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PHASE CHARACTERISTICS OF THE COUNTERMOVEMENT
JUMP FORCE-TIME CURVE:ACOMPARISON OF
ATHLETES BY JUMPING ABILITY
CHRISTOPHER J. SOLE,
1
SATOSHI MIZUGUCHI,
2
KIMITAKE SATO,
2
GAVIN L. MOIR,
3
AND
MICHAEL H. STONE
2
1
Department of Health, Exercise, and Sport Science, The Citadel—The Military College of South Carolina, Charleston, South
Carolina;
2
Center of Excellence for Sport Science and Coach Education, Department of Sport, Exercise, Recreation, and
Kinesiology, East Tennessee State University, Johnson City, Tennessee; and
3
Department of Exercise Science, East Stroudsburg
University, East Stroudsburg, Pennsylvania
ABSTRACT
Sole, CJ, Mizuguchi, S, Sato, K, Moir, GL, and Stone, MH.
Phase characteristics of the countermovement jump force-time
curve: a comparison of athletes by jumping ability. J Strength
Cond Res 32(4): 1155–1165, 2018—The purpose of this
study was to compare the phase characteristics of the coun-
termovement jump (CMJ) force-time (F-t) curve between ath-
letes based on jumping ability. An initial sample of one-hundred
fifty Division-I collegiate athletes were ranked based on CMJ
height. Three performance groups were then formed by taking
the top, middle, and lower 30 athletes (15 men and 15 women)
from the sample. Phases of the CMJ F-t curve were determined
and then characterized by their duration, magnitude, area
(impulse), and shape (shape factor). A series of 3-way mixed
analysis of variance were used to determine statistical differ-
ences in phase characteristics between performance groups
as well as between male and female athletes. Statistically sig-
nificant phase-by-performance group interactions were
observed for relative phase magnitude (p,0.001), relative
phase impulse (p,0.001), and shape factor (p= 0.002).
Phase-by-sex interactions were statistically significant for both
relative phase magnitude (p,0.001) and relative phase
impulse (p,0.001). Post hoc comparisons indicated that
higher jumpers exhibited larger relative magnitude and impulse
in the phases contained within the positive area of the F-t
curve. Similarly, relative phase magnitude and impulse were
the only phase characteristics to be statically different between
men and women. Finally, the relative shape of the phase rep-
resenting the initial rise in force was found to relate to jump
height. These results provide some information regarding the
diagnostic value of qualitative analysis of the CMJ F-t curve.
KEY WORDS jump height, shape factor, force platform, athlete
monitoring
INTRODUCTION
The countermovement vertical jump (CMJ) is reli-
able, noninvasive, and relatively nonfatiguing
assessment used in athlete performance monitor-
ing (12,23,29–31,37). Along with jump height
(JH), CMJ performance is commonly characterized using
instantaneous variables, such as peak force, peak velocity,
and peak power. Although effective indicators of perfor-
mance, these variables are limited in they represent, or are
calculated from, single points throughout the kinetic and
kinematic history of the movement. Consequently, analysis
of CMJ using only instantaneous variables provides limited
mechanistic insight into the movement or neuromuscular
characteristics underpinning performance (32). These limi-
tations may be viewed as problematic for the strength and
conditioning practitioner or sport scientist using these data
to make training decisions or evaluate training progress.
The force-time (F-t) curve of the CMJ contains valuable
information regarding kinetic and temporal characteristics of
the movement. Analysis of the F-t curves of athletic move-
ments, CMJ in particular, has received considerable attention
in biomechanics and sport science research. Previous
research has investigated relationships between factors such
as training background and jumping ability and character-
istics of the CMJ F-t curve (5,9,11,16,20,25,38). In addition,
researchers have investigated the influence of various
neuromuscular training interventions on CMJ F-t curve
characteristics (5–8). These investigations suggest that differ-
ences can be observed in both instantaneous variables and in
the actual shape of the F-t curve itself between individuals
and after training interventions. Furthermore, alterations in
F-t characteristics after interventions may be specific to the
Address correspondence to Dr. Christopher J. Sole, christopher.j.sole@
gmail.com.
32(4)/1155–1165
Journal of Strength and Conditioning Research
Ó2017 National Strength and Conditioning Association
VOLUME 32 | NUMBER 4 | APRIL 2018 | 1155
Copyright © National Strength and Conditioning Association Unauthorized reproduction of this article is prohibited.
type of training performed (e.g., strength- vs. power-focused
training) (6). Collectively, these results suggest that a qualitative
analysis of the CMJ F-t curve may yield diagnostic data regard-
ing an athlete’s performance state that may be used in perfor-
mance evaluation or monitoring. Moreover, this form of
analysis is attractive, considering its potential capability of pro-
viding a mechanistic understanding of performance; something
difficult to accomplish using only instantaneous variables.
Although the previously mentioned studies do provide
information regarding F-t curve characteristics between
jumpers and in response to training, they are limited in their
general approach to examining
the F-t curve itself. For exam-
ple, Cormie et al. (4–6,8)
examined the CMJ F-t curve
in its entirety, whereas others
(20,38) assessed portions of
the curve that encompass mul-
tiple aspects or phases of the
movement (e.g., eccentric and
concentric phases). Consider-
ing the CMJ F-t curve contains
multiple phases, each corre-
sponding to specific aspects
of the movement (17,22,28),
perhaps a more advantageous
method of CMJ F-t curve anal-
ysis would be to take into con-
sideration each of these
specific phases. Detailed infor-
mation regarding the charac-
teristics (duration, size, shape,
etc.) of individual F-t curve
phases as they relate to perfor-
mance may greatly increase the diagnostic potential of CMJ
F-t curve analysis. Unfortunately, with the exception of net
impulse (18,24), little information exists regarding character-
istics of individual CMJ F-t curve phases and performance.
Although a phase-by-phase analysis may be promising,
information must first be established regarding specific phase
characteristics as it relates to performance. Considering the
criterion variable used to characterize CMJ performance is
commonly JH, a logical first step may be to establish F-t
curve phase characteristic behavior based on JH. Therefore,
the purpose of this study was to perform a comparison of the
TABLE 1. Athlete demographic data (n= 150, mean 6SD).
Sport nAge (y) Body mass (kg) Height (cm)
Males
Baseball 24 20.0 61.3 83.2 68.4 181.7 66.3
Basketball 11 21.0 61.3 89.0 612.4 188.7 66.3
Soccer 21 21.0 61.5 77.9 68.8 180.1 66.9
Tennis 6 20.9 61.7 72.6 68.2 180.0 64.9
Track and field
Jumps 7 20.6 61.6 78.9 69.3 186.6 64.9
Throws 4 20.6 61.1 99.2 619.2 188.8 66.6
Multievent 2 19.4 61.4 77.1 65.7 183.0 69.9
Females
Soccer 20 20.0 61.0 67.1 64.8 167.8 64.8
Softball 23 20.5 60.9 69.1 68.2 167.1 66.9
Volleyball 19 19.6 60.9 69.7 67.6 174.1 67.1
Track and field
Jumps 8 20.0 61.5 58.7 65.1 163.9 67.4
Throws 2 19.7 60.4 100.6 643.3 174.5 63.5
Sprints 3 20.9 61.3 60.1 66.1 166.3 610.1
TABLE 2. Jump height performance groups (n= 90, mean 6SD).*
nJH (cm) Age (y) HT (cm) BM (kg) Sport
HPG
Male 15 47.4 64.4 20.9 61.4 183.9 66.8 82.7 69.8 MBB = 6, MS = 2, MTF = 7
Female 15 36.0 62.1 19.7 61.3 170.6 68.3 67.7 68.5 SB = 1, VB = 9, WS = 1, WTF = 4
MPG
Male 15 36.4 61.5 20.3 61.3 182.7 64.7 82.2 68.6 BB = 8, MBB = 3, MS = 2, MT = 1,
MTF = 1,
Female 15 27.5 60.9 19.8 60.9 171.5 66.5 63.4 65.7 SB = 3, VB = 4, WS = 4, WTF = 4
LPG
Male 15 28.4 62.4 20.7 61.4 179.3 68.5 81.4 616.7 BB = 2, MS = 6, MT = 5, MTF = 2
Female 15 19.7 62.3 20.3 60.8 170.6 65.4 76.7 65.4 SB = 7, WS = 7, WTF = 1
*JH = jump height; HT = height; BM = body mass; HPG = high-performance group; MBB = men’s basketball; MS = men’s soccer;
MTF = men’s track and field; SB = softball; VB = women’s volleyball; WS = women’s soccer; WTF = women’s track and field; BB =
baseball; MT = men’s tennis; MPG = middle-performance group; LPG = low-performance group.
Phase Characteristics of the CMJ Force-Time Curve
1156
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individual CMJ F-t curve phases between athletes of various
jumping abilities.
METHODS
Experimental Approach to the Problem
All data included in this study were collected as part of an
ongoing athlete performance monitoring program. To com-
pare CMJ F-t curve phase characteristics based on jumping
ability, CMJ data from a sample of one-hundred fifty male (n
= 75) and female (n= 75) athletes were independently
ranked and then stratified into performance groups based
on JH. Performance groups were formed by taking the top
(high-performance group [HPG]), middle (middle-perfor-
mance group [MPG]), and lower (low-performance group
[LPG]) 15 men and 15 women from the ranked samples.
The remaining 60 athletes’ data were not further used in this
analysis. A 2-way analysis of variance (ANOVA) found JH to
be statistically different between both performance groups
and sex (performance group: F(2,89) = 370,
h
2
= 0.637, p,
0.001; sex: F(1,89) = 333,
h
2
= 0.287, p,0.001). In addition,
there was no statistically significant group-by-sex interaction
effect present. These results support the researcher’s decision
to independently rank male and female athletes when form-
ing performance groups to avoiding overrepresentation of
one sex in any one performance group.
Subjects
Data from one-hundred fifty athletes (men: n= 75; age = 20.5
61.4 years [age range: 18-24 years old], body mass = 82.0 6
11.3 kg, height = 182.1 67.4 cm; women: n= 75; age = 20.1
61.1 years, body mass = 68.1 611.3 kg, height = 169.1 67.1
cm) were initially included in this study. All athletes were
National Collegiate Athletic Association (NCAA) Division-I
athletes representing various sport disciplines (Table 1). After
the formation of the JH performance groups, the initial sample
was reduced to 90 athletes. Descriptive data for athletes
included in each JH performance group are displayed in Table
2. The methodology of the study was approved by East Ten-
nessee State University, and written informed consent was
obtained from each participant at the time of data collection.
Procedures
Before testing, all participants performed a general warm-up
consisting of 25 jumping jacks, 1 set of 5 dynamic mid-thigh
clean pulls with a 20-kg barbell, and 3 sets of 5 mid-thigh
Figure 1. The countermovement jump force-time curve. Point A: initiation of the unweighted phase. Point B: time point where the vertical ground reaction force
returns to system weight. Point C: the end of the eccentric phase and initiation of the propulsive phase, as well as peak negative displacement of the jumper’s
center of mass, and the time point when center of mass velocity transitions from negative to positive. Point D: the end of net impulse. Point E: the vertical ground
reaction force falls below system weight and peak velocity of the jumper’s center of mass. Point F: takeoff, where the jumper leaves the force platform. Points A
to B: unweighted phase. Points B to C: stretching phase. Points C to D: net impulse phase. Points C to E: propulsion-acceleration I phase. Points D to E:
propulsion-acceleration II phase. Points E to F: propulsion-deceleration phase. Area 1: unweighted impulse. Area 2: stretching impulse. Area 3: net impulse.
Combined areas 3 and 4: propulsion-acceleration I impulse. Area 4: propulsion-acceleration II impulse. Area 5: propulsion-deceleration impulse.
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clean pulls with 60 kg for men and 40 kg for women
(19,34,35). Immediately after the general warm-up, partici-
pants proceeded to jump testing. Countermovement jump
(CMJ) testing began with a specific warm-up consisting of
2 submaximal CMJs (50% and 75% of perceived maximal
effort). Athletes then performed 2 maximal effort CMJs with
approximately 60 seconds of rest between trials. Jumps were
performed on a force platform (91.0 cm 391.0 cm; Rice
Lake Weighing Systems, Rice Lake, WI, USA). To prevent
arm swing and only measure lower-body performance (21),
athletes performed all jumps while holding a nearly weight-
less plastic bar across the shoulders approximately between
the seventh cervical and third thoracic vertebrae (19). The
analog signal from the force platform was collected using
an analog-to-analog BNC interface box (BNC-2110), and
16-bit analog-to-digital board (NI PCI-6036E; National
Instruments, Austin, TX, USA). All trials were collected at
a sampling frequency of 1,000
Hz. Voltage data from the force
platform were converted to
vertical ground reaction force
using laboratory calibrations,
and F-t curves were con-
structed. To remove random
noise, all data were filtered
using a fourth-order low-pass
Butterworth filter with a cutoff
frequency of 40 Hz (40). All
data collection and analysis
were performed using custom
programs (LabVIEW Version
12.0; National Instruments,
Austin, TX, USA).
From the CM J F-t curve, the
following6phases(Figure1)
weredeterminedbasedonpre-
vious research (17,22,28,38):
unweighted phase, stretching
phase, net impulse phase,
propulsion-acceleration I phase,
propulsion-acceleration II
phase, and propulsion-
deceleration phase. The fol-
lowing variables were then
calculated for each phase: (a)
duration, calculated as the
length of the phase in millisec-
onds, (b) magnitude, calcu-
lated as the height of the
phase in newtons (N), (c)
impulse, calculated through
integration of the normalized
F-t curve phase, expressed in
newton-seconds (Ns), and (d)
shape factor, calculated as
a ratio of phase impulse relative to a rectangle shape formed
around the impulse, expressed as a percentage (10,27).
Phase magnitude and impulse were scaled to system mass
and expressed as newtons per kg (N$kg
21
) and newton-
seconds per kg (Ns$kg
21
), respectively.
Test-retest reliability was assessed using intraclass correlation
coefficient (ICC) and estimations of typical error expressed as
a coefficient of variation (CV) (15). Intraclass correlation coef-
ficient and CV for JH measures ranged from 0.900 to 0.993 and
1.8–3.2%, respectively. Test-retestreliabilityforCMJF-tcurve
phase characteristics was found to be acceptable (ICC .0.750;
CV ,10.8%) with the only exception being stretching phase
magnitude with a CV of 15.3%. To reduce random error and
represent a more true score, mean variables from the 2 maximal
trials were used for all analyses (13).
Comparisons of CMJ F-t curve phases were performed
using a resampling technique similar to that of previous
TABLE 3. Force-time curve phase characteristics for performance groups (n= 90,
mean 6SD).*
Phase HPG MPG LPG
Duration (ms)
UW 355.1 652.1 345.2 654.8 359.6 657.6
STR 168.6 631.8 181.9 640.5 197.7 646.2
NI 237.7 635.3 237.9 645.4 243.8 637.7
PA-I 263.0 637.0 271.6 647.3 279.0 640.0
PA-II 25.3 63.7 29.0 64.1 35.2 68.2
PD 22.6 63.3 26.3 64.0 30.8 65.6
Relative
magnitude (N$kg
21
)
UW 7.62 61.28 6.77 61.57 5.92 61.31
STR 14.87 62.85 12.36 62.46 10.52 62.15
NI 15.19 62.32 13.20 62.25 11.41 62.11
PA-I 15.19 62.32 13.20 62.25 11.41 62.11
PA-II 9.17 60.83 9.14 60.97 8.48 60.97
PD 9.81 60.06 9.79 60.07 9.77 60.04
Relative
impulse (Ns$kg
21
)
UW 1.45 60.18 1.26 60.19 1.07 60.16
STR 1.41 60.17 1.22 60.18 1.05 60.15
NI 2.85 60.21 2.52 60.22 2.25 60.29
PA-I 3.00 60.21 2.68 60.22 2.44 60.28
PA-II 0.14 60.02 0.16 60.03 0.18 60.03
PD 0.12 60.02 0.15 60.03 0.17 60.03
Shape factor (%)
UW 54.8 64.1 56.3 66.0 52.2 64.1
STR 58.7 69.0 57.0 68.5 52.9 67.6
NI 81.0 68.1 83.1 68.8 83.5 68.5
PA-I 76.9 67.6 77.5 68.7 79.0 67.8
PA-II 58.3 62.0 58.9 62.2 61.0 63.0
PD 55.7 63.9 57.3 63.5 57.5 62.2
*HPG = high-performance group; MPG = middle-performance group; LPG = low-perfor-
mance group; UW = unweighted phase; STR = stretching phase; NI = net impulse phase;
PA-I = propulsion-acceleration I phase; PA-II = propulsion-acceleration II phase; PD = pro-
pulsion-deceleration phase.
Phase Characteristics of the CMJ Force-Time Curve
1158
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researchers (4–8). All-phase F-t curves were modified
to an equal number of samples by adjusting the time delta
between samples and resampling the signal. Once
complete, curves were normalized to time allowing for
point-by-point comparisons. After resampling, the
mean sampling frequency for the modified curves was
633 6125 Hz.
Statistical Analyses
Four 3-way mixed ANOVAs (3 groups by 2 sexes by 6
phases) were used to determine differences between levels of
the independent variables. Simple post hoc interaction tests
were performed when necessary with type I error controlled
using Scheffe
´’s adjusted Fvalue (36). In addition, Cohen’s
deffect size was used to provide a practical estimation of the
magnitude of any statistical differences observed during post
hoc comparisons. For the comparison of F-t curves, all
curves were aggregated by group and expressed as a single
curve. To determine differences between curves, 95% confi-
dence limits were plotted to form upper and lower control
limits. All statistical analyses were performed using SPSS 22
(IBM, Armonk, NY, USA). Statistical significance for all
analyses was set at p#0.05. Holm’s sequential rejective test
(14) was used to adjust the critical alpha from p#0.05 to
further control for type I error.
RESULTS
Force-Time Curve Phase Characteristics
The 3-way mixed ANOVAs identified statistically significant
phase main effects for all variables (duration: F(2.91, 244) =
1679,
h
2
= 0.914, p,0.001; relative magnitude: F(2.05, 244)
= 395,
h
2
= 0.573, p,0.001;
relative impulse: F(1.79, 244) =
7830,
h
2
= 0.949, p,0.001;
and shape factor: F(2.90, 244)
=340,
h
2
= 0.730, p,0.001).
The phase-by-performance
group interactions were statis-
tically significant for relative
magnitude (F(4.11, 172) =
15.5,
h
2
= 0.044, p,0.001),
relative impulse (F(3.33, 139)
= 43.3,
h
2
= 0.010, p,0.001),
and shape factor (F(5.81, 243)
= 3.60,
h
2
= 0.015, p= 0.002),
but not duration. Phase-by-sex
interactions were statistically
significant for both relative
magnitude (F(2.05, 172) =
12.3,
h
2
= 0.017, p,0.001)
and relative impulse (F(1.66,
139) = 55.2,
h
2
= 0.006, p,
0.001), but not for duration or
shape factor. The phase-by-
sex-by-performance group and
performance group-by-sex interaction effects were not sta-
tistically significant for any variable.
Post hoc simple phase-by-performance group compari-
sons were performed for all statistically significant interac-
tions. Table 3 displays the mean phase characteristic values
for each of the 3 jump performance groups. For relative
magnitude, statistically significant interactions (Scheffe
´’s
adjusted F$9.95) were observed between the HPG and
LPG when comparing the unweighted phase with the
stretching, net impulse, propulsion-acceleration I, and
propulsion-deceleration phases. Statistically significant inter-
actions were observed between the HPG and LPG and the
HPG and MPG when comparing the stretching phase with
the propulsion-acceleration II and propulsion-deceleration
phases; the net impulse phase with the propulsion-
acceleration II and propulsion-deceleration phases; and
when comparing the propulsion-acceleration I and
propulsion-acceleration II phases. These interactions indi-
cate that jumpers in the HPG and MPG exhibited greater
relative magnitudes in the stretching (HPG vs. LPG: d=
1.72; MPG vs. LPG: d= 0.38), net impulse (HPG vs.
LPG: d= 1.71; MPG vs. LPG: d= 0.46), and propulsion-
acceleration I (HPG vs. LPG: d= 1.71; MPG vs. LPG: d=
0.46) phases as compared to those in the LPG.
For relative impulse, statistically significant interactions
(Scheffe
´’s adjusted F$8.88) were observed between the
HPG and LPG when comparing the unweighted phase with
the stretching phase; the stretching phase with the net
impulse phase; the net impulse phase and the propulsion-
acceleration I phase; and when comparing the propulsion-
acceleration II and propulsion-deceleration phases.
Figure 2. Plot of post hoc interaction effect for shape factor between the stretching and propulsion-acceleration
II phases. HPG = high-performance group; LPG = low-performance group; MPG = middle-performance group.
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Statistically significant interactions were identified between
the MPG and LPG only when comparing the net impulse
and propulsion-acceleration I phases. Statistically significant
interactions were observed between all groups (HPG, MPG,
and LPG) when comparing the unweighted phase with the
propulsion-acceleration II and propulsion-deceleration
phases; the stretching phase with the propulsion-
acceleration II and propulsion-deceleration phases; the net
impulse phase with the propulsion-acceleration II and
propulsion-deceleration phases; the propulsion-acceleration
I phase with the propulsion-acceleration II and propulsion-
deceleration phases; and when comparing the propulsion-
acceleration II and propulsion-deceleration phases. The
direction of these interactions indicates that relative impulse
differed between all performance groups in the unweighted
(HPG vs. MPG: d= 0.99; HPG vs. LPG: d= 2.20; MPG vs.
LPG: d= 0.35), stretching (HPG vs. MPG: d= 1.08; HPG
vs. LPG: d= 2.22; MPG vs. LPG: d= 0.32), net impulse
(HPG vs. MPG: d= 1.56; HPG vs. LPG: d= 2.34; MPG vs.
LPG: d= 0.58), and propulsion-acceleration I (HPG vs.
MPG: d= 1.49; HPG vs. LPG: d= 2.26; MPG vs. LPG:
d= 0.52) phases, with the greatest values observed in the
higher performance groups.
For shape factor, post hoc comparisons revealed a statis-
tical (Scheffe
´’s adjusted F$13.07) disordinal interaction
pattern in the plotted means (Figure 2). Specifically, jump-
ers in the HPG decreased shape factor from the stretching
phase to the propulsion-acceleration II phase, whereas
those in the LPG exhibited the opposite. This pattern in-
dicates that jumpers in the HPG exhibited high stretching
phase shape factors relative their propulsion-acceleration II
shape factor, with the opposite being true for the LPG
(stretching phase—MPG vs. LPG: d= 0.70; propulsion-
acceleration II phase—MPG vs. LPG: d= 1.04). Because
of this interaction pattern, further examination was con-
ducted to investigate how a change in shape factor between
the 2 phases was related to JH. A ratio of stretching-to-
propulsion-acceleration II phase shape factor was calcu-
lated. A 1-way ANOVA found the ratios to be statistically
different between performance groups (F(2, 87) = 7.21,
h
2
=
0.142, p= 0.001). The mean ratio of stretching shape factor
to propulsion-acceleration II shape factor was 1.00 60.16
for the HPG, 0.97 60.15 for the MPG group, and 0.87 6
0.13 for the LPG. In addition, a statistically significant lin-
ear trend (p,0.001) was identified when comparing ratios
between groups, indicating that as stretching-to-
propulsion-acceleration II shape factor ratio increased, so
did JH in a linear fashion.
Table 4 displays mean phase characteristic values for
male and female jumpers. When examining statistically sig-
nificant interactions (Scheffe
´’s adjusted F$6.26) for rela-
tive magnitude, male jumpers exhibited greater magnitudes
in the stretching (d= 0.57), net impulse (d=0.77),and
propulsion-acceleration I (d= 0.77) phases as compared
to female jumpers, whereas relative magnitudes in the
unweighted, propulsion-acceleration II, and propulsion-
deceleration phases were similar between men and women.
For relative impulse, statistically significant interactions
(Scheffe
´’s adjusted F$6.50) revealed that males exhibited
greater relative impulse values in the net impulse (d= 1.35)
and propulsion-acceleration I (d= 1.42) phases as com-
pared to their female counterparts. In the unweighted,
stretching, propulsion-acceleration II, and propulsion-
deceleration phases, relative impulse was found to be sim-
ilar between sexes.
Averaged Phase Comparisons
Comparisons of the average phase curves found several areas
of nonoverlap between 95% confidence limits. In the
unweighted phase (Figure 3A), a greater negative amplitude
was observed in the HPG as compared to the LPG from
29.5% to 100% of the normalized phase, and the MPG was
TABLE 4. Force-time curve phase characteristics
for males and females (n= 90, mean 6SD).*
Phase Males Females
Duration (ms)
UW 365.1 653.2 341.5 654.0
STR 182.4 639.2 183.2 643.7
NI 234.8 635.2 244.8 642.9
PA-I 266.5 637.8 275.8 645.2
PA-II 28.6 65.8 31.1 67.9
PD 25.9 64.8 27.2 66.1
Relative
magnitude
(N$kg
21
)
UW 6.77 61.53 6.77 61.57
STR 13.43 63.24 11.74 62.63
NI 14.24 62.54 12.29 62.51
PA-I 14.24 62.54 12.29 62.51
PA-II 9.19 60.90 8.67 60.98
PD 9.80 60.05 9.78 60.06
Relative impulse
(Ns$kg
21
)
UW 1.29 60.23 1.23 60.23
STR 1.26 60.23 1.19 60.22
NI 2.73 60.27 2.35 60.30
PA-I 2.90 60.26 2.52 60.28
PA-II 0.15 60.03 0.16 60.04
PD 0.14 60.03 0.15 60.04
Shape factor (%)
UW 54.0 65.2 54.9 65.0
STR 54.2 68.7 58.1 68.2
NI 84.1 68.0 80.9 68.6
PA-I 78.7 68.4 76.9 67.6
PA-II 58.5 62.3 60.2 62.8
PD 56.5 64.0 57.2 62.6
*UW = unweighted phase; STR = stretching phase;
NI = net impulse phase; PA-I = propulsion-acceleration I
phase; PA-II = propulsion-acceleration II phase; PD =
propulsion-deceleration phase.
Phase Characteristics of the CMJ Force-Time Curve
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greater than the LPG from 18.1% to 31.0% and 74.5% to
100% of the phase. Confidence limits overlapped during
the entire phase between the HPG and MPG. In addition,
there were no areas of nonoverlap present when comparing
the unweighted phase of men and women (Figure 4A).
In the stretching phase (Figure 3B), the HPG was greater
than the MPG from 70.0% to 100.0% of the phase. The
MPG was greater than the LPG from 15.0% to 100%, and
the HPG was greater than the LPG throughout the entire
phase. Confidence limits overlapped throughout the entire
stretching phase when comparing men and women (Figure
4B). For the net impulse phase (Figure 3C), the HPG was
greater than the MPG from 0% to 16.0% of the phase. The
MPG was greater than the LPG from 0% to 10.5%, and the
Figure 3. Normalized resampled countermovement jump F-t curve phases by performance group. A) Unweighted phase, (B) stretching phase, (C) net impulse
phase, (D) propulsion-acceleration I phase, (E) propulsion-acceleration II phase, and (F) propulsion-deceleration phase. Shaded areas represent 95% upper and
lower confidence limits for mean curves. HPG = high-performance group; LPG = low-performance group; MPG = middle-performance group.
Figure 4. Normalized resampled countermovement jump F-t curve phases between male and female athletes. A) Unweighted phase, (B) stretching phase, (C)
net impulse phase, (D) propulsion-acceleration I phase, (E) propulsion-acceleration II phase, and (F) propulsion-deceleration phase. Shaded areas represent
95% upper and lower confidence limits for the mean curves.
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HPG was greater than the LPG throughout the entire net
impulse phase. In addition, when comparing men and
women, men were greater from 2.0% to 98.0% of the net
impulse phase (Figure 4C). Analysis of the propulsion-
acceleration II phase (Figure 3E) found the MPG to be
greater than the LPG from 0% to 47.0% of the phase, and
the HPG to be greater than the LPG from 0% to 11.7% of
the phase. Areas of nonoverlapping confidence limits were
not found between the HPG and the MPG or when com-
paring men and women (Figure 4E). Finally, areas of non-
overlapping were not observed for any comparison of the
propulsion-deceleration phase (Figures 3F and 4F).
DISCUSSION
The purpose of the study was to examine phase character-
istics of the CMJ F-t curve between athletes based on
jumping ability (JH). Considering this investigation
included both male and female athletes, a secondary
purpose of this study was to compare these phase
characteristics between sexes. The primary findings of the
study were (a) the performance groups differed for relative
phase magnitude in the stretching, net impulse, and
propulsion-acceleration I phase, and for relative phase
impulse in the unweighted, stretching, net impulse, and
propulsion-acceleration I phases, with highest jumpers
achieving the greatest values, (b) men and women differed
in relative phase magnitude and impulse with men exhibit-
ing greater magnitudes in the stretching, net impulse, and
propulsion-acceleration I phases and greater relative
impulse in the net impulse and propulsion-acceleration I
phases, (c) phase duration did not differ statistically
between performance groups or between men and women,
(d) for shape factor, performance groups only differed
when comparing the stretching and propulsion-
acceleration II phases, with the highest jumpers producing
greater shape factors in the stretching phase.
Before interpreting the results of this study, 2 limita-
tions must be addressed. First, because of the sampling
procedures and the formation of performance groups,
a lack of homogeneity with regard to sport representation
was created within the groups. Previous research has
noted the existence of sport-specific F-t signatures in the
CMJs (20). Therefore, differences observed between
groups may potentially be attributed to sport-specific
jumping strategies. However, the influence of jump strat-
egies is not entirely understood. Therefore, it is unclear
how this factor may have influenced the results of this
study. A second limitation of this study results from the
fact that this analysis was delimited to F-t data only, and
derivatives (displacement, velocity, and acceleration) were
not considered. The inclusion of displacement data in
particular may have contributed to an enhanced under-
standing of the differences observed in this study.
The finding that better jumpers were associated with
greater phase impulse and magnitude was somewhat
expected. Previous research has identified relative impulse
as a determining factor in vertical JH (18,24). In addition,
maximizing the size of positive impulse (Figure 1: points B–
E) has been theorized to result in enhanced JH (1). These
results indicate that better jumpers display greater relative
magnitudes throughout the positive impulse of the F-t curve,
and greater relative impulse throughout the unweighted,
stretching, net impulse, and propulsion-acceleration I phases.
These differences can be observed when viewing the average
curves displayed in Figure 3. Clear differences between
curves can also be observed for the remaining phases con-
tained within positive impulse; particularly the latter portion
of the stretching phase and early net impulse phase (Figures
3B, C). In addition to a greater magnitude, better jumpers
also maintained greater relative force throughout the net
impulse/propulsion-acceleration I phase, consequently pro-
ducing a greater impulse overall. Moreover, it was during
these phases that the greatest separation was exhibited
between the HPG and LPG curves (Figures 3C, D). Average
curves for both the propulsion-acceleration II and
propulsion-deceleration phases were similar for all compar-
isons, suggesting that the characteristics of these phases have
little influence on JH.
As illustrated by the average curve comparison, jumpers
capable of producing greater relative magnitudes late in the
stretching phase initiate the concentric/propulsive phase
with greater forces and maintain these forces throughout the
propulsive phase contributing to a greater JH. This obser-
vation is in agreement with previous research regarding the
proposed contribution of the eccentric phase to jump
performance (2,3). In addition, the stretching phase is spec-
ulated to reflect the jumper’s ability to transition to concen-
tric action as well as the stretch experienced by the
musculotendinous unit after the countermovement (17).
Therefore, the characteristics of this phase may provide
information regarding stretch-shortening cycle function
and eccentric force production capacity. A pronounced mag-
nitude (peak) during this phase has been previously noted in
proficient jumpers (criterion: JH) (25). In addition, this fea-
ture of the F-t curve has been found to appear after power-
focused training (5). Thus, these characteristics may be an
indicator of impulsive ability or “explosiveness” (39) and
potentially useful in performance monitoring. However,
future research is warranted to elucidate the exact mecha-
nisms influencing characteristic of the stretching phase as
well as its role in jump performance.
Interestingly, this study found that CMJ phase duration
did not differ between performance groups or between men
and women. These results are in agreement with the
findings of Laffaye, Wagner, and Tombleson (20) who re-
ported that time-based CMJ variables alone were weak pre-
dictors of JH. In addition, previous reports have noted
similar jump durations between jumpers of different abilities
(5) and neuromuscular training backgrounds (38). Individual
phase durations were also markedly similar between men
Phase Characteristics of the CMJ Force-Time Curve
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and women, with the greatest mean difference (224 ms)
found in the unweighted phase (men: 365 653 ms vs.
women: 341 654 ms). These similarities in duration are
in agreement with previous studies, indicating that the tem-
poral structure of the CMJ F-t curve is comparable between
men and women (20). The similarities in the F-t curve phase
temporal structure suggest that phase duration plays
a minor role in performance and other factors hold greater
influence over JH.
Sex differences were found for both relative phase
magnitude and relative phase impulse. Specifically, men
produced greater relative magnitudes during the stretching,
net impulse, and propulsion-acceleration I phases and
greater relative impulse in the net impulse and propulsion-
acceleration I phases. In other words, the primary difference
between men and women was related to the rate and
magnitude of relative force production during phases
encompassing peak eccentric and concentric force produc-
tion. This result is illustrated by the difference in averaged
curves when comparing men and women (Figures 4B–D).
Between men and women, the average curves for the
unweighted and propulsion-acceleration II and propulsion-
deceleration phases were relatively similar. However, in the
stretching phase, as well as in the net impulse/propulsion-
acceleration I phases, a shift in the shape of the curve can be
seen resulting in areas of nonoverlap from 2.0% to 87.5% of
the normalized propulsion-acceleration I phase. A similar
pattern in the stretching and net impulse/propulsion-
acceleration I phases was exhibited by the HPG (Figures
3B–D). This observation suggests that there may be some
characteristic shared between males and jumpers exhibiting
the greatest JHs influencing the shape of the F-t curve. This
characteristic is presently unknown. However, research has
demonstrated that, in general, males possess greater relative
muscular strength as compared to their female counterparts
(26,33). The greater relative phase magnitudes and impulse
observed in male athletes may be reflective of greater force
production capacity likely influenced by characteristics of
the neuromuscular system such as increased neural drive
or percentage of type II muscle fibers. Thus, the sex differ-
ences found in CMJ F-t curve phase characteristics may in
fact reflect differences in strength.
The relative shape of the impulse produced during
a phase was found to provide little information about JH.
However, an unexpected finding of the study was the
disordinal interaction pattern (Figure 2) produced when
comparing shape factors between the stretching and
propulsion-acceleration II phases. This pattern suggested
that higher jumpers exhibit a greater congruency in the
relative shape of the impulse between the stretching and
propulsion-acceleration II phases. Calculation of the shape
factor ratio suggested that these jumpers (HPG) possess
a stretching-to-propulsion-acceleration II shape factor ratio
of close to 1.0, whereas lower jumpers (LPG) produce
ratios of ,1.0. A comparison of the mean values indicates
that the primary factor influencing this ratio shift was the
stretching shape factor, as the propulsion-acceleration II
shape factor was relatively similar between groups. This
increased shape factor exhibited by the HPG could be
related to the greater rise in force (i.e., eccentric rate of
force development) visible when comparing the average
curves of the stretching phase (Figure 3B). This finding
suggests that the athletes exhibiting the greatest JHs not
only produce a stretching phase with a greater magnitude
and area as discussed above; in addition, these jumpers
produce an impulse that is more rectangular in shape (i.e.,
occupies a greater portion of the rectangle drawn around
the phase). This finding supports the theory outlined by
Adamson and Whitney (1) detailing how impulse may be
optimized to improve jump performance. Based on this
result, increased JH may be achieved by identifying and
implementing training methods aimed at increasing
stretching phase shape factor.
In conclusion, this study was successful in identifying
several CMJ F-t phase characteristics that differ between
jumpers based on jumping ability (JH). Relative magnitude
of the stretching, net impulse, and propulsion-acceleration I
phases as well as the relative impulse of the unweighted,
stretching, net impulse, and propulsion-acceleration I phases
are primary characteristics influencing JH. Differences were
exhibited between men and women and are perhaps the
result of differences in relative strength and force production
capacity. Interestingly, phase duration was similar between
groups as well as between men and women, suggesting that
this characteristic is of little importance to JH. Finally,
a potentially meaningful relationship was found when
comparing the shape factors of the stretching and
propulsion-acceleration II phases with respect to JH. It
should be noted that this study was the first of its kind by
attempting a phase-by-phase analysis of F-t characteristics.
Consequently, additional research is warranted to support
these findings and further elucidate mechanisms underpin-
ning characteristics of the CMJ F-t curve phases. Future
research may consider investigating the influence of muscu-
lar strength or perhaps fatigue on characteristics of these F-t
curve phases.
PRACTICAL APPLICATIONS
Force platform analysis of CMJs has become increasingly
popular for the purpose of athlete performance monitoring.
Despite this popularity, questions still exist as to the most
appropriate variables and analyses practitioners should use
when characterizing CMJ performance. From a practical
standpoint, the results of this investigation may provide
practitioners with the following information related to the
diagnostic value of qualitative CMJ F-t curve analysis.
Greater relative magnitude (height) and impulse (area)
throughout the positive portions of the F-t curve were found
to be the primary characteristics differentiating performance
groups. Consequently, selecting training methods aimed at
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increasing the height and area of positive impulse may be
most effective if increased JH is your target training
adaptation. Moreover, if these characteristics are observed
in response to training, they likely indicate positive adapta-
tion. The size and shape of the initial rise in force after the
unweighted phase (the stretching phase), both in isolation
and in relation to other phases, was found to relate to JH.
Consequently, this portion of the CMJ F-t curve may prove
useful in monitoring an athlete’s impulsive (“explosive”)
state. Furthermore, considering this portion of the curve
represents the transition from eccentric to concentric muscle
action (i.e., the stretch-shortening cycle), the characteristics
of this phase may yield diagnostic information related to
stretch-shortening cycle performance state (fatigue or adap-
tation). Finally, phase duration and the temporal structure of
the F-t curve was not found to statistically differ based on
jumping ability, suggesting that phase timing provides little
diagnostic insight regarding jump performance.
ACKNOWLEDGMENTS
The authors thank all the athletes who participated in this
study. The results of this study do not constitute endorse-
ment of the product by the authors or the National Strength
and Conditioning Association. There are no conflicts of
interest. There are no professional relationships with com-
panies or manufacturers who will benefit from the results of
this study for each author.
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