Original Article
Repeatable techniques for assessing changes in passive swimming resistance
Proc IMechE Part P: J Sports Engineering and Technology 1–10 Ó IMechE 2014 Reprints and permissions: sagepub.co.uk/journalsPermissions.nav DOI: 10.1177/1754337114562875 pip.sagepub.com
Angus P Webb, Dominic J Taunton, Dominic A Hudson, Alexander IJ Forrester and Stephen R Turnock
Abstract Two different methods of measuring the passive resistance of swimmers are used to compare system accuracy and repeatability. Method I uses a submerged glide tow, and Method II, a novel, simpler approach, is based on measuring deceleration during a submerged push-off glide. The comparison of each method is made for specific changes in passive resistance. A set of three male and three female swimmers compare the use of drag shorts to make swimmer-specific increases in drag. In a second study, the effect of hair removal is quantified on a single male swimmer (Method I 9.7% reduction and Method II 9.4% reduction). For five repeat tests, a 1.8% difference in resistance can be resolved with 95% and 70% confidence levels for the passive tow and push-off glide experiments, respectively.
Keywords Swimming, resistance, hair removal, measurement, drag
Date received: 8 August 2014; accepted: 20 October 2014
Introduction It is known that selecting alternative equipment (such as suits, hats and goggles) or changing body posture can reduce swimming resistance with the potential to reduce race time.1 The development of full-body swimming suits with their eventual banning by Fe´de´ration Internationale de Natation (FINA) in January 2010 is indicative of this. What is more challenging is quantifying such changes and thereby allowing swimmers, coaches and national federations to make rational decisions with regard to race kit selection and swimming styles. Measurement of swimming resistance has usually focused on active resistance, with the velocity perturbation method commonly used.2,3 A system which measures hand forces, assumed equal to the thrust delivered by a swimmer, known as the measurement of active drag (MAD) system, has been developed.3,4 Other methods have performed both passive and active swimming experiments to determine active swimming resistance.5,6 Since it is not possible to measure active resistance directly, these methods rely on assumptions which have been found to influence the predicted resistance.7 Alternatively, passive resistance can be measured directly and is generally conducted by a handle tow2,8 or use of a tether in a circulating water channel.6
Passive tow experiments have been used to investigate the effects of body size2 and swimming depth.9,10 These methods require complex bespoke equipment, and therefore, a simpler pool-side method is desirable. The deceleration during a push-off glide is affected by a swimmer’s passive resistance. Therefore, it is proposed that by measuring this deceleration, swimming passive resistance may be determined. A similar method has been developed to determine resistance for autonomous underwater vehicles, in the open sea, by measuring rate of vertical ascent.11 Sharp and Costill12 identified the effect of body hair removal on deceleration during a push-off glide; however, this study did not attempt to deduce swimmer resistance from these measurements. It is proposed that a specific form of resistance change can be used to compare the measurement accuracy of the existing passive tow experiment and this new simpler process. To validate this test Performance Sports Engineering Laboratory, Faculty of Engineering and the Environment, University of Southampton, Southampton, UK Corresponding author: Angus P Webb, Performance Sports Engineering Laboratory, Faculty of Engineering and the Environment, University of Southampton, University Road, Southampton SO17 1BJ, UK. Email:
[email protected]
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Figure 1. Tow system setup, displaying the mechanical and electrical components used to measure the passive drag of a swimmer.
method, six participants were tested with and without drag shorts using both methods, and the accuracy of each method is compared. Few studies have investigated methods of improving swimming performance through reduction of passive resistance.12,13,21 A common approach is to remove exposed body hair; however, no published research has quantified the actual resistance reduction achieved. Sharp et al.13 used blood lactate concentrations as a measure of performance over two identical swims, with and without body hair, and found a reduction of up to 28% in blood lactate in the glabrous condition. Blood lactate measurements depend on many variables specific to an athlete and therefore can only provide an indirect approach to assessing a resistance change.14 Therefore, this study further aims to quantify the reduction in passive resistance experienced by a single male swimmer, after body hair removal, using both the pushoff glide and a passive tow experiments. In this study, an alternative more efficient experimental process, based on measuring deceleration during a push-off glide, is proposed – with the aim to assess its repeatability against an existing over-speed winch tow– based method. It is hypothesised that the push-off glide method can detect changes in swimmer resistance; however, the number of repeat tests required is unknown. The ability of both methods to determine small changes in passive resistance for a reasonable number of swimmer trials is measured through the use of standard ‘drag shorts’ for a test cohort of six swimmers. In addition, as a real-life case study, passive resistance is measured for a single swimmer, before/after shaving. Due to fatigue in the human participants, all tests have been limited to a small sample. Therefore, statistical methods bootstrapping and permutation are utilised to quantify the variance in the measured data for each method.
Methodology Three male and three female non-elite swimmers (aged 20–25 years) participated in the validation study. One male non-elite swimmer (aged 25 years) participated in the hair removal case study. All studies were under ethical approval RGO7207 of the Faculty of Engineering and the Environment, University of Southampton; swimmers also provided written consent. The validation study was conducted over three sessions. The hair removal case study was conducted over 1 day with the hirsute condition tested in the morning and glabrous condition tested in the afternoon after hair removal. The height and weight of all the swimmers were recorded on the day of testing. Passive tow experiments were conducted over a distance of 25 m with a constant depth of 2 m in lane 2. The water temperature was assumed constant at 27 °C.15
Passive tow experiment A portable tow system has been developed, shown schematically in Figure 1, where a swimmer is towed at a range of velocities and tow depths with the resistance measured. Body immersion and attitude are monitored using synchronised video. The force exerted on the swimmer by the tow system is measured with bespoke force transducers. The force transducers consist of four flexures, with a linear shear response, and a centrally mounted linear varying displacement transducer (LVDT) to measure the displacement of the flexures. The analogue output of the LVDT therefore has a linear response to the applied force. Due to this linearity, calibration of the system is performed by applying a single known load. Calibration is repeated after installation and prior to each session to ensure any temperature change does not affect the
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3 where R is the passive resistance, r is the water density, V is the mean tow velocity and S is the estimated wetted surface area of the swimmer.16
Push-off glide experiment The proposed alternative method to measuring passive resistance is by the means of a push-off glide experiment, measuring velocity, from which a passive resistance coefficient is derived. Assume a point mass experiencing the following forces ð2Þ
Z
Figure 2. Resistance trace of a swimmer during a passive tow, with acceleration peak, constant velocity region and measurement window.
linear response. The tow velocity is derived from the rotational velocity of the winch drum and measured using a rotary encoder. The analogue force and speed signals are input into a 14-bit analogue-to-digital converter, and the data are acquired at 250 Hz on a laptop. A 20 Hz digital filter is used to eliminate electrical noise in the data. A typical passive resistance force trace containing an acceleration peak and constant velocity phase can be seen in Figure 2. The region at which the mean drag is calculated is manually selected and displayed in Figure 2. The number of repeat tests was limited to 5 per configuration in the validation study and 10 in the hair removal case study. Statistical methods are used to determine whether sufficient data have been gathered. To ensure an accurate comparison of resistance between the two methods, a tow velocity was chosen to match the mean underwater push-off velocity of the swimmer. The test run was conducted over 25 m, with a measurement time of 6–8 s. The swimmer was towed holding a 0.2-m-long cylindrical aluminium bar with hands side by side and the towline extending between the hands. During the tow, the swimmer adopted a glide position. To ensure repeatability in body posture between tests, swimmers pointed toes to maximum extension, maintained a full breath and focused upward peripheral vision on a specific point on the towline to ensure a consistent head position. Video footage capturing the sagittal plane of the swimmer was inspected, for each test, to ensure body positions remained constant. A constant tow depth of 1 m was chosen to minimise wave-making resistance.9 Surface elevation measurements were performed to ensure this assumption remained true. To eliminate the potential effects of the small inter run velocity variation, a drag coefficient is calculated from CD =
R 1 2 2 rV S
ð1Þ
where R is the velocity-dependent resistance of the swimmer and the term on the right hand side is the inertial force of the swimmer and the surrounding water. M represents the mass of the swimmer and m is the added mass from the surrounding fluid (assumed 20% of body mass), with dV=dt, the rate of change of velocity at any point in time. Therefore, the equation of motion for the swimmer is expressed as RðVÞ ðM + mÞ
dV =0 dt
ð3Þ
If the resistance coefficient CD is assumed constant over the velocity range evaluated in the glide test, equation (1) can be substituted into equation (3) to give CD =
ðM + mÞ dV dt 1 2 2 rV S
ð4Þ
It is worth noting that although the frictional resistance coefficient of the swimmer will increase as they slow down, the fractional change in viscous form resistance will be small between the start and finish speeds of the recording period.17 For a typical push-off velocity range of 2.5–1.5 m s21, this provides a change in skin friction coefficient of 3.4 3 1024; this is not considered to significantly affect the predicted drag coefficient. A velocity measurement system has been developed based on this approach. The system, shown schematically in Figure 3, operates by fastening a 0.4 mm Dyneemaä line to the swimmer, which is led back to a rotary encoder used to measure the line velocity. Two pulleys fixed to a frame allow the line to be pulled out at various depths underwater. The line is attached to a thin, tight-fitting waist belt worn by the swimmer. The rotary encoder and data acquisition system are identical to that described for the tow system. The swimmer initiates a push-off and the velocity trace is recorded at 250 Hz. Figure 4 displays a velocity profile measured during a push-off glide experiment. It contains a steep increase
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Figure 3. Velocity measurement system setup, displaying the push-off method and system components.
Figure 4. Push-off glide experiment velocity trace with measurement window.
in velocity during the push-off, a peak where the feet leave the wall and a deceleration region where the swimmer is gliding through the water. The data during the deceleration period are selected to perform the analysis. Second-order central difference numerical differentiation is performed to determine the rate of change of velocity for each point in time. The mean resistance coefficient throughout the deceleration period is determined from equation (4). Five push-off tests were performed for each configuration, with push-off effort kept approximately constant. The pull-out depth of the line was set to 1 m, to match the depth of the tow experiment.
Statistical analysis Due to the limited number of repeat experiments, the true variance of the population is unknown.
Bootstrapping is a method used to resample existing data, generating a normal distribution of measurements taken and providing an estimation of the true variance.18 In addition, a permutation significance test has been used to determine the probability of the observed differences between the conditions.18 The bootstrap method allows a normal distribution, emulating a large sample size, to be estimated from a small sample. Where the original sample may be skewed due to differences in push-off position and depth, the random resampling process can alleviate these effects. Although this method is used to estimate the true variance of a population, it cannot eliminate the effects of extreme outliers in a small sample size. Therefore for all tests, the synchronised video was used to monitor swimmer immersion and attitude to ensure any extreme outliers were negated. For all analysis, 10,000 bootstrap resamples were used. The permutation significance test is used to quantify the probability of the observed drag change based on the variability of the data. To conduct a permutation test, a null hypothesis is assumed, that is, all the drag measurements from both conditions are in fact the same condition. A probability distribution is generated for a range of potential drag changes, with the most probable being zero according to the null hypothesis. Therefore, the probability of the actual observed drag change is the proportion (p value) of the data outside this region on the distribution. Large drag changes are therefore less probable on the distribution, disproving the null hypothesis and confirming the observed drag change is in fact another condition. The more variability in the data and therefore the wider the distribution, the larger the drag change required to disprove the null hypothesis; p values less than 0.05 are assumed significant. When comparing the measured differences from both the passive tow and push-off glide methods, a
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Figure 5. Drag shorts used to provide drag change to compare push-off glide and passive tow experiments.
paired sample Student’s t-test will be used.19 This will determine whether discrepancy between the two methods is significant.
Validation drag change Drag shorts (Figure 5) were used to provide a change in resistance which could be tested by both methods. For a single participant, tests with and without drag shorts were alternated to ensure that any progressive technique change would not create a bias to either condition.
Hair removal case study A hair length of approximately 2–3 cm was present on the chest, back and arm pits, and a hair length of approximately 1.5 cm was present on the legs and arms on the swimmer. Hair removal was performed on the
chest, back, arm pits, arms and legs. The head in both conditions was shaved. Figure 6 displays the chest and back, before and after hair removal. The time between the testing of hirsute and glabrous conditions was approximately 4 h. The same cap, goggles and trunks were used for both test conditions. Since it was not possible to alternate the tested conditions, progressive technique change may have affected the measured resistance. It cannot be predicted whether this technique change will cause a reduction or increase in resistance. However, this effect is assumed to be small since test subject gained extensive experience in both the passive tow and push-off glide experiments prior to this study.
Results and discussion The average time per run for the passive tow and the push-off glide experiments was 1 min 51 s and 1 min 24 s per run, respectively.
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Figure 6. From left to right: (1) Chest – hirsute, (2) Chest – glabrous, (3) Back – hirsute and (4) Back – glabrous.
Validation study Table 1 displays the mean resistance coefficients determined from the validation study. Male and female data are displayed separately since the resistance data fall into two distinct groups – likely caused by differences in body size and shape (visible in height and weight data). When comparing the drag change measured using the two different experiments for each participant, it can be seen that they match within a few percentage points. In certain cases, there is a difference between the measured changes from the tow and push-off glide experiments. However, a paired sample t-test finds this difference non-significant (p = 0.58). Figure 7 displays the bootstrapped distributions of the data from the validation study. As displayed in Table 1, these distributions identify more clearly that the outputs from both experimental methods reflect the increase in drag associated with wearing drag shorts. Although both methods predict similar relative changes in drag, in some instances, the absolute drag coefficient measured is quite different. For all participants, the drag coefficient measured by the tow experiment is greater than that measured by the push-off glide experiment. A potential reason for this is that during the tow experiment, directional instability of the swimmer sometimes occurs. Therefore, any angle of attack the swimmer may adopt during a tow will increase measured drag. Directional instability is likely dependent both on the shape of the swimmer and skill required to keep the body travelling straight. Any selfalignment actions taken by the swimmer will also increase drag. These factors may explain the consistent higher drag coefficient measured by the tow experiment. An improvement to this method would be to include a measure of angle of attack using video analysis; this may enable fewer repeat tests if angle of attack is the main source of variance in passive resistance. For the push-off glide experiment, an added mass, m, was assumed proportional to body mass. However, this may not fully capture variations in body shape and could explain why the differences between the measured drag coefficients differ for each participant.
Figure 8 displays the output from the permutation tests, identifying the confidence in the measured drag change for both methods. On each plot, the black line represents the probability of differences between the conditions, assuming the null hypothesis (conditions are the same). The circle marker on the x-axis identifies the observed difference. Comparing the p values for male and female, the female data show greater confidence. This is because the drag shorts provided a greater relative drag increase for females. The fit of the drag shorts varied depending on body size, and therefore, the larger the participant, the tighter the fit and the less absolute drag increase that was observed. For the female data, both methods demonstrated sufficient confidence to quantify the difference between conditions. There is greater confidence in the tow experiment observation; however, the longer measurement period for the passive tow experiment, with typically 1750 samples per run versus 375 for the push-off glide experiment, will provide a more statistically significant result. For the male data, where the drag difference between conditions is small, both methods produce similar predictions; however, they are unable to provide significant confidence. To achieve greater confidence, more repeat tests would be necessary.
Hair removal case study Table 2 displays the resistance coefficients measured using both experimental methods for hirsute and glabrous conditions. In total, 10 repeat tests were performed for the passive tow experiment and 5 for the push-off glide experiment. Both methods predicted a similar drag change of within 0.3%. The passive tow experiment measured an absolute drag reduction of 13.25 N at 2.2 m s21 which equates to an effective power reduction (DRV) of 29 W. The change in deceleration at fixed speed values, before and after hair removal, may be considered the same as the change in resistance. These findings are similar to the measurements of Sharp and Costill,12 where an 11.2% reduction in deceleration was found for nine male participants.
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Coefficient
SD: standard deviation.
0.04 0.04 6.99 3.63
0.003 0.001
0.03 0.03 10.6
Coefficient
With Without % Change Difference
Coefficient
Tow
Method
SD
Push-off
Female 1, H = 1.68, W = 57
Participant
0.001 5E204
0.03 0.03 4.79 0.56
With Without % Change Difference
0.03 0.02 5.35
Coefficient
Tow
Method
SD
Push-off
Male 1, H = 1.75, W = 81
Participant
0.002 0.005
SD
0.002 0.001
SD 0.001 0.003
SD
0.03 0.03 10.7 4.81
Coefficient
Tow
9E-04 6E-04
SD
Female 2, H = 1.68, W = 52
0.03 0.03 20.61 2.04
Coefficient
Tow
Male 2, H = 1.93, W = 83.5
0.03 0.02 5.85
Coefficient
Push-off
0.03 0.03 1.43
Coefficient
Push-off
9E-04 6E-04
SD
0.002 0.002
SD 0.002 0.002
SD
0.03 0.03 18.6 2.49
Coefficient
Tow
8E-04 0.002
SD
Female 3, H = 1.57, W = 50
0.02 0.02 1.5 0.42
Coefficient
Tow
Male 3, H = 1.88, W = 77
0.03 0.02 21.1
Coefficient
Push-off
0.02 0.02 1.92
Coefficient
Push-off
0.003 0.002
SD
8E-04 0.001
SD
Table 1. Mean resistance coefficient data determined with and without drag shorts for both push-off glide and passive tow experiments. The height (m) and weight (kg) for each participant is also displayed.
Webb et al. 7
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Figure 7. Bootstrapped distributions for each participant displaying the resistance change from drag shorts for both methods. On the x-axis is resistance coefficient and y-axis is probability density.
Figure 8. Permutation test results comparing the data for with and without drag shorts for each participant and each method. A plot displays the probability of a range of drag changes according to the null hypothesis that the conditions (with and without) are the same. The circle marker identifies the observed change in drag, and the difference and probability are quantified above.
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Figure 9. Bootstrapped distributions for hirsute and glabrous conditions for passive tow and push-off glide methods. Table 2. Mean resistance coefficient data determined for hirsute and glabrous conditions for both push-off glide and passive tow experiments. Participant
Male 4, H = 1.78, W = 66
Method
Tow Coefficient
Hirsute Glabrous % Change Difference
0.031 0.028 9.67 0.27
Push-off SD 0.0009 0.0007
Coefficient 0.021 0.019 9.40
SD 0.0012 0.0012
SD: standard deviation.
Table 3. Simulated glide times and distances for various resistance reductions. Resistance reduction (%)
Time for 5 m glide (s)
Glide distance in 1 s (m)
0 1 5 10
2.95 2.94 2.91 2.88
2.34 2.37 2.38 2.39
Figure 9 displays the bootstrapped mean distributions of the resistance data. As noted in Table 2, both methods have identified a similar reduction in resistance due to hair removal. The effect of performing a greater number of repeat tests for the passive tow experiment is evident, producing sharper distributions. Figure 10 displays the results from the permutation test comparing hirsute and glabrous conditions. For both methods, the observed differences have high confidence values, with the passive tow experiment producing a very low p value of 1 3 1025 evident from the sharp distributions and little overlap in Figure 9. Assuming that the distributions in Figure 9 represent the true variance of the population, the permutation test was used to investigate the minimum resistance change that could be measured with each method to a confidence of 95%. This was achieved by shifting the glabrous data until a p value of 0.05 is reached. This resulted in a minimum resistance change that could be measured of 1.8% and 7% for the passive tow and push-off glide experiments, respectively. To measure a resistance, difference of 1.8% with the push-off glide experiment will result in a confidence of 70%. Hair removal provided a resistance reduction of 9.5% for the specific swimmer tested. To quantify the effect of this resistance change in terms of swimming performance, a simulation method by Lyttle and Elliott8 was adopted. Time to travel 5 m and distance travelled in 1 s immediately after push-off, for a range of resistance reductions, are tabulated (Table 3). This identifies the importance of minimising swimming resistance to improve performance. Additionally, where swimmers train entirely with increased resistance, they will not be prepared for the swimming speeds experienced during a race.20 A resistance change as little as 1% may be desirable for race performance and therefore to measure such a change with confidence would require many repeat tests for both methods.
Conclusion The repeatability of two methods for measuring swimming passive resistance has been assessed. The conventional passive tow experiment is compared with a new
Figure 10. Permutation test results comparing the data for hirsute and glabrous conditions for passive tow and push-off glide methods.
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more efficient method, the push-off glide experiment. A study comparing the effect of drag shorts on three male and three female non-elite participants was performed using both methods. Both methods demonstrated sufficient precision to identify the drag change associated with drag shorts with five repeat tests. However, the passive tow experiment in both the validation study and hair removal case study shows greater precision, but at the expense of a more complex experimental setup and a longer measurement period. The hair removal case study was performed on one male non-elite participant, identifying a 9.7% and 9.4% reduction in passive resistance using the passive tow and push-off glide experiments, respectively. These results were compared to the 11.2% reduction in deceleration measured after hair removal by Sharp and Costill.12 Overall, both methods have shown that with five repeat tests, a 1.8% difference in resistance can be resolved with 95% and 70% confidence for the passive tow and push-off glide experiments, respectively. Where the variance in the data is large, or small drag changes are measured, a greater number of repeat tests are necessary to ensure significant confidence. Declaration of conflicting interests The authors declare that there is no conflict of interest. Funding This research has been supported by a grant from UK Sport and the University of Southampton primarily to fund the PhD programmes of J. Banks, C. Phillips and A. Webb. In addition, British Swimming has funded pool access. British Swimming staff assisted in the testing. Jonty Skinner has provided support throughout the development of the testing procedures. References 1. Mollendorf JC, Termin AC, Oppenheim E, et al. Effect of swim suit design on passive drag. Med Sci Sports Exerc 2004; 36(6): 1029–1035. 2. Kolmogorov SV and Duplishcheva OA. Active drag, useful mechanical power output and hydrodynamic force coefficient in different swimming strokes at maximal velocity. J Biomech 1992; 25(3): 311–318. 3. Mason B, Formosa D and Rollason S. A comparison between the values obtained from active drag analysis compared to forces produced in tethered swimming. In: International Society of Biomechanics in Sport Proceedings Archive, 2009, vol. 1, no. 1.
4. Toussaint HM, De Groot G, Savelberg H, et al. Active drag related to velocity in male and female swimmers. J Biomech 1988; 21(5): 435–438. 5. Webb A, Banks J, Phillips C, et al. Prediction of passive and active drag in swimming. Procedia Eng 2011; 13: 133–140. 6. Takagi H. A hydrodynamic study of active drag in swimming. JSME Int J B: Fluid T 1998; 42(2): 171–177. 7. Toussaint HM, Roos PE and Kolmogorov S. The determination of drag in front crawl swimming. J Biomech 2004; 37(11): 1655–1663. 8. Lyttle A and Elliott C. The effect of depth and velocity on drag during the streamlined glide. J Swimming Res 1998; 13: 15–22. 9. Vennell R, Pease D and Wilson B. Wave drag on human swimmers. J Biomech 2006; 39(4): 664–671. 10. Taunton DJ, Turnock SR, Hudson DA, et al. Predicting wave drag of swimmers using slender body theory (Department report). Southampton: Fluid Structure Interactions, University of Southampton, 2012. 11. Babb RJ. Instrumentation for a low drag hydrodynamic test vehicle. In: Sixth international conference on electronic engineering in oceanography, Cambridge, 19–21 July 1994, pp.24–29. Institute of Oceanographic Sciences Deacon Laboratory. 12. Sharp R and Costill D. Influence of body hair removal on physiological responses during breaststroke swimming. Med Sci Sports Exerc 1989; 21(5): 576–580. 13. Sharp R, Hackney A and Cain S. The effect of shaving body hair on the physiological cost of freestyle swimming. J Swimming Res 1988; 4(1): 9–13. 14. Billat V. Use of blood lactate measurements for prediction of exercise performance and for control of training. Sports Med 1996; 3: 157–175. 15. Fe´de´ration Internationale de Natation (FINA). Facility rules 2 – swimming pools. Lausanne: FINA, 2012. 16. DuBois D and DuBois E. A formula to estimate the approximate surface area if height and weight be known. Arch Intern Med 1916; 17: 863–871. 17. Molland AF, Turnock SR and Hudson DA. Ship resistance and propulsion: practical estimation of ship propulsive power. London: Cambridge University Press, 2011, pp.51–57. 18. Hesterberg T, Moore D and Monaghan S. Bootstrap methods and permutation tests. In: Moore D and McCabe G (eds) Introduction to the practice of statistics. 7th ed.Boston, MA: W.H. Freeman, 2010, pp.14.1–14.70. 19. Student. The probable error of a mean. Biometrika 1908; 6(1): 1–25. 20. Maglischo EW. Swimming fastest. 3rd ed.Champaign, IL: Human Kinetics, 2002. 21. Toussaint HM, Truijens M, Elzinga MJ, et al. Effect of a fast-skin ‘Body’ suit on drag during front crawl swimming. Sports Biomech 2002; 1: 1–10.
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