A “laminar express” pitch is a two-seam fastball whose term was coined by Trevor Bauer years ago when he developed a pitch that had dramatically more movement to the arm side than he previously would have had. It was the opinion of coaches at Driveline Baseball that this was happening due to the laminar/turbulent effect on a baseball, as first discussed in regarding baseball by Dr. Alan Nathan on The Hardball Times (images are unfortunately broken on this older post) in 2012, with the underlying science discovered by Dr. Rod Cross and demonstrated in this Veritasium video.
Dr. Nathan was able to derive coefficients for the components of movement with regard to acceleration when the boundary layer of air is asymmetrical:
From that, I can use the experimental relationship between the rotation rate and the Magnus force to estimate the magnitude of the latter. Since the movement is determined from the components of acceleration, and since the Magnus contribution can be estimated, the additional acceleration due to the roughness asymmetry can also be estimated.
Here is what I find for the forces, all normalized to the weight of the ball:
gravity = 1.00
drag = 0.78
Magnus = 0.32
roughness = 0.63
Boundary layer asymmetry – laminar/turbulent airflow – was responsible for quite a high percentage of acceleration change per Dr. Nathan’s calculations, which was tremendously interesting!
The science behind such movement of a baseball was exciting to analyze and actually deploy in a game situation, which Trevor was able to do after months of practice. Eric Jagers demonstrated clear evidence that two pitches that had dramatically different movement on high-fidelity high-speed video from our Edgertronic cameras could read vastly differently on a launch monitor device like Rapsodo, with the numbers being dramatically different and outside the tolerances for margin of error – driving up the statistically likelihood of the effect existing.
Eric’s trial below features a chart of two fastballs thrown with nearly identical vertical and horizontal break as measured by Rapsodo. The launch monitor detects the ball’s spin rate, spin direction, and velocity and recalculates trajectory based on a physics model – hence why it thinks both pitches shown in the video have nearly identical movement when in reality they are quite different.
|2sFastball||85.0 MPH||2238 RPM||1763 RPM||78.8%||15.2 in.||6.7 in.|
|4sFastball||86.6 MPH||2225 RPM||1832 RPM||82.3%||16.2 in.||6.8 in.|
You could chalk the “misread” up to an error on Rapsodo, but this is extremely uncommon on clean takes with the Rapsodo launch monitor, and when errors do occur, they almost always report missing data or seriously incorrect reads.
In December 2018, Dr. Barton Smith from Utah State University wrote about how a “laminar express” pitch might work.
The idea of a “Laminar Express” is to cause the flow on one side of the ball to be laminar, and thus have an early separation from the ball surface, while the other side is turbulent and has a later separation. The difference in these separations would cause a lateral force on the ball.
I’ve sketched the situation below. The pitch requires a 2-seam orientation, which produces large areas of smooth surface on the two sides of the ball. As I pointed out in the pressure gradient post, if a seam is near the front of the ball, it will disturb the boundary layer, but it will return to smooth, laminar flow because of the strong, favorable pressure gradient there. This is the case for the seam on the first base side near the front of the ball. The seam on the first base side near the back has no impact, because the boundary layer has already separated there.
Despite all this work and tweetstorms around the effect, it was unclear to many people – including Dr. Nathan himself – if the “laminar” effect was truly happening, and how to measure it.
So, what did we do? We decided to visit Dr. Barton Smith in Logan, Utah ourselves and subject some of our coaches to a grueling trial of throwing hundreds of pitches with the correct laminar orientation through his very specialized and expensive Particle Image Velocimetry machine.
Science in the Mountains of Utah
On January 15, 2019, a team from Driveline Baseball including Eric Jagers, Kyle Boddy, Joe Marsh and Dean Jackson visited the USU Experimental Fluid Dynamics Laboratory to attempt to capture the air velocity field around a “Laminar Express” pitch. Dr. Barton Smith, Nazmus Sakib, and Andrew Smith (not pictured) took the measurements.
(You can find Dr. Barton Smith’s post on the topic on his blog, Baseball Aero.)
Here’s what it looks like in high-speed when throwing baseballs into Dr. Smith’s amazing contraption!
I won’t reproduce all of Dr. Smith’s work, but I’ll post a sweet image from his PIV analysis as well as his opinion which he tweeted out:
The figure below shows a PIV dataset of one Laminar Express pitch. Note that this is viewed from above. We successfully captured 3 Laminar Express pitches during the day. All three showed an important feature: the wake is tilted upward (to the left from the pitcher’s view). In the dataset below, the boundary layer on top appears laminar, in that it separates from the ball near 12 o’clock. On the other hand, on the other side of the ball, the flow is turbulent, and remains attached to the ball far longer. The net result is a tilted wake. The pattern fits my sketch from a month ago. This ball has a downward force on it (in the data frame of reference) which is to the right from the pitcher’s frame of reference. The PIV data near the ball are poor (and there is a large region of missing data at the bottom of the ball), but this does not affect my conclusions.
The preliminary results from the @EngineeringUSU PIV air velocity measurements of "Laminar Express" pitches in conjunction with @DrivelineBB. I am now a believer. This thing exists. Comments/questions welcome.
— 𝔹𝕒𝕣𝕥𝕠𝕟 𝕊𝕞𝕚𝕥𝕙 (@NotRealCertain) January 20, 2019
Conclusion: So What?
It’s a rich tradition of Driveline R&D dating back a decade now to replicate results we already knew were true. Some people would call this “wasting time,” but it’s actually the soul of science to confirm things, not always seek novelty. In this case, we were pretty sure our high-speed video, launch monitor numbers, and anecdotal experience just playing catch indicated that we were right, but science generally demands a higher bar to clear. Dr. Barton Smith’s lab at Utah State allowed us the possibility to delve deeper and see the mechanism by which the “laminar express” really does work, and the results astounded all of us (except for Dr. Barton Smith, who called his shot and was basically correct).
The end result is that we know how to add additional movement not currently tracked or understood by models used by Trackman, Rapsodo, or Flightscope (all for different reasons due to different underlying technologies and assumptions, but that’s a post for another day), and that’s really damn cool. It’s not every day you get to throw baseballs in an expensive materials science laboratory and do hardcore science, finding out things that no one else has discovered, but in January 2019, a bunch of nerds from Driveline Baseball got to do just that.
And, oh yeah, it’s always fun to watch the fruits of your labor…
(95 MPH two-seam laminar express for strike three, delivered by Trevor Bauer)