response to my email.

Automobiles are all built with metric. The illusion that they are still imperial is preserved with a speedometer in miles per hour, and bolts on the battery that are imperial. At this point I have no way of knowing if SpaceX is simply the reverse. They use all imperial to build their vehicles with some meters and kilometers thrown in at launch to provide an illusion of possible metric usage? We need legislation and leadership or metric will never happen in this country. Otherwise we will never know if SpaceX is hard metric or just metric snake oil.

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