First Steps into Freestyle Swimming Analysis

Photo by Arisa Chattasa on Unsplash

Introduction

Over the past 6–7 months, I’ve been diving into the field of knowledge engineering, aiming to apply this knowledge in practical ways. My first attempt was modeling a ReBAC access control system and extracting a knowledge component from it, which I documented in an article. This is my second attempt, where I focus on something even more practical — modeling my freestyle swimming technique.

I consider myself an average swimmer, practicing about twice a week, but I’m eager to enhance my efficiency and speed. This inspired me to explore whether I could model swimming itself. My goal was to develop a mental model that would allow me to reason about swimming mechanics and use this understanding to improve my technique. The underlying hypothesis is simple: knowledge isn’t acquired magically. By actively building a model, I would gain the required understanding, which could then be encoded into a structured form, enabling systematic improvements.

Recently, I came across Michael Weisberg’s book Simulation and Similarity (link), and the methods described there inspired me to start modeling the physical process.

Modeling

I began with a simple conceptual model: when I swim, my hands generate a forward force to propel me through the water, while the water exerts a resistive drag force that slows me down. However, this model was too general and lacked actionable parameters I could adjust. To make progress, I decided to study the theoretical aspects of swimming. My sources included the book Science of Swimming Faster (link), ChatGPT, various articles, and Wikipedia.

It turns out that two primary forces influence a swimmer’s body:

1. Propulsion Force — Produced by the swimmer’s hands and legs.
2. Drag Force — Resists the swimmer’s movement through the water.

This theoretical understanding allowed me to break down each force and identify parameters that could be optimized.

Let’s begin with the drag force.

Drag Force

The formula for drag force from fluid dynamic theory is as follows:

From this, it’s clear that:

1. The higher the speed, the greater the drag force. However, since the goal of modeling is to increase speed, reducing speed isn’t an option.

2. The drag coefficient (C_d) should be as small as possible. This coefficient depends on the shape of the body and how streamlined it is in the water.

3. The frontal area (A), or the projection of the swimmer’s body, should be minimized.

Drag Coefficient (C_d)

Diving deeper into the drag coefficient: as per this article, the coefficient ranges from 0.7 for professional swimmers to 2.0 for inexperienced swimmers with inefficient techniques. For freestyle swimming specifically, the range is narrower: around 0.92–1.07.

It’s worth noting that the level of expertise of the “university swimmers” measured in this study isn’t clearly defined. Based on available data, we can approximate the drag coefficient for casual swimmers as 0.9–1.5 and for elite swimmers as low as 0.5–0.7.

The drag coefficient becomes particularly critical when other means of increasing speed (e.g., technique or propulsion) are maxed out. For instance, the authors of this study stated:

“CDA explained 63.8% of the variance in swimming speed, with higher CDA values resulting in slower swimming speeds. This means that the fastest swimmers were able to reduce water resistance more and therefore achieve the fastest swimming speeds.”

Here, CDA refers to the active drag coefficient, which combines active and passive drag effects.

This insight suggests that by optimizing my body position in the water, I can significantly reduce drag force and improve my swimming speed. The following observations highlight ways to reduce the drag coefficient:

1. Maintain a streamlined body: Keep the body as horizontal as possible. On page 140 of Science of Swimming Faster, the authors provide an image illustrating the relative contributions of various body parts to drag. The areas contributing the most drag include the wrists, elbows, neck, hips, knees, mid-trunk, and feet.
2. Keep legs submerged: Ensure legs remain under the water’s surface at all times.
3. Rotate shoulders: Proper shoulder rotation helps streamline the body.
4. Wear appropriate gear: A high-performance swimsuit and swimming cap can reduce drag.

Frontal Area (A)

The second major factor is the swimmer’s frontal area. Reducing this projection is another way to minimize drag force. Key observations include:

1. Head alignment: I should keep the head in line with the body and avoid raising the head; the eyes should face straight down at the bottom of the pool.
2. Leg alignment: I should ensure the legs don’t sink and remain in line with the rest of the body.
3. Full extension: I should extend arms and legs completely to reduce the area exposed to resistance.

With drag force covered, the next step is to examine propulsion — the force that moves me forward.

Propulsion

There are two sources of propulsion: arm strokes and leg kicks. Arm strokes are the primary contributors, accounting for approximately 90% of the total propulsion force. However, according to this study, swimmers using only their arms can achieve about 90% of their usual speed, while those using only their legs can reach around 60%. While these figures are not additive, they emphasize the importance of both arms and legs. Nevertheless, legs primarily serve an additional purpose: maintaining alignment in a horizontal position to streamline the body and reduce drag.

Modeling Arm Propulsion

How do arms create propulsion? Freestyle technique involves a repetitive pattern of arm movements divided into four stages:

1. Entry: The arm enters the water and aligns horizontally for a brief moment.
2. Pull: The arm pulls water, moving until it reaches a 90-degree angle with the body.
3. Push: The arm pushes water until it exits the water, akin to pushing the body forward.
4. Recovery: The arm moves through the air to re-enter the water in front of the body.

According to Science of Swimming Faster (Scott Riewald, Scott Rodeo, p. 148), the push stage generates the most force. The work (force multiplied by time) done during the pull stage is approximately 10 times less than during the push stage. While the other stages contribute less to propulsion, they are crucial for preparing the arm for the push phase and minimizing drag (e.g., recovery occurs in air, where drag is significantly lower than in water).

One key point about the pull stage: if the palm is not vertical, it may waste force by moving the body laterally or vertically instead of forward. For example, a palm that pushes slightly downward during the pull stage generates rotational momentum, causing the body to rise and the legs to sink, which increases drag. Thus, even though push generates most of the propulsion, the model must account for all stages.

Arm propulsion depends on two primary factors:

1. Frontal area of the arm pushing water: During the push phase, keeping the arm perpendicular to the direction of movement maximizes the frontal area. Any bending or rotation of the palm reduces the effective area by the cosine of the rotation angle. Additionally, incorrect angles generate forces in unintended directions, potentially disrupting body alignment and increasing drag. At the end of the push stage, the arm should rotate carefully to avoid upward pressure on the water, which could drag the body down.

2. Force applied: The greater the applied force, the greater the propulsion. While a longer arm provides better leverage, fully extended arms generate less force because they rely primarily on shoulder muscles, which are weaker than the chest and lats that power bent-arm movements. Furthermore, bent-arm motions keep the palm closer to the body’s center, ensuring stability. To engage these stronger muscles effectively, the body must slightly rotate, positioning the pushing arm under the body’s side.

Modeling Leg Propulsion

Legs perform repetitive downward sweeps to propel the body forward. Acting like fins, their efficiency depends on the flexibility of the ankles — greater flexibility results in more effective kicks (Science of Swimming Faster, p. 143). While there aren’t many variables to adjust, the key is to mimic fin-like, wave-like movements to optimize backward force.

This concludes my swimming model at this level of abstraction. While it’s a relatively simple model, it has already provided significant insight into the swimming process and the parameters I can adjust to improve efficiency.

Final Simple Model of a Swimmer

To summarize: a swimmer contracts and relaxes muscles to control the movement of their arms, legs, head, and body. Efficient movements — those that follow optimal trajectories — propel the swimmer forward while minimizing energy spending. Inefficient movements, on the other hand, generate less propulsion and more drag, leading to higher energy consumption and slower speeds.

Swimming is an intricate, dynamic system where, at every moment, each part of the body must not only be positioned precisely but also move with the correct speed, acceleration, and direction. This requires muscles that are flexible enough and strong enough to guide each body part along its predefined trajectory.

Testing the Model against Reality

To refine the model, I wanted to measure key parameters that could be adjusted through training or technique improvement. One effective way to do this is by using devices attached to the palms, which measure propulsion forces and track palm movements. These measurements provide insights into how my movements and forces align with the model I’ve developed. For example, this article describes one of the most popular devices for such purposes.

The parameters I ideally wanted to measure were:

1. Trajectories of each arm: To evaluate symmetry, efficiency, and the parameters of each freestyle stage.
2. Propulsion forces generated by each arm: To understand the direction and magnitude of forces and assess propulsion efficiency.
3. Metrics reflecting body streamlining: To estimate drag force based on streamline metrics and arm trajectories.
4. Propulsion force from kicks: To quantify the contribution of leg movements to overall propulsion.
5. Leg trajectories: To estimate drag caused by leg movements.

I found a coach who owned such a device and booked a session to collect these metrics. The session took place on October 1, 2024. I wasn’t in top physical condition that day due to illness, but this likely didn’t significantly affect the patterns or trajectories, as they depend more on muscle fatigue than overall physical state.

Results from the Session

Here are the key findings:

1. Arm Trajectories

• Side View: The trajectories resembled ovals for both hands. For the right hand, the oval was less consistent but still acceptable. The ovals had a radius of approximately 80 cm horizontally and vertically in the water. Above water, the vertical radius was about 25–35 cm.

• Top View: The trajectories appeared banana-shaped. The recovery phase formed a smooth arc with a radius of about 50 cm, while the pull phase created an inward arc. Notably, both hands did not cross the body’s midline. The arc radius during the pull phase varied: around 20 cm (likely during breathing) and 10 cm otherwise.

2. Propulsion Forces

• Force Values: Both hands generated similar propulsion forces. The right hand produced consistent forces of 2.5–3 N, peaking at 3.5 N. The left hand generally produced 2.5 N, peaking at 3–3.4 N, likely during breathing.

• Direction of Forces: Significant lateral (inward) movements: 27% for the right hand and 17% for the left. Substantial downward movements: 30–40% for the right hand and 40–50% for the left. Minimal upward movements: 0–3% for both hands. Negligible backward drag movement: 0–1% for the right hand, 2–4% for the left. Overall, only ~30% of the force contributed to effective propulsion.

• Forces During Stroke: Hands expended considerable force on lateral movements. Some drag force was evident during the glide (entry and catch) stages for both hands, more so for the right hand. Upward parasitic forces were visible at the end of the push phase due to incorrect hand recovery, where my palm faced upwards instead of towards my feet. The left hand initiated downward movement only during the push phase, which seems unusual.

• Total forces:

• Vertical forces:

• Lateral forces:

3. Body Streamlining Unfortunately, the device didn’t provide metrics for how streamlined my body was.

4. Leg Propulsion and Trajectories The device was attached only to my arms, so no data was available for kicks or leg trajectories.

Analysis and Inferences

After analyzing the metrics from the testing session, I drew the following conclusions.

The average propulsion force generated by my arms is around 2–4 N, which seems acceptable for now. However, the primary issues stem from inefficient use of this force due to incorrect trajectories.

The most noticeable discrepancies from ideal trajectories are as follows:

1. Significant lateral movements: Both hands exhibit large inward and outward motions during the pull and push phases. This not only wastes energy but also reduces forward propulsion.
2. Excessive depth of hands in water: Both hands descend too deep — up to 70 cm. This suggests that I’m not bending my arms enough, leading to overloading my shoulders while failing to fully engage my lats. Additionally, this might contribute to the lateral movements, as the shoulders struggle to stabilize the arms.
3. Stroke discrepancies between breath and non-breath phases: The left arm produces significantly better propulsion during strokes when I breathe (on the right side). This might be because breathing forces me to rotate my body more, improving the mechanics of the stroke.
4. Drag during entry and catch: Both hands generate drag at these stages, likely due to the palms being tilted slightly up or down instead of aligned with the flow of water.
5. Excessive downward force: A considerable portion of force is directed downward during both pull and push phases, which is counterproductive for propulsion.
6. Upward force before recovery: Just before the recovery phase, both hands generate upward force as I lift them out of the water. This happens because I fail to rotate my hands properly, causing the palms to push upwards instead of exiting cleanly.

A proper catching technique — bending the arms with a high elbow after the glide phase — should address the following key issues:

1. Reducing lateral movements: A more controlled, high-elbow catch can stabilize the arms and minimize unnecessary side-to-side motion.
2. Correcting hand depth: Bending the arms properly will prevent them from going too deep, distributing the workload more effectively between the shoulders and lats.
3. Reducing downward force: Proper arm alignment and trajectory during the catch phase can direct more force backward, where it contributes to propulsion, rather than downward, where it increases drag.

Using the Model to identify the reasons of my bad technique

The model has helped me understand the ideal trajectories and forces for my arms, allowing me to compare them with my actual movements. The next question is, “Why can’t I maintain the ideal trajectory for my arms and body movements?” After some thought, I’ve identified several possible reasons:

1. Lack of knowledge: I don’t know what the ideal trajectory is in each case.
2. Inability to observe: I know the ideal trajectory but can’t observe my current trajectory in real-time during swimming to compare it with the target.
3. Control limitations: I see discrepancies between my actual and ideal trajectories, but I can’t control my muscles accurately enough to correct them.
4. Physical limitations: My muscles may lack the strength or flexibility to execute the desired movements with the necessary accuracy, speed, or acceleration.
5. Biomechanical constraints: Physical features of my body, such as small palm surface area or short arms, might make it physically impossible to achieve ideal movement patterns.

These reasons are hypotheses, but they align with existing theory because this is still modeling.

Control theory (link) provides a useful framework for understanding these issues. It describes a system, like a swimmer, as a closed-loop controller that adjusts outputs (muscle movements) to align measured variables (trajectories, velocities, accelerations) with target values. Two essential properties determine whether a controller works:

1. Controllability: The controller (swimmer) can manipulate outputs (muscles).
2. Observability: The controller (swimmer) can observe inputs (trajectories, velocities, and accelerations).

Control theory also assumes that the controller “knows” the target values it is trying to achieve and adjusts outputs to minimize the difference between the actual and target values.

Using control theory terms, I can reframe the possible causes of my poor technique as follows:

1. No target values: The controller doesn’t know what it’s aiming for. (I don’t know the ideal trajectory.)
2. Broken observability: The inputs (current trajectories, velocities, accelerations) aren’t observable. (I know the ideal trajectory but can’t observe my own trajectory in real-time during swimming.)

3. Broken controllability:

• Control signal distortion: The signal from the controller to the system is lost or distorted. (I can’t control my muscles accurately enough to follow the ideal trajectory.)
• System incapacity: The system (muscles and body) can’t respond correctly to the control signal. (My muscles lack the strength, flexibility, or precision to execute the required movements. Physical limitations, such as small palms or short arms, may also contribute.)

After further consideration, I believe all these issues contribute to some degree. Let’s explore each:

1. Knowledge of the ideal trajectory: I have a general understanding of the ideal trajectory, but it’s not perfect.
2. Observation in real-time: I can observe my movements to some extent, but the accuracy is low, especially during swimming when my attention is divided across multiple factors.
3. Muscle control: This seems to be the primary problem: I don’t always know which muscles to engage to follow the ideal trajectory under load. I can’t control many muscles with the precision required — this ability only improves after extensive training.
4. Muscle strength and flexibility: I don’t know how to assess whether my muscles are strong or flexible enough to perform the movements correctly. However, I know that this ability degrades rapidly during a swim. After about 800 meters, all the previous issues worsen significantly.
5. Physical limitations: Certain physical attributes likely contribute to my slower speeds compared to elite swimmers, but these are minor factors compared to the issues above.

Model Limitations

The model has highlighted the gaps in my technique, but it’s not enough on its own. The real challenge is linking the ideal arm trajectory to each muscle and joint, then identifying discrepancies in muscle tension and joint positioning. With an enhanced model that includes these details, I could identify which muscles or joints need improvement and how to address them.

Unfortunately, building such a model and performing the required measurements seems unrealistic. While the insights I’ve gained are valuable, the complexity of human biomechanics and the lack of precise measurement tools make this next level of modeling impractical for now.

Modeling vs. Building

Another option for improving my swimming would be to consult a coach. A coach could observe my swimming, identify which muscles or joints are functioning incorrectly, propose exercises to train those muscles, develop a training plan, and guide me through it. If I followed such a plan diligently, I would likely see improvements in my swimming.

However, this approach doesn’t resemble traditional physical modeling or even the application of control theory. Instead, it feels more like creating a process for “building” a swimmer. This involves numerous choices — selecting the right coach, defining clear goals, undergoing diagnostics, organizing my time for training, and so on. It’s not just physics; it’s a combination of management and engineering.

When modeling a physical system or process, the task, while challenging, is relatively straightforward. You work with equations describing deterministic relationships in the real world: applying more force along an optimal trajectory increases speed, streamlining the body reduces drag, and so forth. The cause-and-effect relationships are clear.

But my goal isn’t just to model a swimmer — I want to create a good swimmer out of myself. This shifts the challenge from physical modeling to engineering. Engineering involves creating something artificial, and in this case, the “system” I’m trying to create — a proficient swimmer — is extraordinarily complex. There are countless interconnected parts, and the relationships between cause and effect aren’t always obvious. For instance, will swimming five times a week make me faster? Not necessarily — it depends on factors like session duration, intensity, technique, and specific activities in the pool.

When I began considering all of this, I felt overwhelmed by the complexity. I realized I needed a framework or discipline to help me manage this complexity and continue improving. Eventually, I discovered Systems Engineering.

Systems Engineering: A Solution for Complexity

Systems Engineering is a transdisciplinary field designed to model and organize the process of creation. Whether you’re building an airplane or training a swimmer, Systems Engineering provides a framework, set of practices, and a structured way of thinking. It doesn’t just focus on the system you want to create (the target system) — it also considers the creation system (the processes and tools used to build the target system) and the entire lifecycle of the system, including conceptualization, design, construction, maintenance, and eventual retirement.

I began studying Systems Engineering some time ago, and my next article will build on this one by applying its principles to my goal of creating a better swimmer out of myself. In hindsight, I should have started with Systems Engineering from the beginning. However, this journey has been a valuable lesson — I now have a clear understanding of my current swimming technique thanks to the modeling and measurements I’ve performed.