Launch Physics
A vertical jump is the purest expression of human explosive power — the body becomes a projectile the instant the feet leave the ground. Once airborne, the center of mass follows a perfect parabolic trajectory governed by gravity alone: h = v₀²/(2g). A takeoff velocity of 2.8 m/s (average adult) produces 40 cm of flight, while an elite athlete at 4.4 m/s achieves nearly 100 cm. Every additional 0.1 m/s of takeoff velocity is hard-won through years of power training.
The Push-Off Phase
Before flight, the body must generate a net upward impulse (force × time) sufficient to achieve the desired takeoff velocity. Starting from rest, the average force during push-off must equal m(v₀²/(2d) + g), where d is the push-off displacement. Deeper countermovement provides more distance and time to develop force, reducing peak force requirements. This simulation visualizes the force-displacement curve and computes the work done during push-off.
Stretch-Shortening Cycle
The countermovement (pre-stretch) before jumping enhances performance by 10-20% through three mechanisms: elastic energy storage in series elastic elements (tendons and titin), enhanced muscle activation via the stretch reflex, and force potentiation from the force-velocity relationship (muscles generate more force when pre-stretched). This is why athletes instinctively dip before jumping — and why a squat jump from a static bent position is always lower.
From the Court to the Lab
The vertical jump test is the most widely used field assessment of lower-body power in sports science. The NBA Combine measures standing vertical reach differences averaging 70-80 cm for drafted players. In the laboratory, force platforms reveal the complete force-time history of the jump, enabling coaches to identify whether an athlete is force-limited (needs strength training) or velocity-limited (needs ballistic training).