有關全壘打距離之問題？ - 美國職棒

http://www.hittrackeronline.com/howitworks.php

How Hit Tracker Works: Hit Tracker is a spreadsheet tool that takes as inputs
atmospheric information and observation data, and gives as an output the true
distance that the home run traveled, along with the initial speed of the hit
off the bat and the precise angles at which the ball left the bat. It does
this by creating as a starting point an initial “best-guess” three
dimensional trajectory for the home run, and then modifying that trajectory,
a little bit at a time, until the trajectory matches the observed data from
the actual home run event. An example follows:



Hit Tracker Example: A player hit a “walkoff” home run at Fenway Park on
May 10, 2005, the ball striking one of the light towers above the left field
wall and seats before caroming back onto the playing field. How far would
this home run have traveled if it had not struck the light tower or any other
obstruction?

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)

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.


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.

--