## Hand Force and Swimming Velocity

**Hand Force and Swimming Velocity**

Rod Havriluk, Ph.D.

XVth Federation Internationale de Natation World Congress

Indianapolis, IN, 2004

The relationship between force and velocity in swimming has been investigated under both passive and active conditions. The most basic form of the equation is expressed as: D = kv

^{n}, where D is the drag force on the body; k includes the coefficient of drag and an area variable; and v is the swimming velocity raised to an exponent of n.A wide range of values for the velocity exponent has been determined. Values were calculated for passive drag from 1.66 to 2.42 (Shimonagata, Taguchi, Taba, & Aoyagi, 1999) and for active drag from 1.2 (di Prampero, 1986) to 2.76 (Nomura, 1994). Non-quadratic equations have also been used (Keskinen, Tilli, & Komi, 1989).

A recently conducted meta-analysis on passive drag confirmed the quadratic relationship between resistance and velocity (Havriluk, 2004). If the resistance increases quadratically with velocity, then propulsion must increase in the same manner. The purpose of this study was to determine the relationship of hand force and swimming velocity. It was hypothesized that there would be a quadratic relationship between force and velocity.

**Method**

The subjects were competitive swimmers between the ages of 16 and 23. Hand force and swimming velocity were measured with Aquanex. The instrumentation and testing protocol were originally described and validated in 1988 by Havriluk. Subsequent studies confirmed the validity of Aquanex for measuring forces in aquatics (Prins, Hartung, Merritt, Blancq, & Goebert, 1994; Prins & Havriluk, 1991; Havriluk, 2003).

Pressure sensors were placed on the swimmer’s hands. Each swimmer was asked to sprint crawlstroke over a 20 m distance to a wall. Data were collected at a rate of 85 samples per sec over the last 10 m of the swim. Average hand force and swimming velocity were calculated. The above figure shows the force curves and video image of one trial. The sensor on the left hand is visible. The vertical gray lines on the force curves are synchronized with the video image.

The hypothesis was addressed with both within and between subjects designs. For the within subjects design, 12 swimmers (6 male, 6 female) were tested. Each subject was asked to increase hand force over a series of ten trials from minimal on trial 1 to maximal on trial 10. For the between subjects design, 60 swimmers (30 male, 30 female) were tested. Each subject was asked to swim at maximum velocity for one trial.

**Results**

For the within subjects design a quadratic relationship of hand force and swimming velocity was found for each subject. All ten data points for the fastest and slowest male and female subjects are plotted on the graph below.

For each subject, the data points fit a quadratic equation with p<.01. The mean k was found to be .145 for males (R

^{2}= .94) and .166 for females (R^{2}= .88). The mean values for age, height, and mass were 21.8 ± 2.1 yrs,193 ± 9 cm, and 90.7 ± 6.0 kg for males and 18.0 ± 1.4 yrs, 173 ± 7 cm, and 65.2 ± 8.4 kg for females.For the between subjects design, a quadratic relationship of hand force and swimming velocity was also found. The individual data points for each subject are plotted on the graph below.

The mean k was found to be .154 for males (R

^{2}= .55, p<.001) and .165 for females (R^{2}= .56, p<.001). The mean values for age, height, and mass were 18.3 ± 1.6 yrs,184 ± 8 cm, and 77.6 ± 8.8 kg for males and 17.9 ± 1.4 yrs, 169 ± 8 cm, and 62.7 ± 8.8 kg for females.**Conclusion**

The results support the hypothesis that there is a quadratic relationship between force and velocity in swimming. The within subjects design shows that a swimmer will swim faster with an increase in hand force. The between subjects design shows that swimmers who exert more hand force swim faster than swimmers who exert less hand force. Any differences in the k values for the within and between designs can be attributed to the components of k: cross-sectional area of the body and drag coefficient.

Understanding the force/velocity relationship is paramount to optimizing performance. Since a disproportionately larger increase in hand force is required to continue to increase swimming velocity, swimmers must be very conscious of generating maximum force and optimally directing the force at the higher swimming velocities.

This information is critical to coaches and can be used in many ways. In the most obvious approach, coaches can encourage swimmers to exert maximum hand force throughout the entire stroke and to maintain high force values throughout a training session. In a more refined approach that usually requires quantitative feedback they can adjust bilateral differences and minimize force losses and wasted motion.

**References**

di Prampero, P. E. (1986). The energy cost of human locomotion on land and in water.

*International Journal of Sports Medicine*,*7*, 55-72.Havriluk, R. (1988). Validation of a criterion measure for swimming technique.

*Journal of Swimming Research*,*4*(4), 11-16.Havriluk, R. (2003). Performance Level Differences in Active Drag Coefficient.

*Proceedings of the IOC Olympic World Congress on Sport Sciences*, Athens.Havriluk, R. (2005). Performance Level Differences in Swimming: A Meta-Analysis of Resistive Forces, in press.

Keskinen, K. L., Tilli, L. J., & Komi, P. V. (1989). Maximum velocity swimming: interrelationships of stroking characteristics, force production and anthropometric variables.

*Scandinavian Journal of Sports Science*,*11*(2), 87-92.Nomura, T., Goya, T., Matsui, A., & Takagi, H. (1994). Determination of active drag during swimming. In M. Miyashita, Y. Mutoh, & A. B. Richardson (Eds

*.), Medicine and Science in Aquatic Sports*(pp. 131-136). Karger: Basel.Prins, J. H., Hartung, G. H., Merritt, D. J., Blancq, R. J., & Goebert, D. A. (1994). Effects of aquatic exercise training in persons with poliomyelitis disability.

*Sports Medicine, Training and Rehabilitation*,*5*, 1-11.Prins, J. H. & Havriluk, R. (1991).

*Measurement of changes in muscular strength in aquatic rehabilitation*. Paper presented at the XIIth International Congress on Biomechanics, Perth, Australia.Shimonagata, S., Taguchi, M., Taba, S., & Aoyagi, M. (1999). Estimation of propulsion and drag force in front crawl stroke. In K. L. Keskinen, P. V. Komi, & A. P. Hollander (Eds.),

*Biomechanics and Medicine in Swimming VIII*(pp.107-112). Jyvaskyla: University of Jyvaskyla.