Atmospheric data: Hit Tracker
accounts for all the atmospheric factors that
significantly influence the flight of a batted ball:
wind, temperature, altitude and spin. Wind speed and
direction, temperature and altitude
must be specified by the user, based on the conditions
at the time of the home run. The spin of the ball
is determined by a series of assumptions related to the
direction and speed of the ball as it leaves the bat.
So, for the particular home run in question, the
atmospheric data would be entered:
Wind: in from RF at 5 mph
Temperature: 57 degrees F
Altitude: 21 ft. above sea level
Spin: automatically calculated
Observed data: To determine the trajectory
of a batted ball, Hit Tracker uses two points: an
initial point, which is always assumed to be about 3
feet above home plate, and a final point, which is a
point typically near the end of the ball’s flight. For
this “final” point, Hit Tracker needs to know the
location of the final point and the time of
flight of the ball to reach the final point. On the
home run in question, the location of the point of
impact of the ball against the light tower was
determined using a scale model of Fenway Park, and the
time of flight was measured with a stopwatch, yielding
the following data:
Distance from home plate: 314 ft.
Vertical distance above field level: 43 ft.
Horizontal angle: 7.4 degrees to the right of the left
field line
Time of Flight: 3.20 sec.
Initial trajectory: To determine the
trajectory that the ball followed, Hit Tracker begins by
making a “best guess”. The inputs to this best guess
trajectory consist of three parameters:
SOB: the initial speed of the baseball off the bat
VLA: the vertical launch angle; small for a line drive,
large for a popup
HLA: the horizontal launch angle; the direction on the
field, e.g. right-center field
Given these three initial parameters, Hit Tracker
constructs the complete trajectory for the initial
guess, breaking the flight of the ball into small
increments of time (1/100th of a second) and applying
the forces acting on the ball during flight:
Gravity
Wind resistance
Magnus force - the force due to the spin of the ball
(what makes a curveball curve)
Figure 1: “initial guess” trajectory and
impact point of actual home run
In the case shown here, the initial guess trajectory
point for 3.20 seconds is a bit high and a bit short
compared to the actual observation point (with the
horizontal angle not shown here, but also taken into
account), so the initial trajectory needs to be changed.
Using a proprietary method, Hit Tracker rapidly adjusts
the three inputs (SOB, VLA, HLA) until the Hit Tracker
trajectory point for 3.20 seconds matches the actual
observation point. Once this occurs, Hit Tracker has
reconstructed the actual trajectory the ball followed in
flight; the true distance of the home run is then read
from the Hit Tracker trajectory, representing the actual
distance the ball would have traveled had its flight not
been interrupted.
Figure 2: “initial guess” trajectory,
final trajectory and impact point of actual home run
Summary of Hit Tracker results: For the
home run in question, the final values for the three
input parameters are as follows:
SOB (Speed off Bat): 107.9 mph
VLA (Vertical Launch Angle): 26.6 degrees
HLA (Horizontal Launch Angle): 12.3 degrees to the right
of the left field line
These inputs to the ball trajectory, combined with the
atmospheric data, result in a true distance for this
home run of 372 ft. |