Spring Chicken

Chicken-ManBy 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:

Metric_Car_Guy

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:

PigFish-Springs

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.

Spring-ColorsSome 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.

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4 thoughts on “Spring Chicken

  1. The kilogram-force (aka kilopond) is certainly obsolete and was never part of the SI. However, it appears that it was part of the older metric system (perhaps more properly metric systems). Prior to the SI, there were a number of competing systems that used metric in a variety of ways. One was “gravitational” metric system:
    https://en.wikipedia.org/wiki/Gravitational_metric_system

    As your link points out, the kilogram-force was not well defined until the CGPM declared the value of standard gravity (in 1901) at which 1 kilogram-mass exerts a 1 kilogram-force.

    The first publication of a separate unit of force in the MKS system appears to be a 1946 decision by the CIPM introducing the “unit of force” or “MKS unit of force” as well as defining modern electrical units. This recommendation was ratified by the CPGM, and the name newton assigned in 1948, (Source: Appendix 1 of SI Brochure). At that point, the kilogram-force should have become obsolete.

    The kilogram-force or kilopond had quite a few uses in Europe and Russia. It was widely used as part of a unit of pressure, the basis of the metric horsepower, etc. It remained a legal unit in Germany until 1978-01-01. (And the metric horsepower, PS, is still used there).

    We are not the only ones with problems obsoleting obsolete units. Multiply it by 9.80665, call it newtons and be done with it.

    • I’m not sure what the tolerances are on these springs, but I would think that for practical purposes and easy in the head computations, multiplying the mass in kilograms by 10 to get newtons would be perfectly acceptable.

      As with electromagnetism and the continued use of CGS sub-units, it isn’t a surprise that the kilogram force continues as a metric equivalent of the pound.

  2. Was it really necessary for the author of the article quoted to write “It turns out that the rest of the world uses something called the metric system…” as though he and his audience have never heard of it before?

    Why can’t American writers mention the metric system without sniping at it?

  3. The workman wouldn’t even need a “device” per se. All he would need to do would be to hang a weight from the spring and observe how far the spring got stretched. With two hooks, and two identical weights, he would be able to make the comparison quickly, accurately, and intuitively. (Unless, of course, the springs weren’t the same length to begin with, in which case it’s back to square one.)

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