Peter R Greene | BGKT Consulting Engineers Ltd. (original) (raw)
Papers by Peter R Greene
EC Ophthalmology Journ., 2023
A 3-element minimal complexity AC/DC equivalent circuit is shown to represent the time course of ... more A 3-element minimal complexity AC/DC equivalent circuit is shown to represent the time course of progressive myopia during the student's educational years, consisting of a Resistor R, Capacitor C, Battery Vo, and ON/OFF switch. This circuit is accurate over several decades of myopia progression, typically age 10 to age 30, accounting for the average accomodation diopter-hours (work load) from near point study, periodic increases in the strength of negative corrective lenses, individual subject's time-constant response to the near work demands, and active myopia-control techniques, using positive (+) Add reading glasses during study.
J. Ophthal. Path., 2021
A 4-element analog series circuit is developed to represent the time-course of progressive myopia... more A 4-element analog series circuit is developed to represent the time-course of progressive myopia development during the student's educational years, consisting of a Resistor R, Capacitor C, Battery Vo, and square wave oscillator V(t). This circuit is accurate over several decades of myopia progression (typically from age 10 to age 30) and can account for the accumulated diopter-hours (work load) of nearpoint study, yearly increases in the strength of negative corrective lenses, individual patient response to the nearwork demands on the visual system, and the positive effects of using reading glasses during study.
International ophthalmology, Jan 12, 2016
The objective herein is to provide refraction data, myopia progression rate, prevalence, and 1st ... more The objective herein is to provide refraction data, myopia progression rate, prevalence, and 1st and 2nd generation correlations, relevant to whether myopia is random or inherited. First- and second-generation ocular refraction data are assembled from N = 34 families, average of 2.8 children per family. From this group, data are available from N = 165 subjects. Inter-generation regressions are performed on all the data sets, including correlation coefficient r, and myopia prevalence [%]. Prevalence of myopia is [M] = 38.5 %. Prevalence of high myopes with |R| >6 D is [M-] = 20.5 %. Average refraction is <R> = -1.84 D ± 3.22 (N = 165). For the high myopes, |R| >6 D, prevalence for the parents is [M-] = 25 %, for the 2nd generation [M-] = 16.5 %. Average myopia level for the high myopes, both generations, is <S> = -7.52 D ± 1.31 D (N = 33). Regression parameters are calculated for all the data sets, yielding correlation coefficients in the range r = 0.48-0.72 for som...
Optometry Open Journal, 2016
The literature on intra-ocular pressure dynamics is reviewed, including tonometer design and cali... more The literature on intra-ocular pressure dynamics is reviewed, including tonometer design and calibration, the influence of corneal-scleral mechanics, and scleral rigidity factors. Drugs that influence the outflow facility of the trabecular meshwork (TM) are discussed. Transmural pressure drop across the lamina cribosa (LC) is an important parameter, in terms of quantifying potential glaucoma damage to the optic nerve.
Pub Med Sci Am, 2019
On a springy new indoor track at Harvard University runners can run faster than they can on stand... more On a springy new indoor track at Harvard University runners can run faster than they can on standard tracks. The design of the track was arrived at through a close analysis of the mechanics of human running.
New Frontiers Ophthalmology, Oatxt, 2017
Purpose: The purpose of this report is to develop analog electrical circuits, using resistors, ca... more Purpose: The purpose of this report is to develop analog electrical circuits, using resistors, capacitors, and constant current sources, which automatically calculate the stress and strain-rate response of viscoelastic biomaterials in response to arbitrary loading history, and to compare these with experimental strain-rate results from sclera subjected to constant and square-wave pressure loads. Methods: Electro-mechanical models of reversible and irreversible viscoelasticity are analyzed, using series and parallel combinations of springs and dashpots from the Kelvin-Voigt, Maxwell, and Jeffrey's viscoelastic models. Experiments include strain-rate response of the sclera, applicable to the development of axial myopia. Results: The resulting strain ε(t) versus time t is shown to vary exponentially for Kelvin-Voigt, as a linear step-ramp for Maxwell, and as a curved step-ramp for Jeffrey's materials, consistent with experimental observations from cornea and sclera, corresponding to output voltage at the analog circuit capacitor V(t) in response to a step change in applied load σ(t) from 0 to σ o and a step change in applied current from 0 to Io at time t = 0. The cornea and sclera are rate-sensitive viscoelastic materials which stretch up to 12% in response to constant or repetitive loads. This is equivalent to an accumulated-9.00 diopters of axial myopia. Conclusions: The resulting analog equivalent circuits can be used as general purpose analog computers, to calculate system strain-rate ε(t), in response to arbitrary applied stress loading σ(t), including ramps, steps, sinusoids, and square waves, with variable intermittency factor. Results are applicable to collagen, cornea, sclera.
Int'l J Adv Res Botany, 2019
SAE Intl Jour Aerospace Engr, 2020
Experimental design phase of a pilot study at Annapolis is described, using reading glasses, +1.5... more Experimental design phase of a pilot study at Annapolis is described, using reading glasses, +1.5 D. to +3.0 D. to alleviate college myopia. College students often become 1.0-2.0 diopters more myopic, so reading glasses were explored to partially cancel the effects of the study environment. N = 25 different sets of (+)Add lenses are evaluated, for required adjustment period and reading comfort. Three computer models are developed to predict refraction versus time. Basic control system equations predict exponential myopia shift of refractive state R(t). Linear, exponential and Gompertz computer results are compared calculating refraction R(t) during the college years, showing correlation coefficients |r| = 0.96-0.97, accurate ±0.31 D. over a 14 year interval. Typical college myopia rate is −0.3 to −0.4 D/yr. Reading glasses may be a simple, practical solution to stabilize college myopia.
Experimental design phase of a pilot study at Annapolis is described, using reading glasses, +1.5... more Experimental design phase of a pilot study at Annapolis is described, using reading glasses, +1.5 D. to +3.0 D. to alleviate college myopia. College students often become 1.0 to 2.0 diopters more myopic, so reading glasses were explored to partially cancel the effects of the study environment. N = 25 different sets of (+)Add lenses are evaluated, for required adjustment period and reading comfort. Three computer models are developed to predict refraction versus time. Basic control system equations predict exponential myopia shift of refractive state R(t) with time constant t0 = 100 days. Linear, exponential and Gompertz computer results are compared calculating refraction R(t) during the college years, showing correlation coefficients |r| = 0.96 to 0.97, accurate +/−0.31 D. over a 14 year interval. Typical college myopia rate is −0.3 to −0.4 D/yr. Reading glasses may be a simple, practical solution to stabilize college myopia.
Dark rearing has been shown to protect against the development of lid-suture myopia in monkeys an... more Dark rearing has been shown to protect against the development of lid-suture myopia in monkeys and tree shrews. Dark-reared monkeys and cats, with or without lid suture, are significantly hyperopic in comparison to light-reared controls. The time course of refractive change during dark rearing has only been systematically investigated in chicks, with hyperopia increasing from 14 to 42 days after hatching. Longitudinal refractions of dark-reared monkeys have not been reported previously. Five infant rhesus monkeys were dark reared with their mothers from the first day of life until 58 to 161 days of age. Cycloplegic retinoscopies were performed at 2-week intervals and were compared with cross-sectional data from 18 normal monkeys at ages 1 to 81 days. The normal monkeys typically had hyperopic refractions from +4 to +8 diopters at birth with an average refraction of +2.8 diopters between 30 and 81 days of age, compared with an average refraction of +5.3 diopters between 30 and 81 days of age for the monkeys raised in darkness (difference significant at P < 0.05). Three of the dark-reared animals retained an average of 7.0 diopters of hyperopia. Darkness thus slowed or interrupted the normal loss of hyperopia in three of the five experimental subjects, and may be useful for creating model hyperopic animals on the order of +5 to +8 diopters. Invest Ophthalmol Vis Sci 30:761-764,1989 Dark rearing has been used for control purposes in studies of visual development. The absence of visual experience in dark-reared animals has yielded interesting alterations in the ocular refractive state. In a study on vision development, three pigtail monkeys dark-reared from age 2 weeks to 6 months showed an average hyperopia of 5 diopters compared to one control animal showing mild myopia. 1 In a study on lid-suture myopia in two monkeys, dark rearing not only protected the monkeys from the development of lid-suture myopia, but also resulted in 2 diopters of hyperopia in both the control and lid-sutured eyes of both monkeys. 2 Dark rearing has also yielded hyper-opia in cats, both with and without lids sutured. 3
Background: Scaling laws for cylindrical column buckling are reviewed, applicable to the cardio-v... more Background: Scaling laws for cylindrical column buckling are reviewed, applicable to the cardio-vascular system arteries or veins of various thicknesses to diameter ratios.
Weeping Willow (Salix babylonica) growth rates are quantified in terms of tree height, trunk diam... more Weeping Willow (Salix babylonica) growth rates are quantified in terms of tree height, trunk diameter at base, leaf stem length, and root system expansion. Experimentally, these rates are found to be the same for the parent and replanted cutting-in other words, "like father, like son". Leaf stem growth is stimulated by gravity induced tensile stress, whereas root system growth is stimulated by compressive stress ahead of the root tip. These results may be applicable to the concept of mechanosensing. The aim of this study is regenerating the Salix babylonicae (Weeping Willow Trees) rapidly from branch cuttings. The results indicate that the success rate for replanting the entire willow tree is 75% [68% CI: 54% to 96% (N=4)]. The leaf stem and root system growth rates differ by a factor of 50 or more, but are observed to be the same, 16 ft/yr (5.0 m/yr) and 3.0 in/yr (6-7 cm/yr) respectively, both for the branch cutting, and the tree. The conclusion is that the the success rate of propagating branch cuttings, i.e. "branch rooting", is 25% [68% CI: 15% to 40% (N=8)], similar values are reported by others. This may require branch diameters from 0.6 cm to 1.6 cm.
A model of running is proposed in which the leg is represented as a rack-and-pinion element in se... more A model of running is proposed in which the leg is represented as a rack-and-pinion element in series with a damped spring. The rack-and-pinion element emphasizes the role of descending commands, while the damped spring represents the dynamic properties of muscles and the position and the rate sensitivity of reflexes. This model is used to predict separately the effect of track compliance on step length and ground contact time. The predictions are compared with experiments in which athletes ran over tracks of controlled spring stiffness. A sharp spike in foot force up to 5 times body weight was found on hard surfaces, but this spike disappeared as the athletes ran on soft experimental tracks. Both ground contact time and step length increased on very compliant surfaces, leading to moderately reduced running speeds, but a range of track stiffness was discovered which actually enhances speed. ISTRODCC-lION Running is essentially a series of collisions with the ground. As the animal strikes the surface, its muscles contract and ultimately reverse the downward velocity of the body. Intuition argues that a surface of suitably large compliance is bound to change running performance. Running on a diving springboard slows a man down considerably, while running on a trampoline is all but impossible. Our goal in this paper will be to find an analytic expression for the change in the runner's speed, step length and foot contact time as a function of the track stiffness, and to compare these predictions with experiment. The simplification that the muscles of locomotion and their reflexes act essentially as springs is lent support by recent developments in the study of neural motor control. Reflexes, however, require some time to act-anyone who has unexpectedly stepped off a curb will recall the sharp jolt which results when the antigravity muscles of the leg are not prepared for the impact. Melville Jones and Watt (1971) have shown that approximately 102 msec are required for reflex activity from the otolith apparatus to activate the antigravity muscles in man, so that unexpected falls of less than about 5.0cm are unaccompanied by reflex accommodation. Even the simple stretch reflex requires a substantial portion of the running step cycle. The latency of EMG changes associated with automatic responses to a change in limb load are found to be in the range of 79 msec for elbow flexion in man (Crag0 er al., 1976) and near 25 msec for soleus muscles in decerebrate cats (Nichols and Houk, 1976). Since the supported period in human running is typically IOOmsec, neither reflexes of vestibular nor stretch origin can beexpected to participate in the first quarter of the stance phase, and therefore the antigravity muscles of the leg must be principally under the l Receiced 17 July 1978. control ofcommand signals from higher motor centers during this time. In the later portion of the stance phase, however, the stretch reflex can be expected to make important modifications of the efferent activity of *-motorneurons. Houk (1976) has argued that muscle stiffness, rather than muscle length, is the property which is regulated by the stretch reflex. He points out that a competition between length-related excitation contributed by muscle spindle receptors and force-related inhibition contributed by Golgi tendon Fig. 1. Schematic representing the separate role of descending commands (rack-and-pinion) and muscle properties plus local reflexes (damped spring). The motion of the rack and pinion element determines the influence of track stiffness on step length. The runner's mass and the damped spring determine the influence of track stiffness on ground contact time. 893
EC Ophthalmology Journ., 2023
A 3-element minimal complexity AC/DC equivalent circuit is shown to represent the time course of ... more A 3-element minimal complexity AC/DC equivalent circuit is shown to represent the time course of progressive myopia during the student's educational years, consisting of a Resistor R, Capacitor C, Battery Vo, and ON/OFF switch. This circuit is accurate over several decades of myopia progression, typically age 10 to age 30, accounting for the average accomodation diopter-hours (work load) from near point study, periodic increases in the strength of negative corrective lenses, individual subject's time-constant response to the near work demands, and active myopia-control techniques, using positive (+) Add reading glasses during study.
J. Ophthal. Path., 2021
A 4-element analog series circuit is developed to represent the time-course of progressive myopia... more A 4-element analog series circuit is developed to represent the time-course of progressive myopia development during the student's educational years, consisting of a Resistor R, Capacitor C, Battery Vo, and square wave oscillator V(t). This circuit is accurate over several decades of myopia progression (typically from age 10 to age 30) and can account for the accumulated diopter-hours (work load) of nearpoint study, yearly increases in the strength of negative corrective lenses, individual patient response to the nearwork demands on the visual system, and the positive effects of using reading glasses during study.
International ophthalmology, Jan 12, 2016
The objective herein is to provide refraction data, myopia progression rate, prevalence, and 1st ... more The objective herein is to provide refraction data, myopia progression rate, prevalence, and 1st and 2nd generation correlations, relevant to whether myopia is random or inherited. First- and second-generation ocular refraction data are assembled from N = 34 families, average of 2.8 children per family. From this group, data are available from N = 165 subjects. Inter-generation regressions are performed on all the data sets, including correlation coefficient r, and myopia prevalence [%]. Prevalence of myopia is [M] = 38.5 %. Prevalence of high myopes with |R| >6 D is [M-] = 20.5 %. Average refraction is <R> = -1.84 D ± 3.22 (N = 165). For the high myopes, |R| >6 D, prevalence for the parents is [M-] = 25 %, for the 2nd generation [M-] = 16.5 %. Average myopia level for the high myopes, both generations, is <S> = -7.52 D ± 1.31 D (N = 33). Regression parameters are calculated for all the data sets, yielding correlation coefficients in the range r = 0.48-0.72 for som...
Optometry Open Journal, 2016
The literature on intra-ocular pressure dynamics is reviewed, including tonometer design and cali... more The literature on intra-ocular pressure dynamics is reviewed, including tonometer design and calibration, the influence of corneal-scleral mechanics, and scleral rigidity factors. Drugs that influence the outflow facility of the trabecular meshwork (TM) are discussed. Transmural pressure drop across the lamina cribosa (LC) is an important parameter, in terms of quantifying potential glaucoma damage to the optic nerve.
Pub Med Sci Am, 2019
On a springy new indoor track at Harvard University runners can run faster than they can on stand... more On a springy new indoor track at Harvard University runners can run faster than they can on standard tracks. The design of the track was arrived at through a close analysis of the mechanics of human running.
New Frontiers Ophthalmology, Oatxt, 2017
Purpose: The purpose of this report is to develop analog electrical circuits, using resistors, ca... more Purpose: The purpose of this report is to develop analog electrical circuits, using resistors, capacitors, and constant current sources, which automatically calculate the stress and strain-rate response of viscoelastic biomaterials in response to arbitrary loading history, and to compare these with experimental strain-rate results from sclera subjected to constant and square-wave pressure loads. Methods: Electro-mechanical models of reversible and irreversible viscoelasticity are analyzed, using series and parallel combinations of springs and dashpots from the Kelvin-Voigt, Maxwell, and Jeffrey's viscoelastic models. Experiments include strain-rate response of the sclera, applicable to the development of axial myopia. Results: The resulting strain ε(t) versus time t is shown to vary exponentially for Kelvin-Voigt, as a linear step-ramp for Maxwell, and as a curved step-ramp for Jeffrey's materials, consistent with experimental observations from cornea and sclera, corresponding to output voltage at the analog circuit capacitor V(t) in response to a step change in applied load σ(t) from 0 to σ o and a step change in applied current from 0 to Io at time t = 0. The cornea and sclera are rate-sensitive viscoelastic materials which stretch up to 12% in response to constant or repetitive loads. This is equivalent to an accumulated-9.00 diopters of axial myopia. Conclusions: The resulting analog equivalent circuits can be used as general purpose analog computers, to calculate system strain-rate ε(t), in response to arbitrary applied stress loading σ(t), including ramps, steps, sinusoids, and square waves, with variable intermittency factor. Results are applicable to collagen, cornea, sclera.
Int'l J Adv Res Botany, 2019
SAE Intl Jour Aerospace Engr, 2020
Experimental design phase of a pilot study at Annapolis is described, using reading glasses, +1.5... more Experimental design phase of a pilot study at Annapolis is described, using reading glasses, +1.5 D. to +3.0 D. to alleviate college myopia. College students often become 1.0-2.0 diopters more myopic, so reading glasses were explored to partially cancel the effects of the study environment. N = 25 different sets of (+)Add lenses are evaluated, for required adjustment period and reading comfort. Three computer models are developed to predict refraction versus time. Basic control system equations predict exponential myopia shift of refractive state R(t). Linear, exponential and Gompertz computer results are compared calculating refraction R(t) during the college years, showing correlation coefficients |r| = 0.96-0.97, accurate ±0.31 D. over a 14 year interval. Typical college myopia rate is −0.3 to −0.4 D/yr. Reading glasses may be a simple, practical solution to stabilize college myopia.
Experimental design phase of a pilot study at Annapolis is described, using reading glasses, +1.5... more Experimental design phase of a pilot study at Annapolis is described, using reading glasses, +1.5 D. to +3.0 D. to alleviate college myopia. College students often become 1.0 to 2.0 diopters more myopic, so reading glasses were explored to partially cancel the effects of the study environment. N = 25 different sets of (+)Add lenses are evaluated, for required adjustment period and reading comfort. Three computer models are developed to predict refraction versus time. Basic control system equations predict exponential myopia shift of refractive state R(t) with time constant t0 = 100 days. Linear, exponential and Gompertz computer results are compared calculating refraction R(t) during the college years, showing correlation coefficients |r| = 0.96 to 0.97, accurate +/−0.31 D. over a 14 year interval. Typical college myopia rate is −0.3 to −0.4 D/yr. Reading glasses may be a simple, practical solution to stabilize college myopia.
Dark rearing has been shown to protect against the development of lid-suture myopia in monkeys an... more Dark rearing has been shown to protect against the development of lid-suture myopia in monkeys and tree shrews. Dark-reared monkeys and cats, with or without lid suture, are significantly hyperopic in comparison to light-reared controls. The time course of refractive change during dark rearing has only been systematically investigated in chicks, with hyperopia increasing from 14 to 42 days after hatching. Longitudinal refractions of dark-reared monkeys have not been reported previously. Five infant rhesus monkeys were dark reared with their mothers from the first day of life until 58 to 161 days of age. Cycloplegic retinoscopies were performed at 2-week intervals and were compared with cross-sectional data from 18 normal monkeys at ages 1 to 81 days. The normal monkeys typically had hyperopic refractions from +4 to +8 diopters at birth with an average refraction of +2.8 diopters between 30 and 81 days of age, compared with an average refraction of +5.3 diopters between 30 and 81 days of age for the monkeys raised in darkness (difference significant at P < 0.05). Three of the dark-reared animals retained an average of 7.0 diopters of hyperopia. Darkness thus slowed or interrupted the normal loss of hyperopia in three of the five experimental subjects, and may be useful for creating model hyperopic animals on the order of +5 to +8 diopters. Invest Ophthalmol Vis Sci 30:761-764,1989 Dark rearing has been used for control purposes in studies of visual development. The absence of visual experience in dark-reared animals has yielded interesting alterations in the ocular refractive state. In a study on vision development, three pigtail monkeys dark-reared from age 2 weeks to 6 months showed an average hyperopia of 5 diopters compared to one control animal showing mild myopia. 1 In a study on lid-suture myopia in two monkeys, dark rearing not only protected the monkeys from the development of lid-suture myopia, but also resulted in 2 diopters of hyperopia in both the control and lid-sutured eyes of both monkeys. 2 Dark rearing has also yielded hyper-opia in cats, both with and without lids sutured. 3
Background: Scaling laws for cylindrical column buckling are reviewed, applicable to the cardio-v... more Background: Scaling laws for cylindrical column buckling are reviewed, applicable to the cardio-vascular system arteries or veins of various thicknesses to diameter ratios.
Weeping Willow (Salix babylonica) growth rates are quantified in terms of tree height, trunk diam... more Weeping Willow (Salix babylonica) growth rates are quantified in terms of tree height, trunk diameter at base, leaf stem length, and root system expansion. Experimentally, these rates are found to be the same for the parent and replanted cutting-in other words, "like father, like son". Leaf stem growth is stimulated by gravity induced tensile stress, whereas root system growth is stimulated by compressive stress ahead of the root tip. These results may be applicable to the concept of mechanosensing. The aim of this study is regenerating the Salix babylonicae (Weeping Willow Trees) rapidly from branch cuttings. The results indicate that the success rate for replanting the entire willow tree is 75% [68% CI: 54% to 96% (N=4)]. The leaf stem and root system growth rates differ by a factor of 50 or more, but are observed to be the same, 16 ft/yr (5.0 m/yr) and 3.0 in/yr (6-7 cm/yr) respectively, both for the branch cutting, and the tree. The conclusion is that the the success rate of propagating branch cuttings, i.e. "branch rooting", is 25% [68% CI: 15% to 40% (N=8)], similar values are reported by others. This may require branch diameters from 0.6 cm to 1.6 cm.
A model of running is proposed in which the leg is represented as a rack-and-pinion element in se... more A model of running is proposed in which the leg is represented as a rack-and-pinion element in series with a damped spring. The rack-and-pinion element emphasizes the role of descending commands, while the damped spring represents the dynamic properties of muscles and the position and the rate sensitivity of reflexes. This model is used to predict separately the effect of track compliance on step length and ground contact time. The predictions are compared with experiments in which athletes ran over tracks of controlled spring stiffness. A sharp spike in foot force up to 5 times body weight was found on hard surfaces, but this spike disappeared as the athletes ran on soft experimental tracks. Both ground contact time and step length increased on very compliant surfaces, leading to moderately reduced running speeds, but a range of track stiffness was discovered which actually enhances speed. ISTRODCC-lION Running is essentially a series of collisions with the ground. As the animal strikes the surface, its muscles contract and ultimately reverse the downward velocity of the body. Intuition argues that a surface of suitably large compliance is bound to change running performance. Running on a diving springboard slows a man down considerably, while running on a trampoline is all but impossible. Our goal in this paper will be to find an analytic expression for the change in the runner's speed, step length and foot contact time as a function of the track stiffness, and to compare these predictions with experiment. The simplification that the muscles of locomotion and their reflexes act essentially as springs is lent support by recent developments in the study of neural motor control. Reflexes, however, require some time to act-anyone who has unexpectedly stepped off a curb will recall the sharp jolt which results when the antigravity muscles of the leg are not prepared for the impact. Melville Jones and Watt (1971) have shown that approximately 102 msec are required for reflex activity from the otolith apparatus to activate the antigravity muscles in man, so that unexpected falls of less than about 5.0cm are unaccompanied by reflex accommodation. Even the simple stretch reflex requires a substantial portion of the running step cycle. The latency of EMG changes associated with automatic responses to a change in limb load are found to be in the range of 79 msec for elbow flexion in man (Crag0 er al., 1976) and near 25 msec for soleus muscles in decerebrate cats (Nichols and Houk, 1976). Since the supported period in human running is typically IOOmsec, neither reflexes of vestibular nor stretch origin can beexpected to participate in the first quarter of the stance phase, and therefore the antigravity muscles of the leg must be principally under the l Receiced 17 July 1978. control ofcommand signals from higher motor centers during this time. In the later portion of the stance phase, however, the stretch reflex can be expected to make important modifications of the efferent activity of *-motorneurons. Houk (1976) has argued that muscle stiffness, rather than muscle length, is the property which is regulated by the stretch reflex. He points out that a competition between length-related excitation contributed by muscle spindle receptors and force-related inhibition contributed by Golgi tendon Fig. 1. Schematic representing the separate role of descending commands (rack-and-pinion) and muscle properties plus local reflexes (damped spring). The motion of the rack and pinion element determines the influence of track stiffness on step length. The runner's mass and the damped spring determine the influence of track stiffness on ground contact time. 893