Moment of inertia is the key to power

Moment of inertia is the key to power

Written by: Brian Laposa

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Time to read 3 min

The data analysis conducted by the Coretek Analytics Team provides a quantitative, data-driven understanding of what truly creates paddle power, moving beyond subjective marketing terms. This analysis reveals several key physical principles underlying paddle design and their impact on power generation:


* **Engineered Features are Paramount**: The most critical step in the analysis involved creating **engineered features** that capture real-world physics. These features proved to be the most important predictors of paddle power, validating Coretek's physics-based approach.

    * **Rotational_Mass**: This engineered feature is calculated as **Weight (oz) * Balance Point (mm)**.

        * **Why it Matters (Physics)**: It directly measures how "head-heavy" a paddle is, which is a **direct proxy for its ability to generate momentum during a swing**. More momentum translates to more power transfer to the ball.

        * **Importance**: Rotational_Mass was identified as the **clear #1 most important predictor of power**. To maximize power, engineers must design paddles that are **heavier, more head-heavy, or both**.

    * **Power_to_Stiffness_Ratio**: This engineered feature is calculated as **Swingweight / Core Thickness (mm)**.

        * **Why it Matters (Physics)**: It captures the **interplay between the paddle's overall mass in motion (Swingweight) and the "trampoline effect" of its core (Core Thickness)**. A **thin, stiff core returns more energy to the ball**.

        * **Importance**: This ratio is the second most important predictor of paddle power. For high-power paddles, it's crucial to pair high rotational mass with a **high swingweight relative to its core thickness (i.e., a thinner, stiffer core)**.


* **Hierarchy of Power**: The Gradient Boosting model, which was the most accurate for capturing complex relationships, provided a clear ranking of feature importance based on physics:

    1. **Rotational_Mass** (The clear #1).

    2. **Power_to_Stiffness_Ratio**.

    3. **Twistweight**: This characteristic is crucial for **usable power** by contributing to the paddle's stability during a swing.

    4. **Swingweight**: The overall mass in motion.

    5. **Core Thickness (mm)**: Directly impacts the "trampoline effect".


* **Engineer's Decision Tree Insights**: The data analysis was translated into a practical **decision tree for paddle engineers**, which highlights the hierarchical impact of controllable physical characteristics on power.

    * The design process should **begin with optimizing Rotational_Mass** as the primary lever for power.

    * Following that, **optimizing the Power-to-Stiffness-Ratio** is the secondary goal for maximum power.

    * The tree also quantifies **design trade-offs**, showing, for example, that choosing a thicker, more forgiving core on a paddle with low rotational mass will result in the lowest power output.


* **Other Physical Characteristics Influencing Power**: Outlier analysis further revealed common physical characteristics among paddles with unusually high or low 'Usable Power Index':

    * **Paddle Shape**: **Non-widebody shapes** are predominantly found among high-power outliers, suggesting that narrower, more elongated shapes might contribute to higher power. Conversely, widebody shapes are associated with lower power.

    * **Grit Type**: **'Grit Type_Raw Texture/Peel Ply'** is significantly more prevalent in high-power paddles.

    * **Build Generation**: Paddles belonging to **'Generation/Build_Gen 3/Edgeless'** are frequently observed in high-power outliers, indicating that these material and construction choices are conducive to higher usable power. 'Generation/Build_Gen 2' is associated with lower power.

    * **Paddle Type**: Paddles classified as **'Paddle Type_Control'** inherently exhibit much lower power, as their design prioritizes feel and placement over raw power.


In summary, the data analysis moves beyond qualitative descriptions to provide **precise, actionable insights** into how physical design choices, particularly **Rotational_Mass and Power_to_Stiffness_Ratio**, directly influence a paddle's power output. It shows that **power is driven by a system of interacting features**, and optimizing these physics-based metrics is key to designing demonstrably better paddles.

It's important to note that we trained our model on physical characteristics of paddles without any power data. However we later verified it on power of power data and found that our model was able to predict power with 0.47 r squared. And an Mae of about one mile per hour. Why is this all important? We discovered that rotational Mass is without doubt the best indicator of power in a paddle that we can find. This is understandable as it combines multiple features of paddle performance. Our engineered rotational Mass feature was essentially identical to the moment of inertia used in pickleball coefficient of restitution testing.

In fact based on the significance of this engineered feature it's hard to understand why moment of inertia alone would not be sufficient for regulatory purposes. It's also important to question considering the importance of balance and paddles weight is allowing modified paddles in Pro play reasonable? If it is, the end weight of paddle should be considered in trying to regulate manufacturers. Pickleball coefficient of restitution is still as far as we are concerned a very pointless and damaging regulation as it essentially only is important for pro play and it doesn't even test the paddles as they are used. It's hard to see what the purpose of this regulation is.

 

Brian Laposa

Coretek Pickleball 

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