This is the 2D side-view companion to the 3D lumbar-spine model, built on the exact same moment-balance equations. The trunk is a lever pivoting at the L4–L5 disc. Taking moments about the disc balances the erector-spinae muscle force Fm (moment arm ≈ 5 cm) against the torque of the upper-body weight Wt and any hand-held load WL, each acting at its own moment arm, which grows with effective trunk flexion angle θ and with reach:
d_trunk = 0.02 + 0.10·sin(θ_eff) [m]
d_load = reach + 0.10·sin(θ_eff) [m]
F_m·d_m = W_t·d_trunk + W_L·d_load
Compressive force C = F_m + (W_t + W_L)·cos(θ_eff)
Intradiscal pressure P ≈ 1.5 · C / A_disc (A_disc ≈ 16 cm²)
The 1.5× factor and the ≈0.5 MPa relaxed-standing baseline follow in-vivo intradiscal pressure measurements (Nachemson & Elfström 1970; Wilke et al. 1999): pressure rises roughly linearly with the vertical compressive load carried by the disc.
- Trunk flexion — bending the spine forward multiplies the trunk's own moment arm, so the erector-spinae muscles must contract far harder just to hold the posture up — the dominant cause of disc loading, even with no external weight.
- Load & reach — a weight held at arm's length loads the disc several times more than the same weight held close to the body, because torque scales with distance, not just mass.
- Squat vs stoop — switching to a bent-knee squat lift lets the hips and knees do more of the work, cutting the *effective* spinal flexion angle θeff to about 35% of the visible trunk bend — which is exactly why "lift with your legs, not your back" lowers intradiscal pressure.
This is a simplified single-level sagittal-plane model used for physical-therapy patient education, not a full musculoskeletal simulation — real loading also depends on individual anatomy, spinal curvature and co-contraction of stabilising muscles.