Computational Units

Why are units so confusing?

Nobel Prize physicist Richard Feynman once remarked it was an embarrassment that with everything Physics had accomplished, they had never been able to settle on a consistent set of units.

Europe uses Meters, Kilograms, Secs while the United States uses Feet, Slugs, Secs.  lbs and kgs are both used to describe mass and force confusing everyone.

The answer is no one forced the issue, and scientists continued to insist on doing things the way they always have. At times, the United States has considered switching to the Metric SI system, but the cost of changing any signs such as mileage from one unit to the other is expensive.

Keeping units straight is one of the key challenges in Physics, and converting units to their correct form are one of the sources of mistakes in computing results.

What are Systems of Units?

Systems of Units were formulated when Newton developed computational physics. Metric, CGS, and MKS are European units that have evolved over time into SI. These systems include many other quantities, so for our purposes, MKS and SI units are the same. The Imperial System used in the United States was developed in England, and while they eventually migrated to the Metric systems, the United States did not.

Which system should we use?

The choice is between Imperial or SI. The answer is we will use both. Whether inputs are provided using Imperial units or modified SI such as kms,we will first convert them into SI and use them to perform the calculations. When we have our final results, we will present results where appropriate using both units.

Keeping Things Straight: Distances

Keeping units straight means being clear with what you are working with. Here are a few hints as to how to do that.

Distances are often quoted in kilometers, meters, miles, and feet. Converting to SI units means converting to the SI unit of meters. However, some base units may use a mixture of terms and so it will be important to keep track of how each term is measured.

Keeping Things Straight: Mass and Weight

Mass and Weight are both object properties. All objects have a mass which occupies a volume. Mass is an unchanging object property.
On the other hand, weight is a dynamic property which changes depending on where the object is located. Objects on Earth have a different weight from when they are on the moon.

https://www.engadget.com/2017/01/09/the-best-bathroom-scales/

 

Cycling is done on the surface of the earth which means that we can use weight to estimate mass and vice versa. I say estimate because the force of gravity does slightly vary even on the surface of the earth. Fortunately, most of our key calculations depend on Weight and we will only have minimal need for an object’s mass.

Keeping Things Straight: Force

Force in these two units are SI Newtons or Imperial Pounds. While Newton’s are unfamiliar to Americans, just think of them as a fifth of a pound. Just another way to measure force, but in the end the same thing.

Keeping Things Straight: Work, Energy, and Power

These terms are fundamental to cycling. Work is sometimes called Energy. Both in SI Units are defined in terms of Joules. Power is defined in terms of Watts and is how work is performed in a second.

Here is where things can get confusing with Imperial units. Watts are often used in discussions which otherwise use Imperial Units. For this reason, I have gone to performing calculations using SI units.