A force platform analysis of vertical jumping provides an engaging demonstration of the kinematics and dynamics of one-dimensional motion. The height of the jump may be calculated (1) from the flight time of the jump, (2) by applying the impulse–momentum theorem to the force–time curve, and (3) by applying the work–energy theorem to the force-displacement curve.

1.
R.
Cross
, “
Standing, walking, running, and jumping on a force plate
,”
Am. J. Phys.
67
(
4
),
304
309
(
1998
).
2.
J. A.
Major
,
W. A.
Sands
,
J. R.
McNeal
,
D. D.
Paine
, and
R.
Kipp
, “
Design, construction, and validation of a portable one-dimensional force-platform
,”
J. Strength Conditioning Res.
12
(
1
),
37
41
(
1998
).
3.
Our teaching laboratory is equipped with a Kistler force platform (type 9281A, with amplifier type 9803). Available from Kistler Instrument Corporation, Amherst, NY (www.kistler.com).
4.
P. V. Komi, “Stretch-shortening cycle,” in Strength and Power in Sport, edited by P. V. Komi (Blackwell Science, Oxford, 1992), pp. 169–179.
5.
A.
Kibele
, “
Possibilities and limitations in the biomechanical analysis of countermovement jumps: A methodological study
,”
J. Appl. Biomech.
14
(
1
),
105
117
(
1998
).
6.
The most common method of measuring the height a person can jump is with the “jump-and-reach” test. The jumper stands next to a wall with the arm stretched overhead and holding a piece of chalk. The jumper makes a mark on the wall, then performs a jump and makes another mark on the wall when at the peak of the jump. The difference between the two marks is the jump height. The presence of the wall and the requirement to make a mark on the wall restricts the performance of some jumpers.
7.
Another method of measuring the flight height is with a calibrated video analysis to monitor the motion of the jumper’s c.m. Unfortunately, the jumper’s c.m. is not at a fixed position within the body; its location changes in response to the bending of the legs, the position of the arms, and the inclination of the trunk. In the “segmentation” method, the location of the c.m. of the body is determined by summing the effects of the component segments of the body (head, trunk, limbs, etc.) The mass and location of the c.m. of each of the body segments are estimated from data based on cadaver studies. The segmentation method is usually performed using computer-assisted digitizing, calibration, and calculation techniques, and is relatively time consuming. For further information see R. Bartlett, Introduction to Sports Biomechanics (E & FN Spon, London, 1997), pp. 164–205.
8.
The flight time of a vertical jump may be measured using a “contact mat” instead of a force platform. A contact mat is a thin sheet of foam rubber that is sandwiched by two layers of conducting foil. When the jumper is standing on the mat, the foam is compressed and the foil sheets are in contact, thus closing a timing switch. Available from Innervations, Muncie, IN (www.innervations.com) for about $600.
9.
M. F.
Bobbert
,
K. G. M.
Gerritsen
,
M. C. A.
Litjens
, and
A. J.
van Soest
, “
Why is countermovement jump height greater than squat jump height
,”
Med. Sci. Sports Exercise
28
(
11
),
1402
1412
(
1996
).
10.
G. J.
van Ingen Schenau
,
M. F.
Bobbert
, and
A.
de Haan
, “
Does elastic energy enhance work and efficiency in the stretch-shorten cycle?
,”
J. Appl. Biomech.
13
(
4
),
389
415
(
1997
).
11.
R.
McN. Alexander
, “
Optimum techniques for high and long jumps
,”
Philos. Trans. R. Soc. London, Ser. B
329
,
3
10
(
1990
).
12.
J. G.
Dowling
and
L.
Vamos
, “
Identification of kinetic and temporal factors related to vertical jump performance
,”
J. Appl. Biomech.
9
(
4
),
95
110
(
1993
).
13.
J. Hamill and K. M. Knutzen, Biomechanical Basis of Human Movement (Williams & Wilkins, Baltimore, 1995), pp. 476–478.
14.
E. A.
Harman
,
M. T.
Rosenstein
,
P. N.
Frykman
,
R. M.
Rosenstein
, and
W. J.
Kraemer
, “
Estimation of human power output from vertical jump
,”
J. Appl. Sport Sci. Research
5
(
3
),
116
120
(
1991
).
15.
QUATTRO JUMP. Available from Kistler Instrument Corporation, Amherst, NY (www.kistler.com).
16.
J.
Dapena
and
C. S.
Chung
, “
Vertical and radial motions of the body during the take-off phase of high jumping
,”
Med. Sci. Sports Exercise
20
(
3
),
290
302
(
1988
).
17.
A.
Lees
,
P.
Graham-Smith
, and
N.
Fowler
, “
A biomechanical analysis of the last stride, touchdown, and takeoff characteristics of the men’s long jump
,”
J. Appl. Biomech.
10
(
1
),
61
78
(
1994
).
18.
E. L.
Offenbacher
, “
Physics of the vertical jump
,”
Am. J. Phys.
38
(
7
),
829
836
(
1970
).
19.
P. H. Gerrish, “A dynamical analysis of the standing vertical jump,” Ph.D thesis, Teachers College, Columbia University, 1934.
This content is only available via PDF.
AAPT members receive access to the American Journal of Physics and The Physics Teacher as a member benefit. To learn more about this member benefit and becoming an AAPT member, visit the Joining AAPT page.