The effects of leg prosthesis stiffness and take-off board stiffness on long jump performance

Abstract

Run-up velocity and take-off step technique influence long jump performance. We determined run-up velocity and jump distance of two athletes with transtibial amputation (TTA) who used a manufacturer-recommended stiffness running-specific prosthesis (RSP; 39.5 kN/m), and a less (36.0 kN/m) and more stiff RSP (43.9 kN/m) and eight non-amputee athletes who used a regulation run-up surface with a regulation (1630 kN/m), and two compliant (84.0 and 90.0 kN/m) take-off platforms. Athletes with TTA had no significant difference in maximum run-up velocity or jump distance between RSP stiffnesses, but jump distance was positively associated with run-up velocity (p = 0.002). Non-amputee athletes had no significant difference in maximum run-up velocity between take-off platforms but jump distance increased as platform stiffness decreased (p = 6.07 × 10⁻⁵) and as maximum run-up velocity increased (p = 0.001). Non-amputee athletes jumped 7% farther when they used the most compliant compared to regulation take-off platform and had the same run up velocity (p = 0.82) but jumped 16% further (p = 0.01) than athletes with TTA using the recommended stiffness RSP despite the RSP storing 45% more elastic energy than the most compliant take-off platform (p = 6.73 × 10⁻⁴). These results suggest take-off platform stiffness affects long jump performance in non-amputees.

Introduction

In the sport of long jump, an athlete’s horizontal run-up velocity and take-off step technique are the main determinants of jump distance^1,2. Maximum horizontal run-up velocity is strongly correlated with jump distance^2,3 and primarily determined by an athlete’s ability to produce large vertical ground reaction forces (vGRF)^4–6. Horizontal running velocity is the product of stride frequency and stride length, where a stride is comprised of two steps, and a step is the period of ground contact and subsequent aerial time of a single leg⁷. Step frequency (f_step) is the number of steps taken per second, and step length equals the forward distance traveled by the body’s center of mass, relative to the ground, during each step. At a given velocity, step length can be expressed as the product of the stance-average vGRF normalized to body weight (vGRF_avg) and contact length (L_c), which is the product of contact time and forward velocity. Thus, running velocity equals the product of f_step, vGRF_avg, and L_c and faster horizontal velocity is primarily realized by generating large vGRF_avg⁷. In the sport of long jump, the maximum horizontal velocity attained during the run-up is redirected during the jump take-off step to increase vertical velocity while losing as little horizontal velocity as possible^1,3,4,8. Thus, an optimal take-off technique is one where an athlete generates large vGRF_avg to increase vertical velocity and minimizes horizontal braking GRF to retain horizontal velocity^8–11.

Changes in horizontal and vertical velocity during the long jump take-off step result from muscle force generation and the storage and return of elastic energy within the take-off leg. In the long jump, the leg acts as a spring in series with the take-off surface, where the reciprocal of total system stiffness (k_total) equals the sum of the reciprocal of leg (k_leg) and surface (k_surf) stiffness. Leg stiffness, defined as the ratio of peak vGRF to leg spring displacement, affects elastic energy return, which affects the force produced by the leg. Humans adjust leg stiffness to accommodate different surface stiffnesses and retain total system stiffness primarily by adjusting the range of motion at the knee¹² As surface stiffness decreases, the stance leg resists compression through decreases in knee flexion, when compared to stiffer surfaces^12,13. Thus, a less stiff surface would presumably result in a stiffer leg, which could reduce the force required by the leg and allow a more efficient take-off technique. Further, Coward and Halsey (2014) showed that when athletes performed a broad jump for horizontal distance from a compliant (k_surf = 22.7 N/m) versus a stiff surface (k_surf = 881 N/m), their vertical take-off velocity increased significantly, and they jumped a greater horizontal distance¹⁴. Thus, decreasing surface stiffness and increasing the elastic energy storage and return of the take-off surface could improve long jump performance^9,15,16.

Competitive long jump athletes with a transtibial amputation (TTA) use a running-specific prosthesis (RSP) to enable running and jumping, where previous studies have shown that these athletes achieve slower horizontal run-up velocities but elicit better take-off step technique when they use their affected leg as their take-off leg than non-amputee long jump athletes who jump the same distance^10,17,18. An RSP acts in-series with the residual limb of an athlete with a TTA and functions mechanically as a passive-elastic spring. An RSP includes a socket that is typically made of carbon fiber and attaches to and surrounds an athlete’s residual limb. Unlike a biological lower limb, an RSP does not have an articulating ankle and has a fixed stiffness that is prescribed by the manufacturer using arbitrary numerical stiffness categories based on an athlete’s body mass and activity level¹⁹. RSP stiffness dictates affected leg stiffness in athletes with a TTA across a range of running velocities²⁰. Further, though previous studies have shown that RSP stiffness has no significant effect on maximum sprinting velocity²¹, athletes with a TTA using a recommended stiffness category RSP elicit 9% lower vGRF_avg in their affected leg than their unaffected leg across a range of velocities, which likely limits their maximum horizontal velocity compared to non-amputees⁷. Moreover, long jump athletes with a TTA have 7.6% slower maximum horizontal velocity but similar jump distances than non-amputee long jump athletes¹⁰. Previous research has found that athletes with a TTA are able to jump the same distance as non-amputees by increasing vertical velocity by a similar magnitude while losing 45% less horizontal velocity during the take-off step¹⁰. It has been previously reported that long jump athletes with a TTA exhibit a reduced knee range of motion in the take-off leg during the take-off step, indicating that a stiffer leg may enable the RSP to function more effectively as a springboard compared to athletes using a biological limb²². This unique take-off step technique is likely related to the use of the affected leg as the take-off leg and to the elastic energy storage and return of the RSP.

The stiffness of an RSP likely affects take-off technique in athletes with a TTA due to differences in elastic energy storage and return within an RSP²³. The magnitude of RSP energy storage and return during ground contact is inversely related to the in-series stiffness of the RSP (k_RSP), such that use of a less stiff RSP results in longer ground contact time and greater deformation of the RSP for a given force than a stiffer RSP²⁴. Greater elastic energy return from an RSP may result in more efficient conversion of negative to positive mechanical work performed on the athlete’s center of mass and thus less horizontal velocity loss during the take-off step in athletes with a TTA compared to non-amputee athletes¹⁰. Further, while previous studies have found k_RSP to have no significant effect on maximum running velocity²¹, decreasing the in-series stiffness of an RSP could affect long jump take-off step technique and potentially increase jump distance in athletes with a TTA by allowing them to lose less horizontal velocity^25–27. Further, decreasing the in-series stiffness of a long jump take-off platform could affect long jump take-off step technique and potentially increase jump distance in non-amputee athletes by allowing them to lose less horizontal velocity.

Previous studies found that athletes with a TTA who use their affected leg as their take-off leg have slower run-up velocity and an improved take-off step technique, yet jump the same distance compared to non-amputees¹⁰. Improvements in take-off technique are likely due to elastic energy storage and return from the in-series RSP. To discern how in-series stiffness affects long jump performance, we measured the maximum jump distance of athletes with a TTA using an RSP with different stiffness categories and of non-amputee athletes using a regulation run-up surface and different take-off platform surface stiffness (k_surf). We hypothesized that use of an RSP one category less-stiff than manufacturer-recommended (− 1 Cat) would have no effect on maximum run-up velocity but increase jump distance due to increased elastic energy storage of the RSP compared to the manufacturer-recommended stiffness category (Rec Cat) and an RSP one category more stiff than recommended (+ 1 Cat) in athletes with a TTA. We also hypothesized that jumping from a less stiff take-off platform would not affect run-up velocity but increase jump distance due to increased elastic energy storage and return of the surface, compared to a regulation track surface in non-amputee long jump athletes.

Results

Athletes with TTA

We constructed linear mixed-effects models to determine the effect of RSP stiffness on maximum run-up velocity, and the effect of RSP stiffness, elastic energy storage within the RSP, and maximum run-up velocity on jump distance in athletes with a TTA. We found no statistically significant effect of RSP stiffness on maximum run-up velocity when athletes with a TTA used the − 1 Cat compared to the Rec Cat RSP (p = 0.16; Table 1) or the − 1 Cat compared to the + 1 Cat RSP (p = 0.21; Table 1). Additionally, we found faster maximum run-up velocity was significantly associated with increased jump distance, such that athletes with a TTA increased jump distance by 0.55 m for every 1.00 m/s increase in run-up velocity (B = 0.55 m; p = 0.002; Fig. 1a). We also found no significant effect of RSP stiffness on jump distance when athletes with a TTA used the − 1 Cat versus the Rec Cat RSP (p = 0.08), nor when they used the -1 Cat versus the + 1 Cat RSP (p = 0.31). We found use of the − 1 Cat RSP resulted in significantly more elastic energy storage within the RSP during the take-off step than the Rec Cat (B = 12.45 J; p = 8.65 × 10⁻¹¹) and the + 1 Cat (B = 19.22 J; p = 6.66 × 10⁻¹³) RSP, but elastic energy storage within the RSP had no significant effect on jump distance (p = 0.55; Fig. 1b).

Table 1.

Average [SE] jump distance, maximum (Max.) run-up velocity, displacement, and elastic energy storage within the running-specific prosthesis (RSP) or take-off platform for athletes with a transtibial amputation (TTA) using an RSP stiffness category (Cat) that was recommended (Rec) and one Cat less stiff (− 1 Cat) and more stiff (+ 1 Cat) than Rec and for non-amputee athletes using each of the take-off platform stiffnesses, respectively.

	Athletes with a TTA			Non-amputee athletes
RSP or take-off platform stiffness (kN/m)	37.0 (− 1 Cat)	39.0 (Rec Cat)	41.0 (+ 1 Cat)	84.0	90.0	1630.0
Jump distance (m)	5.20 [0.16]	5.26 [0.20]	5.25 [0.34]	5.95 [0.16]	6.07 [0.11]	5.68 [0.11]
Max. run-up velocity (m/s)	8.66 [0.19]	8.34 [0.31]	8.46 [0.29]	8.60 [0.12]	8.57 [0.09]	8.52 [0.09]
Displacement (m)	0.111 [0.003]	0.105 [0.003]	0.103 [0.003]	0.055 [0.002]	0.050 [0.002]	0.002 [0.001]
Elastic energy storage of the RSP or take-off platform (J)	225.47 [13.79]	213.02 [12.75]	206.17 [14.81]	129.55 [10.76]	116.87 [7.62]	4.20 [0.23]

Figure 1.

(a) Box and whisker plot of long jump distance (m) when two athletes with a transtibial amputation (TTA) used a running-specific prosthesis (RSP) stiffness category (Cat) that was recommended (Rec—triangles) and one Cat less stiff (− 1 Cat—circles) and one Cat stiffer (+ 1 Cat—diamonds) than Rec. Both athletes used their affected leg as their take-off leg. Colored symbols represent subject-specific data from up to three maximum effort jumps per Cat, with the median per category shown as a horizontal black line. The median is derived using the lower and upper quartile values. The maximum and minimum values are displayed with vertical lines (“whiskers”) connecting the points to the center box. Data points lying outside of the whiskers represent outliers. Subject-specific data points may obscure whiskers and are offset for clarity. (b) Jump Distance (m) versus maximum run-up velocity (m/s) and elastic energy storage within the RSP (J) when two athletes with TTA used a − 1 Cat, Rec Cat, and + 1 Cat RSP. Colored symbols represent subject-specific data from up to three maximum effort jumps per Cat. The black line represents the model’s overall predictions from maximum run-up velocity (p = 0.002; R = 0.88; Jump Distance [m] = 0.61 *velocity [m/s]).

Non-amputee athletes

We constructed ANOVAs to test for the effect of take-off platform surface stiffness (k_surf) on maximum run-up velocity, and linear mixed effects models to test the effect of maximum run-up velocity, k_surf, and elastic energy storage within the take-off platform on jump distance in non-amputee athletes. We found no statistically significant difference in maximum run-up velocity attained when athletes jumped from take-off platforms with different stiffnesses (p = 0.56; Table 1). We found that faster maximum run-up velocity was significantly associated with increased jump distance such that non-amputee athletes increased jump distance by 0.80 m, on average, for every 1.00 m/s increase in run-up velocity (B = 0.78 m; p = 0.001; Fig. 2a). We also found non-amputee athletes significantly increased jump distance with decreased k_surf (B = 1.93 × 10⁻⁴ m; p = 6.07 × 10⁻⁵; Fig. 2b). We found elastic energy storage within the take-off platform increased with lower k_surf (B = 0.08; p < 0.001; Fig. 2b), but elastic energy storage within the take-off platform had no significant effect on jump distance in non-amputee athletes (p = 0.14; Fig. 3).

Figure 2.

(a) Jump distance (m) versus maximum run-up velocity (m/s) when eight non-amputee athletes jumped from take-off platforms with stiffness values (k_surf) of 84.0 kN/m (circles), 90.0 kN/m (triangles), and 1630 kN/m (regulation—diamonds). Colored symbols represent subject-specific data from up to three maximum effort jumps per k_surf. The solid black line represents the model’s overall predictions (p = 0.02; R = 0.85; Jump Distance [m] = 0.69*velocity [m/s]). (b) Box and whisker plot of jump distance (m) of eight non-amputee athletes for up to three maximum effort jumps from 84.0 kN/m, 90.0 kN/m, and 1630 kN/m take-off platforms. Colored symbols represent subject-specific data from up to three maximum effort jumps per k_surf, with group median shown as a horizontal black line. The median is derived using the lower and upper quartile values. The maximum and minimum values are displayed with vertical lines (“whiskers”) connecting the points to the center box. Data points outside of the whiskers represent outliers. Subject-specific data points may obscure whiskers and are offset for clarity.

Figure 3.

Jump distance (m) versus elastic energy storage (U) within the take-off platform (J) when eight non-amputee athletes jumped from take-off platforms with stiffness values (k_surf) of 84.0 kN/m (circles), 90.0 kN/m (triangles), and 1630 kN/m (regulation—diamonds). Colored symbols represent subject-specific data from up to three maximum effort jumps per k_surf. The black line represents the model’s overall predictions across elastic energy storage values (p = 5.54 × 10⁻⁸; R = 0.58; Jump Distance [m] = 0.003*U [J]).

Athletes with and without TTA

We used the non-parametric Wilcoxon rank sum test to compare jump distance, maximum run-up velocity, and elastic energy storage within the RSP or take-off platform in athletes with a TTA using the Rec Cat RSP and non-amputee athletes using the regulation track surface (1630 kN/m). We found no significant difference in maximum run-up velocity between athletes with a TTA and non-amputee athletes (8.34 m/s and 8.52 m/s, respectively; p = 0.90). Additionally, we found no significant difference in jump distance between athletes with a TTA and non-amputee athletes (5.26 m and 5.67 m, respectively; p = 0.10). However, we found that the Rec Cat RSP stored 98.0% more elastic energy than the regulation track surface (213 J and 4.20 J, respectively; Table 1; p = 1.88 × 10⁻⁴).

We then used the non-parametric Wilcoxon rank sum test to compare jump distance, maximum run-up velocity, and elastic energy storage within the RSP or take-off platform in athletes with a TTA using the Rec Cat RSP and non-amputee athletes using the 90.0 kN/m take-off platform, respectively, as these conditions resulted in the longest average jump distances. We found no significant difference in maximum run-up velocity between athletes with a TTA and non-amputee athletes (8.34 m/s and 8.57 m/s, respectively; p = 0.66; Table 1). We found that athletes with a TTA had 15.6% shorter jump distances than non-amputee athletes (5.26 m and 6.07 m, respectively; p = 0.01; Table 1), and that the Rec Cat RSP stored 45.1% more elastic energy than the 90.0 kN/m take-off platform (213 J and 117 J, respectively; p = 6.73 × 10⁻⁴; Table 1).

Discussion

We determined how use of an RSP with different stiffness affects long jump distance in athletes with a TTA. When athletes with a TTA used an RSP one category more or less stiff than recommended and at the recommended category, we found no significant effect on maximum horizontal run-up velocity or jump distance, which partially supports our first hypothesis. These findings are consistent with a previous study that found that use of an RSP one category more or less stiff than recommended and at the recommended category did not affect maximum sprinting velocity in athletes with a TTA²¹. We found that the RSP that was one category less stiff than recommended stored a greater amount of elastic energy than the RSP that was one category stiffer than recommended. However, longer jump distance was significantly associated with faster maximum run-up velocity in athletes with a TTA, rather than with elastic energy storage within the RSP. This finding does not support our hypothesis. Our results are in alignment with numerous previous studies of athletes with and without a TTA that have found and associations between increased jump distance and faster maximum run-up velocity^1,3,18.

In support of our second hypothesis, we found that jump distance was associated with maximum run-up velocity and take-off platform stiffness in non-amputee athletes. Specifically, we found that jump distance increased by 0.80 m for every 1 m/s increase in maximum horizontal run-up velocity, regardless of the take-off platform stiffness. This result is in line with previous studies that found horizontal run-up velocity to be the strongest determinant of jump distance in non-amputee athletes^1,2,28. Additionally, we found that for a given maximum horizontal run-up velocity, lower take-off platform stiffness was associated with greater jump distance in non-amputee athletes (Fig. 2a). Previous studies have shown that ~ 60% of the mechanical energy stored within the leg is returned during the take-off step in non-amputee athletes on a regulation track surface¹⁰. Thus, a more compliant take-off platform, and greater elastic energy storage within the take-off platform could minimize horizontal velocity loss and enhance long jump performance in non-amputee athletes²⁹. Overall, our results suggest that take-off platform stiffness affects jump distance in non-amputee athletes. Further, elastic energy return within the RSP or take-off platform during the second half of the take-off step likely improves take-off technique by decreasing horizontal velocity loss in athletes with and without a TTA, respectively.

Previous studies have reported that athletes with a TTA have 7.6% slower maximum horizontal velocity compared to non-amputee athletes^10,30. However, athletes with a TTA compensate by using a more effective take-off step technique. This allows them to jump comparable distances by storing and returning more elastic energy within their RSP than is possible in the biological leg of non-amputee athletes^10,24. Increased elastic energy return of take-off leg has been hypothesized to result in a more efficient conversion of negative to positive mechanical work performed on the athlete’s center of mass and thus less horizontal velocity loss during the take-off step⁹. We found that for every 1 kN/m increase in k_RSP, elastic energy storage within the RSP decreased by 5.6 J during the take-off step for athletes with a TTA. Whereas for every 1 kN/m increase in k_surf, elastic energy storage within the compliant take-off platforms decreased by 2.35 J during the take-off step for non-amputees. The elastic energy stored within the RSP is in line with values reported for the long jump take-off step in athletes with a TTA¹⁰ and the elastic energy stored within the platforms is in line with values reported for non-amputee athletes running on surfaces of different stiffness^31,32.

Despite greater elastic energy storage within the RSP and maximum run-up velocities that were not significantly different, the distance jumped by athletes with a TTA was not significantly different when they used the − 1 Cat compared to the + 1 Cat RSP. Further, though the elastic energy storage of the regulation track surface was 98% less than that of a Rec Cat RSP, non-amputee athletes attained maximum run-up velocities and jump distances that were not significantly different than those of athletes with a TTA using the Rec Cat RSP. Thus, it is likely that non-amputee athletes adjust leg stiffness in response to the stiffness of the take-off surface to optimize elastic energy storage and return within the take-off leg. In contrast, the stiffness of the take-off leg in athletes with a TTA is dictated and fixed by RSP stiffness, when athletes with a TTA use their affected-leg as their take-off leg to jump²⁰. In non-amputee athletes, our results suggest that decreasing the stiffness of the take-off platform significantly improves jump distance, regardless of maximum run-up velocity, by increasing elastic energy storage and return within the surface.

Our study had some potential limitations. The sample size of two athletes with a TTA limited our statistical power. Additional research is needed to determine if RSP stiffness that is one category stiffer and less stiff than recommended affects long jump performance in a larger sample size or with a larger range of RSP stiffnesses. Moreover, faster horizontal run-up velocity may relate with greater vertical velocity gain and less horizontal velocity loss during the take-off step through greater elastic energy storage and return within the take-off leg^3,33, where it is predicted that maximum jump distance is achieved with high stance-average vertical ground reaction forces and low take-off leg stiffness during the take-off step⁴. We measured the energy storage within the RSP or surface but could not determine the elastic energy storage and return in the leg or the ground reaction forces and center of mass velocity during the take-off step, which may explain the differences in performance between athletes with and without a TTA. Future studies are warranted to determine the overall elastic energy storage and return and ground reaction forces when using different in-series stiffness RSPs or take-off platforms. Further, elements of an athlete’s take-off technique, such as take-off angle (vertical-to-horizontal velocity ratio), knee angle at touchdown, and leg angle (the horizontal distance between the center of mass and the foot at touchdown), and positioning of the swing leg, influence overall jump distance, which we could not calculate in this study and may explain the lack of significant differences between RSP conditions in athletes with a TTA^3,34–36. Vertical displacement of the take-off board during the take-off step was measured using a high-speed camera, placed perpendicular to it, which may have introduced parallax at the lateral borders of the video. However, the take-off board was placed within the center of the field of view of the camera, thus any parallax that may have been present should not have meaningfully affected the vertical displacement measurement. Despite randomizing the trial order and using a repeated measured design, the accommodation time provided to athletes may have been too short. This limited accommodation period may have attenuated performance, potentially contributing to non-significant differences between conditions and jump distances that did not fully reflect participants’ maximal jumping capacity. Further, although participants were instructed to perform maximal-effort jumps, voluntary performance may have been subconsciously modulated in response to participating in a research study rather than competing, which may have limited the jump distance achieved. Future studies that allow athletes to train with each RSP or take-off platform stiffness are needed to determine if greater accommodation time can affect long jump performance. For non-amputee athletes, we designed the take-off platform to constrain the springs to compress vertically. However, the platform surface was not evenly compressed and thus there was energy loss that we could not account for in the calculations of elastic energy storage in the platform. Further, the elastic energy storage within the leg affects running and jumping^9,37. Future studies are needed that quantify the overall stiffness of the leg and in-series RSP or platform stiffness during the long jump take-off step.

Overall, the current study provides novel insight on the effect that maximum run-up velocity and elastic energy storage during the take-off step have on jump distance in athletes with and without a TTA. Further, the current findings may prove useful for researchers, RSP manufacturers prosthetists, athletes, and decision makers in the field of competitive sports. We found that maximum run-up velocity was not significantly different between athletes with and without a TTA. We found that despite changing elastic energy storage within the RSP, use of an RSP at the recommended stiffness and at one category more or less stiff than recommended did not significantly affect long jump distance in athletes with a TTA. We also found that increasing the elastic energy stored within a take-off platform improved jump distance in non-amputee athletes, suggesting coaches might adjust take-off step technique to more closely mirror that of athletes with a TTA to potentially reduce the loss of horizontal velocity at touchdown. This could include utilizing a more extended leg at touchdown^22,30, and increasing hip strength to increase sagittal plane motion during jump take-off, though further studies are needed to support these adjustments. Ultimately, it is important to note we found no significant difference in maximum run-up velocity or jump distance when athletes with a TTA used their manufacturer-recommended stiffness category RSP and non-amputee athletes used a regulation track surface for the take-off step This was observed despite significantly more elastic energy stored within the RSP. These results suggest that though the energy storage capacities of RSPs used by athletes with a TTA exceed the energy storage capacities within the regulation track surface for non-amputees, use of a carbon-fiber RSP does not allow long jump athletes with a TTA to jump further than non-amputee long jump athletes. Therefore, future technical regulations regarding inclusion of Paralympic and Olympic athletes should consider the overall ability of the athlete to utilize technology for long jump competition.

Methods

Participants

Two elite long jump athletes with a unilateral transtibial amputation (2 M; Class T44) and eight National Collegiate Athletic Association (NCAA) Division 1 long jump athletes (4 M, 4 F) without an amputation gave informed written consent and participated. Athletes with an amputation were competitive at an international level and had competed in the Paralympic Games (Table 2). Non-amputees were competitive collegiate athletes (Table 2). Participants reported no musculoskeletal injury, or cardiovascular, pulmonary, or neurological disease or disorder beyond a TTA. The University of Colorado Boulder Institutional Review Board approved this protocol (IRB 16-0106). All research was performed in accordance with relevant guidelines and regulations.

Table 2.

Average [SD] age, mass including the manufacturer-recommended stiffness category prosthesis, standing height, and long jump distance personal record (PR) for athletes with a transtibial amputation (TTA) and non-amputee athletes.

	Age (years)	Body mass (kg)	Standing height (m)	Long jump distance PR (m)
Athletes with a TTA	34.7 [6.4]	73.6 [8.2]	1.77 [0.02]	6.89 [0.89]
Non-Amputee Athletes	21.3 [1.9]	71.4 [9.9]	1.79 [0.11]	6.20 [0.80]

Experimental protocol

Athletes participated in a 3-day protocol using the long jump runway and sand pit within an indoor track. Each athlete completed the protocol within a 2-week time-period. Athletes with a TTA completed the protocol following the completion the World Para Athletics Championships. Non-amputee athletes completed the protocol immediately following the completion of their Fall competition season. On each day, each athlete performed their own typical competition warm-up and then was asked to complete 2–3 maximum effort jumps using an RSP with one of three different stiffness categories or a take-off platform with one of three different stiffnesses. All athletes were thus aware of the RSP or take-off platform stiffness prior to the maximum effort jumps. All athletes were allowed to utilize their personal competition take-off run-up distance, which complied with NCAA rules and regulations for non-amputee athletes, and Paralympic rules and regulations for athletes with a TTA. All athletes performed up to six attempts per condition. The three longest jump distances were used for analysis. Between each maximum effort jump, athletes were given a minimum of 3 min rest. Athletes jumped using only one RSP stiffness category or take-off platform stiffness per day to avoid any potential effects of fatigue and minimize the risk of injury.

Athletes with a TTA completed maximum effort jumps along a regulation surface runway and take-off platform using an RSP with the manufacturer recommended stiffness category (Rec Cat) based on their body mass and a high activity level, and one category less stiff (− 1 Cat) and stiffer (+ 1 Cat) than the Rec Cat RSP. Prior to the warm-up and maximum effort jumps, each RSP was aligned by a certified prosthetist to match the height and alignment typically used by each athlete. Both athletes with a TTA used the same Rec Cat of the Cheetah® Xtend RSP with a Nike spike plate (Össur, Reykjavik, Iceland). To attach each RSP to an athlete’s prosthetic socket, we constructed a custom aluminum bracket²⁰ that allowed us to preserve the RSP, secure it to the back of the prosthetic socket, and alter height and/or alignment between athletes. The order of RSP stiffness was randomized for athletes with a TTA. Non-amputee athletes completed maximum effort jumps along a regulation surface runway with three different take-off platform stiffnesses (k_surf) using their own track spikes. One platform was a regulation mondo-covered track surface, and the two other platforms were custom-built and less stiff than the regulation surface. The order of platform stiffnesses was randomized across data collection days, but not between athletes. Changing take-off platform stiffness required full reconstruction for each stiffness condition. Thus, all non-amputee athletes were tested on the same stiffness condition each day. We measured and analyzed up to three successful jumps per athlete and deemed a jump as successful according to athletics regulations³⁸.

Set-up/materials

We calculated RSP stiffness values in kN/m (k_RSP) using the mean peak vertical ground reaction force (GRF) magnitude measured during the ground contact phase of the take-off step from previous studies of long jump athletes with a TTA¹⁰, and estimated RSP displacement (d_RSP) using the force–displacement equations at 6 m/s from Beck et al.²⁴. for Össur Cheetah Xtend RSPs at a height of 38.0 cm, which matched the height within 2.0 cm that was set for both athletes in the present study. For athletes with a TTA, average (SE) k_RSP was 36.0 kN/m, 39.5 kN/m, and 43.9 kN/m for the − 1 Cat, Rec Cat, and + 1 Cat RSPs, respectively. Both athletes with a TTA used their affected leg as their take-off leg in competition and were thus instructed to do so for this study. We used a video camera with a 240 Hz sampling frequency (Casio Exilim Ex-zr70; Casio America Inc., Dover, NJ, USA) placed 1.8 m perpendicular to the take-off board to record d_RSP during the take-off step in the sagittal plane of athletes with a TTA. We calculated elastic energy storage (U_RSP; Eq. 1) within each RSP Cat during the take-off step from measurements of d_RSP using Kinovea (Roubaix, France) and the calculated k_RSP values.

1

We changed take-off platform stiffness (k_surf) for non-amputee athletes using a custom-built compliant platform (Fig. 4). We mounted the platform within the indoor track long jump runway to be flush with the running surface (Fig. 4a). The top of the platform was comprised of a 1.2 m × 0.6 m × 0.0064 m aluminum plate covered with 0.02 m of Mondo (Mondo International, Alba, Piedmont, Italy) and a plywood take-off board (Fig. 4b). We attached 28–30 linear stiffness metal coil springs that had a 0.14 m resting length beneath the top of the platform. The top of the platform was suspended on the springs and constrained to move vertically by eight low friction linear bearings that were placed along the lateral edges and aligned on eight steel rods that were secured to the base of the platform (Fig. 4c). Thus, when force was applied to the take-off platform surface, the top of the platform and springs were constrained to compress vertically. We secured the compliant platform between two rigid boxes using three 0.0064 m thick aluminum C-shaped brackets. One C-shaped bracket fit tightly over the top edges of each box and was 1.2 m long (Fig. 4a). The third C-shaped bracket comprised the base of the spring platform, was 1.19 m long and was attached with bolts to each of the C-shaped brackets that were placed over the boxes and rigidly secured the take-off platform in place (Fig. 4a,c). There was approximately 0.0064 m of space between the top of the spring platform and each edge of the boxes to allow unobstructed vertical movement of the spring platform during the take-off step (Fig. 4a).

Figure 4.

Custom built compliant take-off platform. (a) We installed the take-off platform within the indoor track long jump runway to be flush with the surrounding surface. (b) Top view of the take-off platform. The top of the take-off platform was covered with 2.2 cm of Mondo and a regulation take-off board. (c) Side view of the take-off platform. We changed the take-off platform stiffness by attaching linear stiffness metal coil springs beneath the top of the take-off platform, and vertical compression of the springs was constrained by linear bearings mounted within the top of the take-off platform.

We measured the stiffness of each linear spring used in the platform with a materials testing machine (Instron Series 5859; Norwood, MA, USA). We averaged force and displacement from three successive loading and unloading cycles of one spring at 3.40 N/s and a sampling frequency of 10 Hz, to a maximum load of 250 N. The average linear stiffness (quotient of force and displacement) of each spring was 3 kN/m. We varied the number of springs within the platform and arranged them in a balanced pattern to create two compliant platforms with an overall k_surf of 84.0 kN/m (28 spring pattern) and 90.0 kN/m (30 spring pattern). The 6.0 kN/m difference in k_surf between the compliant platforms is similar to the difference in k_RSP between the − 1 Cat and + 1 Cat RSP stiffness categories, which was ~ 7.9 kN/m. The k_surf of the regulation track surface was 1630.0 kN/m³⁹. We used a video camera with a 240 Hz sampling frequency (Casio Exilim Ex-zr70; Casio America Inc., Dover, NJ, USA) placed 1.8 m perpendicular to the take-off board to record the maximum vertical displacement of the top of the platform during the take-off step (d_platform) in the sagittal plane of non-amputee athletes. Vertical displacement (d_platform) was measured in Kinovea, using the length of the take-off board (known distance) to calibrate the field of view. We calculated elastic energy storage (U_platform; Joules) within each take-off platform (Eq. 2) during the take-off step from measurements of d_platform using Kinovea (Roubaix, France) and the take-off platform stiffness (k_surf).

2

We measured horizontal velocity during the entire run-up of all athletes using a radar gun (Stalker; 47 Hz, Stalker Sport, Plano, TX). The radar gun was mounted on a tripod at a height corresponding to each subject’s approximate center of mass and thus was positioned ~ 1.5 m above the ground, and 42 m behind the take-off board to allow each athlete to complete their full run-up sprint. We measured jump distances for all completed jumps with a tape measure according to athletics regulations³⁸; we measured the distance from the forward edge of the take-off board to the impression in the sand pit closest to the take-off board made by any part of the body of the athlete. This measurement excluded the distance between the distal end of the athlete’s take-off foot or RSP and the take-off board. A jump was classified as a foul if any part of the take-off foot or RSP crossed the forward edge of the board, and such attempts were excluded from analysis.

Statistical analysis

We constructed linear mixed-effects models to determine the effect of RSP stiffness on maximum horizontal run-up velocity and the effect of RSP stiffness, elastic energy storage of the RSP, and maximum horizontal run-up velocity on jump distance in athletes with a TTA⁴⁰. The fixed effects in the linear mixed models were RSP stiffness category (categorical; − 1 stiffness category, recommended, and + 1 stiffness category), elastic energy storage (continuous; J) and maximum horizontal run-up velocity (continuous; velocity in m/s) and interactions between each RSP Cat, elastic energy storage, and maximum horizontal run-up velocity. We constructed additional linear mixed effects models to test for the effect of take-off platform stiffness (k_surf) on maximum horizontal run-up velocity and the effects of k_surf, elastic energy storage, and maximum horizontal run-up velocity on jump distance in non-amputee athletes⁴⁰. Separate models were used to test for the effect of k_surf on maximum horizontal run-up velocity, and the effect of k_surf, elastic energy storage, and maximum run-up velocity on jump distance. The fixed effects in each linear model were k_surf (continuous; stiffness in kN/m), elastic energy storage (continuous; J and maximum horizontal run-up velocity (continuous; velocity in m/s). Subject was set as a random effect for all models. We report unstandardized model coefficients (B) for each significant association (dependent variable = B · independent variable + intercept). B represents the change in the dependent variable related to a unit change in the independent variable. We used a significance level of p < 0.05. All statistical tests were done in RStudio (Boston, MA, USA)⁴⁰.

We compared maximum horizontal run-up velocity, jump distance and elastic energy storage of the RSP and the take-off platform between athletes with a TTA and non-amputee athletes, respectively, using a non-parametric test (Wilcoxon rank sum test). Separate tests were run to compare the recommended category RSP (Rec Cat) with the regulation track surface (1630 kN/m) and to compare the Rec Cat RSP with the 90.0 kN/m take-off platform. We used a significance level of p < 0.05.

Author contributions

AG contributed to conception and design of the study. KA acquired the data, performed the statistical analyses, interpreted the results, prepared figures, and drafted the manuscript. Both authors contributed to manuscript revision and read and approved the submitted version.

Data availability

Our data and code can be accessed through the electronic supplementary material ⁴¹. LongJumpData.csv is a csv file of the data from the study. LongJump_Stats.rmd and LJgraphing.rmd are RStudio files of the code used for the statistics and to create the figures for the study, respectively. LongJump_Stats.pdf is a PDF version of the code. 10.6084/m9.figshare.24247159.

Competing interests

The author(s) declare no competing interests.