Longitudinal Bending Stiffness Research Articles

Effect of increased shoe longitudinal bending stiffness on ankle and foot biomechanics in jump-cut movements of low and high degrees

Lateral ankle sprains are the most common injuries in indoor and court sports, with ankle inversion being a primary injury driver. Stabilising the ankle during multidirectional changes is crucial for injury prevention. Conversely, increased shoe stiffness has been hypothesised to influence the magnitude of ankle inversion and may raise the risk for ankle injuries. Therefore, the purpose of this study was to investigate the influence of shoe longitudinal bending stiffness on ankle biomechanics during indoor and court sport-specific cutting movements. Biomechanical data from 19 participants were collected using a motion capture system and force plate. A jump-cut protocol with two different cutting directions after landing was performed in indoor shoes with and without carbon plate inserts of varying stiffness. Ankle kinematics and kinetics were analysed with statistical parametric mapping and repeated measures analysis of variance. A significant increase in ankle inversion during the 180° cut and a reduction in forefoot inversion (foot torsion) for stiffer footwear conditions during both the 45° and 180° cut were observed. While dorsiflexion moments differed during the last 10% of ground contact, ankle inversion moments did not significantly diverge between shoe conditions. Furthermore, a noteworthy correlation between footwear longitudinal bending stiffness and torsional stiffness was identified. In conclusion, increased bending stiffness significantly affected ankle and foot kinematics. The ankle compensated for restricted mobility and higher demands during high-degree jump-cuts, while foot torsion played a more prominent role in low-degree cuts. The heightened ankle inversion during high-degree cuts may induce an elevated risk for lateral ankle sprains. Further longitudinal studies are necessary to comprehensively understand injury incidence and the role of shoe stiffness in injury prevention.

Influence of Running Shoe Longitudinal Bending Stiffness on Running Economy and Performance in Trained and National Level Runners.

Previous results about shoe longitudinal bending stiffness (LBS) and running economy (RE) show high variability. This study aimed to assess the effects of shoes with increased LBS on RE and performance in trained and national runners. Twenty-eight male runners were divided into two groups according to their 10-km performance times (trained, 38-45 min and national runners, <34 min). Subjects ran 2 × 3 min (at 9 and 13 km·h -1 for trained, and 13 and 17 km·h -1 for national runners) with an experimental shoe with carbon fiber plate to increase the LBS (Increased LBS) and a control shoe (without carbon fiber plate). We measured energy cost of running (W·kg -1 ) and spatiotemporal parameters in visit one and participants performed a 3000 m time trial (TT) in two successive visits. Increased LBS improved RE in the trained group at slow (11.41 ± 0.93 W·kg -1 vs 11.86 ± 0.93 W·kg -1 ) and fast velocity (15.89 ± 1.24 W·kg -1 vs 16.39 ± 1.24 W·kg -1 ) and only at the fast velocity in the national group (20.35 ± 1.45 W·kg -1 vs 20.78 ± 1.18 W·kg -1 ). The improvements in RE were accompanied by different changes in biomechanical variables between groups. There were a similar improvement in the 3000 m TT test in Increased LBS for trained (639 ± 59 vs 644 ± 61 s in control shoes) and national runners (569 ± 21 vs 574 ± 21 s in control shoes) with more constant pace in increased LBS compared with control shoes in both groups. Increasing shoe LBS improved RE at slow and fast velocities in trained runners and only at fast velocity in national runners. However, the 3000 m TT test improved similarly in both levels of runners with increased LBS. The improvements in RE are accompanied by small modifications in running kinematics that could explain the difference between the different levels of runners.

Effects of longitudinal bending stiffness and midsole foam on running energetics and biomechanics

Effects of longitudinal bending stiffness and midsole foam on running energetics and biomechanics

Peak plantar pressures in running footwear with increased longitudinal bending stiffness

Peak plantar pressures in running footwear with increased longitudinal bending stiffness

Model test investigation on the longitudinal mechanical property of shield tunnels considering internal structure

Reasonable evaluation of longitudinal mechanical property of shield tunnel is critical to the design and maintenance of tunnel structures. Traditionally, the internal structure has not been involved in the existing studies on the longitudinal mechanical properties of shield tunnels, of which the effect on the longitudinal mechanical properties of shield tunnels remains unknown. In this study, a series of physical similar model tests were conducted on homogeneous model (HM), non-homogeneous model (NHM) and non-homogeneous model with internal structure (NHMI), the effect of internal structure and longitudinal force on the longitudinal mechanical properties of road-metro shield tunnels were investigated. The longitudinal strain, displacement, curvature, and circumferential joint deformation of the tunnels were analyzed in depth. The experimental results show that the internal structure can reduce the longitudinal deformation of shield tunnels greatly, and the maximum displacement of tunnels with internal structure can be reduced by 70.58 %, the curvature radius can be increased by 1.73 to 2.36 times, the dislocation of the circumferential joint can be reduced by up to 70.4 %, and the opening of the circumferential joint can be reduced by up to 67.37 %. The longitudinal bending stiffness efficiency of tunnels ranges from 0.66 to 0.86 after taking into account the effect of internal structures. Increasing the longitudinal force from 0 MPa to 0.3 MPa significantly improves the longitudinal bending stiffness efficiency of tunnels, after which increasing the longitudinal force has no significant effect on the longitudinal mechanical properties of the tunnel.

Evaluation of Longitudinal Equivalent Bending Stiffness of Shield Tunnel with Residual Jacking Force

Existing tunnels are often subject to longitudinal bending when undercrossing tunnelling. It is of significance to more accurately evaluate the longitudinal equivalent bending stiffness (LEBS) of the existing tunnel within the influential zone. A new analytical method is proposed for the LEBS of tunnel segmental lining joints with consideration of incorporating combined action of residual jacking force and bending moment. The solution can degenerate into a special case with no residual jacking force, which agrees well with other classical solutions and validates the model and solutions. Sensitivity analyses are carried out for the bending moment, tunnel geometry, tensile stiffness of bolts and concrete grade on the LEBS, and effective ratio of the LEBS considering residual jacking force. The LEBS and the effective ratio of LEBS increase nonlinearly as an S-curve with the residual jacking force and decrease with an increasing bending moment. The results show that the LEBS of the shield tunnel is variable stiffness, which exhibits a significant nonlinearity. The maximum increment of the LEBS reaches 80.3% as the ring width increases from 1 m to 2 m, and the LEBS of the shield tunnel increases by approximately 1.3 × 107 kN·m2 for every 4-bolt added. The influential order on the LEBS of shield tunnels is the tunnel diameter &gt; lining thickness &gt; bolts diameter &gt; ring width &gt; the number of bolts &gt; elastic modulus of bolts. When the effective ratio of LEBS is more than 0.85, it does not change with the ring width, lining thickness, tensile stiffness of bolts, and concrete grade. The response characteristics of the tunnel parameters on the LEBS, considering the residual jacking force, could provide a theoretical basis for the design and deformation control of shield tunnels when undercrossing tunnelling.

Analytical algorithm of longitudinal bending stiffness of shield tunnel considering longitudinal residual jacking force

Longitudinal bending stiffness is a fundamental parameter of shield tunnels, and its value directly affects the analysis of their longitudinal response. Existing studies have not considered the tensile stiffness of segment ring joints and longitudinal residual jacking force when determining the value of the longitudinal bending stiffness of an existing shield tunnel. Therefore, through theoretical analysis, this study considered the longitudinal bending deformation under an external load action as two parts, namely the longitudinal bending deformation of the homogeneous pipe and the longitudinal bending deformation induced by the opening of the segment ring joints. An analytical algorithm of the longitudinal bending stiffness of the shield tunnel was obtained, considering that this longitudinal bending stiffness was related to various factors such as the elastic modulus of the material of the segment ring, outer diameter of the shield tunnel, width of the segment ring, number of the segment ring joints and tensile stiffness of the connecting bolt. A scaled shield tunnel model that considered tensile stiffness of the segment ring joints and longitudinal residual jacking force was designed, and longitudinal bending stiffness tests of the model were conducted accordingly. The tests were designed to measure the longitudinal bending deformation and opening of the segment ring joints. The validation of the theoretical analysis result based on the test data demonstrates that the longitudinal residual jacking force could only reduce the longitudinal bending deformation and the opening of the segment ring joints at small loads, it had almost no effect under larger loads. The measured longitudinal bending stiffness of the shield tunnel model was generally consistent with that obtained using the theoretical algorithm. Thus, in the longitudinal response analysis of the shield tunnel, the effect of the longitudinal residual jacking force on the enhancement of the longitudinal bending stiffness need not be considered.

Increasing Shoe Longitudinal Bending Stiffness Is Not Beneficial to Reduce Energy Cost During Graded Running

Carbon plates have been used to increase running shoes' longitudinal bending stiffness (LBS), leading to reductions in the energy cost of level running (Cr). However, whether or not this is true during uphill (UH) running remains unknown. The aim of our study was to identify the effect of LBS on Cr during UH running. Twenty well-trained male runners participated in this study. Cr was determined using gas exchange during nine 4-minute bouts performed using 3 different LBS shoe conditions at 2.22 and 4.44m/s on level and 2.22m/s UH (gradient: + 15%) running. All variables were compared using 2-way analyses of variance (LBS × speed/grade effects). There was no significant effect of LBS (F = 2.04; P = .14, ηp2=.11) and no significant LBS × grade interaction (F = 0.31; P = .87, ηp2=.02). Results were characterized by a very large interindividual variability in response to LBS changes. The current study contributes to a growing body of literature reporting no effect of LBS on Cr during level and UH running. Yet, the very large interindividual differences in response to changes in LBS suggest that increasing shoe LBS may be beneficial for some runners.

Theoretical analysis on the deformation of existing tunnel caused by under-crossing of large-diameter slurry shield considering construction factors

With the expansion of underground space networks, new tunnels especially large-diameter shields under-crossing existing tunnels have been commonly practiced. To obtain a better understanding of the effect of large-diameter slurry shield under-crossing on the existing tunnel and provide a quick and effective tool for evaluating the deformation behaviors of the existing tunnel before construction, in this study a simplified analytical method is proposed. Based on the two-stage method, and considering the characteristics of construction factors such as additional thrust on the shield excavation face of the slurry shield machine, friction force of the shield shell, and grouting pressure of the shield tail, deformation of the existing tunnel caused by the crossing of the large-diameter slurry shield in saturated soil is calculated. The proposed method is verified with field measurement data from a case study. A parametric analysis is conducted to study the influence of typical factors on tunnel responses, including longitudinal bending stiffness, elastic modulus, clearance between two tunnels, and shield crossing angle. The parametric study indicates a significant influence of the crossing angle on maximum settlement and the influence range of settlement of the existing tunnel. Recommendations for safe values of shield crossing clearance are given. The proposed analytical solution can be used as a reference to predict the potential risk of new large-diameter slurry shield crossing on the existing tunnel in engineering practices.

Influence of Footwear Features on Oxygen Consumption and Running Economy: A Review

It has been reported that the new technology applied to current racing shoes has increased the performance of runners who use this kind of footwear. This improvement has been proven in the scientific literature in relation to oxygen consumption. Nevertheless, as it is a novel topic, there is a lack of knowledge about which specific features achieve a decrease in oxygen consumption during running. Thus, the purpose of this study was to determine the influence of the features of footwear, specifically the shoe mass, the cushioning system, the longitudinal bending stiffness and the comfort feeling on running economy. This review was carried out from the bibliographic search in the main databases such as PubMed, Cochrane Plus and Medline and considering the PRISMA statement as a reference so that an analysis of the results has been obtained together with the methodological quality and risk of bias of the studies. Nineteen articles met the inclusion criteria, which presented a moderate/high methodological quality, and an analysis of their results was carried out. Footwear features such as the shoe mass, the cushioning system and the longitudinal bending stiffness produce advantages compared to other footwear that does not include this technology. Due to the lack of evidence, the influence of comfort feeling on oxygen consumption has not been proved.

Running Velocity and Longitudinal Bending Stiffness Influence the Asymmetry of Kinematic Variables of the Lower Limb Joints.

Running-related limb asymmetries suggest specific sports injuries and recovery circumstances. It is debatable if running speed affected asymmetry, and more research is required to determine how longitudinal bending stiffness (LBS) affected asymmetry. The purpose of this study was to investigate the influence of running velocity and LBS on kinematic characteristics of the hip, knee, ankle, metatarsophalangeal joint (MTP) and the corresponding asymmetry. Kinematic (200 Hz) running stance phase data were collected bilaterally for 16 healthy male recreational runners (age: 23.13 ± 1.17, height: 175.2 ± 1.6 cm, body mass: 75.7 ± 3.6 kg, BMI: 24.7 ± 1.3 kg/m2) running on a force plate at three different velocities (10, 12 and 14 km/h) and three increasing-LBS shoes in a randomized order. The symmetry angle (SA) was calculated to quantify gait asymmetry magnitude at each running velocity and LBS. Changes in running velocity and LBS led to differences in kinematic variables between the hip, knee, ankle and MTP (p &lt; 0.05). Significant changes in SA caused by running velocity were found in the knee flexion angle (p = 0.001) and flexion angle peak velocity (p &lt; 0.001), ankle plantarflexion angle (p = 0.001) and plantarflexion angle peak velocity (p = 0.043) and MTP dorsiflexion angle (p = 0.001) and dorsiflexion angle peak velocity (p = 0.019). A significant change in the SA caused by LBS was found in the MTP dorsiflexion peak angle velocity (p = 0.014). There were interaction effects between running velocity and LBS on the MTP plantarflexion angle (p = 0.033) and plantarflexion angle peak velocity (p = 0.038). These findings indicate the existence of bilateral lower limb asymmetry. Meanwhile, it was proved that running velocity and LBS can influence the asymmetry of lower limb joints. Additionally, there was an interaction between running velocity and LBS on the asymmetry of the lower limb. These findings can provide some information for sports injuries, such as metatarsal stress fractures and anterior cruciate ligament injuries. They can also provide some useful information for running velocities and running shoes.

Individual physiological responses to changes in shoe bending stiffness: a cluster analysis study on 96 runners.

Shoe longitudinal bending stiffness is known to influence running economy (RE). Recent studies showed divergent results ranging from 3% deterioration to 3% improvement in RE when bending stiffness increases. The variability of these results highlights inter-individual differences. Thus, our purpose was to study the runner-specific metabolic responses to changes in shoe bending stiffness. After assessing their maximal oxygen consumption ([Formula: see text] max) and aerobic speed (MAS) during a first visit, 96 heterogeneous runners performed two treadmill 5min runs at 75% [Formula: see text] max with two different prototypes of shoes on a second day. Prototypes differed only by their forefoot bending stiffness (17N/mm vs. 10.4N/mm). RE and stride kinematics were recorded during each trial. A clustering analysis was computed by comparing the measured RE and the technical measurement error of our gas exchange analyzer to identify functional groups of runners, i.e., responding similarly to footwear interventions. ANOVAs were then computed on biomechanical and morphological variables to compare the functional groups. Considering the whole sample (n = 96), there was no significant difference in RE between the two conditions. Cluster 1 (n = 29) improves RE in the stiffest condition (2.7 ± 2.1%). Cluster 2 (n = 26) impairs RE in the stiffest condition (2.7 ± 1.3%). Cluster 3 (n = 41) demonstrated no change in RE (0.28 ± 0.65%). Cluster 1 demonstrated 1.7km·h-1 greater MAS compared to cluster 2 (p = 0.014). The present study highlights that the effect of shoe bending stiffness on RE is runner-specific. High-level runners took advantage of increased bending stiffness, whereas medium-level runners did not. Finally, this study emphasizes the importance of individual response examination to understand the effect of footwear on runner's performance.

The Implications of Sports Biomechanics Studies on the Research and Development of Running Shoes: A Systematic Review.

Although various sports footwear demonstrated marked changes in running biomechanical variables, few studies have yielded definitive findings on the underlying mechanisms of shoe constructions affecting running-related performance and injuries. Therefore, this study focused on examining the effect of basic shoe constructions on running biomechanics and assessing the current state of sports shoe production in terms of injury and efficiency. Relevant literature was searched on five databases using Boolean logic operation and then screened by eligibility criteria. A total of 1260 related articles were retrieved in this review, and 41 articles that met the requirements were finally included, mainly covering the influence of midsole, longitudinal bending stiffness, heel-toe drop, shoe mass, heel flare, and heel stabilizer on running-related performance and injuries. The results of this review study were: (1) The functional positioning of running shoe design and the target groups tend to influence running performance and injury risk; (2) Thickness of 15–20 mm, hardness of Asker C50-C55 of the midsole, the design of the medial or lateral heel flares of 15°, the curved carbon plate, and the 3D printed heel cup may be beneficial to optimize performance and reduce running-related injuries; (3) The update of research and development concepts in sports biomechanics may further contribute to the development of running shoes; (4) Footwear design and optimization should also consider the influences of runners’ strike patterns.

The Influence of Footwear Longitudinal Bending Stiffness on Running Economy and Biomechanics in Older Runners

ABSTRACTPurpose: This study assessed the effects of footwear longitudinal bending stiffness on running economy and biomechanics of rearfoot striking older runners. Methods: Nine runners over 60 years of age completed two running bouts at their preferred running pace in each of three footwear conditions: low (4.4 ± 1.8 N·m-1), moderate (5.7 ± 1.7 N·m-1), and high (6.4 ± 1.6 N·m-1) bending stiffness. Testing order was randomized and a mirror protocol was used (i.e., A,B,C,C,B,A). Expired gases, lower limb kinematics, and ground reaction forces were collected simultaneously and lower limb joint kinetics, running economy (i.e., VO2), leg stiffness, and spatio-temporal variables were calculated. Results: Running economy was not different among stiffness conditions (p = 0.60, p = 0.53 [mass adjusted]). Greater footwear stiffness reduced step length (p = 0.046) and increased peak vertical ground reaction force (p = 0.019) but did not change peak ankle plantarflexor torque (p = 0.65), peak positive ankle power (p = 0.48), ankle positive work (p = 0.86), propulsive force (p = 0.081), and leg stiffness (p = 0.46). Moderate footwear stiffness yielded greater peak negative knee power compared to low (p = 0.04) and high (p = 0.03) stiffness. Conclusions: These novel findings demonstrate that increasing footwear longitudinal bending stiffness using flat carbon fiber inserts does not improve running economy and generally does not alter lower limb joint mechanics of rearfoot strike runners over 60 years. Future studies should investigate how other footwear characteristics (e.g., midsole material, plate location, and sole curvature) influence economy and biomechanics in this population.

Energy Storage And Return From Footwear And Biological Structures While Running

Energy Storage and Return from Footwear and Biological Structures While Running Extraordinary performances have been achieved by runners using advanced footwear. Previous research has found energetically favorable changes in biological joint kinetics while running in such footwear. However, there is limited research that also quantifies footwear kinetics during running. PURPOSE: To compare energy storage and return from footwear and biological structures while running in shoes of varying constructions. METHODS: Fifteen male runners ran in a motion analysis lab while kinematics and ground reaction forces were collected. Three footwear conditions of varying construction were evaluated (Shoe A, B, C). Shoe A had the greatest midsole compliance and longitudinal bending stiffness. Hip, knee, and ankle joint powers were computed using inverse dynamics to evaluate the mechanical work at biological joints. Distal rearfoot power was computed to evaluate the net mechanical work from the biological foot and footwear structures (Foot + Footwear). Kruskal-Wallis and Wilcoxon signed-rank tests were used for between footwear comparisons. RESULTS: Negative Foot + Footwear work (energy storage) was significantly greater in Shoe A (0.29 ± 0.07 J/kg) than Shoe B (0.21 ± 0.06 J/kg, p < 0.001), but not Shoe C (0.26 ± 0.08 J/kg, p = 0.055). Positive Foot + Footwear work (energy return) was significantly greater in Shoe A (0.30 ± 0.09 J/kg) than both other shoes (Shoe B: 0.19 ± 0.08 J/kg, p = 0.001; Shoe C: 0.15 ± 0.07 J/kg, p < 0.001). Positive ankle work was significantly lower in Shoe A (0.61 ± 0.08 J/kg) than both other shoes (Shoe B: 0.68 ± 0.09 J/kg, p < 0.001; Shoe C: 0.67 ± 0.06 J/kg, p = 0.003). Hip and knee work were not significantly different between shoe conditions (p > 0.05). CONCLUSION: Understanding how advanced footwear stores and returns energy during running may explain the reduction in work required by biological structures and resulting increased performance. Supported by Li-Ning.

Effects of footwear with different longitudinal bending stiffness on biomechanical characteristics and muscular mechanics of lower limbs in adolescent runners.

Background: Running shoes with carbon plates have been identified to have positive effects on improving running performance from a biomechanical perspective. However, the specific difference between the effects of carbon plates with different longitudinal bending stiffness (LBS)on biomechanical characteristics and muscular mechanics of lower limbs in adolescent runners remains unclear. This study aimed to identify the difference in biomechanical characteristics and muscular mechanics in lower limbs during running stance phases between wearing shoes with low longitudinal bending stiffness (Llbs) and high longitudinal bending stiffness (Hlbs) carbon plates in adolescent runners. Methods: 10 male adolescent runners with a habit of daily running exercise (age: 13.5 ± 0.6 years; height: 166.3 ± 1.9 cm; bodyweight: 50.8 ± 3.1 kg; foot length: 25.4 ± 0.2 cm) were recruited and asked to conduct two times of tests by wearing shoes with Llbs and Hlbs carbon plates in a randomized order. Paired t-test and statistical parametric mapping (SPM) analysis were used to identify the difference in biomechanical characteristics and muscular mechanics in lower limbs during running stance phases. Result: Under the condition of wearing shoes with Hlbs, the time of foot contact significantly increased, whereas the range of motion (ROM) of hip and metatarsophalangeal (MTP) in the sagittal plane significantly reduced as well as the peak moment of ankle joint in the sagittal plane. The activations of vastus medialis, vastus lateralis, flexor digitorum brevis (flex dig brevis), and flexor hallucis longus (flex hall long) significantly increased under the condition of wearing shoes with Hlbs. According to the results of the SPM analysis, the joint angles (hip, ankle, and MTP), the net joint moments (knee, ankle, and MTP), and the muscle forces (gluteus maximus and tibialis anterior) were significant difference during the running stance phase between conditions of wearing shoes with Hlbs and Llbs. Conclusion: Running shoes with Llb carbon plates are appropriate for adolescent runners due to the advantages of biomechanical characteristics and muscular mechanics.

An enhanced analytical model for predicting the nonlinear longitudinal equivalent bending stiffness of shield tunnels incorporating combined N-M actions

The longitudinal equivalent bending stiffness (LEBS) is a key parameter of the longitudinal equivalent continuous model (LECM) of shield tunnels. When the incorporating combined actions of axial force and bending moment, i.e., N-M actions, is considered, the LEBS exhibits a significant nonlinearity. In this study, to reflect the actual action range of the circumferential joint and the coupling effect generated by the transverse and longitudinal performance of the shield tunnel, the impact factor of circumferential joint (λ) and the impact factor of transverse bending stiffness of the segmental lining (ψ) are introduced, and an enhanced analytical model for calculating the LBSE is proposed. Four types of longitudinal bending deformation modes of the shield tunnel are divided based on the contact state of circumferential joint and the corresponding neutral axis position. The LEBS of each mode is derived based on the strict elliptical integrals, and the load condition conditions to distinguish the different deformation modes are expressed. Then the performance of the proposed model is verified via the calibrated FEM model, available model tests, and other analytical models. Next, the influences of λ and ψ on the robustness of the proposed model are analyzed. Results show that there is a significant influence of ψ on the LBSE, especially the load combination is compression-bending, and λ also affects the LBSE significantly if λ ≤ 1.

Rapid fiber alignment quantification in direct write printing of short fiber reinforced composites

Short fiber reinforced polymer composites fabricated by direct ink writing (DW) have design flexibility, low cost, and tailored property advantages over traditional composite materials. Controlling fiber alignment in these composite systems can be used to design unique materials with direction-dependent properties, especially when coupled to topology optimization for light weighting and high strength. . This study focuses on controlling fiber alignment in short carbon fiber composites with two printing parameters common in DW systems: nozzle diameter and velocity ratio. To do so, a novel rapid fiber alignment analysis (RFAA) was developed to quickly collect large amounts of fiber alignment data. Compared to the conventional fiber alignment quantification technique, X-Ray CT, RFAA is a rapid, accurate, and low-cost alternative. It was determined that fiber alignment can be enhanced by printing with smaller nozzle diameters and higher velocity ratios. Longitudinal bending stiffness and bending strength improved as the fiber alignment increased. Composites printed with low fiber alignment exhibited isotropic mechanical properties. However, aligning the fibers in the composite resulted in direction-dependent properties with significantly enhanced modulus and strength in the alignment direction.

Can We Quantify the Benefits of “Super Spikes” in Track Running?

The recent and rapid developments in track spike innovation have been followed by a wave of record-breaking times and top performances. This has led many to question what role “super spikes” play in improving running performance. To date, the specific contributions of new innovations in footwear, including lightweight, resilient, and compliant midsole foam, altered geometry, and increased longitudinal bending stiffness, to track running performance are unknown. Based on current literature, we speculate about what advantages these features provide. Importantly, the effects of super spikes will vary based on several factors including the event (e.g., 100 m vs. 10,000 m) and the characteristics of the athlete wearing them. Further confounding our understanding of super spikes is the difficulty of testing them. Unlike marathon shoes, testing track spikes comes with a unique challenge of quantifying the metabolic energy demands of middle-distance running events, which are partly anaerobic. Quantifying the exact benefits from super spikes is difficult and we may need to rely on comparison of track performances pre- and post- the introduction of super spikes.

Algorithm for an Effective Ratio of the Transverse Bending Rigidity Based on the Segment Joint Bending Stiffness

An algorithm for calculating the effective ratio of the transverse bending rigidity is established based on the segment longitudinal joint bending stiffness. With the knowledge of this effective ratio, the bending rigidity of a modified uniform rigidity ring is fully defined. To verify this developed algorithm, the effective ratios and convergence deformations of the modified uniform rigidity rings obtained with different methods are compared. Moreover, the responses of the modified uniform rigidity ring model under loading obtained from this algorithm are compared to those obtained with the existing generally accepted beam-spring model. The results show that although the bending moments obtained from these two models are different, the axial forces, horizontal convergent deformations, and vertical convergent deformations are quite consistent with each other. The modified uniform rigidity ring model built on the developed effective ratio algorithm is applicable for the analysis of the tunnel convergence deformation and the interaction between the tunnel structure and the ground during operation. This modified uniform rigidity ring model is simpler and easier to use than the beam-spring model; thus, the significance of the developed algorithm for the effective ratio of the transverse bending rigidity is demonstrated.