Eighty-eight participants (45 female, 43 male; 43.4 ± 12.3 years old; 80.1 ± 16.9 kg; 170.9 ± 9.2 cm) were enrolled in the study based upon an a priori power analysis completed for the broader study (logistic regression that assumed an odds ratio of 3 for 1 standard deviation shift in the regressor; α = 0.008; β = 0.2; average slip rate of 0.5). Participants were eligible if they were 18–65 years, climbed ladders at least 10 times in the previous year, weighed under 136 kg (due to harness system restrictions), had a height of less than 196 cm (due to ceiling restrictions), had a BMI under 35, and were generally healthy. Ethical approval was obtained from the University of Pittsburgh Institutional Review Board (Study 19100204) and all participants provided informed consent. This research was performed in accordance with the Declaration of Helsinki of 1975.

This study used a custom instrumented ladder apparatus which could rotate to three discrete angles and had interchangeable rungs (Fig. 1). The third rung (chosen to ensure steady-state climbing) of the ladder was rigidly attached to a force plate (AMTI Inc., Watertown, MA, USA; 1080 Hz) to collect kinetic data at the shoe-rung interface, while 12 motion tracking cameras (Vicon Motion System Ltd., Centennial, CO, USA: 120 Hz), positioned around the ladder apparatus, collected time-synced kinematic data. A set of seventy-nine reflective markers (Moyer, 2006) were secured to anatomical landmarks. This anatomical marker set, required to capture full-body kinematics for the broader study, included five foot markers relevant to the foot kinematics investigated here: a medial heel marker (inferior to the medial malleolus), a lateral heel marker (inferior to the lateral malleolus), an inferior heel marker (inferior on the posterior of the calcaneus), a medial toe marker (distal end of the hallux), and a lateral toe marker (distal end of the 4th phalange). Participants were outfitted with tight fitting athletic wear, helmet, shin guards, knee pads, elbow pads, gloves, shoes (Vans Authentic Wide Shoe, Cost Mesa, CA), and a safety harness attached to a fall arrest system (Self Retracting Lanyard, Ropes Park Equipment, Fairfield, CT, USA). Participant height and weight were recorded at the beginning of testing with and without all the worn equipment.

Participants climbed a series of ladder configurations consisting of eight unique rung designs and three angles (Fig. 2). The order of configurations was randomized for each participant to ensure that a range of ladder rungs and ladder angles were encountered in the slippery condition. Three climbing trials were completed in each configuration. Participants were instructed to climb up the ladder urgently, stopping at the 5th rung, and then descend the ladder. Climbing speed was not constrained, to ensure the generalizability of this work across physical ability levels. During the last configuration, participants climbed the ladder a fourth time, for their final trial, in which a liquid contaminant (90 % glycerol +10 % water by volume) was added to the third rung. Participants completed a word puzzle task to distract them from contaminant application and ensure the slip was unexpected. Some participants (n = 46) completed this task on the fifth rung of the ladder and the contaminant was applied prior to their ladder descent. The remaining participants (n = 42) completed this task on the ground while facing away from the ladder allowing for contaminant application prior to their ladder ascent. To increase the slipping rate, 59 participants climbed a ladder with plexiglass plates installed in front of the rung to limit toe clearance (Pliner, 2020; Pliner et al., 2014). The lights were dimmed to prevent subjects from noticing the contaminant.

Perturbation trials were included in the analysis if the participant was unaware of the contaminant prior to their climb. For participants who had the contaminant applied prior to their ladder ascent, the descending perturbation trial was also included if the participant did not notice the contaminant after the ascending climb and did not have a slip during the ascent (Albert et al., 2017; Iraqi and Beschorner, 2017; Iraqi et al., 2018).

A local coordinate system was defined for the foot using four anatomical markers. An x vector pointed to the right with an origin defined as the midway point between the medial and lateral heel markers. A z vector, perpendicular to a plane formed by the x vector and an anterior vector pointing from the midpoint of the heel markers to the midpoint of the front foot markers, pointed superiorly. A y vector, orthogonal to the x vector and z vector, pointed anteriorly. (Fig. 3a). The foot position while standing in a static reference orientation was used to define a neutral (0°) position for the shoe plane in the global system. The foot center was calculated as the average position of the medial and lateral heel markers and the two front foot markers (Fig. 3a). This local coordinate system and foot center were used to define slipping speed, normal force, shear force, shoe-rung angle, transverse foot angle, foot position, and slip distance. These variables (except slip distance) were quantified at the start of the slip and the time of peak slipping speed (Fig. 4). Slipping speed was the resultant velocity of the foot center along the shoe-rung plane (defined by the shoe angle). Peak slipping speed was the maximum resultant speed of the foot center during contact. Local minima around the peak slipping speed defined the start and end of slip. Slipping speed (resultant velocity), anterior posterior (AP) velocity, and medial–lateral (ML) velocity were reported. Normal force was the force component perpendicular to the sole (z-axis, Fig. 3) in the local foot coordinate system. Shear force was the resultant of the force components within the plane of the foot (x and y-axis, Fig. 3). Shoe-rung angle was calculated as the angle, between the long axis of the foot and the rung surface in the sagittal plane where 0°corresponds to the foot being perpendicular to the ladder plane (Fig. 3b). Transverse foot angle was calculated as the angle between the foot and the rung in the transverse plane, with 0°corresponding to the foot being perpendicular to the ladder rung, and a positive value indicating that the toe is rotated laterally from this orientation (Fig. 3a). AP foot position was quantified as a percentage of foot length based on the rung position relative to the foot, where 0 % corresponds to contact at the medial toe marker and 100 % corresponds to contact at the posterior heel marker. ML foot position was quantified as the point along the rung where shoe contact was made, where 0 % corresponds to the foot center being at the leftmost point of the rung and 100 % corresponds to the foot center being at the rightmost point of the rung. Slip distance was the displacement of the foot center between the start of slip and the end of slip, defined as the local minima in resultant velocity just after peak slipping speed.

Slips were classified using a k-means cluster analysis that grouped the trials based on the peak slipping speed and slip distance (Beschorner et al., 2016; Chambers and Cham, 2007; Jones et al., 2018; Moyer et al., 2006). Both parameters were transformed into z-score distributions to prevent variable scales from influencing the clustering. This analysis minimizes the sum of distances between data points and cluster centroids with the algorithm iterating through groupings until this minimization is complete. The Davies-Bouldin Index and the Silhouette score were used to determine the optimal number of groups for this classification. The Davies-Bouldin index determines how well clusters are separated in a model and the Silhouette determines how well-defined clusters are based upon inter-cluster distances and intra-cluster distances. Two reviewers, with an inter-rater reliability of 93 %, observed each slip trial classified by the cluster analysis to confirm each classification or remove it from the slip group if it was found to be incorrectly classified. The cluster analysis and reviewer observations provided both objective and subjective classification methods that increased confidence in the final slip classifications. Mean values and 95 % confidence intervals were calculated for all metrics (slipping speed, shoe-rung angle, transverse foot angle, normal force, shear force, AP foot position, and ML foot position) at the time of slip start and peak slipping speed.

The Davies-Bouldin Index (0.31) and the Silhouette score (0.90) returned an optimal grouping of four clusters based on slip distance and peak slipping speed (Fig. 5). The k-means cluster analysis minimized the total sum of distances to 21.2 over three iterations. Group A consisted of low peak slipping speed values (0.09 ± 0.04 m/s) and low slip distance values (1.54 ± 1.21 % of foot length). Group B consisted of higher peak slipping speed values (0.31 ± 0.08 m/s) and higher displacements (9.56 ± 2.72 % of foot length). Groups C and D each contained one individual point, both of which had high peak slipping speeds (0.61 & 1.00 m/s) and slip displacement (22.77 & 37.74 % of foot length). As Groups C and D each only had a single point and were characterized by more severe slipping (higher speed and larger distance), these two clusters were combined with Group B. These grouped points (B, C, & D) were classified as slips, resulting in a total of 15 slip events (Fig. 5). Group A was classified as non-slips, resulting in a total of 87 non-slip trials (Fig. 6). Of the 15 slips identified by the cluster analysis, 4 were removed following the reviewer analysis, resulting in 11 slips.

Of the eleven slip trials, nine were forward slips and two were backward slips. Due to the low number of backward slips, kinematic and kinetic averages and confidence intervals were only calculated from the nine forward slips. Forward slips primarily occurred in early stance with a mean slip time that was 11.5 ± 15.2 % into stance. Forward slips had a mean slipping speed of 0.05 m/s at slip start and 0.34 m/s at the peak slipping speed (Table 1). The mean AP component was 0.33 ± 0.08 m/s and the mean ML component was −0.02 ± 0.08 m/s, indicating that slips were primarily in the AP direction. The average total slip displacement was 28.1 ± 4.6 mm. Forward slips had mean shoe-rung angles of 7.6 ± 7.6° at the start of slip and 7.0 ± 4.5° at peak slipping speed, resulting in slightly dorsiflexed foot orientations for both time points. Normal forces were around half of bodyweight for both time points, with means of 38.3 ± 34.8 % BW (288.9 ± 240.8 N) at the start of slip and 58.6 ± 24.6 % BW (460.1 ± 224.5 N) at peak slipping speed. The remaining kinematic and kinetic metric means and confidence intervals can be found in Table 1. The two backward slips had lower peak sliding speeds (0.20 m/s & 0.29 m/s), lower slip displacements (17.9 mm & 17.5 mm), and more dorsiflexed shoe-rung angles (21.4° & 20.6°) compared to the forward slip averages.

One limitation of this study is the low number of slip events. This primarily limits comparisons between slipping direction because there were only 2 backward and 9 forward slips. Another limitation is the use of a single liquid contaminant and shoe design, limiting the generalizability of these results to other shoes and contaminants (Chander et al., 2017; Jones et al., 2018). Finally, the laboratory setting may have caused participants to climb differently than they would in typical outdoor settings, which may have impacted their climbing kinematics/kinetics.