How to Calculate Jump Height: Flight Time vs Impulse Momentum

This post compares the two prevalent methods for calculating jump height, flight time and impulse momentum, and guide practitioners in choosing the most suitable approach for their needs.

With advancements in technology, assessing jump height has become more sophisticated. A force plate, a device that measures the ground reaction forces generated by a body standing on it, is often used for this purpose. There are two primary methods to calculate jump height using a force plate: the flight time method and the impulse momentum method.

This post will compare the flight time and impulse momentum methods and determine the most appropriate one for calculating jump height.

Reviewing the Force Time Curve

Traditionally, jump height may have been assessed with some form of jump and reach test. However, when using a force plate, jump height is defined as the vertical displacement of the centre of mass. In the case where an Abalakov jump is used for example, i.e. a countermovement jump with arm swing, the jump height will still relate to the centre of mass rather than how high the arms may reach.

To understand jump height calculations, it is essential to comprehend the force-time curve of a countermovement jump on a force plate. This curve illustrates the various phases of the jump, from the initial unweighting to the propulsion phase, followed by the flight phase, and finally the landing. The flight time method uses the flight phase whereas, the impulse-momentum method uses data from the takeoff phase to calculate jump height.

Flight Time Method

The flight time method calculates jump height based on the duration an athlete spends in the air. By accurately determining the take-off and landing times, we can input the flight time value into the projectile motion equation, where:

Given that when an objective is in the air, the only thing acting upon it is gravity (9.81m/s/s), we know a constant force is trying to pull the object back down to Earth. So by knowing how long an individual is in the air, we can calculate the jump height. The simplicity of this method lies in its reliance solely on the time of flight. There are limitations to this method however, as I'll discuss further below.

Impulse-Momentum Method

The impulse-momentum method, while more complex, involves calculating the take-off velocity from the data collected before take-off. Understanding the relationship between impulse (force applied over time) and momentum (mass times velocity) is critical here.

This figure from Jordan et al., (2020) in the Aspetar Journal displays how the takeoff velocity in the vertical jump is determined using the impulse momentum relationship.

In short, if the initial velocity is zero (i.e. the athlete is completely still before they start their jump), the change in momentum directly equals the net impulse (i.e. area under the force-time curve). This allows for an accurate calculation of take-off velocity and subsequently, the jump height.

Here is a more detailed breakdown courtesy of VALD Product Manager, Lucas Thomeer:

• If the jumper is perfectly still when the rep begins, then their velocity is zero, which means that their momentum is also zero (mass * velocity).

• If that initial momentum is 0, then impulse and momentum for the jumper are the same thing (Impulse = Current_Momentum - Initial_Momentum ->  Impulse = Current_Momentum).

• Once we know that, we can calculate the area under the force-time curve that we measure with ForceDecks to find both impulse & momentum, and then we can calculate velocity from momentum using the mass of the jumper that we measured at the beginning of the test.

Illustration with Real ForceDecks Data

Using real data from VALD’s ForceDecks, we compared jump heights calculated via both methods. Generally, jump heights obtained using the flight time method tend to be higher than those computed with the impulse momentum method. This discrepancy, well-documented in literature, indicates that the flight time method may overestimate jump height.

However, we also identified an outlier based on limitations with the impulse-momentum method. Have a look at the video below for more information on the two methods and the comparison of real ForceDecks data:

Which Method to Choose?

As I discussed in the video above taken from the Global Performance Insights YouTube channel, the jump height method you choose depends on your setting. The table below displays the key advantages and disadvantages of each.

	Advantages	Disadvantages
Flight Time Method	Simple, quick, and consistent.	Tends to overestimate jump height. Assumes the same position for take-off and landing, which can lead to inaccuracies.
Impulse-Momentum Method	More accurate as it accounts for actual physical displacement of the centre of mass.	Requires a stable initial still phase, making it susceptible to inaccuracies if body mass measurements are compromised.

Crucially, given it is not a perfect relationship between the two methods, you should not use them interchangeably.

Conclusion

In summary, while the flight time method is convenient and straightforward, it may not always be accurate. On the other hand, the impulse momentum method, although more precise, requires stringent conditions for accurate data collection, specifically the individual's body mass in the quiet phase before the start of the jump. Practitioners should choose the method best suited to their environment and the constraints they face, and always avoid using them interchangeably.

Frequently Asked Questions (FAQs)

How does the flight time method calculate jump height?

This method calculates jump height based on the duration the individual spends in the air, using the projectile motion equation.

Why might the flight time method overestimate jump height?

It assumes identical body positions at take-off and landing. This is not accurate as individuals tend to land later with some knee flexion, and can also be manipulated to increase air time.

What is the impulse-momentum method for calculating jump height?

This method calculates jump height using the velocity at take-off, derived from the impulse (force over time) applied during the jump. As long as the individual is still at the start of their jump, the change in momentum directly equals the net impulse (i.e. area under the force-time curve). This allows for an accurate calculation of take-off velocity and subsequently, the jump height.

Which jump height method should I use?

Choose based on your setting: the flight time method for simplicity and speed, or the impulse momentum method for accuracy if you can ensure reliable body mass measurements. But do not use data from the two methods interchangeably.

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This article is support by VALD Performance. For more information, about their technology, visit their website.

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