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“Load, Force and Power-Velocity Relationships in the Prone Pull-Up Exercise” by Muñoz-López M et al.

International Journal of Sports Physiology and Performance

© 2017 Human Kinetics, Inc.

Note. This article will be published in a forthcoming issue of the

International Journal of Sports Physiology and Performance. The

article appears here in its accepted, peer-reviewed form, as it was

provided by the submitting author. It has not been copyedited,

proofread, or formatted by the publisher.

Section: Original Investigation

Article Title: Load, Force and Power-Velocity Relationships in the Prone Pull-Up Exercise

Authors: Mario Muñoz-López1, David Marchante1, Miguel A. Cano-Ruiz1, José López

Chicharro2 and Carlos Balsalobre-Fernández3

Affiliations: 1Powerexplosive Center, Madrid, Spain. 2Complutense University of Madrid,

Madrid, Spain. 3Department of Sport Sciences, European University of Madrid, Spain.

Journal: International Journal of Sports Physiology and Performance

Acceptance Date: February 9, 2017

©2017 Human Kinetics, Inc.

DOI: https://doi.org/10.1123/ijspp.2016-0657

“Load, Force and Power-Velocity Relationships in the Prone Pull-Up Exercise” by Muñoz-López M et al.

International Journal of Sports Physiology and Performance

© 2017 Human Kinetics, Inc.

LOAD, FORCE AND POWER-VELOCITY RELATIONSHIPS IN THE PRONE PULL-

UP EXERCISE

Mario Muñoz-López1, David Marchante1, Miguel A. Cano-Ruiz1, José López Chicharro2 &

Carlos Balsalobre-Fernández3

1Powerexplosive Center, Madrid, Spain

2Complutense University of Madrid, Madrid, Spain

3Department of Sport Sciences, European University of Madrid, Spain

Running head: LOAD-VELOCITY PROFILE IN THE PULL-UP EXERCISE

Submission type: Original investigation

Abstract word count: 249

Text-only word count: 3291

Number of figures: 4

Number of tables: 1

Corresponding author

Carlos Balsalobre-Fernández

Department of Sport Sciences, European University of Madrid, Spain

Address: C/ Tajo, Villaviciosa de Odón 28670, Madrid, Spain

Telephone: +34 606798498

E-mail: carlos.balsalobre@icloud.com

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“Load, Force and Power-Velocity Relationships in the Prone Pull-Up Exercise” by Muñoz-López M et al.

International Journal of Sports Physiology and Performance

© 2017 Human Kinetics, Inc.

ABSTRACT

Purpose: To analyze the load, force and power-velocity relationships, as well as to determine

the load that optimizes power output on the pull-up exercise. Methods: Eighty-two resistance

trained males (Age = 26.8 5.0 yrs.; Pull-up 1RM – normalized per kg of body mass– = 1.5

0.34) performed two repetitions with 4 incremental loads (ranging 70-100%1-RM) in the pull-

up exercise while mean propulsive velocity (MPV), force (MPF) and power (MPP) were

measured using a linear transducer. Relationships between variables were studied using first

and second order least-squares regression, and subjects were divided into three groups

depending on their 1-RM for comparison purposes. Results: Almost perfect individual load-

velocity (R2 = 0.975 0.02), force-velocity (R2 = 0.954 0.04) and power-velocity (R2 = 0.966

0.04) relationships, which allowed to determine the velocity at each %1-RM as well as the

maximal theoretical force (F0), velocity (V0) and power (Pmax) for each subject were

observed. Statistically significant differences between groups were observed for F0 (p<0.01)

but not for MPV at each %1-RM, V0 or Pmax (p>0.05). Also, high correlations between F0

and 1-RM (r = 0.811) and V0 and Pmax (r = 0.865) were observed. Finally, we observed that

the load that maximized MPP was 71.0 6.6 %1-RM. Conclusions: The very high load-

velocity, force-velocity and power-velocity relationships allows to estimate 1-RM by

measuring movement velocity, as well as to determine maximal force, velocity and power

capabilities. This information could be of great interest for strength and conditioning coaches

who wish to monitor pull-up performance.

KEYWORDS: resistance training; monitoring; biomechanics; physical performance

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“Load, Force and Power-Velocity Relationships in the Prone Pull-Up Exercise” by Muñoz-López M et al.

International Journal of Sports Physiology and Performance

© 2017 Human Kinetics, Inc.

INTRODUCTION

Resistance training has been previously reported to improve health, fitness and

performance 1–3. In order to optimize the response to resistance training, monitoring training

load has been suggested as a key factor; specifically, training intensity is generally

acknowledged as the most important variable to produce the desired neuromuscular adaptations

4,5. In this sense, strength and conditioning coaches often faces an issue when designing

resistance training programs, that’s it, how to objectively quantify and prescribe intensity in

resistance exercises. The most common method to quantify intensity is the measurement of the

1-Repetition maximum (1-RM, i.e., the load that can be lifted just once) 6,7; however, in the

recent years less demanding methodologies have emerged as an alternative to the 1-RM

paradigm 8–10. Among them, movement velocity was shown to be an accurate, effective and

non-fatiguing method to quantify relative intensity in resistance exercises 8,11,12. This method

is based on the load-velocity relationship observed in different resistance exercises, by which

the load (in terms of %1-RM) is highly related to the velocity at which that load is lifted 11,12.

Thus, the measurement of movement velocity has successfully been probed to estimate the 1-

RM and each of its percentages on different resistance exercises such as bench-press 11, bench-

pull 13, squat or leg press 12.

In addition to the measurement of the load-velocity relationship, several studies have

analyzed the well-known force and power-velocity relationships in order to understand the

maximal force, velocity and power capabilities of the athletes 14–16. Thus, the analysis of the

maximal theoretical force (F0), velocity (V0) and power (Pmax), and the slope of the force-

velocity profile has been shown to be of great interest to study the maximal neuromuscular

capabilities in different exercises 15,17. For example, Pmax and the slope of the force-velocity

profile have been probed to significantly influence the ballistic performance in vertical jumping

18. Also, a very high relationship between F0 and 1-RM has been recently observed in the

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“Load, Force and Power-Velocity Relationships in the Prone Pull-Up Exercise” by Muñoz-López M et al.

International Journal of Sports Physiology and Performance

© 2017 Human Kinetics, Inc.

bench-press exercise 19. Finally, the load that maximizes power output has been extensively

studied in different exercises, since that load has been commonly used to improve ballistic

performance 7,20,21. Thus, the analysis of individual force-power-velocity characteristics could

be of great interest for coaches and sport practitioners.

However, research has shown that load-velocity, force-velocity and power-velocity

relationships are specific of each exercise 12,15,21, meaning that the velocity associated at each

%1-RM, as well as the load that maximizes power output or the maximal expressions of F0

and V0 depend on the movement pattern and muscle groups used 12,21. Therefore, more research

is needed in order to analyze the load, force and power-velocity relationships in other common

resistance exercises. Specifically, one of the most used multi-joint, closed-chain, upper-body

resistance exercises, the prone pull-up, has not been analyzed yet in this sense. The prone pull-

up has been used to assess the strength of the upper limbs in different populations such as

fitness practitioners 22, firefighters 23, swimmers 24 or climbers 25. However, to our knowledge,

there are no studies in the literature that analyze the specific relationships between load, force,

power and velocity on the prone pull-up exercise. Consequently, the aim of the present study

is to analyze the load, force, power-velocity relationships in this exercise.

METHODS

Subjects

Eighty-two resistance-trained males, with more than 4 years of experience in the prone

pull-up exercise, participated in this study (N = 82 men; Age = 26.8 5.0 yrs., Height = 1.80

0.1m; Body mass = 81.6 9.3 kg; Pull-up 1RM – normalized per kg of body mass– = 1.47

0.19). Participants were divided into three groups according to their normalized weighted pull-

up 1-RM (1-RM/kg): group 1 (G1: N = 27; 1-RM/kg < 1.4), group 2 (G2: N=27; 1-RM/kg <

1.52) and group 3 (G3: N = 28; 1-RM/kg > 1.52).

Downloaded by UPV Biblioteca Central on 03/03/17, Volume 0, Article Number 0

“Load, Force and Power-Velocity Relationships in the Prone Pull-Up Exercise” by Muñoz-López M et al.

International Journal of Sports Physiology and Performance

© 2017 Human Kinetics, Inc.

No physical limitations or musculoskeletal injuries that could affect testing were

reported. To join the study, each participant needed to perform a minimum of 15 repetitions to

failure in the un-weighted prone pull-up exercise and train the weighted prone pull-up exercise

at least once per week for the last 6 months. The study complained with the Declaration of

Helsinki and all participants signed informed-consent forms before participation. The study

was approved by the institutional review board.

Design

Least-squares regression analysis aiming to identify the load, force and power-velocity

relationships was conducted. All participants performed a 4-loads incremental test in the prone

pull-up exercise with loads ranging 70-100% of their 1RM (considered as body mass plus

external load) while mean propulsive velocity (MPV), force (MPF) and power (MPP) were

being registered at a sampling frequency of 1000Hz using the Smartcoach Power Encoder

linear position transducer (LPT) (Smartcoach Europe, Stockholm, Sweden). The software of

the LPT determined the propulsive phase of each repetition as the part of the concentric phase

in which measured acceleration was higher than g (i.e. a > 9.81 m/s2) as described elsewhere

11. MPF was indirectly calculated from propulsive velocity using the well-known impulse-

momentum theorem as follows:

F = m * (vf –v0) / t

where F is MPF (in N), m the system mass (i.e. body mass plus external load, in kg), vf is the

final velocity of the propulsive phase (in m/s), v0 is the initial propulsive velocity of the

concentric phase (in m/s) and t is the duration of the propulsive phase (in s). Finally, MPP was

computed as the product of MPF and MPV: MPP = MPF * MPV. The load that maximized

MPP was also registered accordingly. Each participant performed 2 repetitions with each load,

and the one with higher MPV was registered.

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“Load, Force and Power-Velocity Relationships in the Prone Pull-Up Exercise” by Muñoz-López M et al.

International Journal of Sports Physiology and Performance

© 2017 Human Kinetics, Inc.

Furthermore, individual force-velocity and power-velocity relationships were used in

order to determine theoretical maximal force (F0), velocity (F0) and power (Pmax) production,

which represent the maximal neuromuscular capabilities of the participants 14. The values of

F0 and V0 were calculated as the y-intercept and x-intercept of the force-velocity linear

regression, and Pmax was computed as Pmax = F0*V0/4 as described elsewhere 14. It should

be noted that Pmax is a theoretical expression of the maximal power capabilities of the subject,

while maximal MPP is the actual maximal power attained within the incremental test.

Methodology

Body measures

At the beginning of the testing session, height was measured to the nearest 0.5 cm

during a maximum inhalation using a wall-mounted stadiometer (Seca 202, Seca Ltd,

Hamburg, Germany). Then, body mass was measured using the Jata 531 scale (Jata S.A.,

Bizcaia, Spain).

Pull-up incremental test

One week prior to the testing session, a familiarization session was conducted so that

participants could get used to isoinertial testing. After conducting a proper 15-minutes warm-

up consisting on dynamic stretching and preparatory exercises (i.e., glenohumeral joint external

rotations, scapular retractions and 1 set of 5 un-weighted prone pull-ups), athletes performed 4

different sets on the prone pull-up exercise. Initial external load was set at 0kg (i.e., un-

weighted prone pull-up), and it was incremented until the 1-RM (i.e., weighted prone pull-up)

was reached. The magnitude of the increment in the external load was based in the drop of

velocity from the previous set, so that each set could be performed at least 0.1m/s slower than

the previous set. If the 1-RM was not reached in the 4th set, an additional set with 5-10% more

kg was performed. Consequently, the loads used ranged 70-100% 1RM approximately. Two

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“Load, Force and Power-Velocity Relationships in the Prone Pull-Up Exercise” by Muñoz-López M et al.

International Journal of Sports Physiology and Performance

© 2017 Human Kinetics, Inc.

repetitions were performed with each load and the one with higher MPV was recorded. Sets

where separated by 3 minutes of passive rest.

The pull-up was performed with a prone grip and hands were separated by a distance

equivalent to participant’s acromion-to-acromion length. In order to consider a repetition valid,

the participant needed to start the movement hanging in the bar with the elbows fully extended

and the feet in the air with the knees flexed and the hip in neutral position. After holding that

position for 2 seconds, participants were encouraged to perform the pull-up as fast as possible

until their chins were above the bar.

Weight plates were located in the ventral section of the coronal plane using a specific

belt (Maniak Fitness, Málaga, Spain). The cable of the LPT was fixed to the rear label of

participants’ shorts at the sacral vertebrae height because of its proximity to the Center of Mass

and to avoid any contact with the weight plates.

Instrumental

The Smartcoach Power Encoder (Smartcoach Europe, Stockholm, Sweden) LPT was

used to register MPV (in m/s), MPF (in N) and MPP (in W) at a sampling frequency of 1kHz.

Butterworth filtering was used by this instrument to smooth the data. The LPT was placed in

the floor below participants’ Center of Mass so its cable could be aligned with the Z-axis (i.e.,

vertical position) following the criteria described by the manufacturer. Then, the LPT was

connected to the Smartcoach 5.0.0 software which was installed on a personal computer

running the Windows 10 operating system and all the data were exported to a spreadsheet for

further analyses.

Statistical analysis

Standard statistical methods were used for calculation of means and SDs. The normality

of the data was analyzed using the Kolmogorov-Smirnov test. To analyze the load-velocity (i.e.

%1-RM-MPV) and force-velocity relationship (i.e. MPF-MPV), first order least-squares

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“Load, Force and Power-Velocity Relationships in the Prone Pull-Up Exercise” by Muñoz-López M et al.

International Journal of Sports Physiology and Performance

© 2017 Human Kinetics, Inc.

regression was used, and to analyze the power-velocity relationship (i.e. MPP-MPV), second

order least-squares regression was used.

One-way ANOVA with Bonferroni post hoc comparisons was used to detect potential

differences between groups in the studied variables, as well as to analyze differences between

power output with different loads. Finally, the relationships between variables were calculated

using Pearson’s product–moment correlation coefficient and bootstrapping (N= 1000)

determined the 95% Confidence Interval (CI). The level of significance was set at .05, and the

IBM® SPSS® V.23 software (IBM Co., USA) was used for the analyses.

RESULTS

Load-velocity relationship

When analyzing individual load-velocity profiles for each participant, an almost perfect

relationship between %1-RM and MPV was observed in all cases (Mean (SD) from individual

values: R2 = 0.975 0.02, SEE = 0.035 0.02 m/s). Moreover, the slope (s = -0.017 0.004)

and intercept (i = 1.933 0.44 m/s) of the load-velocity relationship were similar for all

participants. See Figure 1 for more details.

When using each participant’s regression equation to estimate MPV for a certain %1-

RM, an almost perfect correlation, with no significant differences was observed between the

estimated and actual MPV for each %1-RM used in the incremental tests (r = 0.987 0.01,

Mean difference = 0.033 0.07 m/s, p = 1.00).

Force-power-velocity relationships

Almost perfect relationships between mean propulsive force (MPF) and MPV (R2 =

0.954 0.04), and mean propulsive power (MPP) and MPV (R2 = 0.966 0.04) were observed

for each participant. Using the force-velocity and power-velocity relationships, descriptive data

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“Load, Force and Power-Velocity Relationships in the Prone Pull-Up Exercise” by Muñoz-López M et al.

International Journal of Sports Physiology and Performance

© 2017 Human Kinetics, Inc.

for F0, V0, Pmax and the slope of the force-velocity profile were calculated for each

participant. See Figure 2.

There were no statistically significant differences between groups of strength for V0 or

Pmax as revealed by the one-way ANOVA (p> 0.05). However, significant differences were

observed for F0 (p< 0.001) and the slope of the force-velocity profile (p< 0.05). See Table 1

for more details. Finally, it was observed that the load that maximized MPP was 71.0 6.6

%1-RM i.e., the first load of the incremental test in most cases. The absolute value of maximal

mean power output was 645.4 171.4 W. See Figure 2 for more details.

Correlations between variables

Finally, high, significant correlations were observed between 1-RM and F0 (r = 0.811,

CI: 0.623-0.930, p< 0.001) and V0 and Pmax (r = 0.865, CI: 0.801-0.917, p< 0.001). See Figure

3.

DISCUSSION

The results of our study showed a very close individual load-velocity (R2 = 0.975

0.02) relationship. Given the very high correlation between MPV and the load at which that

velocity was produced, individual regression equations allowed to estimate the velocity at

which each percentage of the 1-RM was performed. Moreover, no significant differences

(0.046 0.27 m/s, p = 1.00) were observed between the estimated and actual velocity

performed with the loads used in the incremental test. Therefore, results in our study showed

that the load used in the prone pull-up exercise can be accurately determined by measuring the

velocity at which that load is moved. This is in line with previous research that found similar,

very high correlations between load (in terms of %1-RM) and movement velocity in different

exercises such as bench press 11, bench-pull 13 or squat 12. However, unlike previous research

that showed an almost perfect fit (R2 > 0.98) when velocities at each %1-RM from each

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“Load, Force and Power-Velocity Relationships in the Prone Pull-Up Exercise” by Muñoz-López M et al.

International Journal of Sports Physiology and Performance

© 2017 Human Kinetics, Inc.

participant were computed in the same regression equation 11, we observed a much lower value

(R2 = 0.780), meaning that an individual regression equations, and not a global one, should be

used to estimate the %1-RM of each participant. This could be due to a particularity of the

prone pull-up exercise: unlike other exercises where the athlete mainly faces the load that

represents the barbell and plates, the prone pull-up exercise is demanding with a load as low as

0kg of external load (i.e., the un-weighted pull-up) due to subject’s own body mass. Thus,

subjects with higher 1-RM find easier to perform the exercise without any load and,

consequently, can produce higher velocities. In fact, the one-way ANOVA showed significant

differences in the MPV of the unweighted pull-up as detailed in Table 1 (p<0.001). However,

when a maximal lift is performed (i.e., 100%1-RM) all participants produced the same velocity

(in our study the velocity at 1-RM = 0.26 0.05), which confirms previous research that

showed that velocity at 1-RM is very stable and doesn’t depend on athletes’ fitness 8,11,12. For

this, to accurately determine the percentage of 1-RM from movement velocity, individual

analysis to determine the athlete’s own load-velocity profile is highly recommended.

Also, very high force-velocity (R2 = 0.954 0.04), and power-velocity (R2 = 0.966

0.04) relationships, which allowed the calculations of F0, V0 and Pmax were observed. Thus,

our study confirmed that the very high, linear force-velocity relationship and the very high

quadratic power-velocity relationship observed in different activities 15 are also present in the

prone pull-up exercise. There is an increasing interest in the analysis of the force-power-

velocity relationships since F0, V0 and Pmax have been proposed to represent the maximal

theoretical neuromuscular capabilities of the athletes 14,15. For example, vertical jump

performance was shown to be significantly influenced by participants’ Pmax 18, while bench

press 1-RM has shown to be very highly correlated with F0 19. Therefore, the analysis of the

force-power-velocity relationships has been proposed to provide interesting additional

information on the athletes’ neuromuscular performance for different activities such as jumping

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“Load, Force and Power-Velocity Relationships in the Prone Pull-Up Exercise” by Muñoz-López M et al.

International Journal of Sports Physiology and Performance

© 2017 Human Kinetics, Inc.

26, sprinting 17, or bench-pressing 19. This is the first study that analyzed the force-power-

velocity relationships in the prone pull-up exercise. Also, to the best of our knowledge, this

study shows for the first time normative values of F0, V0 and Pmax for resistance-trained males

in this exercise. However, one important limitation should be noted when analyzing the force-

power-velocity characteristics in the pull-up exercise, that’s it, the instrumental used to

measure force. The gold standard for the measurement of force are force platforms since they

register the reaction forces applied to the ground directly 27. Meanwhile, linear transducers

estimate force using the impulse-momentum theorem, providing an indirect measurement of

force in the basis of system mass and changes in velocity 27. Thus, to obtain a direct

measurement of force in this exercise, a special device that would register “bar reaction forces”

should be used; however, to the best of our knowledge, such device doesn’t exist yet. Therefore,

until technology provides a direct measurement of force in the pull-up exercise, the force (and

consequently, power) measures obtained with a linear transducer should be interpreted with

caution.

Interestingly, none of the variables analyzed in the force-power-velocity relationships

differed among groups of strength with the exception of F0 (p<0.001) and the slope of the

force-velocity profile (p<0.05) which were higher and lower, respectively, in G3 with respect

to the other two groups. Therefore, it seems that while strongest athletes had significantly

higher values of F0, none Pmax nor V0 were different from less strong subjects. In this sense,

it was observed that F0 and 1-RM were significantly correlated (r = 0.811), as well as Pmax

and V0 (r = 0.865), but no other pair of variables. Thus, it seems that high values of 1-RM are

related with high values of F0, but not with high V0 or Pmax. Therefore, considering our

results, athletes who wish to develop their 1-RM in the prone pull-up exercise might benefit

from increasing their maximal force capabilities, while those who want to increase their

maximal power might need to focus on developing maximal velocity.

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“Load, Force and Power-Velocity Relationships in the Prone Pull-Up Exercise” by Muñoz-López M et al.

International Journal of Sports Physiology and Performance

© 2017 Human Kinetics, Inc.

Developing maximal power output is, in fact, one of the most common goals in strength

and conditioning since ballistic performance has shown to be influenced by muscular power in

several activities such as sprinting, jumping, lifting or tackling, among others 28,29. Thus, there

is a large body of research investigating which range of loads produce the higher maximal

power output, since it was proposed that training with the maximal power load could have

superior benefits to increase power production 20,30,31. For example, a recent meta-analysis on

the maximal power load on upper-body exercises has shown that power output on the bench

press exercise is maximized with loads ranging 30-70%1-RM 21. However, to date, no research

has described the range of loads that maximize the power output in the prone pull-up exercise.

In this sense, our study shows that, in most cases, the load that produced the greatest power

output was the first load on the incremental test which corresponded to 71.0 6.6 %1-RM. It

should be noted that this value corresponds to the maximal MPP production within the

incremental test, while Pmax (which is calculated from F0 and V0 as described in the methods

section) is a theoretical expression of the maximal power production capabilities of the subject.

In this sense, it was observed that the value of Pmax, derived from the force-power-velocity

relationships was higher than the actual maximal MPP produced in the incremental test (747.4

232.9 vs. 645.4 171.4 W). Thus, we can conclude that the lightest load on the incremental

test (i.e. the unweighted pull-up) is not enough to express the absolute maximal power

capabilities of the subjects and, consequently, Pmax would only be reached with an assistance

that would reduce the body weight of the athlete and, therefore, could allow a highest

movement velocity.

To the best of our knowledge, this is the first study which analyzes the load-force-

power-velocity relationships in the prone pull-up exercise.

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“Load, Force and Power-Velocity Relationships in the Prone Pull-Up Exercise” by Muñoz-López M et al.

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© 2017 Human Kinetics, Inc.

PRACTICAL APPLICATIONS

First, results in our study showed that there is an almost perfect relationship between

the load (in terms of %1-RM) and mean propulsive velocity in the prone pull-up exercise. Thus,

strength and conditioning coaches who wish to monitor training intensity when prescribing the

prone pull-up exercise might benefit from measuring movement velocity, because it would

allow to know athlete’s 1-RM without conducting an actual 1-RM test; however, individual

load-velocity profiles should be used for accurate estimations. Second, it was observed that the

load that produced higher power outputs was about 71.0 %1-RM in most cases (i.e., un-

weighted pull-up), although this value was lower than the maximal theoretical power (Pmax)

derived from the force-power-velocity relationships. Therefore, if absolute maximal power

capabilities are to be developed, subjects should use an assistance that would reduce body

weight and, therefore, could produce higher movement velocities. Also, Pmax was shown to

be highly correlated with maximal velocity (V0) but not to maximal force (F0). Therefore,

athletes who wish to focus on power development might benefit from training with no load, or

very light loads moved at high speeds to produce high power outputs. Finally, it was observed

that 1-RM was highly related with F0, meaning that if maximal force capability is to be

developed, athletes should probably focus on increasing their maximal load in the prone pull-

up exercise.

CONCLUSIONS

Very high load-velocity, force-velocity and power-velocity relationships which allows

to estimate training intensity (in terms of %1-RM) by measuring movement velocity, and to

estimate the maximal force (F0), velocity (V0) and power (Pmax) capabilities were observed

in the prone pull-up exercise. Our results could have potential practical applications for strength

and conditioning coaches who wish to use the prone pull-up exercise in their training programs.

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© 2017 Human Kinetics, Inc.

ACKNOWLEDGEMENTS

The authors want to thank the participants, fitness centers and SéMovimiento team for their

involvement in this study.

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“Load, Force and Power-Velocity Relationships in the Prone Pull-Up Exercise” by Muñoz-López M et al.

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© 2017 Human Kinetics, Inc.

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Figure 1. Load-velocity linear regression from a typical participant.

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“Load, Force and Power-Velocity Relationships in the Prone Pull-Up Exercise” by Muñoz-López M et al.

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Figure 2. Force-velocity linear regression and power-velocity quadratic regression. Data

represents average values from the whole group.

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“Load, Force and Power-Velocity Relationships in the Prone Pull-Up Exercise” by Muñoz-López M et al.

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Figure 3. Correlation between A) F0 and 1-RM/kg and B) Pmax and V0.

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© 2017 Human Kinetics, Inc.

Table 1: Mean and standard deviations values for F0, V0, Pmax, slope of the force-velocity relationship, mean propulsive velocity without an

external load and mean propulsive velocity at typical percentage of the 1-RM (calculated from individual regression equations)

Measure

G1

G2

G3

Total

F0(N/kg) *

14.8 2.1

16.3 1.1

19.0 2.6

16.7 2.6

V0 (m/s)

2.4 0.9

2.2 0.4

2.0 0.8

2.2 0.7

Pmax (W/kg)

8.6 2.8

9.1 1.9

9.6 3.1

9.1 2.7

F-V Slope *

-7.4 4.1

-7.5 1.8

-10.4 3.4

-8.5 3.5

MPV UP (m/s)*

0.61 0.12

0.80 0.1

0.81 0.15

0.73 0.16

MPV @80%1-RM (m/s)

0.61 0.09

0.61 0.09

0.56 0.12

0.59 0.1

MPV @85%1-RM (m/s)

0.52 0.07

0.52 0.08

0.49 0.1

0.51 0.09

MPV @90%1-RM (m/s)

0.43 0.06

0.44 0.07

0.41 0.09

0.43 0.07

MPV @95%1-RM (m/s)

0.34 0.04

0.35 0.06

0.33 .07

0.34 0.06

MPV @100%1-RM (m/s)

0.25 0.03

0.26 0.06

0.25 0.04

0.26 0.05

*p< 0.001; F0 = maximal theoretical force production at 0 velocity; V0 = maximal theoretical velocity at 0 force; Pmax = theoretical maximal power output; F-V slope =

slope of the force-velocity linear relationship; MPV @ = mean propulsive velocity at each percentage of 1-RM; UP = unweighted pull-up (i.e. 0kg of external load)

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