J. &mechanics Printed

Vol. 25. No. 6, pp. 565-571,

in Great

W21-9290/92

1992.

Pergamon

Britian

ICE FRICTION

DURING

SS.OO+ .oO Press Ltd

SPEED SKATING

Jos J. DE KONING, GERT DE GROOT and GERRIT JAN VAN INGEN SCHENAU Faculty of Human Movement Sciences, Vrije Universiteit, v.d. Boechorststraat 9, 1081 BT Amsterdam, The Netherlands Abstract-During speed skating, the external power output delivered by the athlete is predominantly used to overcome the air and ice frictional forces. Special skates were developed and used to measure the ice frictional forces during actual speed skating. The mean coefficients of friction for the straights and curves were, respectively, 0.0046 and 0.0059. The minimum value of the coefficient of ice friction was measured at an ice surface temperature of about - 7 “C. It was found that the coefficient of friction increases with increasing speed. In the literature, it is suggested that the relatively low friction in skating results from a thin film of liquid water on the ice surface. Theories about the presence of water between the rubbing surfaces are focused on the formation of water by pressure-melting, melting due to frictional heating and on the ‘liquid-like’ properties of the ice surface. From our measurements and calculations, it is concluded that the liquid-like surface properties of ice seem to be a reasonable explanation for the low friction during speed skating.

INTRODUCTION

speed skating, the external power output produced by the athlete is predominantly used to overcome the air and ice frictional forces (Ingen Schenau and Cavanagh, 1990). Air friction is the largest resisting force. During skating at a velocity of lOms_ ‘, the total frictional losses can be roughly divided into 15% air friction and 25% ice friction. The influence of air frictional losses on speed-skating performance was extensively discussed by Ingen Schenau (1982). The reported coefficients of ice friction vary between 0.003 (Kobayashi, 1973) and 0.030 (Zatsiorski et al., 1987). The friction of ice can be measured in different ways. Kobayashi (1973) performed measurements with a special sledge which was propelled by a catapult mechanism. The sledge consisted of a pair of skate blades mounted parallel, which were always perpendicular to the ice surface. Bowden and Hughes (1939) performed measurements with an apparatus with a rotating disk of ice on which sliders slide. It is likely that there will be differences between ice friction during these types of measurements and that during actual speed skating. Probably, the best way to correctly quantify the coefficient of ice friction during speed skating is to measure it during actual skating. For this purpose a system of instrumented skates was built (Jobse et al., 1990). These skates allow the measurements of ice friction and of the normal forces during actual speed skating. The purpose of this study was to determine the magnitude of the ice frictional forces during skating at different ice conditions and to find a reasonable explanation for the relatively low friction during skating on ice. During

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11 July 1991.

Friction Friction can best be understood by considering the free-body diagram shown in Fig. 1. This figure represents a skater of weight W gliding on ice. The skater encounters resistance by the forces Fair and Ficc known as, respectively, the air and the ice frictional forces. The weight W is counterbalanced by the normal force N. Obeying Amontons law, the frictional force Ficc is proportional to the normal force N and independent of the magnitude of the geometrical contact area. The ratio between the horizontal ice frictional force and the vertical normal force is assumed to be a constant. This constant is called the coefficient of friction (p). About the mechanism to be held responsible for the relatively low friction coefficient of ice, some theories are available. It is generally accepted that friction is caused by adhesion and plastic and elastic deformation of the surfaces. If a low-viscosity fluid as lubricant is present, the two rubbing surfaces are more or less separated. This separation leads to a large reduction in friction.

Fig. 1. Free-body diagram of a skater with W the weight of the skater, N the normal force, and Fai, and Fi,,, respectively, the air and the ice frictional forces. 565

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In the literature, many suggestions are made for the low friction in skating and skiing being due to a thin film of liquid water between the ice surface and the skate or ski (Bowden and Hughes, 1939; Bowden, 1953; Tabor and Walker, 1970). Theories about the presence of water between the surfaces are focused on the ‘liquid-like’ properties of the ice surface, the formation of water by pressure-melting and by melting due to frictional heating. Pressure-melting. Pressure lowers the melting point of ice. This results from the larger molar volume of ice compared to liquid water. Using the ClausiusClapeyron equation, the decrease of the melting point (d7) for a given pressure change (dp) is given by dT -AV -=-= dp AS

-0.0074”C/105Nm-2,

(1)

with AV, the ice-water volume change, and AS, the ice-water change in entropy (Barnes and Tabor, 1966) calculated from the molar heat of phase transition. For a skater of 75 kg mass on skates with a contact area of 0.5 cm2 the pressure is 150 x lo5 Nm- 2. From equation (1) it follows that this pressure can form water only if the ice temperature is not lower than -1.l”C. Bowden (1953), therefore, suggested that pressure-melting of ice is a factor only at temperatures very close to 0°C and with slowmoving surfaces (glaciers). He reported that at appreciable sliding speeds, local surface melting is produced, not by pressure-melting, but by the frictional heating of the sliding surfaces. Melting due to frictional heating. Bowden (1953) suggests that the heat generated by friction is sufficient to melt some of the ice. The rate of heat supplied to the rubbing surfaces can be calculated from the energy flow caused by friction: P=pNv,

(2)

with ~1representing the coefficient of friction, N the normal force and v the sliding velocity. For speed skating, this energy flow equals 37.5 W when a coefficient of ice friction p of 0.005, a normal force of 750N and a velocity of 10 m s - ’ is used in equation (2). The heat of this plane source is conducted away into the two rubbing bodies (skate and ice). Archard (1959) describes the problem of the heat flow distribution over two rubbing bodies. But the theory first requires the solution of the equations for the heat flow into each body. Furey (1971) describes a method to obtain the increase of temperature dT over a circular contact area moving with a velocity v over a flat surface (for instance, ice). If all the heat given by equation (2) flows into the ice then dT of the ice surface is given by

where a is the radius of the circular rubbing surface, k is the thermal conductivity of ice (2.1 W m-i ‘C-l), r is the specific heat (2200 J kg- ’ ‘C-l), c is the density

(917 kgmm3) and v is the sliding velocity. Application of equation (3) to speed skating results in dT=7”C, assuming that a = 4 mm (corresponding to the magnitude of the actual contact surface of the skate blade) and v=lOms- i. This increase in ice temperature will be lower if not all the heat flows into the ice, but also to the skate. Arguments in favour of the theory of ice melting due to frictional heating are the experimentally observed inverse relation between sliding velocity and ice friction (Bowden, 1953) and the influence of thermal conductivity of the sliders on ice friction (Bowden and Hughes, 1939). Both frictional heating and pressure-melting should result in the formation of a lubricant during the skating action. There are also theories which take their starting point as the intrinsic properties of the ice surface itself, in particular, the liquid-like properties of the ice surface. Liquid-like surface properties of ice. A long time ago, Faraday and Tyndall postulated that sintering of ice results from a liquid layer covering the ice surface (Hobbs, 1974). Later, the existence of such a layer was incorporated in theories about the ice surface on a molecular level. The polarity of the molecules results in a transition layer with characteristics of a liquid (Weyl, 1951; Nakaya and Matsumoto, 1953), and this layer lowers the free energy (Fletcher, 1961,1963). For an extensive review of these theories see Hobbs (1974). The properties, but probably not the existence of such a liquid layer, depend on the adjacent medium (Jellinek, 1959, 1961). It may be that this layer is responsible for the low ice friction in speed skating. The friction between ice and steel could be explained then by an intrinsic property of the ice surface. Niven (1959) proposed that single Hz0 molecules or small groups of molecules can act somewhat like roller bearings. Molecular rotations at the surface would be possible because of the incomplete hydrogen bonds to lock the molecules into place. At this moment it is impossible to say which mechanism causes the low friction on ice. Evidence for both the melting-due-to-frictional-heat theory and the liquid-like layer theory can be found in the literature. The pressure-melting theory, however, seems to be an unrealistic theory for the explanation of the low coefficient of friction between ice and skates.

METHODS

Measuring system

The measuring system consists of a pair of instrumented skates and a portable data acquisition microcomputer. The force signals of the skates are amplified, low-pass-filtered, 13-bit analog-to-digital-converted, and fed into the microcomputer system. The microcomputer stores the sampled data in memory. The prototype of this measuring system was described

Ice friction during speed skating earlier (Jobse et al., 1990). Some alterations and improvements are made, which will be described here in more detail. The instrumented skates. A construction with three temperature-compensated strain gages (Wheatstone bridges) was built between the shoe and the blade of the skate to measure force in both horizontal (friction) and vertical (normal) directions. Relative to the pushoff forces during speed skating the ice frictional forces are very small. In designing the measuring unit special attention was paid to minimize the cross-talk from the normal-force to the frictional-force transducer. A transducer for normal-force measurements (A in Fig. 2) was built in both the front end and the rear end of the unit, which allowed the calculation of the point of application of the normal force. The transducer consists of a Wheatstone bridge, glued to a plate (thickness 1.3 mm) perpendicular in the middle of a cube. Exerting a load causes a rhombic transformation in the plate, in response to which the Wheatstone bridge produces a proportional electrical signal. The transducer for frictional-force measurements (B in Fig. 2) was positioned in the middle of the unit and was designed to be highly sensitive to frictional forces and insensitive to moments and forces in other directions. If a horizontal force is exerted on the transducer, the leaf springs of the element will bend and cause a rhomboid transformation in the central plate (thickness 0.3 mm) on which a Wheatstone bridge is glued. Shear stress will develop at an angle of 45”. The measuring unit was designed symmetrically to minimize the cross-talk from the normal-force to the frictional-force transducer. When the point of application of the normal force is situated near the middle of

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the skate, the cross-talk is only 0.03% of the normal force. On the front end of the skate the cross-talk is maximally 0.08%. The measuring unit is protected by an aluminium cover (C in Fig. 2). On this cover the shoes were mounted (sizes in the range from 23 to 29cm). Skate blades type ‘Viking special’ (Viking Skates, Amsterdam) were adapted. The strain gage elements for the normal-force and the frictional-force measurements can be loaded up to 1400 and 40 N, respectively. The electrical signals from the force transducers were pre-amplified (INA 102) and the offset was compensated previous to the transmission of signals to the data acquisition computer. The mass of the skates (0.93 kg per skate) is 55% higher than the mass of the normal skates (0.6 kg per skate). The data acquisition computer. The main task to this unit is to amplify, filter, digitize and store both the frictional force and the normal force. (This specially designed unit was built with surface-mounted devices technology.) Each force transducer in the skate is connected to an instrumentation amplifier (INA 102). Each amplifier is followed by a second-order Butterworth filter (cutoff frequency 50 Hz). A 13-bit analog-to-digital convertor (ML2208) provides the link to the on-board microcomputer system with a Hitachi 6309E microprocessor. The operating software is held in 32 kbyte ROM and 32kbyte RAM. The acquired data are stored in 32 kbytes of RAM and on a interchangeable memory card (ITT Cannon) with optional 1 Mbyte external RAM. After the test, the sampled data and the calculated values can be transferred to a host computer by the memory cards or by using RS232C format, and saved on a disk.

Fig. 2. Drawing of the measuring unit between the shoe and skate blade: the push-off force measuring elements (A), the frictional-force measuring element (B) and the protective cover(C).

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Amplification and sample frequency (from 200 to 1500 Hz) of the force signals can be set under software control and automatic offset nulling can be done. Graphs of the measured signals can be inspected on a 64 x 256 dot graphic liquid-crystal display of the hand terminal. In the measure mode (the hand terminal is disconnected) sampling is initiated by the subject during the experiment by pressing a hand-held button. The skate-to-ice contact is software-detected. During the ice contact, the sampled data are stored in the memory. After one or more strokes, the sampling can be stopped by the subject. In the measure mode the software calculates the coefficient of ice friction of the sampled data. The calculated coefficients of successive sessions are stored in the RAM and on the data card. Power supply is from a rechargeable 7.2 V, 1.2 Ah NiCd battery. The microcomputer (5 x 9 x 22 cm and 0.7 kg) is carried by the skater on his back. Measurements The experiments were carried out on three 400m artificial speed-skating ice rinks, the indoor rink in Heerenveen, The Netherlands, the indoor Olympic rink in Calgary, Canada, and the outdoor rink in Haarlem, The Netherlands. The ice. was properly

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prepared with ice-rink machines (Zamboni). These machines polish the ice surface and apply fresh water. During the experiments, the temperature of the ice surface was varied between - 1.8 and - 11 “C. The surface temperature of the ice was measured with an infrared surface thermometer (Horiba IT330). The blades of the skate were treated with a whetstone and polished with diamond polishing paper. The experiments were done with one experienced speed skater (1.80 m and 72 kg), who was very familiar with the measuring equipment. The experiments were carried out on a part of the ice rink that was not used by other skaters. The velocity of the skater was determined by measuring 100 m times. Each measurement was done for a couple (4-6) of strokes, both on the straightaways and in the curves. The coefficients of ice friction were calculated as the frictional force divided by the push-off force. The differences were tested for significance with a twotailed Student’s t-test (p < 0.05). RESULTS

Measurements of both the ice frictional force and the push-off force were done. Figure 3(a) shows an

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time (s) Fig. 3. An example of the push-off force (a) and the frictional force (b) of four strokes during skating the straight part of the track at 8 m s-l and with an ice temperature of - 5 “C. The frictional force divided by the push-off force gives the coefficient of ice friction (c).

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example of a push-off force registration and Fig. 3(b) shows the simultaneously measured frictional force. The frictional force samples divided by the push-off force samples gives for every sample a coefficient of ice friction. Figure 3(c) shows these coefficients calculated from the measured strokes of Fig. 3(a) and (b). The coefficients of ice friction for each run are the means of the varying values during the four strokes. The frictional and the push-off forces were measured on the straightaways as well as on the curves. Ice friction was measured at ice surface temperatures between - 1.8 and - 11 “C. In all these experiments the measurements appear to be consistent and reproducible. Figure 4 gives the relation between the coefficient of ice friction and ice surface temperature as measured on the straights when skating with a velocity of8ms- ‘. The data on ice friction while skating the curves show a comparable relation, only with 28% higher values. A second-order polynomial function was fitted through the data. The minimum value of p was found at an ice surface temperature between -6 and - 9 “C. The average value of the measured frictional force within the temperature interval of - 1.8 to - 11 “C was 3.77 N ( f 0.32) and 4.87 N (+ 0.36) for the straights and the curves, respectively. The corresponding averaged values of the coefficients of friction for the straights and curves were 0.0046 (+O.OOM) and 0.0059 (* 0.0004), respectively. The relation between the skating velocity and friction at an ice temperature of - 4.6 “C is plotted in Fig. 5. The coefficient of friction appears to increase with increasing speed. DISCUSSION Magnitude

of ice friction during speed skating

The experiments were carried out under different circumstances with a variety of ice temperatures. The mean frictional forces were registered in the range 3-6N. The mean coefficients of ice friction (p) were

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Fig. 4. Relation between the coe.flicient of friction and ice temperature during skating the straight parts of the track with a velocity of 8 m s- ‘.

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Fig. 5. Relation between the coefficient of friction and &ating velocity during skating the straight part of the track at an ice temperature of -4.6 “C.

found in the range 0.003-0.007 during skating the straights. The graphs of p against time during a couple of strokes [Fig. 3(c)] show that at the beginning and the end of every stroke p exceeds the values of the midphase. During the stroke, the skate rotates through its length axis from one edge to the other. During that rotation, first the outer edge makes a groove into the ice. Then the skate glides smoothly, but during the push-off, the skate rotates to the inner edge and makes again a groove into the ice. These penetrations in the ice can explain the increase of p. When ice friction is compared to friction in other endurance sports, it is found that the ice frictional force has more or less the same magnitude as the rolling resistance in competitive cycling (Di Prampero et al., 1979). The resistance during roller skating is five times higher (Boer et al., 1987) and during skiing on snow, approximately 10 times higher than that during speed skating (Bowden, 1953). The value of p influences the speed-skating performances. With the power balance model described by Ingen Schenau (1982), the effect of different values for the coefficients of friction on the skating velocity can be calculated. Ice conditions can easily change from 0.004 to 0.006 within competitions. A change in p from 0.004 to 0.006 has an effect of roughly 0.3 m s -. ’ on the mean velocity at all the competitive distances under the assumption of an unchanged external power output. Such a change in speed means, for example, an increase in the final performance time of 0.8 s at the 5OOm sprint and 23.5 s at the 10,OOOm race. These differences are larger than the variation in the final time among the fastest six competitors during the 1988 Winter Olympic Games. Friction on the straightaway

ice temperature (0C)

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and in the curve

The averaged p found during skating the curves with a velocity of 8ms-’ is 28% higher than the coefficients measured during skating the straights. The larger values found in the curves can be explained by a

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larger deformation of ice during skating the curve. In the curves the edge of the skate blade penetrates during the complete stroke into the ice, which causes a larger deformation and, consequently, larger values of ~1are observed when compared to the straights. InJuence

of ice temperature

on friction

Within a time span of 9 h the ice temperature of the indoor ice rink in Heerenveen was changed from - 1.8 to - 11.0 “C. The air in the indoor ice rink was at 12 “C, with a relative humidity of 55%. The track was polished every 30min. The experiments were done with a skating velocity of 8 m s-r. Figure 4 shows the measured coefficients of ice friction on the straights, ranging from 0.0038 to 0.0057, with an average p of 0.0046. A second-order polynomial function was fitted through the data. The minimum value of this fitted curve (0.0043) was reached at an ice surface temperature of - 7.4 “C. Obviously, the best surface temperature for speed skating on artificial ice lies between - 6 and -9°C. The lubrication between the blade of the skates and the ice surface may be expected to increase with increasing ice temperatures, irrespective of the underlying mechanism. However, the friction is also determined by the hardness of the ice (deformation) and, since the hardness increases with lower temperatures, an optimum ice surface temperature is to be expected. The advantages of a higher temperature (better lubrication), and those of a lower temperature minimizing the deformation, cancel out each other at a particular ice temperature. The optimum ice surface temperature for speed skating found in this study differs from the values published by Kobayashi (1973). He found an optimum surface temperature of -2.2 “C for speed skating on artifical ice and a value of - 0.6 “C for natural ice on a lake. The origin of the difference between our experiments and the experiments of Kobayashi can be found in the methodology used in measuring ice friction. The optimum value for the used sledge with fixed skates (25 kg, 1.4 ms-‘) will lie at a higher ice surface temperature, because the deformation of ice will play a smaller role. Injkence

of velocity on ice friction

The relation between the velocity of the skater and the coefficient of ice friction with an ice temperature of -4.6”C is shown in Fig. 5. The coefficient of friction rises with increasing speed. The increasing p at higher velocities is in contradiction with the measurements of Bowden (1953), who found a decreasing ~1at higher velocities with skis on ice. His explanation of a decreasing p was the larger surface melting and, thus, better lubrication due to a larger frictional heating at higher speeds. This conclusion is not confirmed by our experiments. But it cannot be excluded that the increase of friction is due to a different skating technique at different skating speeds.

Which mechansim causes the low friction?

From calculations and experiments described in the literature it may be concluded that pressure-melting seems to be an unrealistic theory for the explanation of the low coefficient of friction between ice and skates. From our experiments no clear answer can be given to the question of the mechanism causing the low friction on ice. Evidence for both the melting-due-to-frictional-heat theory and the liquid-like layer theory can be found in the literature. One interesting phenomenon and an argument in favour of the liquid-like layer theory is the effect of surface-active agents on ice. These surfactants lower the surface tension of ice and cause a change in the surface equilibrium film thickness. As a consequence, the liquid-like layer will be thicker and, probably, the lubrication of the two rubbing surfaces better. Ice makers of some speedskating rinks used these surfactants as their secret to give ice a superior quality. Kobayashi (1973) reported results of experiments with small quantities of ethylene glycol. On ice with temperatures lower than - 6 “C, he found 30% better results with treated ice. We measured at the artificial speed-skating rink of Haarlem, significant differences between ice (- 5.5 “C) prepared with normal water (~=0.0042) and ice treated with water with an added ‘secret’ chemical substance (~=0.0036). It may be assumed that these chemicals do not influence the thermal properties and frictional heating processes of ice; so it is likely that the liquid-like surface properties of ice are responsible for the lower coefficient of friction. Acknowledgements-Theauthors gratefully acknowledge the technical assistance of H. Jobse, F. &rep, F. de Boer and W. Schreurs and express their gratitude to B. Butter and J. de Jong for their support during the experiments. REFERENCES Archard, J. F. (1959) The temperature of rubbing surfaces. Wear 2,438-455. Barnes, P. and Tabor, D. (1966) Plastic flow and pressure melting in the deformation of ice I. Nature 210, 878-882. Boer, R. W. dc, Vos, E., Hutter, W., Groot, G. de and Ingen Schenau, G. J. van (1987) Physiological and biomechanical comparison of roller skating and speed skating on ice. Eur. J. app. Physiol. 56, 562-569.

Bowden, F.4. (1953) Friction on snow and ice. Proc. R. Sot. A 217,462-478. Bowden, F. P. and Hughes, T. P. (1939) The mechanics of sliding on ice and snow. Proc. R. Sot. A 172,280-298. Di Prampero, P. E., Cortilli, G., Morgnoni, P. and Saibene, F. (1979) Equation of motion of a cyclist. J. appl. Physiol. 47,201-206.

Furey, M. J. (1971) Friction, wear and lubrication. In Chemistry and Physics of Interfaces II (Edited by Ross, S.). American Chemical Society Publications, Washington DC. Fletcher, N. H. (1961) Surface structure of water and ice. Phil. Mag. 7, 255-296.

Fletcher, N. H. (1963) Surface structure of water and ice-a reply and a correction. Phil. Man. 10, 1425-1426. Hobbs, P. V. (1974) Ice Physics. Ciarenhon Press, Oxford. Ingen Schenau, G. J. van (1982) The influence of air friction in speed skating. J. Biomechanics 15, 449-458.

Ice friction during speed skating Ingen Schenau, G. J. van and Cavanagh, P. R. (1990) Power equations in endurance sports. J. Biomechanics 23, 865-881. Jellinek, H. H. G. (1959) Adhesive properties of ice. J. Coil. Sci. 14, 268-280. Jellinek, H. H. G. (1961) Liquid layers on ice. J. appl. Physics 32, 1793.

Jobse, H., Schuurhof, R., Cserep, F., Schreurs, A. W. and Koning, J. J. de (1990) Measurement of push-off force and ice friction during speed skating. Int. J. Sport Biomechanics 6,92-100. Kobayashi, T. (1973) Studies of the properties of ice in speed skating rinks. Ashrae. J. 73, 51-56. Nakaya, U. and Matsumoto. A. (1953) Simple experiment

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showing the existence of ‘liquid water’ film on the ice surface. J. Coil. Sci. 9, 41-49. Niven (1959) In Physics of Ice (Edited by Pounder, E. R.). Pergamon Press, Oxford. Tabor, D. and Walker, J. C. F. (1970) Creep and friction of ice. Nature 22% 137-139. Weyl, W. A. (1951) Surface structure of water and some of its phvsical and chemical manifestations. J. Co& Sci. 6, 389-405. Zatsiorski, W. M., Aljeschinski, S. J. and Jakuninm, N. A. (1987) Biomechanischer Grundlagen der Ausdauer (Biomechanical principles in endurance sports). Sportverlag, Berlin.

Ice friction during speed skating.

During speed skating, the external power output delivered by the athlete is predominantly used to overcome the air and ice frictional forces. Special ...
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