Leg Spring Stiffness

Definition

“Leg spring stiffness” (LSS) is the spring stiffness of the leg during the ground contact phase of running. It describes the ratio between peak vertical ground reaction force and the shortening of the leg from touchdown to maximum compression. The unit is kilonewtons per metre (kN/m).

k_leg = F_max / ΔL

The term comes from the spring-mass model of running: the body is treated as a mass on a spring that is compressed on every step and returns energy. This is distinct from vertical stiffness (k_vert), which considers only the displacement of the centre of mass and takes markedly higher values.

Why it matters

Leg stiffness describes how efficiently tendons and muscles store and return elastic energy while running. Higher stiffness usually goes with shorter ground contact time, higher cadence and better running economy. For the same person at the same speed it is relatively stable.

That is exactly why its trend is informative. If stiffness falls within a long run at constant pace, the muscle-tendon unit is fatiguing. If it falls over weeks, that can point to insufficient recovery or an emerging overload problem. If it rises after a strength or plyometric block, the training has worked.

Stiffness depends on speed, cadence, surface and shoe. Comparisons are therefore only meaningful under similar conditions.

How obseed measures it

obseed imports leg spring stiffness from the recording when a sensor provides it, such as a Stryd running pod. Watches without this value do not record it, and it cannot be computed from GPS data alone.

If ground contact time, flight time and body mass are available, vertical stiffness can be estimated using the model of Morin et al. (2005). Leg stiffness additionally requires leg length and speed. Such estimates are approximations and do not replace a force plate.

Example

A 70 kg runner runs at 4.0 m/s (4:10/km) with a ground contact time of 240 ms and a flight time of 120 ms. Leg length 0.95 m.

Peak ground reaction force after Morin et al.:

F_max = m × g × (π/2) × (t_flight / t_contact + 1)
      = 70 × 9.81 × 1.571 × (0.12 / 0.24 + 1)
      = 1618 N

Centre-of-mass displacement and vertical stiffness:

Δz = F_max × t_contact² / (m × π²) − g × t_contact² / 8
   = 1618 × 0.0576 / 690.9 − 9.81 × 0.0576 / 8
   = 0.135 − 0.071 = 0.064 m

k_vert = 1618 / 0.064 = 25.3 kN/m

Leg compression and leg stiffness:

ΔL = L − √(L² − (v × t_contact / 2)²) + Δz
   = 0.95 − √(0.9025 − 0.2304) + 0.064
   = 0.95 − 0.820 + 0.064 = 0.194 m

k_leg = 1618 / 0.194 = 8.3 kN/m

If the same runner shows a contact time of 262 ms and only 7.2 kN/m at the end of a 30 km run at the same pace, the spring action of the leg has declined by about 13 %.

References

• Farley, C. T., González, O. (1996). Leg stiffness and stride frequency in human running. Journal of Biomechanics.
• Morin, J. B., Dalleau, G., Kyröläinen, H., Jeannin, T., Belli, A. (2005). A simple method for measuring stiffness during running. Journal of Applied Biomechanics.