Standing Vertical Jump
Optimum Push-Off Range
The standing vertical jump is a popular test of leg power and it is routinely used to monitor the effectiveness of an athlete's conditioning program.
In most tests the athlete is asked to perform a 'countermovement jump' (with armswing) for maximum height.
A countermovement jump is where the jumper starts from an upright standing position, makes a preliminary downward movement by flexing at the knees and hips, then immediately extends the knees and hips again to jump vertically up off the ground (Figure 1a).
Such a movement makes use of the ‘stretch-shorten cycle’, where the muscles are ‘pre-stretched’ before shortening in the desired direction.
A less common type of jump is the 'squat jump', where the jumper starts from a stationary semi-squatted position (Figure 1b).
The jumper does not employ a preliminary downward phase (i.e., a countermovement) and so the jump does not involve pre-stretching of muscles.
Most athletes can jump 3 - 6 cm higher in a countermovement jump than in a squat jump.
Figure 1.Sequence of actions (a) in a countermovement jump and (b) in a squat jump.
Optimum Vertical Push-Off Range
A few years ago I witnessed some good vertical jumps by a masters pole vaulter.
This athlete outperformed most of the WA Institute of Sport athletes by using a squat jump, rather than a countermovement jump.
(He recorded 76 cm on a standard 'jump-and-reach test'.)
He chose to use a squat jump because he was unfamiliar with the countermovement jump, and it was suspected that he could improve his jump score even more if he learned to jump using a countermovement.
This highlighted an important consideration in obtaining valid results in athlete testing.
If an athlete uses a sub-optimal technique because of lack of familiarity with the test, then his test score will underestimate his true capabilities.
Vertical jump tests require good movement coordination, especially in the timing of the armswing and the extension of the hips and legs.
A jumper must also choose the right depth of movement (amount of knee and hip flexion).
A study was conducted to identify the optimum depth of squat in vertical jumping.
(Optimal timing of armswing and leg extension was not the focus of this study.)
The subject was an experienced athlete with good technique in both the countermovement jump and squat jump.
A series of jumps were performed on a force platform using various depths of squat.
The motion of the jumper’s centre of mass was calculated by numerical integration of the force-time record from a force platform.
The study confirmed the advantage of the countermovement jump over the squat jump, and showed that selecting the optimum depth of squat is not crucial to performance (Figure 2).
A jumper can achieve very close to their best performance using a wide range of techniques (depth of squat).
Figure 2. Dependence of flight height on vertical push-off range.
One of the reasons you can jump higher in a countermovement jump than in a squat jump is because of muscle 'pre-tensing' (Figure 3).
In a countermovement jump the levels of activation in the jumper’s leg muscles are higher at the start of the upward phase because the jumper has to slow and then reverse the initial downward motion.
A countermovement eliminates the vertical push-off range that is wasted in a squat jump while the muscles build up to maximum force.
The jumper thus performs more work early in the upward phase of the jump, and so the jumper has a higher takeoff velocity and a greater jump height.
Figure 3. Force-displacement traces for a squat jump and a countermovement jump with the same vertical push-off range.
To find out more about this study, see:
Linthorne, N.P. (2000).
Optimum take-off range in vertical jumping.
In "Book of Abstracts, 3rd Australasian Biomechanics Conference, Griffith University, 31 January - 1 February 2000", pp. 49-50.
Vertical Jumping in Undergraduate Teaching
The work on vertical jumping and force platforms has been incorporated into the biomechanics classes in the School of Exercise and Sport Science.
Computer software was developed that produces curves of velocity and displacement of a jumper’s centre of mass by numerical integration of the force-time record from a force platform.
Although vertical jumping is a relatively simple movement skill, the physics of the vertical jump is not immediately obvious.
The students carefully trace the evolution of the jump while identifying the key times and phases.
They are asked to describe the actions of the jumper and note the relations between the force acting on the jumper and the resulting acceleration, velocity and displacement of the jumper’s c.m.
The curves obtained from the force platform are also used to calculate the height of the jump.
The most straight-forward method is to determine the time spent in the airborne phase and then use the kinematic equations for one-dimensional motion under constant acceleration.
A more accurate method of determining the jump height is to apply the impulse-momentum theorem to the force-time record, and this provides an interesting example of numerical integration.
The jump height may also be calculated by applying the work-energy theorem to the force-displacement curve, again using numerical integration.
I have written about my teaching experiences for a paper in American Journal of Physics.
My aim is to enlighten the physics teaching community about the use of sports and human movement examples to liven up the teaching of undergraduate mechanics.
Although much of the material is already well-known to biomechanists, there are some important novel aspects in the paper.
Force-displacement curves are not commonly used in force platform studies, and in my view they have considerable potential in assessing the skill level of the jumper and in monitoring the effects of athletic training.
To find out more about this work, see:
Linthorne, N.P. (2001).
Analysis of standing vertical jumps using a force platform.
American Journal of Physics, 69 (11), 1198-1204.