Applied Biomechanics: Building Intuition with Vectors

Traditionally, quantitative sports biomechanics has only been accessible to those with mathematics, engineering, or physics backgrounds. However, over the past decade, biomechanical analysis of movement patterns and performance has become more commonplace in the realm of elite sport and injury rehabilitation. Sports scientists, athletic trainers, and other sports medicine practitioners can more objectively define the movement of their athletes, leading to better performance outcomes and reducing the risk of injury. This combination of research-backed quantitative evidence, coaches’ practical experience, and athlete-specific responses has opened up the subfield of “applied biomechanics.” It paves the way for an evidence-based approach to sports performance and monitoring.

Scalars vs. Vectors

So how can we actually apply “applied biomechanics”? To start, we must build an intuition around how movement is quantified. There are two basic building blocks: scalars and vectors.

Scalars are quantities like speed, distance, volume, and time. These are values that can be fully described by their magnitudes alone.

For example, speed is a scalar quantity representing the magnitude of how fast an object (or person) travels (i.e., distance **travelled over time), but it does not tell us directionality.

Check out this good-looking athlete below. It looks like they are running really fast! But without an idea of their direction, do we confidently know if they are running forwards or backwards?

Velocity is the “vector equivalent” to speed. It quantifies the displacement of an object or person over time instead of distance, assigning the direction of the movement (up, down, forward, backward, or a combination).

Vectors are quantities like velocity, acceleration, and force. These are values that must be described by both magnitude and direction. Why do we care? Because vectors allow us to objectively describe motion in an amount of detail that scalar quantities alone cannot match.

Now check out this speed racer! They are obviously running forward.

Did you have a flashback to your school days? We get it… vectors can be intimidating, but hopefully, by the end of this post, you will have a more intuitive understanding of what they mean in the real world instead of just watching your teacher draw arrows on a whiteboard.

Now that we know that difference, we can see how velocity is a more powerful metric of athletic performance than just speed, as it provides key descriptors of task performance.

Force Vectors

Let's expand on the application of vectors in sports with a familiar concept to many sports practitioners: force application.

Force is the interaction of two or more objects that changes the state of motion (by either pushing or pulling). Force applied to an object can induce motion, stop it, accelerate it, or change its direction. When represented as vectors, the magnitude of each force is the amount of force being applied, and the direction of the arrow indicates the direction of the force. Direction is important because it will influence the result (e.g., whether it is a pushing or a pulling force).

Let’s take the barbell deadlift as an example. The minimum required upward pull force (Fa) that needs to be applied to the barbell to lift it off the ground must be greater than the downward pull of gravity (Fg) due to its weight.

Acceleration Vectors

Now, how does that relate to acceleration? According to Newton’s Second Law, force equals mass times acceleration (F = ma), where mass is the size of the weight in kg. So acceleration is essentially the movement result of the force. In this barbell example, the acceleration applied is larger than the acceleration of gravity, so the net acceleration is upward.

A larger applied force means a larger applied acceleration, so the weight will move off the ground faster.

In the real world, forces act in all directions, not just up and down. There are many combinations and directional possibilities in gameplay's dynamic environments, so to understand these complex movements, we need to understand how they are produced. This is why vectors and movement measurements are critical in applied biomechanics.

With so many different components in play, the question then becomes, what do we focus on to create meaningful improvement with the unique performance demands of different athletes? This depends on the situation, so stay tuned for upcoming posts on some of our favourite metrics and how they can help quantify propulsive and absorptive capacities to identify trainable deficits with vectors.