Graphical Analysis: Visualizing Stone Skips on Water

Minitab Blog Editor 02 July, 2012

The doctor’s advice to beat the heat? Chuck it all and head to the nearest lake, river, or ocean. Stick your bare feet in the cold water, and avoid all strenuous activity—except maybe skipping stones.

Yes, it’s a perfect time to lazily hone your technique and prepare for the upcoming Pennsylvania Qualifying Stone Skipping Tourney. Every year, amateur and professional skippers congregate on the banks of the mighty Allegheny River to compete in this crazy rock-slinging fest, only about 2 hours away by car from Minitab, Inc. 

In fact, the two most recent world record-holders for stone skipping, Kurt “Mountain Man” Steiner (shown at right) and Russ “Rock Bottom” Byars (the current record holder), both hail from small Pennsylvania towns not far from here.

This got me thinking. To throw with the pros, how good a skipper would you have to be?

Individual Value Plots

To find out, I recorded the results from last year’s Pennsylvania stone skipping tournament in Minitab Statistical Software and displayed the results in an individual value plot. There were 29 pro contestants. Each contestant got six tries to skip a stone, once in each round. How did they do?

  • The number of skips in each round is spread fairly evenly, ranging from about 1 to nearly 40 skips. You can see the overall winning throw at the top of Round 1 (39 skips, thrown by “Mountain Man” Steiner, from Emporium, Pa.).
  • The median (blue symbol) for each round shows that that about half of the time, the pros get at least 15 skips on each throw. The zigzag pattern of the connect lines suggests that they don't seem to consistently get better (or worse) with each throw.
  • The pros throw a fair number of stones that skip only once. But, unlike me, they do seem to avoid plonks (stones that sink on the first hit of a run) and skronks (stones that never hit the water at all).  

Note that the plot does not tell us anything about agnews (stones that accidentally hit a bystander).

To Plink or to Pitty-Pat, That Is the Question

The winner of the Pennsylvania regional pro tourney automatically qualifies for the national stone-skipping championship on Mackinac Island. Once you reach the big time, your skips are categorized and recorded as plinkers, the long, clean-cut skips at the head of a run, or pitty-pats, the short, quick mini-skips at the end of a run.

To maximize your skips, should you focus on getting more plinkers or pitty-pats?

Stacked Bar Chart

To help answer this profound question, I created a stacked bar chart in Minitab that shows the number of plinkers and pitty-pats on each throw for each pro finalist in last year's national competition.

Each throw is represented by one color—so you can see the breakdown of skips for each throw by following a single color across the two bars for each contestant.

For example, look at the bars for Mussels Callewaert, who won last year's championship on his first throw. The 26 skips on that winning throw (Throw 1, dark orange) were mostly plinkers. His next best throw (Throw 4, peach) was also mostly plinkers. Treetops Cawood, another top skipper last year, also seems to plink more than he pitty-pats.

But this trend is belied by Rock Bottom Byars, who relies heavily on pitty-pats. Ditto Lefty Kolar, who also turned in a respectable performance last year.

So I don’t see any clear pattern that suggests that you’re better off with plinkers or pitty-pats.

So what can you do to up your skips?

Technique Is Everything—Or Is It?

According to the physicist Lydéric Bocquet, the number of skips depends on the stone's diameter(α), velocity (V), mass (M), tilt (ϴ), angle of attack (ß) and the density of water (ρw):  

Simple isn't it? All you need to do is mentally maximize that formula when you skip the stone. (Changing the density of the water should be a snap—just bring plenty of packets of Sweet-N-Low to pour in the water.)

If you'd prefer a more concrete example, watch this video of Guiness world record holder Russ "Rock Bottom" Ayers, of Franklin, Pa. skipping a stone. (Notice the one-legged windup!)  

Asked about his technique, Byars once commented, "I have to be honest with you. I don't really know how I do that."

Maybe it's better that way.

After all, skipping stones, like many pleasures in life, is about more than just the numbers on the surface.

Related Links

(Better yet, don't click anything. Just go outside and skip some stones!)

Credits: PA Stone-Skipping Tourney Photo by Michael J. Henderson