Velocity loss of a pitched baseball
George Hardy
If a baseball is pitched at 90 mph (132 fps), it will
lose velocity as it travels towards the plate. As the
ballistic coefficient of a baseball is not very good,
the velocity loss should be significant? Can anyone
post what will be the velocity of the baseball as it
crosses the plate?
This velocity loss will effect drift. Drift can be
very significant, even if the cross-wind is only 6
mph (8.8 fps). That means 4.4 feet in a half second.
Of course, drift depends on the loss of velocity.
Please advise -- either calculated velocity loss or
measured velocity loss.
GFH
Ralph Carmichael
The question was posted by George Hardy:
How much velocity does a ball pitched at 90 mph
lose by the time it reaches home plate?
Assume the drag is constant and simply compute
deceleration due to drag and time-of-flight
as follows:
initial velocity = 90 miles/hour = 40.234 m/s
dynamic pressure = 0.5*density*velocity**2
= (0.5)(1,225)(40.234)(40.234)
= 991.5 Pa = 20.7 psf
drag=dragCoefficient*dynamicPressure*area
diameter of a baseball = 74mm
cross-section-area of baseball = pi*.037**2
= .0043 sq.m = 6.67 sq.in
dragCoefficient=0.3
drag=(0.3)(991.5)(0.0043)=1.279 N = 0.288 lb
mass of a baseball = 125g = 0.125kg
acceleration = drag/mass = 1.279/0.125 = 10.23 m/s**2
distance = 60.5 ft = 18.44 m
time-of-flight = 18.44/40.234 = 0.458 seconds
delta-V = (10.23)(0.458) = 4.68 m/s
summary:
initial velocity = 40.23 m/s = 90.00 mph
final velocity = 35.55 m/s = 79.52 mph
so it loses 12 percent of its speed.
The drag force is suprisingly high - it is
greater than the weight of the ball.
A more exact analysis would show that the ball does
not lose quite that much speed. The drag decreases
as the ball slows down.
------------------------------------------------------
Ralph Carmichael ralp...@yahoo.com
Public Domain Aeronautical Software
P.O. Box 1438 Santa Cruz CA 95061 USA
http://www.pdas.com
Tom MacIntyre
On 14 Aug 2002 20:45:01 GMT, ralp...@yahoo.com (Ralph Carmichael)
wrote:
It does seem a little high...
When Nolan Ryan was timed at 100.9 in 1973, didn't they base it on the
speed of the ball crossing the plate? I think when they timed Bob
Feller, the device that timed him was about halfway between the mound
and home (I think I saw a picture of that, and I also think I saw a
picture of him throwing in competition against a speeding motorcycle
one time). Where is the ball's trajectory grabbed by modern radar
guns? Isn't that one of the reasons for some guns (earlier ones at
least) having such differences in their readings?
Tom
Gene Nygaard
Tom MacIntyre <tom__ma...@hotmail.com> wrote in message news:<E17mkxx-...@ns15.u-build-it.net>...
There are factors in the calculations by the earlier poster that also
skew the results. Here are a couple of them:
Isn't the weight of a major league baseball 145 g rather than 125 g?
The distance from the pitcher's hand at release to home plate is
probably more like 17 m, not 18.44 m.
Cross-section area of the baseball might not be the proper value for
the drag formula.
Gene Nygaard