Phases for Physical Analysis

Dave Tutelman -- January 21, 2007

This article consists of some random musings from January of 2007. (That's before Frank Schmidberger and I developed TrajectoWare Drive.)

Bear in mind that everything about golf physics is about getting the golf ball where you want it on the course. Here are the phases of getting it there, starting with the golfer's swing. Each phase has inputs and outputs. For instance, the swing has inputs of the forces exerted on the club by the golfer, and the characteristics of the club. The outputs for the swing are the position and motion of the clubhead at the instant it strikes the ball. The table below is a graphical representation of the phases I am fairly familiar with.

So a physical analysis of the swing phase -- or any phase -- would consist of calculating the outputs from the inputs. Ted Jorgensen's book, "The Physics of Golf" has as its first few chapters exactly such an analysis. Max Dupilka's computer program SwingPerfect is a good example of mechanizing the analysis of the swing phase. (Note that neither Jorgensen's nor Dupilka's works addressed shaft flex behavior. But the other factors are there.)

If you have worked with my program TrajectoWare Drive, you will recognize it as a computer mechanization of the impact and ball flight phases.

Swing		Impact		Ball Flight
Input	Output	Input	Output	Input	Output
Forces exerted by golfer on club	Clubhead speed and direction at impact		Ball speed		Carry distance
Club length	Clubface direction		Launch angle		Trajectory: Full path plus...
Shaft flex and flex profile	Position on clubface		Spin		Landing angle
Club mass and mass distribution		Clubhead mass and mass distribution		Atmospherics: density, wind	Final speed
		Ball mass and construction		Ball's surface: dimple pattern	Final spin

Red = Impact conditions
Green = Launch conditions

There's another view that I haven't much experience analyzing. I hope to be able to say enough about it at some point to add it to TrajectoWare Drive.

Ball Flight		Landing		Bounce + Roll
Input	Output	Input	Output	Input	Output
Ball speed	Carry distance	Ground surface elasticity	Ball speed		Distance
Launch angle	Trajectory: Full path plus...	Ground angle	Bounce angle		Direction
Spin	Landing angle		Spin
Atmospherics: density, wind	Final speed			Ground angle
Ball's surface: dimple pattern	Final spin			Grass conditions

Green = Impact conditions
Blue = Landing conditions
Purple = Bounce conditions

I have given no serious analytical thought to this "second impact" and what happens afterwards. Those who work seriously in this realm have to do so. If your business is golf simulators, this is an important part of your software; you must accurately model what happens after the ball reaches the ground. One such company (Gardiner Golf Simulators) divides the "Bounce + Roll" phase into separate Bounce and Roll phases, since it's different math for bounce and roll. Other companies (I believe OptimalFlight falls in this category) lump Bounce and Roll together and estimate a total Bounce + Roll distance based on a subset of the bounce conditions.

Last modified Aug 20, 2007