How far does it fly? The physics inside the Aaron Judge home run tracker
A one-minute painted explainer of the tracker's ball-flight model, followed by the real physics it leaves out and where to read more.
Read the narration
This tracker replays Aaron Judge's first home run back from injury, and asks a physics question: how far does a ball fly? The defaults are an exit velocity of one hundred twelve point four miles an hour and a launch angle of twenty-eight and a half degrees. That's about a hundred sixty-five feet per second, split into forward speed and climb. In a vacuum, that ball would carry about seven hundred feet. But the tool steps the flight every fiftieth of a second: gravity pulls down, and drag pushes back, harder the faster the ball moves. With drag, the ball peaks at seventy-one feet, hangs four point one seconds, and lands at three hundred ninety-four feet. That clears the tool's three hundred eighty-five foot fence by nine. Home run. Angle matters too. The Limited preset, at twenty-one degrees, dies at three hundred ten feet. The Moonshot, at thirty-five degrees, climbs to ninety-three feet and lands at four hundred two. One caution: the tool also turns this single swing into a season slugging of point seven one two, above the page's pre-injury mark. That's a straight-line rule, not Statcast.
What the model includes, and what real baseballs do
Gravity plus drag, stepped in time
The tracker converts mph to ft/s, splits the speed into horizontal and vertical parts, then updates position every 0.02 s with gravity (32.174 ft/s²) and a drag term proportional to speed squared (coefficient 0.00185 per foot).
No backspin lift
Real fly balls carry backspin, which creates Magnus lift and adds many feet of carry. The tool leaves lift, wind, temperature and altitude out, which is one reason its 394 ft is shorter than what Statcast typically projects for a ball hit this hard at this angle.
Which fence is 385 feet?
The tool calls its 385 ft, 8 ft wall 'left-center'. At Yankee Stadium the posted distances are about 399 ft to left-center and 385 ft to right-center, so treat the fence as the tool's simplification.
Slugging from one swing
Projected slugging is 0.620 + 0.006 × (exit velocity − 100) + 0.003 × (recovery − 90), clamped to .480–.740. It is a hand-set rule linking a single hit to a season rate, not a statistical projection.
Try it in the tool
Click Limited 103 mph, then Moonshot 35°, and compare Projected Distance and Apex Height with the default.
Keep Exit Velocity at 112.4 and drag Launch Angle from 12° to 45° to find where distance peaks.
Move the Physical Bat-Speed Recovery Index and notice that it changes only the simulated slugging, not the ball's flight.
Why spinning balls curve and carry, the lift the tool omits.
Distances in the video come from this tracker's simplified drag model and default inputs; real Statcast projections include spin, weather and park effects.
Baseball Trajectory Simulation & Recovery Metrics
How does this simulator model batted ball distance, apex height, and slugging outlook from exit velocity and launch angle?
This interactive workbench integrates standard 2D equations of motion for a baseball under gravity and quadratic aerodynamic drag. Using initial contact height, exit velocity, and launch angle, it computes the landing distance and apex height via fixed discrete Euler steps. The page also applies a linear heuristic combining exit speed and bat-speed recovery to estimate post-injury slugging, rather than running a full empirical forecasting model.
The physics solver models only 2D drag with a constant coefficient (0.00185) and gravity, omitting backspin (the Magnus force), wind, humidity, and elevation that heavily dictate real-world Statcast trajectories. Furthermore, the recovery slugging outlook relies on a simplified linear weighting formula rather than Statcast expected statistics or validated medical recovery curves.
Try a worked example
Clicking the 'Peak 117 mph' preset loads an exit velocity of 117.2 mph, a 27.0° launch angle, and 102.0% bat speed recovery. Running these inputs through the page's trajectory integration updates the projected distance display to 407 ft, sets the apex height to 69 ft, adjusts fence clearance to +22 ft past the left-center fence, and sets the simulated slugging percentage to .740.
Statcast Exit Velocity and Hard-Hit Classifications
Statcast tracks exit velocity as the speed of the baseball immediately off the bat on all batted ball events. In Major League Baseball analysis, batted balls struck at 95 mph or higher are classified as hard-hit, giving fielders less time to react and significantly increasing on-base probabilities. Exit Velocity (EV) | Glossary | MLB.com
While this tool captures user-selected exit velocities to simulate flight, its fixed 2D aerodynamic model calculates trajectory paths without accounting for pitch speed conversion or spin dynamics.
Barrel Criteria vs. Simplified Table Rules
Statcast defines a 'Barrel' as a batted ball combining exit velocity and launch angle that has historically produced at least a .500 batting average and a 1.500 slugging percentage. The classification requires at least 98 mph off the bat with an initial 26° to 30° launch window, widening as exit velocity increases up to 116 mph. Barrel | Glossary | MLB.com
In this page's script, the matrix table instead toggles between fixed percentages (25.4% when exit velocity is at least 98 mph and launch angle is between 24° and 32°, otherwise 18.2%), providing an illustrative rule rather than evaluating Statcast's dynamic velocity-dependent barrel cone.