Let’s Talk Physics for a Minute.

What is the fastest route between two points?

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Well, contrary to what you’ve been taught, a straight line is not always the fastest. When gravity is involved, a straight line is actually not an optimal route - enter the Brachistochrone Curve [ bruh-kis-tuh-krohn ]. The Brachistochrone Curve is the curve of fastest descent, when an object slides down a frictionless* surface (an important detail to remember).

The Brachistochrone problem, originally posed by Johann Bernoulli, asked, “given two points A and B in a vertical plane, assign a path AMB to the moving body M, along which the body will arrive to point B, falling by its own gravity and beginning from A, in the least time?” In other words - given two points, A and B, what is the fastest route between them?

YouTuber, V-Sauce, enlisted the help of Mythbusters’ Adam Savage to explore this concept in detail - to learn more click here.

Consider the three slopes below (see video below). 

The direct route will be the shortest distance but the ball will not accelerate to its top speed nearly as fast as the other two slopes. On the other hand, the slope with the steepest drop will initially accelerate an object to its top speed faster than the other two, however, it must travel the greatest distance of the three slopes and may not continue to accelerate through the finish. You can conceptualize the Brachistochrone Curve as the perfect blend of these two routes -- it takes the shortest path while also optimizing the use of gravity to accelerate an object. 

So, what does this have to do with pitching?

Movement efficiency. The objective of the forward move in pitching is to gain momentum while also maintaining positions and a posture that allows the athlete to store rotational energy.

If an athlete drops too much without forward movement or only uses forward movement with no drop, they are taking a less than optimal route and may not be using gravity effectively. This is especially important because faster forward movement can make achieving faster rotational movements much easier - like a car accelerating from a slow roll vs. a car accelerating down a hill. 

It needs to be a blend of both, happening simultaneously. Gravity accelerates the body (drop) and applying pressure through the back leg gets the athlete to front foot plant faster by redirecting their momentum forward. 

The beauty of this curve is that you don’t need to change your mechanics and the athlete does LESS to achieve MORE -- i.e., they don’t extend out of a strong posture early in their delivery in an attempt to accelerate their body, gravity does the work. You can see in the video above that each pitcher’s delivery is different, yet the athletes get their bodies moving by following the curve as they descend out of max leg lift.

The Physical Requirement

Here’s the catch. The descent portion of the Brachistochrone Curve is an incredibly athletic and physically demanding task. 

After the athlete applies pressure (through their back leg) into the rubber to get their momentum moving forward, they then relax their back leg - allowing gravity to accelerate their body downward - before applying the brakes and redirecting their momentum back into the rubber to continue their path towards home plate. 

We’re talking olympic level reactivity, not just strength. The faster an athlete can descend, the greater the physical requirement will be placed on the body to redirect that energy. Watch Jack Leiter in regular speed to get an idea of how quickly he applies the brakes while redirecting his momentum forward after he descends from max leg lift. 

The sensation of redirecting your momentum forward after the descent is similar to that you would get when riding down a half pipe or, for those of you who aren’t X-Games athletes, the feeling you would get from riding your bike down a steep hill that leveled out quickly. 

Common Mistakes

Applying Pressure in the Wrong Direction

After searching for the Brachistochrone Curve in novice athletes, there are a few things to be aware of If an athlete’s center of mass is biased too far rearward, they may not be able to apply pressure in a way that effectively propels them forward (see the image below).

Essentially, these athletes use gravity to accelerate as they descend into their stride but when they apply the brakes, they resist upwards instead of creating a better force vector that propels them towards home plate. It’s like trying to do a pistol squat and then trying to move forward after you’ve stopped most of your downward momentum. 

Never Taking Their Foot Off of the Brakes

Similarly, there are athletes who resist too much on the way down and they don’t use gravity to its full potential. These athletes may even follow a Brachistochrone-like curve, however, by never taking their foot off the brakes, they limit the maximum speed they can reach. Not unlike a car. 

Of course, this does not mean that you should be telling your athletes to try to relax longer because they might not be able to physically do it! Remember that this is a pretty demanding task and most kids can’t even do a controlled descent into a pistol squat, so it’s unrealistic to expect them to replicate that movement without causing a flurry of other issues. 

It’s also important to acknowledge that your athlete may have some sort of physical restriction or limitation in their ankles or hips that limit their ability to perform the ideal movement. Alternatively, it could also be that your pitcher isn’t used to moving at a fast rate of speed and this is their way of decelerating their body to a speed they can manage -- much like the feeling you get from trying to run down a hill with too steep of a slope. 

Your job as a coach is to rule out alternative explanations for why they move the way they do and then provide your pitcher with a training program that will help them move explosively and efficiently. 

Resources

1. “Surfing the Brachistochrone” by Steve Haake
   https://engineeringsport.co.uk/2010/10/29/surfing-the-brachistochrone/

2. “Surfing Brachistochrones” by Bruce Henry and Simon Watt
   https://www.parabola.unsw.edu.au/files/articles/1990-1999/volume-34-1998/issue-3/vol34_no3_2.pdf

3. “The Brachistochrone” by Vsauce
   https://www.youtube.com/watch?v=skvnj67YGmw&t=1077s
   
   

About the Author

Graham Tebbit is one of the lead throwing trainers with Velo Baseball as well as our head data analyst. While attending Hofstra University he earned his bachelor’s degree in psychology and later earned his MSc in Kinesiology while attending the University of Toronto where he studied sub-concussive head impacts to catchers. Contact Graham here.