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:


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.

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.


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.


Popped Secret

By The Metric Maven

Bulldog Edition

Popcorn is a very New World food. It is amazing that in ideal conditions the kernels of unpopped popcorn can be stored almost indefinitely. Corn was first domesticated in Mexico about 9000 years ago. As a young boy, I recall a friend showing me a popcorn pan with a hand-crank on the lid. We were watching an old movie and he wanted to make something special. My friend placed oil into the pan and heated it, he then tossed in a measured amount of popping corn. Normally, at that point one would  immediately put the lid on to keep from being splashed if it started popping immediately. He next tossed in some sugar. The handle was part of a wire sweeper that could push the corn around. This was done until the popcorn had finished popping, and for the first time I had popcorn with a sugar coating. At that age it seemed exotic. At that point in my life I gave no thought to how much extra energy was imparted by the introduction of sugar. The agitator was a nice addition. Generally when popping popcorn in a pan one would need to continuously shake the pan forward and backward to keep the popcorn from burning. Popping popcorn at home was an acquired skill. Popcorn balls (generally colored in some fashion) were often handed out at Halloween in my small town as a treat. The largest documented popcorn ball is 2.4 meters in diameter, 7.5 meters in circumference, with a mass of 1549 Kilograms (well over a Megagram). Popcorn was also strung on thread to decorate Christmas trees during the winter holiday season.

In China and Korea a sealed cast-iron canister with popcorn inside is used like a rotisserie  over a fire.  When a pressure gauge on the container reaches a threshold value, the canister is taken from the flame, a canvas sack placed over the top and the seal broken. With a large boom, the popcorn explodes all at once. It is then poured into the canvas bag.

The first popcorn was popped by hand (sometimes over an open fire), and  was later automated with steam powered mechanisms designed in the late 19th century. This new popcorn popper was introduced at the 1893 Colombian Exposition. When I was a boy we purchased sealed plastic bags of popcorn kernels with Jolly Time printed onto the transparent film. The big change in popcorn preparation came when General Mills obtained the first patent for bagged microwave popcorn in 1981. This made popping popcorn much more convenient and a surge in popcorn consumption followed. People also ceased to see popcorn kernels any longer as they now come in an opaque bag.

Microwave popcorn allows one to eat popcorn with a very consistent serving size in terms of mass and volume. This consistency would be great for those who are trying to monitor their food energy intake. When I first attempted to determine the energy content of popcorn I was very surprised at the low value. The serving size per bag is about 3 and the serving size is 1 cup popped or three cups. This works out to 90 Calories (377 KJ). My significant other (SO) immediately doubted this value. It had to be higher. In recent years it has been emphasized that we should go back to Olde English only nutrition labels. One can see this from the nutrition labels that Ye Olde English is still Kyng. Here is the nutrition label for Pop Secret’s Homestyle Microwave Popcorn:


So if the servings per bag is about three, and the serving size is two tablespoons unpopped, then it would be a total of 3*150 Calories or 450 Calories (1884 KJ). The fact that the serving size is given as 2 tablespoons unpopped and 1 cup popped seems to indicate an equivalence. So which is it? Ninety Calories per bag or 450 Calories per bag? This difference is a factor of five! The range given on the web for a single bag of Pop Secret Homestyle was from around 400-500 Calories or so. When I looked at the bag after popping, and used my 100 mm wide hand to measure it, the bag appeared to be somewhere around two liters in volume, but I had no idea how many cups that might be. I could immediately estimate the value in metric, but could not do the same with Ye Olde English.  My SO and myself then conducted an experiment, we popped a bag and measured it with a one cup measure. It turned out to be somewhere from about 10-12 cups of popped popcorn. It would seem that each bag contains about 6 tablespoons of unpopped popcorn, and 15 cups when popped, but the nutrition label does not say that.

When converted to metric the clarity has not increased much:

Nutrition Facts
Serving Size  15 mL unpopped  237 mL popped

Amount            15 mL     237 mL
Per Serving      Unpopped   Popped

Calories           150        30

So 15 mL of popcorn becomes about half of a 500 mL bottle of soda or water. Does that make sense or not? I was able to estimate the volume of a popped bag at about two liters or 2000 mL.  Given about 200 mL per serving 2 liters would be about ten servings or 300 Calories. Clearly the value would not be 90 Calories.

In my view this label has been designed to confuse. Who eats unpopped popcorn? Who even sees the unpopped popcorn in a sealed opaque paper bag? How would you estimate the unpopped amount when you can’t even see it! One would immediately look  at the label assume 3 cups per bag at 30 Calories per cup and compute 90 Calories total. There have been moves to go back to Ye Olde English from metric for US nutrition labels to make them more “understandable.” The Pop Secret label is unclear in metric and even more inaccessible in Ye Olde English. It could have been written:

Nutrition Facts

Calories per bag: 450

Servings per bag: 3

Calories per serving 150.

Calories per cup 30

Volume of bag: approximately 2500 mL

The nutrition label as it is originally formatted appears to be designed to mislead consumers into believing that microwave popcorn contains far less calories than it does. This in turn causes the person to consume more calories and hence more product while blowing their estimated food energy intake.

Profiting from measurement confusion and misinterpretation is often thought to be a thing of the past. It is clearly not—and never has been. I have a measuring scoop provided inside my laundry detergent box which has a volume twice that recommended for each wash. It has a line halfway up its side which is the recommended volume. People don’t notice the transparent line, or read the tiny instructions, and generally fill the scoop up to the top, using twice the recommended amount of soap. People who see the importance of implementing the metric system, and the teaching of basic numeracy as fringe issues in the United States, are but ignorant marks for our modern industrialized hucksters.


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.