Critical Power and Pacing (Multisport)

📋 What is Critical Threshold

Critical Threshold represents the boundary between sustainable and unsustainable exercise intensity:

• 🚴 Cycling: Critical Power (CP) - The highest power you can sustain without fatigue
• 🏃 Running: Critical Velocity (CV) - The fastest pace you can maintain indefinitely
• 🏊 Swimming: Critical Swim Speed (CSS) - Your sustainable swim speed

Why it matters:

• More accurate than FTP or lactate threshold for some applications
• Predicts performance across different durations
• Helps set precise training zones
• Validated by decades of sports science research

🎯 STEP-BY-STEP GUIDE

STEP 1: Choose Your Sport

Click one of the three sport buttons at the top:

• 🚴 Cycling - Uses power meter data (watts)
• 🏃 Running - Uses distance and time (pace-based)
• 🏊 Swimming - Uses distance and time (pace-based)

STEP 2: Select Test Mode

Choose how you want to analyze your data:

Option A: 2 Tests (Fast, Deterministic) ⚡

Best for:

• Quick estimates
• Retesting to track progress
• When you only have 2 maximal efforts

How it works:

• Fits exact hyperbolic curve to your 2 test points
• No validation (assumes both tests are perfect)
• Fast calculation

Example:

Test 1: 3 min @ 350W
Test 2: 12 min @ 280W
→ Exact fit through both points

Option B: 3 Tests (Pair Validation) ⭐ RECOMMENDED

Best for:

• Most users
• Quality control
• Detecting pacing errors

How it works:

• Tests all 3 combinations of test pairs: (1,2), (1,3), (2,3)
• Fits model to each pair
• Predicts the 3rd point
• Chooses the pair with best validation
• Shows you the error on the unused point

Validation indicators:

• ✅ Green (<3% error): Excellent - very consistent pacing
• ⚠️ Yellow (3-7% error): Acceptable - minor inconsistency
• 🚫 Red (>7% error): Poor - retest recommended

Example:

Test 1: 3 min @ 350W
Test 2: 8 min @ 305W
Test 3: 12 min @ 280W

Calculator tries:
- Fit (1,2), predict 3: 2.1% error ← BEST
- Fit (1,3), predict 2: 5.8% error
- Fit (2,3), predict 1: 4.2% error

Result: Uses tests 1 & 2, validates with test 3
Shows: ✅ Excellent fit (2.1% error)

Option C: 3 Tests (Morton Model) 🎓 ADVANCED

Best for:

• Advanced users
• When you have very short duration tests (<2 min)
• Research or lab testing

How it works:

• Fits 3-parameter model: y = θ + φ/(t + k)
• Adds curvature parameter k for short durations
• More complex but can be more accurate
• Automatically falls back to Pair Validation if it fails

When to use:

• You have a test under 90 seconds
• You want maximum accuracy
• You understand the model limitations

STEP 3: Enter Your Test Data

🚴 CYCLING

What you need:

• Power meter data (average watts)
• Duration of each effort (minutes)

Recommended test durations:

• Test 1 (short): 3-8 minutes
• Test 2 (long): 12-25 minutes
• Test 3 (middle): 6-10 minutes

Example input:

Test 1:
  Duration: 5 (minutes)
  Power: 350 (watts)

Test 2:
  Duration: 20 (minutes)
  Power: 280 (watts)

Important tips:

• Warm up 15-20 minutes before each test
• Ride at maximum sustainable power (not sprinting)
• Keep power as steady as possible
• Indoor trainer preferred (more consistent)
• Rest 24-48 hours between tests

🏃 RUNNING

What you need:

• Distance (meters)
• Time (can enter as MM:SS or total seconds)

Recommended test distances:

• Test 1 (short): 1200-1600 meters
• Test 2 (long): 3200-5000 meters
• Test 3 (middle): 2000-3000 meters

Example input:

Test 1:
  Distance: 1200 (meters)
  Time: 4:30 (or 270 seconds)

Test 2:
  Distance: 3200 (meters)
  Time: 12:15 (or 735 seconds)

Important tips:

• Use a track or flat, measured course
• Pace as evenly as possible
• All-out effort (maximal sustainable pace)
• GPS watches can be inaccurate - use known distances
• Similar conditions for all tests (weather, time of day)

🏊 SWIMMING

What you need:

• Distance (meters)
• Time (can enter as MM:SS.d with tenths of a second)

Recommended test distances:

• Test 1 (short): 200 meters
• Test 2 (long): 400-800 meters
• Test 3 (middle): 300-400 meters

Example input:

Test 1:
  Distance: 200 (meters)
  Time: 2:45.2 (or 165.2 seconds)

Test 2:
  Distance: 400 (meters)
  Time: 6:20.5 (or 380.5 seconds)

Important tips:

• Use pool swimming (more accurate than open water)
• Push-off and turns count (part of your race performance)
• Maximal effort from the start
• Maintain technique (don't thrash)
• Long course (50m) preferred over short course (25m)

STEP 4: Click Calculate

The calculator will:

1. ✅ Validate your inputs (check for errors)
2. 📊 Fit the appropriate model
3. 📈 Generate a graph showing your tests and curve
4. 📋 Display your results
5. 🎯 Enable the pacing calculator

STEP 5: Understand Your Results

📊 THE GRAPH

The graph shows:

• Blue curve - Your power/speed model across all durations
• Purple dots - Test points used to fit the model
• Green/Yellow/Red dot - Validation point (3-test mode)
  • Green: <3% error (excellent)
  • Yellow: 3-7% error (acceptable)
  • Red: >7% error (retest recommended)

What to look for:

• Points should be close to the curve
• No single point far from the line
• Smooth hyperbolic shape

📋 RESULTS METRICS

🚴 Cycling:

• Critical Power (CP): Your threshold in watts
• FTP (95% CP): Training intensity (~1 hour power)
• W' (Anaerobic Capacity): Energy above CP in kilojoules

🏃 Running:

• Critical Velocity (CV): Threshold speed (m/s)
• CV Pace: Threshold pace (min/km)
• Threshold Pace: Training pace (~1 hour)
• D' (Anaerobic Distance): Distance capacity in meters
• Race Predictions: Estimated times for 5K, 10K, Half Marathon

🏊 Swimming:

• CSS (Critical Swim Speed): Threshold speed (m/s)
• CSS Pace: Threshold pace (min/100m)
• T30 Pace: Training pace (~30 min sustainable)
• D' (Anaerobic Capacity): Distance capacity in meters
• Predicted Times: Estimates for 400m, 800m, 1500m

✅ VALIDATION STATUS

3-Test Pair Validation Mode shows:

✅ Excellent fit (2.1% error on test 3)

• Your pacing was very consistent
• High confidence in results
• Use these values for training

⚠️ Acceptable fit (5.2% error on test 2)

• Results are usable but slight inconsistency detected
• Consider retesting for more accuracy
• May have paced one test differently

🚫 Poor fit (9.8% error). Consider retesting with better pacing.

• Significant inconsistency detected
• One test likely paced incorrectly
• Retest with more even pacing
• Results less reliable

STEP 6: Use the Pacing Calculator

After getting your results, scroll down to the Pacing Calculator section.

🚴 Cycling Pacing:

Option 1: Estimate power for a duration

Input: 8 minutes
Output: 313 watts

Use this to: Plan interval training, predict race power

Option 2: Estimate duration for a power

Input: 300 watts
Output: 9.3 minutes

Use this to: See how long you can hold target power

🏃 Running Pacing:

Option 1: Predict race time

Input: 5000 meters (5K)
Output: 19:16

Use this to: Set race goals, predict performance

Option 2: Find max sustainable distance

Input: 4:00/km pace
Output: 8,450 meters

Use this to: Plan long runs, understand pace limits

🏊 Swimming Pacing:

Option 1: Predict swim time

Input: 1500 meters
Output: 26:52

Use this to: Plan race strategy, set goals

Option 2: Find max distance at pace

Input: 1:45/100m pace
Output: 1,240 meters

Use this to: Plan training sets

🎓 INTERPRETING YOUR RESULTS

What is a "good" result?

Validation (3-test mode):

• <3% error: Excellent - your tests are very reliable
• 3-5% error: Good - normal variation
• 5-7% error: Acceptable - some inconsistency
• >7% error: Poor - retest with better pacing

Absolute values depend on your fitness level, but here are some benchmarks:

🚴 Cycling CP (watts/kg):

• 5.0+ W/kg: World-class
• 4.0-5.0 W/kg: Competitive racer
• 3.0-4.0 W/kg: Strong amateur
• 2.5-3.0 W/kg: Recreational cyclist
• <2.5 W/kg: Beginner/fitness

🏃 Running CV (pace):

• <3:00/km: Elite
• 3:00-3:30/km: Competitive
• 3:30-4:30/km: Strong runner
• 4:30-5:30/km: Recreational
• >5:30/km: Beginner/fitness

🏊 Swimming CSS (pace/100m):

• <1:15/100m: Elite
• 1:15-1:30/100m: Competitive
• 1:30-1:50/100m: Strong swimmer
• 1:50-2:15/100m: Recreational
• >2:15/100m: Beginner/fitness

🔧 TROUBLESHOOTING

"Calculation failed. Check inputs and try again."

Possible causes:

• Empty fields - fill in all test data
• Negative numbers - use positive values only
• Test 1 must be shorter than Test 2
• Test 1 must be higher intensity than Test 2

Fix: Double-check your inputs follow the model assumptions

"Test 1 duration must be shorter than Test 2"

Cause: You entered a longer duration for Test 1

Fix:

• Test 1 should be the SHORT effort (3-8 min cycling, 1200-1600m running)
• Test 2 should be the LONG effort (12-25 min cycling, 3200-5000m running)
• Swap your test numbers if needed

"Test 1 value must be higher than Test 2"

Cause: Your shorter test has lower power/speed than longer test

Fix:

• Shorter efforts should be higher intensity
• Check you didn't mix up test data
• If data is correct, you may not have been maximal on the short test

High validation error (>7%)

Possible causes:

1. Inconsistent pacing - One test had surges or fading
2. Different conditions - Tests done in very different weather/fatigue
3. Not maximal - One test wasn't truly all-out effort
4. Equipment issues - Power meter drift, GPS errors, etc.

Solutions:

• Retest with more even pacing
• Use indoor/controlled environment
• Ensure all tests are genuinely maximal
• Check equipment calibration

Graph doesn't show

Cause: Chart.js library not loaded

Fix:

• Check browser console (F12) for errors
• Verify Chart.js CDN is accessible
• Try different browser
• Clear browser cache (Ctrl+Shift+R)

💡 TIPS FOR BEST RESULTS

Testing Protocol:

1. Warm up properly
   • 15-20 minutes easy
   • 2-3 short accelerations
   • Feel ready to give max effort
2. Choose good conditions
   • Similar weather/temperature
   • No headwind (or consistent conditions)
   • Not fatigued from previous training
3. Pace evenly
   • No sprint starts
   • Avoid dying at the end
   • Steady, sustainable max effort
4. Rest between tests
   • Minimum 24 hours
   • Ideally 48 hours
   • Fully recovered for each test
5. Use proper equipment
   • Calibrated power meter (cycling)
   • Measured course (running)
   • Pool with known distance (swimming)

When to Retest:

Retest if:

• Validation error >7%
• Results don't match perceived fitness
• Equipment changed (new bike, power meter)
• Training block completed

6 weeks since last test

How often to test:

• Every 4-6 weeks during training
• Start and end of training block
• Before and after rest/taper
• When fitness changes significantly

📚 UNDERSTANDING THE SCIENCE

The Hyperbolic Model

The calculator uses the equation:

y = θ + φ/t

Where:

• y = performance (power or speed)
• θ = threshold (CP, CV, or CSS)
• φ = capacity (W' or D')
• t = duration (time)

What this means:

• At very short durations, capacity dominates (high power/speed)
• At long durations, threshold dominates (sustainable power/speed)
• The curve connects these two extremes

Why This Works

Scientific basis:

1. Energy systems have limited capacity above threshold
2. This capacity depletes at rate: (intensity - threshold)
3. Hyperbolic model accurately describes this relationship
4. Validated across thousands of athletes and decades of research

Key papers:

• Monod & Scherrer (1965) - Original model
• Jones et al. (2010) - CP in sports
• Poole et al. (2016) - Critical Power concept
• Bundle et al. (2017) - CV predicts running performance

Limitations

The model works best:

• For efforts between 2-30 minutes
• With consistent pacing
• In similar conditions
• When truly maximal

The model breaks down:

• Very short (<90 seconds) - anaerobic dominates
• Very long (>40 minutes) - fatigue/fueling issues
• Inconsistent pacing - violates assumptions
• Different environments - wind, heat, hills

🎯 USING RESULTS FOR TRAINING

🚴 Cycling Training Zones

Based on your CP:

• Zone 1 (Recovery): <55% CP
• Zone 2 (Endurance): 55-75% CP
• Zone 3 (Tempo): 75-90% CP
• Zone 4 (Threshold): 90-105% CP
• Zone 5 (VO2max): 105-120% CP
• Zone 6 (Anaerobic): >120% CP

Example with CP = 250W:

• Z1: <138W
• Z2: 138-188W
• Z3: 188-225W
• Z4: 225-263W
• Z5: 263-300W
• Z6: >300W

🏃 Running Training Paces

Based on your CV:

• Easy: CV pace + 60-90 sec/km
• Tempo: CV pace + 15-30 sec/km
• Threshold: CV pace ± 5 sec/km
• Intervals: CV pace - 10-30 sec/km

Example with CV pace = 4:00/km:

• Easy: 5:00-5:30/km
• Tempo: 4:15-4:30/km
• Threshold: 3:55-4:05/km
• Intervals: 3:30-3:50/km

🏊 Swimming Training Sets

Based on your CSS:

• Aerobic: CSS pace + 10-20 sec/100m
• Threshold: CSS pace ± 5 sec/100m
• VO2max: CSS pace - 5-10 sec/100m

Example with CSS = 1:40/100m:

• Aerobic: 1:50-2:00/100m
• Threshold: 1:35-1:45/100m
• VO2max: 1:30-1:35/100m

✅ QUICK REFERENCE

🚴 CYCLING

• Tests: 3-8 min + 12-25 min
• Input: Duration (min) + Power (W)
• Output: CP (W), FTP (W), W' (kJ)

🏃 RUNNING

• Tests: 1200-1600m + 3200-5000m
• Input: Distance (m) + Time (MM:SS)
• Output: CV (m/s), Pace (min/km), D' (m)

🏊 SWIMMING

• Tests: 200m + 400-800m
• Input: Distance (m) + Time (MM:SS.d)
• Output: CSS (m/s), Pace (min/100m), D' (m)

VALIDATION

• <3%: ✅ Excellent
• 3-7%: ⚠️ Acceptable

7%: 🚫 Retest

📖 FURTHER READING

Want to learn more?

Check out these resources:

• "Training and Racing with a Power Meter" by Hunter Allen & Andrew Coggan
• "Daniels' Running Formula" by Jack Daniels
• "Science of Swimming Faster" by Scott Riewald

Research papers:

• Search "critical power" on PubMed or Google Scholar
• Look for papers by Andy Jones, David Poole, and Matt Bundle