Thanks to scaling, smaller can be better

I became fascinated with the microscopic world when I was very young. This probably happened because I couldn’t see much of anything unless it was about 3 inches from my face.

I was amazed when, in the third grade, I got glasses and discovered that there were actually leaves on trees. Before that, I thought trees were like green clouds.

Most people intuitively know that things are different as the size gets either larger or smaller. I was reminded of this the other day as I passed a bin filled with Hot Wheels at City Market. Hot Wheels are the tiny, metal replicas of actual cars that roll on freely turning wheels. They are only a couple of inches long, but built to scale. 

See, when we were in college, my wife and her sister-in-law were both pregnant at the same time. The two children were born literally within a few days of each other.

My brother-in-law is exceptionally competitive, and he was always bragging that his kid would be first. However, I won!

Now every soon-to-be mother knows that predicting the exact date of delivery is a chancy thing. There was, and still is, a need for more accurate methods of predicting when a baby will come.

While I wasn’t so much into the competition, I was a budding scientist at the time. And I got to thinking I might be able to devise a simple algorithm that could be used by expectant mothers everywhere to accurately predict the time of birth. 

I suggested we race Hot Wheels down our wives’ abdomens while keeping track of the times. With sufficient data, we ought to be able to predict delivery based upon average track times. We just had to establish a benchmark. 

Unfortunately, I didn’t anticipate all the variables that would come into play, the foremost being the unwillingness of our wives to cooperate.

My brother-in-law probably would have cheated anyway. All was not lost, however. Because, while racing Hot Wheels with my brother-in-law, a second phenomenon revealed itself.

Why doesn’t the wreck of a Hot Wheels car result in the same degree of destruction as the wreck of a regular car at similar speeds?

I recognized almost immediately that model airplanes, remote-controlled cars, toy trains and many other small things withstand collisions and accidents much better than full-sized vehicles.

The reason for this lies within a principle called “scaling.” When size is diminished to an extremely small level, Newtonian mechanics don’t work anymore.

I think this is one reason I find microscopic things so intriguing. You know, anything to get out of work. 

Scaling laws are proportionality relations of characteristics of an object, or system, with its length scale.

For example, the volume of an object varies with its cubic length.

On the other hand, surface area of an object scales as length squared. Smaller objects possess larger surface areas to their volume when compared with a larger object of similar geometrical shape.

There are two types of scaling laws. One is related to the scaling of physical size of objects like surface area and volume. The other type is related to the phenomenological behavior of an object.

For example, it is easier to break a long stick of a given diameter than the shorter stick of the same diameter. 

Consequently, a toy vehicle made of the same material as a full-sized car is stronger than the full-sized car. It withstands collisions better.

Can you imagine how much stronger the molecular components of a single cell are compared to the same molecule one hundred times larger?

Somewhere between a fertilized egg and a baby, Newtonian mechanics kicks in.

Building small models of objects intended for production in larger form, which is basically what pregnancy is, creates a need to understand engineering scaling.

So, I still think Hot Wheels could predict time of delivery of a baby.

Gary McCallister, .(JavaScript must be enabled to view this email address), is a professor emeritus of biological sciences at Colorado Mesa University.


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