Validity of Stryd Leg Stiffness Against the Morin (2005) Sine-Wave Method: A Level-1 Assessment on Flat and Uphill Treadmill Running

1. Introduction

The Stryd running foot pod (Stryd Inc., Boulder, CO, USA) has become one of the most widely adopted wearable devices in running and trail running research. An expanding body of peer-reviewed literature has used Stryd-derived data to investigate running power output, biomechanics, and performance across laboratory and field settings [1,2,3,4]. This proliferation creates a scientific obligation: each metric must be independently validated against established references before use with confidence in research or applied practice 5.

Several Stryd metrics have been formally validated. Stride kinematics such as cadence, stride length, and contact time have demonstrated strong concurrent validity against optical and force-plate references across a range of running velocities [2,6]. Running power has been evaluated against metabolic cost and mechanical power with good linear agreement [1]. Reliability under inclined and trail conditions has been confirmed for speed, cadence, and contact time [7], and Stryd biomechanical parameters have been shown to predict performance in trained runners [3]. In contrast, leg spring stiffness (k_leg) has received comparatively little analytical attention. The spring-mass model conceptualizes the runner as a mass oscillating on a linear spring that compresses and recoils during ground contact [8,9], with k_leg directly linked to running economy and stride regulation. To date, only Imbach et al. [1] have compared Stryd k_leg against a laboratory reference (i.e., force platform), finding acceptable agreement in a sample of six recreational runners on flat treadmill running. No study has examined the validity of Stryd k_leg on inclined terrain, even though uphill running is a defining feature of trail running and mountain racing, contexts in which Stryd is increasingly deployed.

The Dhahbi & Chamari [5] standardization framework for wearable assessment technologies prescribes Level-1 analytical validation (i.e., direct comparison against an established reference, with ICC > 0.7, Bland-Altman analysis, and MAPE as primary metrics) as the mandatory first step before applied adoption. Morin et al. [10] validated a sine-wave method to estimate kleg from body mass, velocity, leg length, contact time, and flight time, reporting biases of 0.12–6.93% against force platforms. The purpose of this study is therefore to conduct a Level-1 analytical validation of Stryd kleg against the sine-wave method [10] under flat (0%) and inclined (+12%) treadmill running conditions.

2. Materials and Methods

Twenty-three highly trained trail runners (12 males, 11 females; body mass 67.7 ± 9.4 kg; height: 1.73 ± 0.1; leg length: 0.92 ± 0.1) participated in the parent study (Jaén-Carrillo et al., in press) [11], from which this work constitutes a secondary analysis; full protocol details are reported there. Data were collected under two treadmill conditions (hp cosmos, h/p/cosmos sports & medical GmbH, Nussdorf-Traunstein, Germany) separated by 48 hours: (i) Uphill running: a 12-minute time trial at +12% gradient performed in fresh state (mean speed 2.59 ± 0.34 m·s⁻¹); and (ii) level running: the first hour of a 180-minute submaximal treadmill run at 85% of the speed corresponding to the lactate threshold +0.5 mmol·L−1 at 0% gradient (mean speed 3.10 ± 0.41 m·s⁻¹). All data represent condition-level participant means recorded by the Stryd foot pod. The study conformed to the Declaration of Helsinki; all participants provided written informed consent.

The Stryd foot pod, clipped to the laces of the running shoes, provided contact time (CT, ms), flight time (FT, ms), running speed (v, m·s⁻¹), and leg stiffness (kN·m⁻¹).

Leg stiffness was estimated following Morin et al. sine-wave method 10. Modelled peak ground reaction force:

F^_max = m·g·(π/2)·(t_f/t_c + 1)

(1)

where m is body mass (kg), g = 9.81 m·s⁻², t_f = flight time (s), t_c = contact time (s). Vertical centre-of-mass displacement:

Δŷ_c = F^_max·t_c² / (m·π²) − g·t_c²/8

(2)

Peak leg spring compression:

ΔL^ = L − √(L² − (v·t_c/2)²) + Δŷ_c

(3)

Leg stiffness:

k_leg = F^_max / ΔL^

(4)

Leg length was estimated as L = 0.53·h using sex-based mean heights (males: 1.78 m, L = 0.943 m; females: 1.65 m, L = 0.875 m). Morin et al. [10] reported only 1.94 ± 1.51% error using this approach versus directly measured leg length.

The statistical analysis followed Dhahbi & Chamari [5]. Level-1 validation included: (i) ICC(2,1) with absolute agreement (two-way random effects, single measures), threshold ICC > 0.7; (ii) Pearson r and R²; (iii) Bland-Altman analysis (mean bias and 95% LoA); (iv) MAPE; and (v) paired t-test (α = 0.05). ICC 95% CIs were computed via the F-distribution method 12. All analyses used Python 3.10 (SciPy 1.11).

3. Results

The uphill running condition (+12%) yielded shorter flight times and longer contact times than level running, reflecting the mechanical response to uphill running. Mean k_leg was similar across conditions and methods (Table 1).

3.1. Level-1 Analytical Validation

All Level-1 criteria were met and substantially exceeded in both conditions (Table 2). For TT-Control (+12% grade): ICC(2,1) = 0.959 (95%CI: 0.903–0.982, p < 0.001), Pearson r = 0.958 (R² = 0.919), Bland-Altman bias = −0.016 kN·m⁻¹, 95% LoA [−0.595, +0.628] kN·m⁻¹, MAPE = 2.44%, paired t: p = 0.803. For Stage-S1 (0% grade): ICC(2,1) = 0.970 (95%CI: 0.929–0.987, p < 0.001), Pearson r = 0.969 (R² = 0.940), bias = −0.043 kN·m⁻¹, 95% LoA [−0.549, +0.634] kN·m⁻¹, MAPE = 2.59%, paired t: p = 0.505. Scatter plots and Bland-Altman plots are presented in Figure 1.

4. Discussion

Applying the Level-1 framework of Dhahbi & Chamari [5], Stryd k_leg satisfies all prescribed validation criteria with large margins. ICC(2,1) values of 0.959 and 0.970 far exceeded the threshold of 0.70, falling within the ‘excellent’ range (> 0.90) 12. MAPE values below 3% and near-zero Bland-Altman biases (< 0.05 kN·m−1) are comparable to the reference-model biases of 0.12–6.93% reported by Morin et al. [10] against force platforms. These findings considerably extend the sole prior comparison by Imbach et al. [1], limited to six recreational runners on flat terrain, by confirming validity in a larger sample and under a +12% gradient.

The validity of Stryd k_leg on inclined terrain is particularly relevant given the growing application of Stryd in trail running and mountain racing [4,7]. The +12% gradient condition yielded negligible mean bias (−0.016 kN·m−1) and narrow LoA, despite the fact that the sine-wave model [100] was originally validated for horizontal running. That agreement remained excellent at this gradient suggests that the Stryd algorithm may account for gradient-induced mechanical changes, though the specific mechanism cannot be determined from available data. The slightly wider LoA at +12% versus 0% grade (±0.61 vs. ±0.59 kN·m⁻¹) are consistent with expected additional noise on inclines and remain within acceptable ranges.

While cadence, stride length, contact time, and power have been progressively validated [1,2,6] k_leg had remained the least characterized Stryd output, closing a key evidence gap. Future work should extend this validation to downhill and outdoor trail conditions. Level-2 and Level-3 validation represent the next logical steps.

Leg spring stiffness recorded by the Stryd foot pod can be used with confidence as a valid field measure during both level and uphill treadmill running, requiring no instrumentation beyond the device already used for power and pace monitoring. The low MAPE (< 3%) and negligible systematic bias indicate that Stryd k_leg values are interchangeable with Morin-derived estimates for routine monitoring, eliminating the need for laboratory-based calculations. This is particularly relevant for trail running and mountain racing, where uphill running constitutes a substantial portion of total load and Stryd validity on inclined terrain was previously unvalidated. Given that leg stiffness is associated with running economy, fatigue-induced gait alterations, and musculoskeletal injury risk, continuous Stryd k_leg monitoring may enable real-time detection of stiffness drift during prolonged efforts, with potential applications in pacing strategy and fatigue management.

5. Conclusions

This study provides Level-1 analytical validation of the Stryd leg stiffness metric against the Morin (2005) sine-wave reference method. Stryd k_leg demonstrated excellent agreement under both level running (ICC = 0.970, MAPE = 2.6%) and uphill treadmill running at +12% grade (ICC = 0.959, MAPE = 2.4%), with negligible mean bias and no statistically significant systematic error in either condition. Given the growing use of Stryd in running and trail running research and the scarcity of prior evidence on k_leg validity, particularly on inclined terrain, these results fill a critical evidentiary gap. Stryd k_leg satisfies all Level-1 validity thresholds and may be used with confidence as a continuous wearable field measure of leg spring stiffness.