Stochastic distribution of the required coefficient of friction for level walking--an in-depth study

This study investigated the stochastic distribution of the required coefficient of friction (RCOF) which is a critical element for estimating slip probability. Fifty participants walked under four walking conditions. The results of the Kolmogorov-Smirnov two-sample test indicate that 76% of the RCOF data showed a difference in distribution between both feet for the same participant under each walking condition; the data from both feet were kept separate. The results of the Kolmogorov-Smirnov goodness-of-fit test indicate that most of the distribution of the RCOF appears to have a good match with the normal (85.5%), log-normal (84.5%) and Weibull distributions (81.5%). However, approximately 7.75% of the cases did not have a match with any of these distributions. It is reasonable to use the normal distribution for representation of the RCOF distribution due to its simplicity and familiarity, but each foot had a different distribution from the other foot in 76% of cases. PRACTITIONER SUMMARY: The stochastic distribution of the required coefficient of friction (RCOF) was investigated for use in a statistical model to improve the estimate of slip probability in risk assessment. The results indicate that 85.5% of the distribution of the RCOF appears to have a good match with the normal distribution.     

A methodology to quantify the stochastic distribution of friction coefficient required for level walking

The required friction coefficient is defined as the minimum friction needed at the shoe and floor interface to support human locomotion. The available friction is the maximum friction coefficient that can be supported without a slip at the shoe and floor interface. A statistical model was recently introduced to estimate the probability of slip and fall incidents by comparing the available friction with the required friction, assuming that both the available and required friction coefficients have stochastic distributions. This paper presents a methodology to investigate the stochastic distributions of the required friction coefficient for level walking. In this experiment, a walkway with a layout of three force plates was specially designed in order to capture a large number of successful strikes without causing fatigue in participants. The required coefficient of friction data of one participant, who repeatedly walked on this walkway under four different walking conditions, is presented as an example of the readiness of the methodology examined in this paper. The results of the Kolmogorov-Smirnov goodness-of-fit test indicated that the required friction coefficient generated from each foot and walking condition by this participant appears to fit the normal, log-normal or Weibull distributions with few exceptions. Among these three distributions, the normal distribution appears to fit all the data generated with this participant. The average of successful strikes for each walk achieved with three force plates in this experiment was 2.49, ranging from 2.14 to 2.95 for each walking condition. The methodology and layout of the experimental apparatus presented in this paper are suitable for being applied to a full-scale study.     

Comparison of different methods to extract the required coefficient of friction for level walking

The required coefficient of friction (RCOF) is an important predictor for slip incidents. Despite the wide use of the RCOF there is no standardised method for identifying the RCOF from ground reaction forces. This article presents a comparison of the outcomes from seven different methods, derived from those reported in the literature, for identifying the RCOF from the same data. While commonly used methods are based on a normal force threshold, percentage of stance phase or time from heel contact, a newly introduced hybrid method is based on a combination of normal force, time and direction of increase in coefficient of friction. Although no major differences were found with these methods in more than half the strikes, significant differences were found in a significant portion of strikes. Potential problems with some of these methods were identified and discussed and they appear to be overcome by the hybrid method. PRACTITIONER SUMMARY: No standard method exists for determining the required coefficient of friction (RCOF), an important predictor for slipping. In this study, RCOF values from a single data set, using various methods from the literature, differed considerably for a significant portion of strikes. A hybrid method may yield improved results.     

Available friction of ladder shoes and slip potential for climbing on a straight ladder

Straight ladder accidents are a major safety problem. As a leading cause of injuries involving straight ladders, slips at the ladder base occur when the required friction exceeds the available friction at the ladder shoe and floor interface. The objectives of this experiment were to measure the available friction at the base of a portable straight ladder in contact with a floor and to estimate the slip potential of the ladder. The results of friction measurements indicated that the measured friction coefficient on the oily surfaces differed among the six commercially available ladder shoes evaluated. A statistical model was used to compare the available friction results from the current study with the friction requirements under different climbing conditions from a previous study based on their stochastic distributions to estimate the slip potential at the base of the ladder. The results showed that different climbing conditions used in the previous study could be supported by available friction on dry surfaces. However, when the ladder was put onto oily surfaces, resulting in a significant reduction in the available friction due to contamination, slip potential was significantly increased.     

Available friction of ladder shoes and slip potential for climbing on a straight ladder

Straight ladder accidents are a major safety problem. As a leading cause of injuries involving straight ladders, slips at the ladder base occur when the required friction exceeds the available friction at the ladder shoe and floor interface. The objectives of this experiment were to measure the available friction at the base of a portable straight ladder in contact with a floor and to estimate the slip potential of the ladder. The results of friction measurements indicated that the measured friction coefficient on the oily surfaces differed among the six commercially available ladder shoes evaluated. A statistical model was used to compare the available friction results from the current study with the friction requirements under different climbing conditions from a previous study based on their stochastic distributions to estimate the slip potential at the base of the ladder. The results showed that different climbing conditions used in the previous study could be supported by available friction on dry surfaces. However, when the ladder was put onto oily surfaces, resulting in a significant reduction in the available friction due to contamination, slip potential was significantly increased.     

Predicting slips and falls considering required and available friction

This study investigated the relationship among measurements of friction, the biomechanics of gait, and actual slip and fall events. The goal was to develop a method for estimating the probability of slips and falls based on measurements of available friction and required friction. Five subjects wearing safety harnesses walked down a ramp at various angles with either a tile or carpeted surface under dry, wet or soapy conditions. Ramp angles of 0 degree, 10 degrees and 20 degrees were used to vary the shear and normal foot force requirements. The dynamic coefficient of friction (DCOF) of shoe, floor surface and contaminant interfaces was measured. Required friction was assessed by examining the foot forces during walking trials when no slips occurred. Slips with recoveries and slips resulting in falls were recorded and categorized using a force plate and high-speed video camera. These data were then incorporated into a logistic regression to model the probability of a slip or fall event occurring based on the difference between the COF required by the foot forces generated and the measured DCOF. The results showed that the number of slip and fall events increased as the difference between the required COF and the measured DCOF increased. The logistic regression model fit the data well, resulting in an estimate of the probability of a slip or fall event based on the difference between the measured and required friction. This type of model could be used in the future to evaluate slip resistance measurement devices under various environments and assist in the design of safer work environments.     

Prediction of slips: an evaluation of utilized coefficient of friction and available slip resistance

The purpose of this study was to investigate the relationship between measures of floor surface slip resistance and an individual's peak utilized coefficient of friction (COFU) on the probability of a slip occurring during level walking. Video, kinematic and ground reaction force data were recorded simultaneously as subjects walked at a self-selected speed during conditions of normal and reduced floor surface slip resistance. Peak COFU during weight acceptance was calculated and the available floor surface slip resistance was measured using the variable incidence tribometer (VIT). Separate logistic regression analyses identified that knowledge of the available slip resistance (as measured by the VIT) in combination with an individual's peak COFU allowed for greater accuracy in classifying slip outcomes (89.5%; p = 0.004), while knowledge of only the available slip resistance reduced the accuracy of categorization to 78.9% (p = 0.021).     

A comparison of different postures for scaffold end-frame disassembly

Overexertion and fall injuries comprise the largest category of nonfatal injuries among scaffold workers. This study was conducted to identify the most favourable scaffold end-frame disassembly techniques and evaluate the associated slip potential by measuring whole-body isometric strength capability and required coefficient of friction (RCOF) to reduce the incidence of injury. Forty-six male construction workers were used to study seven typical postures associated with scaffold end-frame disassembly. An analysis of variance (ANOVA) showed that the isometric forces (334.4-676.3 N) resulting from the seven postures were significantly different (p < 0.05). Three of the disassembly postures resulted in considerable biomechanical stress to workers. The symmetric front-lift method with hand locations at knuckle height would be the most favourable posture; at least 93% of the male construction worker population could handle the end frame with minimum overexertion risk. The static RCOF value resulting from this posture during the disassembly phase was less than 0.2, thus the likelihood of a slip should be low.     

Observation of the floor surface topography changes in pedestrian slip resistance measurements

This study is concerned with the changes of the floor surface topography in the early stage of repetitive wear rubbings and the relationships between slip resistance properties and operationally defined geometric characteristics of the floor surfaces. It was assumed that: (1) alterations in surface topography will be associated with changes in the DFC; and (2) wear process will be accompanied by changes in surface topography. For the analysis of initial characterization on the surface topography, specially prepared, dry and clean metal and perspex specimens were chosen. The surface profiles of the fresh and rubbed flooring specimens were recorded using a laser scanning confocal microscope. From the profile ordinate data read at 1 μm intervals, a number of surface roughness parameters – centre line average, root-mean-square roughness, maximum height, maximum mean peak height, maximum mean depth, and absolute average asperity slope were calculated using a computer program. The skew and the kurtosis of the statistical distribution of each surface profile were also computed. The results indicate that the asperity height and the maximum mean depth were significantly reduced after the friction tests. The average slope of asperities was the parameter that most highly correlated with the dynamic friction coefficient. The analyses also showed that the surface parameters underwent large variations initially, but subsequently these changes were less marked, which was explained by the transition from unsteady-state friction to steady-state friction. These results found that slip resistance properties between the shoes and the floor counterfaces were greatly influenced by the manner in which the geometry of the floor surface was modified. It was suggested that measurement of changes in the surface geometry provides additional information on the analysis of slip resistance and could usefully be reported with friction measurements.

Relevance to industry

Slipping and falling accidents are a major ergonomic and safety concern in the workplace and the general community. Prevention of slip hazard has focused on designing “slip resistant” footwear and floor surfaces. This study is primarily concerned with the understanding of friction and wear mechanisms from a tribological point of view. A tribological approach may provide additional useful information about slip resistance performance.     

A comparison of foot/ground interaction during stair negotiation and level walking in young and older women

Stair design and environmental conditions may play a role in slip accidents on stairs in the workplace, but little is known about the slip resistance requirements on stairs compared to level walking. Older adults have an increased risk of falling compared to younger adults and may be at greater risk during stair negotiation. The purpose of this study was to determine whether the ground reaction force profiles and peak required coefficient of friction (RCOF) differed between young and elderly women or between stair ascent, stair descent and overground walking. While there was a trend towards less risky stair descent behaviour in the older women in terms of their peak RCOF values during stair descent, the increased vertical loading rate in the older women may imply reduced dynamic balance control. The largest mean RCOF peaks occurred during stair ascent in both young and older women, but there were several overground walking trials in both groups and a few stair descent trials of the young women, which resulted in RCOF peaks greater than 0.5. These results should be considered when choosing stair surface materials, particularly in occupational and outdoor settings where the tread surfaces may become wet or contaminated.     

A comparison of foot/ground interaction during stair negotiation and level walking in young and older women

Stair design and environmental conditions may play a role in slip accidents on stairs in the workplace, but little is known about the slip resistance requirements on stairs compared to level walking. Older adults have an increased risk of falling compared to younger adults and may be at greater risk during stair negotiation. The purpose of this study was to determine whether the ground reaction force profiles and peak required coefficient of friction (RCOF) differed between young and elderly women or between stair ascent, stair descent and overground walking. While there was a trend towards less risky stair descent behaviour in the older women in terms of their peak RCOF values during stair descent, the increased vertical loading rate in the older women may imply reduced dynamic balance control. The largest mean RCOF peaks occurred during stair ascent in both young and older women, but there were several overground walking trials in both groups and a few stair descent trials of the young women, which resulted in RCOF peaks greater than 0.5. These results should be considered when choosing stair surface materials, particularly in occupational and outdoor settings where the tread surfaces may become wet or contaminated.     

Biomechanics of slips

The biomechanics of slips are an important component in the prevention of fall-related injuries. The purpose of this paper is to review the available literature on the biomechanics of gait relevant to slips. This knowledge can be used to develop slip resistance testing methodologies and to determine critical differences in human behaviour between slips leading to recovery and those resulting in falls. Ground reaction forces at the shoe-floor interface have been extensively studied and are probably the most critical biomechanical factor in slips. The ratio of the shear to normal foot forces generated during gait, known as the required coefficient of friction (RCOF) during normal locomotion on dry surfaces or ‘friction used/achievable’ during slips, has been one biomechanical variable most closely associated with the measured frictional properties of the shoe/floor interface (usually the coefficient of friction or COF). Other biomechanical factors that also play an important role are the kinematics of the foot at heel contact and human responses to slipping perturbations, often evident in the moments generated at the lower extremity joints and postural adaptations. In addition, it must be realized that the biomechanics are dependent upon the capabilities of the postural control system, the mental set of the individual, and the perception of the environment, particularly, the danger of slipping. The focus of this paper is to review what is known regarding the kinematics and kinetics of walking on surfaces under a variety of environmental conditions. Finally, we discuss future biomechanical research needs to help to improve walkway-friction measurements and safety.     

Biomechanics of slips.

The biomechanics of slips are an important component in the prevention of fall-related injuries. The purpose of this paper is to review the available literature on the biomechanics of gait relevant to slips. This knowledge can be used to develop slip resistance testing methodologies and to determine critical differences in human behaviour between slips leading to recovery and those resulting in falls. Ground reaction forces at the shoe-floor interface have been extensively studied and are probably the most critical biomechanical factor in slips. The ratio of the shear to normal foot forces generated during gait, known as the required coefficient of friction (RCOF) during normal locomotion on dry surfaces or 'friction used/achievable' during slips, has been one biomechanical variable most closely associated with the measured frictional properties of the shoe/floor interface (usually the coefficient of friction or COF). Other biomechanical factors that also play an important role are the kinematics of the foot at heel contact and human responses to slipping perturbations, often evident in the moments generated at the lower extremity joints and postural adaptations. In addition, it must be realized that the biomechanics are dependent upon the capabilities of the postural control system, the mental set of the individual, and the perception of the environment, particularly, the danger of slipping. The focus of this paper is to review what is known regarding the kinematics and kinetics of walking on surfaces under a variety of environmental conditions. Finally, we discuss future biomechanical research needs to help to improve walkway-friction measurements and safety.     

Prediction of slips: an evaluation of utilized coefficient of friction and available slip resistance

The purpose of this study was to investigate the relationship between measures of floor surface slip resistance and an individual's peak utilized coefficient of friction (COF_U) on the probability of a slip occurring during level walking. Video, kinematic and ground reaction force data were recorded simultaneously as subjects walked at a self-selected speed during conditions of normal and reduced floor surface slip resistance. Peak COF_U during weight acceptance was calculated and the available floor surface slip resistance was measured using the variable incidence tribometer (VIT). Separate logistic regression analyses identified that knowledge of the available slip resistance (as measured by the VIT) in combination with an individual's peak COF_U allowed for greater accuracy in classifying slip outcomes (89.5%; p = 0.004), while knowledge of only the available slip resistance reduced the accuracy of categorization to 78.9% (p = 0.021).     

Predicting slips based on the STM 603 whole-footwear tribometer under different coefficient of friction testing conditions

Assessing footwear slip-resistance is critical to preventing slip and fall accidents. The STM 603 (SATRA Technology) is commonly used to assess footwear friction but its ability to predict human slips while walking is unclear. This study assessed this apparatus’ ability to predict slips across footwear designs and to determine if modifying the test parameters alters predictions. The available coefficient of friction (ACOF) was measured with the device for nine different footwear designs using 12 testing conditions with varying vertical force, speed and shoe angle. The occurrence of slipping and the required coefficient of friction was quantified from human gait data including 124 exposures to liquid contaminants. ACOF values varied across the test conditions leading to different slip prediction models. Generally, a steeper shoe angle (13°) and higher vertical forces (400 or 500?N) modestly improved predictions of slipping. This study can potentially guide improvements in predictive test conditions for this device.

Practitioner Summary: Frictional measures by the STM603 (SATRA Technology) were able to predict human slips under liquid contaminant conditions. Test parameters did have an influence on the measurements. An increased shoe-floor testing angle resulted in better slip predictions than test methods specified in the ASTM F2913 standard.     

Cluster analysis—an alternative to statistical distributions for determining slotting schemes used in determining indirect work standards

This paper is a follow-up to a research effort by Enscore and Niebel [1] in which various statistical distributions (uniform, normal and gamma) were compared to determine their effectiveness in generating slotting schemes for indirect labor standards. Using the same data as the previous research, cluster analysis is evaluated for its effectiveness as a slotting method. A fourth statistical distribution is introduced as part of this research. It is the log-normal distribution. The determination of the slotting schemes for each method and the simulation used for evaluation of the methods is carried out on a VAX 11/780. Of the five slotting techniques tested, cluster analysis is clearly the best and the uniform distribution clearly the worst. The normal, gamma and log-normal distributions all performed well, with a slight edge going to the normal.     

Existence of an optimum dynamic coefficient of friction and the influence on human gait variability

The existence of a range of optimal coefficient of friction that encompasses safety and comfort has not been addressed before. This paper assesses the existence of such a range and its relationship with the variability of human gait. Six women walked for 15 min over five ceramic tile floorings with friction coefficients (DCOF) ranging from 0.19 to 0.63. Subjective opinions (pain, comfort, etc.) and biomechanical parameters including sagittal plane knee angle, tibia acceleration, and ground reaction forces were gathered. The required coefficient of friction (RCOF) was calculated from ground reaction forces. The results show that as DCOF increases so do reports of pain in the knees and under the metatarsal heads and toes; whereas a low DCOF relates to pain in the thighs and perception of low friction. RCOF showed a quadratic relationship with DCOF indicating the existence of a range of optimal coefficient of friction outside of which walking strategy is modified either to avoid slipping (DCOF < 0.25) or reduce pain (DCOF > 0.55). This result is supported by the results of the analysis of gait variability using non-linear methods. Floors inside the optimal range of friction yielded statistically significant higher entropy for tibia acceleration and knee angle, confirming the hypothesis that gait is more constrained outside that range (i.e. natural variability is reduced).Relevance to the industry: Floor friction is one of the main concerns for the floor industry and for decision makers when choosing public space paving (indoor and outdoor). The false concept ‘the more friction the better’ can induce manufacturers and technicians to make wrong decisions. This paper can assist the industry produce and select solutions encompassing safety and comfort.     

Effects of age-related gait changes on the biomechanics of slips and falls

A laboratory study was conducted to examine gait changes associated with aging and the effect of these changes on initiation of slips and frequency of falls utilizing newly defined biomechanical parameters of slips and falls. Twenty-eight participants from two age groups (young and old) walked around a circular track at a comfortable pace wearing a safety harness. A slippery floor surface was placed on the walking track over the force plate at random time intervals without the participants' awareness. Synchronized kinetic and kinematic measurements were obtained on both slippery and non-slippery walking surfaces. The results indicated that older participants' horizontal heel contact velocity was significantly faster, step length was significantly shorter, and transitional acceleration of the whole body centre-of-mass (COM) was significantly slower than younger participants. Older participants' initial friction demand, as measured by required coefficient of friction (RCOF), was not significantly different than their younger counterparts. Additionally, older participants slipped longer and faster, and fell more often than younger participants. A comparison of horizontal heel contact velocity for participants who fell with participants who did not fall indicated that, in general, fallers' horizontal heel contact velocity was faster than non-fallers. However, a comparison of RCOF for participants who fell with participants who did not fall suggested that RCOF was not a totally deterministic factor influencing actual fall events. These findings suggest that gait changes associated with aging (especially higher horizontal heel contact velocity and slower transition of the whole body COM) affect initiation of slip-induced falls.     

Effects of work experience on work methods during dynamic pushing and pulling

Pushing and pulling are potential risk factors for work-related low back disorders (WRLBDs). While several studies have evaluated differences in work methods related to work experience, such evidence for dynamic pushing and pulling is limited. Eight novices and eight experienced workers completed dynamic push/pull tasks using a cart weighted to 250% of individual body mass in two different configurations (preferred vs. elbow handle heights). Multiple measures [hand forces, torso kinematics and kinetics, and required coefficient of friction (RCOF)] were obtained to assess WRLBD and slip risks. Experienced workers generated higher medio-lateral hand forces, during both pulls and pushes, though with a more substantial difference during pushes (∼74%), and which involved the use of hand force components other than to move the cart in an anterior-posterior direction. Experienced workers also had lower peak torso kinematics in flexion/extension and lateral bending, and lower torso flexion/extension kinetics. The latter is suggestive of a lower risk for WRLBDs, though levels of exposures to WRLBD risk were low to moderate in both groups and were often relatively small and inconsistent across the task configurations. Group-level differences in RCOF were quite small, indicating a comparable slip risk between the two groups. Thus, it was considered inconclusive whether the work methods used by experienced workers during dynamic pushing and pulling are advantageous regarding WRLBD and slip risks.     

Effects of age-related gait changes on the biomechanics of slips and falls

A laboratory study was conducted to examine gait changes associated with aging and the effect of these changes on initiation of slips and frequency of falls utilizing newly defined biomechanical parameters of slips and falls. Twenty-eight participants from two age groups (young and old) walked around a circular track at a comfortable pace wearing a safety harness. A slippery floor surface was placed on the walking track over the force plate at random time intervals without the participants' awareness. Synchronized kinetic and kinematic measurements were obtained on both slippery and non-slippery walking surfaces. The results indicated that older participants' horizontal heel contact velocity was significantly faster, step length was significantly shorter, and transitional acceleration of the whole body centre-of-mass (COM) was significantly slower than younger participants. Older participants' initial friction demand, as measured by required coefficient of friction (RCOF), was not significantly different than their younger counterparts. Additionally, older participants slipped longer and faster, and fell more often than younger participants. A comparison of horizontal heel contact velocity for participants who fell with participants who did not fall indicated that, in general, fallers' horizontal heel contact velocity was faster than non-fallers. However, a comparison of RCOF for participants who fell with participants who did not fall suggested that RCOF was not a totally deterministic factor influencing actual fall events. These findings suggest that gait changes associated with aging (especially higher horizontal heel contact velocity and slower transition of the whole body COM) affect initiation of slip-induced falls.