Return-to-Sport Hop Test: Limb Symmetry Simulator

Test Leg

Athlete & Injury Parameters

Body mass 75 kg

Quadriceps strength deficit (injured leg) 25%

Landing knee flexion (softness) 30°

Ground-contact (push-off) time 0.22 s

Trial Readouts

Hop distance

— m

Peak landing GRF

— BW

Takeoff velocity

— m/s

Knee valgus risk

—

Return-to-Sport Decision

—

Limb Symmetry Index

Run both legs to evaluate

How it works

Each trial models a single-leg hop for distance using impulse–momentum and projectile-motion mechanics, the same variables physical therapists track in a real hop-test battery:

Takeoff:  v0 = F·t_c / m,   F = F_base · (1 − deficit)
Distance: D = v0² sin(2θ) / g          (θ ≈ 22° takeoff angle)
Landing:  F_grf = m·(v0 sinθ) / t_land   (deeper knee flexion → longer t_land → lower peak force)
LSI = (D_injured / D_uninvolved) × 100

Quadriceps deficit — scales the injured leg's propulsive force, directly shortening its hop distance.
Landing flexion — a stiffer (shallower) landing shortens the deceleration time, spiking peak ground-reaction force and knee valgus risk; deeper flexion spreads the impulse over more time.
Contact time — longer push-off contact lets the same muscle force deliver more impulse (F·t_c), raising takeoff velocity.
LSI ≥ 90% is the clinical benchmark used after ACL reconstruction and other lower-limb injuries to clear an athlete for return-to-sport — run both legs and compare.

Real-world relevance: single-leg hop batteries (single hop, triple hop, crossover hop) are a standard quantitative gate in sports-rehab return-to-play protocols, precisely because raw strength recovery alone under-predicts re-injury risk — symmetric hop performance and safe landing mechanics matter just as much.

Injured leg trial Uninvolved leg trial

⚠ Couldn't load the 3D engineThree.js failed to load from the CDN. Check your connection and reload.