# Spring Chicken

By The Metric Maven

Bulldog Edition

It is said that in 1960 Richard Leghorn coined the phrase “information age.” He founded a company that manufactured spy cameras and later worked at the Pentagon. The phrase “information explosion” was also in vogue at the time. In my view there has also been a “non-information explosion” depending on if one is concerned about the veracity of information presented. Klystron sent me a link to an online article where an automotive writer discusses the different types of compression springs one can use in car suspension. The article introduces the reader to “spring rate” which is proportional to the stiffness of a spring:

In simple terms, a spring’s rate is the amount of weight required to compress itself a single inch. It’s a universal measurement, it applies to everything from lowering springs to valve springs, and it’ll look something like this: 500 lbs/in. The bigger the number, the stiffer the spring.

This took me back to my introductory physics class in college where I was introduced to Hooke’s Law. In 1678 Robert Hooke (1635-1703) offered a simple linear mathematical equation that relates the force produced by a spring in terms of its extension or compression (depending on the type of spring). The equation is simple: F = kX. The letter F stands for the force the spring produces, X is the distance you have compressed or stretched the spring. The value k is a number that converts the distance the spring has been compressed or stretched to the amount of force it produces. The value k is called the spring constant, and it is the same as the “spring rate”  offered by the automotive writer. In this case k is in pounds per inch or lbs/in. Indeed, the larger the spring constant k, the stiffer the spring. As I point out in my essay, The Count Only Counts—He Does Not Measure, this relationship was used to produce the first spring mass gauges. Springs often obey this relationship only over a given displacement range, but we will ignore that here and assume we are within the linear range.

The author then points out that the rest of the world is metric and converts the spring constant (rate) over to metric for his readers:

Kilograms are not a force, and so Kg/mm when multiplied by a displacement distance in millimeters produces a mass value and not a force. This is very poor dimensional analysis on the part of this professional automotive writer. When one stands on a bathroom scale in the US, the readout is in pounds of force, but if one flips a switch to metric it instead offers mass in Kilograms. If the scale had a metric readout of force, the value would be in Newtons. If you have a mass of 75 Kg, then your metric weight would be 735 newtons, which is a force value.

A 500 lb/inch spring constant properly converted to metric would instead be 87.8 newtons/mm.

While springs appear rather prosaic they are used ubiquitously in our modern world. Their benefits are enthusiastically portrayed in this 1940s film about the benefits of springs.

Metric springs in the US apparently use non-SI for a spring constant:

click to enlarge

The 60 mm inner diameter spring in the top line of the table above has a metric “spring rate” of 18 kgf/mm or 18 kilogram-force per millimeter. Kilogram force has never been a part of the metric system and is not accepted for use with the modern metric system. A “kilogram-force” is 9.806 newtons, so the spring constant when actually converted to metric is 9.806*18 = 176.5 newtons/mm.

We are a country that thinks it is technologically unmatched, yet everyday I see that most professions never think quantitatively or technically.

Some years back, one of the tension springs on my garage door snapped making it inoperable. The previous owner had taped a garage repair business card to the wall and I called the number. The fellow who showed up was friendly and had a large number of springs in his truck. He took one look and checked his truck to see if he had a replacement. The technician looked up from his pickup-bed and asked “is the color white or blue?” It was then that I realized the spring had a section along the middle painted white. He returned with a set of blue and a set of white springs, one of which had paint on one end. The workman indicated that both garage springs needed to be replaced so they would have the same “strength.” This made sense. He took out the broken spring and then the intact one, which he then put over a hook on the back of his truck and pulled. He next pulled on a new blue one, and then a new white one.

I asked why he was doing two colors. “They’re all different” he said, “the colors are meaningless. Every manufacturing company is different—I use feeling.”  I immediately suspected this was not a good idea. The interpretation of force (weight) on an object by humans is logarithmic. It struck me that it would be possible to create a device that would measure the spring constant of each spring so there would be no guessing. When I asked if such a device existed, the technician asserted he did not need it. His human measurement perception indicated white was needed as I recall. He put them into the garage door and after opening and closing it a time or two decided the blue spring was probably better. He installed the blue springs and then pronounced them the best. Indeed, my garage door has been fine over the last few years and works well.

It bothers me that people who support what is left of our infrastructure in the US seem so out of tune with the quantitative aspects of it. It would make a lot of sense to me that if one needs a pair of springs with the same spring constant for each side of a garage door that measuring this value would make sure the springs are the same. At the next level, those who write articles to inform the public are often no better. I see this as part of a cultural problem that promotes an anti-intellectual view in the US. The lack of the metric system appears to be but a symptom of this larger problem.

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The Metric Maven has published a new book titled The Dimensions of The Cosmos. It examines the basic quantities of the world from yocto to Yotta with a mixture of scientific anecdotes and may be purchased here.

# Mill-a-Meter

Old Mill on the Iowa River (click to enlarge) Belmond Historical Society

By The Metric Maven

In my single digit youth I often walked across the “old bridge” in my small town. One could see right off of the concrete bed of this truss type bridge over the Iowa River. I noticed that a small dam existed with an opening near the center of the river. People would often walk out on this dam, which had a height of only 1 to 1.5 meters or so, and fish. One day in the local library I saw a painting that showed an old mill had been on the river. I was quite surprised and asked if it had really been there. The librarian said it had, and was washed away during a flood.

Old Bridge Over The Iowa River    (Belmond Historical Society)

It was a decade or so later that I learned photographs of the “old mill” existed. One of them is inset above. On the far right side of this photo is the location of the “new mill.” A local history1 offers little detail about the design of the “old mill.” Before the old mill, there was an original mill. A dam was constructed and:

The river provided the power for the first flour and sawmill built in 1855 or early 1856 by Dr. Cutler and Archer Dumond.” … “After only a few months’ use, this first mill constructed by the early settlers was washed away by flood waters in the spring of 1856.

In 1857, the next mill constructed was a steam mill. The following year, 1858, was so wet that the steam mill was surrounded by water that season. The machinery was sold and moved to Kansas. Apparently, rather than use the river for a source of power, an experimentation with steam took place.

The “old mill” in the photograph was constructed on the site of the “original mill” in 1858 by G.H. Armsbury. It was both a sawmill and gristmill. It is not stated if it was a water powered mill, but judging from the details of the transaction, it probably was. In 1863, George A. Thompson took charge of the gristmill. His relative Joseph Fulton became a part-owner of the mill, which, in 1870, was the only flour mill in Wright County. In the Spring of 1870 Fulton became entangled in the mill workings when he went to the basement to oil some of the parts. He was killed instantly. Assuming this is a mill that utilized a flat mill stone, they could revolve up to 125 RPM, with a considerable mass.

The mill dam was renovated numerous times before the “old mill” was finally retired. The “new mill” was constructed about 1901 and the “old mill” was:

….being torn down. The timbers are rotting away and it would soon be at the mercy of the first serious wind storm. In the days of long ago, it furnished flour to farmers as far away as Spirit Lake.

The last mill in Belmond Iowa was torn down in 1935, the location of the final millstone is a mystery. The bridge I traversed as a boy was the only structure left from this time period. It was replaced decades ago. I suspect the millstone was a flat affair that was common at this time. It is my understanding that some people actually collect old mill stones which have many unique cutting patterns rendered on their surface. Grain would be fed into the hole at the top. It would work its way down into the meeting line of the rotating upper stone and the static lower one. The milled grain then worked its way outward where it was collected.

I thought about this local history when I was re-reading The Ancient Engineers by L. Sprauge de Camp. The grinding of grain was of paramount importance to the creation of bread. This was a consistent staple: (page 243)

“…Throughout the ancient empires, bread was the principal food. To make it, wheat or barley grain had to be ground into flour. At first the grain was painfully pounded with a pestle in a mortar, as you can still see done in Central Africa.

At a later time, the grain was ground between two flat stones, one of which was pushed back and forth over the other. With such a mill, one person—usually a slave girl—could grind each day only enough grain to make bread for eight people. Hence, in a large household, several such women would have to spend their entire day at the weary task of pushing and pulling the upper millstone. The two ever-present sounds of ancient households were the clack of the loom and the grate of the hand mill.”

The implementation of water power to grind grain, is a perfect example of employing engineering to help keep a community fed, and reduce the horrible mind-numbing boredom of an essential all-day repetitive task.

All of the examples of millstones I had seen were a pair of stone cylinders with a flat interface between them. The small hand versions are called quern-stones. The large millstone examples I had seen using water power were always like this. One stone had patterns cut into it for the grain to be ground and then work its way out from the center where it could be collected by a pan at its edge.

I encountered a pair of surprises when L. Sprauge deCamp offered this drawing of a hand mill from ancient Pompeii:

This is known as an hourglass mill and was used in Hellenistic and Roman times. I was quite surprised that it was possible to make stone conform to these shapes, but what really confused me were the dimensions. Throughout The Ancient Engineers, all the dimensions are in Ye Olde English. The book was published in 1960, so this is not surprising, but what on Earth were the units m/m? I knew that ca. meant “approximately,” or “about this dimension,” but m/m was strange. I hypothesized that it was millimeters—even though the entire complement of the book is in Olde English measures. The values 900 mm and 700 mm seemed to make approximate sense. What is wonderful about our modern world is that I can do a web search on hourglass mills and see photographs of the mills at Pompeii:

The dimensions in millimeters found on the drawing make sense, but the use of m/m for millimeters was unknown to me at that point. I consulted with Peter Goodyear, and he found examples of guns drills, and clocks that are still designated with m/m for millimeters! I have no idea where the designation m/m originated, but amazingly it is still in use.  Indeed here is a specification table from a Tawianese company that makes paper cutters:

I’m pleased they used millimeters, but amazed and annoyed that m/m is used for mm. This is another example of an introduced usage from another era that continues to complicate our modern world in an unnecessary manner. It also demonstrates just how hard reform that would simplify our world is to achieve.

[1] History of Belmond, Iowa 1856-2006 Belmond Historical Society

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The Metric Maven has published a new book titled The Dimensions of The Cosmos. It examines the basic quantities of the world from yocto to Yotta with a mixture of scientific anecdotes and may be purchased here.