DYNAMIC EFFECT OF LACROSSE STICK SHAPE ON BALL SPEED DURING THROWING
1
1
Alison L. Sheets and 2Mont Hubbard
The Ohio State University, Columbus, OH, USA
2
University of California, Davis, CA, USA
email: [email protected]
INTRODUCTION
The sport of lacrosse is played with a solid rubber
ball that can be caught, held and thrown with a net
strung inside of a head and attached to a longhandled stick (Fig. 1). Lacrosse was originally
played by Native Americans as a part of ceremonial
rituals, a way to train for war, or a method for
settling disputes between tribes. In the modern
game, teams of 10 players attempt to score by
shooting the ball into the opposing team’s 6ft x 6ft
goal. Although the rules and purpose for playing
have taken many forms over the centuries, the
equipment remained largely unchanged until the
mid 1950’s. At this time, the popularity of lacrosse
began steadily increasing. It is currently the fastest
growing sport in the United States [1].
Stick head design significantly affects shot speed
[2,3] but exactly how the ball and stick head interact
is unclear. The ball speed at release is significantly
faster than the tip of the stick and the velocity
direction varies by as much as 0.31 rad [3]. This
indicates that net curvature is an important factor to
include in the interaction between the ball and stick.
The goal of this study was to create a lacrosse head
model and throwing simulation that can be used to
systematically investigate the effect of stick head
geometry on throwing speed and direction. This tool
could be used by the governing bodies of lacrosse to
attempt to reduce player injury risk by developing
more stringent requirements for approved stick head
designs. This is a concern because the very fast shot
speed has caused fatal injuries in the men’s game,
and has necessitated the addition of protective eyewear to the women’s game.
METHODS
Figure 1: Examples of new, plastic lacrosse head
shape, and older wooden design
(www.southswellsports.com)
In response to the surge in popularity, there have
been fundamental changes to lacrosse stick design.
The most notable change was the replacement of
wooden stick heads with plastic ones in the men’s
and women’s games in 1966 and 1997, respectively.
The use of plastic decreased the variability between
sticks, decreased manufacturing time and cost, and
increased durability. More recently, stick head
designs have been customized to increase shot
speed, throwing distance and ball retention
capabilities. Now there are hundreds of stick heads
with subtle geometric variations (Fig. 1).
A generalized planar lacrosse stick model was
developed and used to propel a one-degree-offreedom ball that was 0.065m in diameter and
weighed 0.1465 kg (Fig. 2). The stick was initially
positioned at a 30º angle from vertical at rest. From
this position it rotated with linearly increasing
angular acceleration =3500*t rad/s2 around a
fixed point 0.1405 m behind, 0.1015 m above the
distal end of shaft. This point was an experimentally
measured instant center at ball release [3].
Four experimentally measured points defined the
geometry and depth of the net in the stick head (Fig.
2). Depth was measured by placing a ball in the net
at numerous locations and applying a load to the
ball. This defined a rigid envelope that the ball rolls
on, which incorporates the non-rigid movement of
the net. From these points, the radius from the
center of the stick head face to the surface of the net
was defined as a piecewise function of  with a
continuous slope:
1.21    0.98
0.403 2  1.565  1.383

if 0.98    0.15
R( )=  0.065 / cos 
0.027 2 +0.170  0.334
0.15    1.57

Figure 2: Side view of stick head (left) and whole
stick including shaft (right)
The ball was assumed to roll without slipping on the
stick head surface. The state variables of the system
were  , the angle to the ball center from a line
passing perpendicularly through the center of the
stick face, and  . Ball release was defined to be
when the ball had rolled past the stick tip,  >1.57.
RESULTS AND DISCUSSION
Ball speed at release, 19.02 m/s, exceeded the speed
of the tip of the stick (Fig. 3) and was similar to
speeds measured for high-level, female collegiate
players, 18.8 m/s-19.7 m/s [3]. The ball velocity
was primarily in the horizontal direction, 19.25 m/s,
with a small downward component, -2.4 m/s.
Additionally, there was a very small angle, 0.015
rad, between the directions of the velocity vectors
of the ball and stick tip. This is smaller than the
experimentally measured differences of 0.23-0.31
rad [3]. It is likely the simulated differences in
velocity direction would increase with a more
realistic model of the ball-stick interaction just prior
to release. The model described in this paper
defines release velocity as the state of the ball when
the contact point reaches the tip of the stick.
Actually, before the contact force becomes zero and
the ball leaves the stick, it continues to rotate about
the very small radius of the stick tip. During this
short additional contact period, the stick tip velocity
would continue rapidly changing direction, since it
is rotating about a fixed point, while the ball
velocity is not constrained in this way. The
marginally longer contact time would also slightly
increase ball speed at release.
Figure 3: Ball speed exceeds that of the stick tip at
ball release
This study describes a method for modeling the
complex geometry of a lacrosse stick head by
defining a radius from the center of the head to the
net as a piecewise function. The dynamic model
was able to reproduce characteristics of
experimentally measured ball velocities, and will be
used to investigate the effects of surface geometry
on throwing speed and technique.
REFERENCES
1.Sterenson S. 2007 US Lacrosse Participation
Survey. 2008.
2.Livingston LA. J Science and Medicine in Sport
9, 299-303, 2006.
3.Crisco JJ, et al. J Applied Biomech, 25, 184-191,
2009.
ACKNOWLEDGEMENTS
The OSU Department of Mechanical Engineering
provided the support for this study.