This is the third post based on **John Garrett’s MS Thesis**. Like 73, this won’t stand on its own. I recommend starting back at 72.

Since the start of this work, all of our measurements have been made at 90 mph. We chose that number using what a friend of mine calls a “rectal pluck.” This post represents the first time we have investigated the effect of speed.

Many baseball nerds know that the effect of spin is offset by velocity. In order to assess spin effects, you must consider spin/velocity. For a particular pitcher, that ratio will generally be constant, so if that pitcher throws a slower pitch, it will generally spin less and visa versa. I bring this up because it is a familiar baseball example of a *dimensionless number.* While RPM/Velo is a popular metric (sometimes associated with a certain player’s name) it’s a proxy for the “spin parameter” S = RPM X D / V where D is the ball diameter. Obviously all baseballs have the same diameter so that certain player saw no point in keeping the D around. The important point is that the units of RPM, D, and V cancel out to form a dimensionless number.

The dimensionless number I want to talk about is called Reynolds number, Re = V D ρ/μ where ρ is the air density and μ is the air viscosity. Seam effects depend on Reynolds number, so this allows is to see that as ρ goes down (such as in Denver), one has to have a higher velocity to have the same Reynolds number and therefore the same seam effects.

Note that Logan, UT where we do these measurements is at 4500 feet, almost as high as Denver. This means that our seam effect measurements at 90 mph in Logan correspond to 76 mph at sea level and 92 mph in Denver. Note I am not saying any other aspect of the pitch (spin effects, batter reactions, whatever) scales this way but the seam effects will. Similarly, our 60 mph test corresponds to 51 mph at sea level and 62 mph in Denver while our 110 mph test correspond to 93 mph at Sea Level and 113 mph in Denver. We were unfortunately not able to test beyond a speed of 110.

If you don’t understand that discussion, the bottom line is we need to shoot balls faster to generate data for sea level. For each of these cases, I’ll quote speed here and at sea level.

There are more details contained in the thesis, but I think the most concise way to describe these results is using the a “separation map”, as shown below. This description of the map is repeated from the previous posts.

The red dot shows the “natural” separation point, or where the flow separates when no seam is nearby. The error bars show one standard deviation of that position based on many samples. In other words, the separation point is within that band 68% of the time. It’s within twice that range 95% of the time.

The green area is where a seam will cause the flow to separate at that location, and the darker green means separation is more likely.

There is also a range of angles (marked blue) that will cause separation of the

laminarboundary layer to separate ahead of the seam, and the location indicated with the blue dot. Note that the flow is never laminar past the hemisphere plane. Also note the blue dot shows where separation occurs, but the blue line is the location of the seam causing that separation. The blue and green together make up “advanced separation”, or SSW potential.

Here is what I see. For the 4S orientation, the natural separation point (red dot), which separation happens when no seam is involved, creeps farther forward as the speed increases (or as altitude decreases) and the variations get smaller. Laminar separation in front of a seam (the blue dot) disappears completely at the highest speed. SO, I am finally vindicated in saying that “laminar flow” has little effect at game speeds and altitudes.

For 2S, the point where separation occurs on the side of the ball *opposite* the seams moves backward with increasing speed. Nothing else changes much with speed. Laminar separation does not disappear completely at 110 mph but it does occur much less often than at lower speeds.