The elbow is a lever. The biceps inserts close to the joint (moment arm dm ≈ 5 cm); the load sits far out at the hand (dL ≈ 30 cm) — a large mechanical disadvantage, so muscle force must vastly exceed the weight's force.
F_muscle = σ · CSA (σ = specific tension ≈ 35 N/cm²)
torque_muscle = F_muscle × d_m
torque_load = (m_load + 0.43·m_forearm) · g · d_L · sin(φ)
lift succeeds when torque_muscle ≥ torque_load, all φ
Cross-sectional area follows an age-and-training model. Past 30, CSA falls ~1%/year; the annual rate itself grows after 60 (rate60+ = 1% + 0.08%×years past 60). Resistance training multiplies the decline down and adds a hypertrophy term that can push CSA back above the untrained curve:
CSA(age,T) = CSA_peak25 · (1 − D(age)·(1 − 0.07T) − 0.006T)
where D(age) is the cumulative fractional loss integrated from the rates above and T is the training slider (0–10). Because σ is constant, % of peak strength = % of peak CSA. The elbow itself is animated with real torque-driven angular dynamics (I·α = torque_muscle·activation(t) − torque_load − damping·ω): too little muscle torque and the forearm visibly trembles near the bottom instead of curling.