Critical Power & W' Model - Advanced Cycling Analytics

🎯 Key Takeaways

Critical Power (CP) is the maximum sustainable power for extended durations—more scientifically robust than FTP
W' (W Prime) is your anaerobic work capacity above CP, measured in kilojoules
W' Balance tracks real-time depletion and recovery of anaerobic capacity during rides
CP ≈ FTP + 5-10W in practice, but CP is derived mathematically from multiple efforts
Critical for MTB and variable efforts where pacing and surge management are essential

What is Critical Power?

Critical Power (CP) is the highest metabolic rate that can be sustained without fatigue for extended periods. It represents the boundary between sustainable aerobic metabolism and unsustainable exercise requiring anaerobic contribution. Unlike FTP (a single 1-hour estimate), CP is mathematically derived from multiple maximal efforts at different durations, making it more robust and scientifically validated.

The Science Behind Critical Power

Critical Power theory emerged from exercise physiology research in the 1960s and was refined for cycling in the 1990s. The model is based on the hyperbolic power-duration relationship:

Power-Duration Relationship

t = W' / (P - CP)

Where:

t = time to exhaustion
P = power output
CP = critical power (watts)
W' = anaerobic work capacity (kilojoules)

What this means: At any power above CP, you have a finite amount of work (W') before exhaustion. At CP itself, you can theoretically continue indefinitely. Below CP, you never tap into W' and can sustain effort for very long durations.

📚 Research Foundation

Critical Power is supported by decades of peer-reviewed research:

Jones et al. (2019): "Critical Power: Theory and Applications" - comprehensive review in Journal of Applied Physiology
Poole et al. (2016): "Critical Power: An Important Fatigue Threshold" - validates CP as physiological threshold
Vanhatalo et al. (2011): Demonstrates CP aligns with maximal lactate steady state

Critical Power vs FTP: Key Differences

Functional Threshold Power (FTP)

Definition: Maximum power sustainable for approximately 1 hour.

Testing: Single 20-minute or 60-minute effort.

Calculation: FTP = 95% of 20-min power (or 100% of 60-min power).

Pros:

Simple to test and understand
Single effort required
Widely used industry standard
Integrated in TrainingPeaks, Zwift, etc.

Cons:

Single-point estimate (less robust)
Mentally demanding 20-60 min effort
Pacing errors affect accuracy
No anaerobic capacity measure

Critical Power (CP)

Definition: Maximum sustainable power for theoretically infinite duration.

Testing: Multiple maximal efforts (3-7 min, 12 min, 20 min typical).

Calculation: Mathematical curve fitting from multiple data points.

Pros:

Scientifically robust (multiple efforts)
Includes W' (anaerobic capacity)
Better accuracy than single FTP test
Enables W' Balance tracking

Cons:

Requires 3-5 separate maximal efforts
More complex to calculate
Less widely understood
Testing protocol more demanding

🔍 In Practice: CP ≈ FTP + 5-10W

For well-trained cyclists, Critical Power is typically 5-10 watts higher than FTP. Example:

FTP: 250W (from 20-min test)
CP: 257W (from 3-min, 12-min, 20-min tests)

CP represents the theoretical infinite-duration threshold, while FTP is a practical 1-hour power estimate. Both are useful—FTP for simplicity, CP for precision and W' tracking.

What is W' (W Prime)?

W' (pronounced "W Prime") is the finite amount of work you can perform above Critical Power. Think of it as your "anaerobic battery"—a limited energy store that depletes when riding above CP and slowly recovers when riding below CP.

W' Definition

W' = (P - CP) × t

Where:

W' = anaerobic work capacity (kilojoules)
P = power output (watts)
CP = critical power (watts)
t = time to exhaustion (seconds)

Example: If you can sustain 350W for 5 minutes and your CP is 250W:
W' = (350 - 250) × 300 = 30,000 joules = 30 kJ

Typical W' Values

Cyclist Level	W' Range (kJ)	What This Means
Recreational	10-15 kJ	Limited surge capacity, shorter attacks
Competitive Amateur	15-20 kJ	Moderate anaerobic capacity, typical range
Elite Road	20-25 kJ	High surge capacity for attacks and sprints
Elite MTB/CX	18-23 kJ	Optimized for repeated surges

💡 Understanding W' in Real Riding

W' = 20 kJ example:

1 minute at 350W (100W above CP = 250W) = 6 kJ depleted → 14 kJ remaining
2 minutes at 300W (50W above CP) = 6 kJ depleted → 8 kJ remaining
30 seconds at 450W (200W above CP) = 6 kJ depleted → 2 kJ remaining
If W' depletes to zero → you're cooked, must drop below CP to recover

How to Calculate Your CP and W'

To determine your Critical Power and W', you need multiple maximal efforts at different durations. The standard protocol uses 3-5 time trials:

Standard CP Testing Protocol

Test 1

3-Minute Maximal Effort

After thorough warm-up, perform an all-out 3-minute effort. Record average power (e.g., 330W). Rest 30-60 minutes before next test (or test on separate day).

Test 2

12-Minute Maximal Effort

Perform a 12-minute time trial at maximum sustainable power. Record average power (e.g., 275W). Rest fully before final test.

Test 3

20-Minute Maximal Effort

Complete a 20-minute FTP-style effort. Record average power (e.g., 260W). This is your longest duration test.

Calculate

Mathematical Curve Fitting

Plot power vs time data and fit to hyperbolic curve. Bike Analytics does this automatically:

CP: Asymptote of power-duration curve (e.g., 250W)
W': Curvature constant (e.g., 18 kJ)

⚠️ Testing Best Practices

Consistent conditions: All tests same location, gearing, equipment
Fully rested: No hard training 24-48h before each test
Proper pacing: Each effort must be truly maximal for that duration
Adequate spacing: 24-48 hours between tests if not same-day protocol
Calibrated power meter: Zero-offset before each test

💡 Alternative: Use Existing Ride Data

If you have power data from recent races or hard rides, Bike Analytics can estimate CP and W' from your power duration curve:

Best 3-minute power from past 90 days
Best 5-minute power
Best 12-minute power
Best 20-minute power

This "historical best" method is less precise than dedicated tests but provides a reasonable starting estimate.

W' Balance: Real-Time Fatigue Tracking

W' Balance (W'bal) tracks your anaerobic capacity depletion and recovery in real-time during rides. This is the most powerful application of the CP model for pacing and race strategy.

How W'bal Works

Depletion Phase (Above CP):

When riding above CP, W' depletes linearly
Rate = (Current Power - CP)
Example: 50W above CP = 50 joules/second depletion

Recovery Phase (Below CP):

When riding below CP, W' recovers exponentially
Recovery rate depends on how far below CP
Lower power = faster recovery rate
Time constant τ ≈ 377 seconds (Skiba model)

W'bal Interpretation

W'bal = 100%: Fully recovered, ready for surges

W'bal = 75%: Still strong, can attack

W'bal = 50%: Moderate fatigue, be cautious

W'bal = 25%: High fatigue, limited surge capacity

W'bal = 0%: Completely exhausted, must ride below CP

Key insight: Even brief recoveries below CP restore W'. A 30-second recovery at 150W (100W below CP) can restore 2-3 kJ of W'.

🚴 Example: MTB Race W'bal Management

Scenario: 90-minute cross-country race, CP = 250W, W' = 20 kJ

Lap 1 (0-15 min): Conservative pace, W'bal stays 80-100%
Lap 2 (15-30 min): Hard climb (350W for 90s) → W'bal drops to 55%
Recovery (30-35 min): Easy descent (150W) → W'bal recovers to 70%
Lap 3 (35-50 min): Technical section with bursts → W'bal fluctuates 60-75%
Lap 4 (50-65 min): Attack on climb (380W for 60s) → W'bal drops to 40%
Final lap (65-90 min): Manage W'bal carefully, save for sprint finish

Result: By monitoring W'bal, rider knows exactly when surges are possible and when recovery is needed. No guessing based on "feel".

Practical Applications of CP and W'

1. Pacing Long Climbs

Use CP to determine sustainable climbing power. If climb duration is 30+ minutes, target power should be ≤ CP. Dipping slightly above CP is okay, but track W'bal to ensure you don't "blow up" before the top.

Example: 40-Minute Climb

CP = 250W: Sustainable target power
260W (10W over CP): Slight dip into W', but sustainable for 40 min
280W (30W over CP): Too high, W' depletes completely in ~11 minutes

2. MTB and Cyclocross Race Strategy

Off-road racing involves constant power surges above CP. Use W'bal to manage "matches burned"—each surge depletes W', and recovery periods must be sufficient to restore capacity.

MTB Surge Management:

Before attack: Check W'bal ≥ 60% (enough reserves)
During surge: Accept W' depletion, but know the cost
After surge: Drop below CP to recover W' before next effort
Late race: If W'bal < 30%, avoid big surges—you'll blow up

3. Criterium and Road Race Tactics

Criteriums require repeated accelerations and attacks. W'bal helps you know when you can respond to attacks and when you need to let the break go.

Crit Attack Decision:

W'bal = 85%: Go with the break—you have reserves
W'bal = 40%: Risky—might blow up chasing
W'bal = 15%: Stay in pack, recover W' for final sprint

4. Interval Training Design

Use CP and W' to structure intervals precisely. For VO₂max intervals, power should be CP + (W' / interval duration).

Example: 5-Minute VO₂max Intervals

CP = 250W, W' = 20 kJ
Target power: 250W + (20,000J / 300s) = 250W + 67W = 317W
This depletes W' completely in 5 minutes
Recovery: 5-10 min below CP to restore W'

5. Time Trial Pacing

For time trials longer than 30 minutes, ride slightly below CP to avoid W' depletion. Save W' for finishing surge.

40K TT Pacing:

First 35K: 95-98% of CP (conserve W')
Final 5K: Gradually increase to CP + 10-20W (use W')
Final 1K: Empty W' completely (sprint finish)

Critical Power & W': Frequently Asked Questions

Is CP better than FTP?

CP is more scientifically robust because it's derived from multiple efforts, not a single test. However, FTP is simpler and widely understood. For most cyclists, FTP is sufficient. Use CP if you want precision, W' tracking, or race pacing models. In practice, CP ≈ FTP + 5-10W.

How long does W' take to fully recover?

Recovery is exponential, not linear. At 100W below CP, W' recovers ~50% in 6 minutes, 75% in 12 minutes, 90% in 20 minutes. Full recovery (99%+) takes 30-40 minutes at very low power. The further below CP you ride, the faster W' recovers. Complete rest (0W) is NOT optimal—light spinning (~100-150W) accelerates recovery.

Can I train to increase W'?

Yes—W' is trainable through anaerobic intervals. VO₂max intervals (3-8 min at 110-120% CP) and repeated surges (30-90s at 150%+ CP) expand W'. Road sprinters and MTB racers typically have higher W' than endurance riders. Training focus: 1-2 sessions/week of high-intensity intervals that deplete W' completely, followed by adequate recovery.

Does W' decrease as a ride progresses?

Yes—W' capacity decreases with accumulated fatigue. Early in a ride, you might have 20 kJ available. After 2-3 hours of hard riding, effective W' may drop to 12-15 kJ. This is why late-race surges feel harder—your anaerobic reserve is compromised. Bike Analytics can model this W' depletion using fatigue factors.

How often should I retest CP and W'?

Every 8-12 weeks during training progression. CP increases more slowly than FTP (it's more stable). W' can change significantly with targeted anaerobic training. Retest after major training blocks, illness, or injury. CP/W' are more resistant to short-term fitness fluctuations than FTP.

Can I use CP for indoor training?

Absolutely—CP is ideal for indoor training. Smart trainers provide stable power, making CP testing highly accurate. Zwift, TrainerRoad, and other platforms support CP-based workouts. W'bal tracking works perfectly indoors where power is consistent. Many coaches prefer CP for structured indoor training.

What is the Skiba W' Balance model?

Dr. Philip Skiba's 2012 model mathematically tracks W' depletion and recovery. It uses differential equations with time constant τ ≈ 377 seconds for recovery kinetics. This model is implemented in WKO5, Golden Cheetah, and Bike Analytics. It's the gold standard for real-time W'bal calculation during rides. Research: Skiba et al. (2012, 2014, 2021) in Medicine & Science in Sports & Exercise.

Can CP and W' predict race performance?

Yes—with high accuracy for efforts 3-60 minutes. The CP model can predict time-to-exhaustion at any given power. Example: If CP = 250W and W' = 20 kJ, you can sustain 300W for exactly 6.67 minutes (20,000J / 50W = 400s). For longer efforts (>60 min), CP slightly overestimates sustainable power due to additional fatigue factors.

How does altitude affect CP and W'?

CP decreases ~1% per 300m above 1500m altitude. W' is less affected because anaerobic capacity doesn't depend on oxygen. At 2500m, expect CP to drop 3-4% but W' remains similar. This means at altitude, your sustainable power drops but your surge capacity (relative to new CP) is maintained. Retest CP at altitude for accurate training zones.

Should I use CP for Zone 4 threshold training?

Yes—CP defines Zone 4 threshold precisely. Threshold intervals should be at 95-105% of CP. Unlike FTP (estimated from a single test), CP provides a mathematically derived threshold. For sustained tempo efforts (2×20 min), ride at CP. For shorter intervals (5×5 min), ride at CP + 3-5%. Bike Analytics calculates training zones from CP automatically.

Research References

Jones, A.M., Burnley, M., Black, M.I., Poole, D.C., & Vanhatalo, A. (2019)

Critical Power: Theory and Applications

Journal of Applied Physiology, 126(6), 1905-1915.

Comprehensive review of critical power theory, physiological underpinnings, and practical applications for athletes and coaches.

Skiba, P.F., Chidnok, W., Vanhatalo, A., & Jones, A.M. (2012)

Modeling the Expenditure and Reconstitution of Work Capacity Above Critical Power

Medicine and Science in Sports and Exercise, 44(8), 1526-1532.

Introduces the W' Balance model with exponential recovery kinetics. Foundation for real-time W'bal tracking.

Skiba, P.F., & Clarke, D.C. (2021)

The W′ Balance: Mathematical and Methodological Considerations

International Journal of Sports Physiology and Performance, 16(11), 1561-1572.

Updated review of W' Balance calculation methods, validation studies, and practical implementation considerations.

Poole, D.C., Burnley, M., Vanhatalo, A., Rossiter, H.B., & Jones, A.M. (2016)

Critical Power: An Important Fatigue Threshold in Exercise Physiology

Medicine and Science in Sports and Exercise, 48(11), 2320-2334.

Validates critical power as a physiological threshold separating heavy from severe exercise domains.

Clark, I.E., Vanhatalo, A., Thompson, C., et al. (2021)

A Comparative Analysis of Critical Power Models in Elite Road Cyclists

European Journal of Applied Physiology, 121, 3027-3037.

Compares different CP calculation methods in elite cyclists. Shows CP aligns with respiratory compensation point.

📚 Further Reading

Training and Racing with a Power Meter (3rd Ed.) by Hunter Allen & Andrew Coggan - Chapter on Critical Power and W'
WKO5 Software Documentation - Detailed CP and W'bal implementation guides
Golden Cheetah CP Analysis - Open-source tools for CP curve fitting

Related Resources

FTP Testing

Learn the standard 20-minute FTP test protocol and how FTP relates to Critical Power.

FTP Guide →

Training Zones

Understand the 7-zone power-based training system derived from CP or FTP.

Training Zones →

Training Load

Learn how CP affects TSS calculation and overall training stress management.

TSS & PMC →

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