Optimum TakeOff Angle
in the
Long Jump
Introduction
Optimum TakeOff Angle
Undergraduate Teaching
Introduction
One of the best known 'results' of the science of mechanics is that the
optimum projection angle for achieving maximum horizontal range is
45°. However, it is also well known that actual performers in
projectilerelated sports seldom use an angle of 45°. For
example, typical takeoff angles of worldclass long jumpers are around
21°. Some researchers have noted that in long jumping the
landing is about 50 cm lower than the takeoff. Even so, this produces
only a small reduction in the calculated optimum takeoff angle (to
about 43°)
The reason for the discrepancy between theory and practice is that the
takeoff speed attained by the athlete are not
independent of the takeoff angle, as is assumed in the conventional
calculation of the optimum takeoff angle. Experiments have shown that
the takeoff speed an athlete can generate decreases
with increasing takeoff angle, and that this substantially reduces
the optimum takeoff angle.
Optimum TakeOff Angle
The
idea that the optimum takeoff angle in the long jump is about
43° may be understood by using the wellknown formula for the
range of a projectile in free flight.
A
series of distance versus takeoff angle curves may be plotted for
selected takeoff speeds. These curves suggest that the optimum
takeoff angle is just under 45°.
This
set of calculations contain a serious error. The calculations do not
include the fact that an athlete cannot jump with
the same speed at all takeoff angles. The takeoff speed an athlete
can generate steadily decreases as the athlete
tries to jump with a higher and higher takeoff angle.
The
optimum takeoff angle for the athlete is obtained by combining the
speedangle relation for the athlete with the equation for the range of
a projectile in free flight. The optimum takeoff angle for the athlete
is not just under 45°, but about 22°.
The
optimum takeoff angle calculated above applies only to the athlete in
question.
Each athlete has a unique speedangle relation that depends on their
size, strength, and jumping technique.
This means that each athlete has their own specific optimum takeoff
angle.
The optimum takeoff angle for a worldclass long jumper may be
anywhere from 15° to 27°.
To
find out more about the long jump takeoff angle study, see:
Linthorne,
N.P., Guzman, M.S., and Bridgett, L.A. (2005).
Optimum takeoff angle in the long jump.
Journal of Sports Sciences,
23 (7), 703712. (Publisher)
Linthorne,
N.P. Optimum angles of projection in the throws and jumps.
SweatPit.com.
Optimum Projection Angles in
Undergraduate Teaching
My
work on optimum projection angles has been incorporated into my
biomechanics classes. I have produced a Microsoft Excel spreadsheet and
graphing tutorial to examine the optimum projection angle in
shotputting.
This tutorial highlights to the student the fact that the optimum
projection angle in sports is not 45°.
