Wbal Model

Work Balance & Power Output Modeling

Interactive Wbal Simulation

Explore how W balance (Wbal) evolves during high-intensity interval training (HIIT) sessions. Adjust the parameters below to see how different session designs and athlete characteristics affect W balance depletion and recovery.

Excel Implementation

You can replicate this Wbal model in Excel using the following step-by-step approach:

Setup Your Spreadsheet

1. Column A: Time (t) in seconds: 0, 1, 2, 3, ...
2. Column B: Power (P) values for your session
3. Column C: W balance calculations
4. Column D: Tau Wp calculations (optional)

Mathematical Implementation

The Wbal model uses different equations depending on whether power is above or below CP:

When Power ≤ CP (Recovery):

When Power > CP (Depletion):

Excel Formula Implementation

Use this formula in cell C3 for $W_{bal,k+1}$:

=IF(B2<=CP, C2+(CP-B2)*((Wp-C2)/Wp), C2-(B2-CP))

Copy this formula down column C for all time points.

Key Points for Excel Implementation

• Row indices: Use $k$ for current row, $k+1$ for next row
• IF statement: Checks if $P_k \leq CP$ to determine recovery or depletion
• Recovery rate: Depends on current Wbal level - the lower the Wbal, the slower the recovery
• Depletion rate: Simple linear subtraction of power above CP

Model Parameters

• CP (Critical Power): The highest sustainable power output
• Wp: The curvature constant of the power/duration relationship
• Interval Parameters: Length, power, and number of intervals
• Recovery: Equal duration at 0 Watts between intervals

Understanding the Model

The Wbal model captures the dynamics of high-intensity exercise capacity:

• Above CP: $W_{bal}$ depletes linearly at rate $P_k - CP$
• Below CP: $W_{bal}$ recovers exponentially
• At CP: $W_{bal}$ remains constant (sustainable intensity)