Part 1

By Wayne Carley

In the continuing revelation of what STEM really means in our lives, let’s continue to explore the STEM skills necessary in participate and excel at a sport so many enjoy. In previous issues of STEM Magazine we’ve looked at the STEM of football, basketball, soccer, hockey and other sports. In the midst of our summer and in honor of the recent U.S. Open, let’s dig into the STEM of Golf.

Golf is intensely mathematical, with strong engineering applications. The math and engineering are personal in application, with the technology being primarily in the equipment. The science of Golf (the systematic accumulation of knowledge) permeates all aspects. What is really interesting is that we don’t actually learn these math applications to be effective at golf. For successful golfers (low scoring), we seem to be born with many of these practical applications and experiential knowledge of the following mathematics.

Math is of course defined as “The science of numbers and their operations, interrelations, combinations, generalizations, and abstractions”. Golf is certainly all of this and includes the math domains of geometry, analysis, topology, combinatorics, number theory, algebra, math physics and more.

If you enjoy any sport, but say you hate or don’t understand math, this is a real contradiction. What I hope you will consider and better understand is that you already know so much math, you just don’t realize it or see it in your daily life. That being said, let’s consider the geometry of golf.

**Geometry** noun

ge·om·e·try | \ jē-ˈä-mə-trē /

**Definition of geometry**

1a **: **a branch of mathematics that deals with the measurement, properties, and relationships of points, lines, angles, surfaces, and solids

Golf is 3 dimensional and requires 3 dimensional thinking to solve golfs primary problem: Get the ball in the hold with as few swings (strokes) as possible.

Geometric considerations are:

– the flight of the golf ball ( apex or height reached, distance desired, possible obstacles to be avoided, velocity of ball flight to get from point A to point B). This geometric problem can only be solved by the golfer by using the engineering method that we will cover later, in conjunction with the technology in the golf bag, the golfers ability to use it well, and a dozen questions that need to be ask for each and every golf shot.

The golfer must visually determine where they want the golf ball to land for the first shot. Once decided, the distance needs to be estimated, usually in yards. A golf club must be chosen with the correct angle of attack for the desired ball flight. Proper physical alignment toward target must be decided, usually in degrees. The speed of the golf swing must be estimated to drive the ball along the chosen flight path. Just when you thought we were done, other consideration must be considered for success. If there is wind, the direction and speed of the wind need to be evaluated. Will a head wind slow the forward movement? If so, how much? Will a tail wind speed the flight progression? If so, how much? Will a cross wind cause a deviation in the alignment of the shot? If so, how much?

Air temperature or density directly
impacts ball flight, thus distance and accuracy. This is measured in degrees.
The hotter the air, the thinner the air, thus less resistance to flight requiring
another recalculation of club use and strike force required. The humidity of
the air is important and often in direct contradiction to air temperature. **Relative
humidity** is the most common consideration and is the ratio of the current
absolute humidity to the highest possible absolute humidity (which depends on
the current air temperature). A reading of 100 percent relative humidity means
that the air is totally saturated with water vapor and cannot hold any more,
creating the possibility of rain. This doesn’t mean that the relative humidity
must be 100 percent in order for it to rain — it must be 100 percent where the
clouds are forming, but the relative humidity near the ground could be much
less. Hot temperatures with low moisture content or low humidity result in thin
air, less resistance to ball flight and longer distances. Hot temperatures with
high moisture content or high humidity result in thick air, more physical air
resistance to flight and shorter distances.

Let’s not forget altitude measured in feet above sea level for golfing purposes. Air density or thickness at sea level is greater than air density at higher altitudes. Therefore, the distance a golf ball travels at the beach is less than the distance it travels in Denver Colorado at 5,280 feet above sea level. Under similar atmospheric conditions using the same club, same ball, and same striking force, the ball in Denver will travel significantly further.

The math and geometry of golf is so very complicated and we’ve only scratched the surface. When all of the aforementioned aspects are decided, the human golfer must physically execute a golf swing the allows for the calculations to be accurately realized. This is where the challenge really exists. The brain has done its work, and now the body is called upon to execute the mental formula.

This was the first shot of our round of golf. Everything we’ve just calculated must be done again, an average of 100 times for the typical golfer. Your results may vary.