Technical Reference & Formulas

Formula:

JavaScript Implementation:

function calculateCRS(distance1, time1, distance2, time2) {
  // Convert times to seconds
  const t1 = typeof time1 === 'string' ? timeToSeconds(time1) : time1;
  const t2 = typeof time2 === 'string' ? timeToSeconds(time2) : time2;

  // Calculate CRS velocity in m/s
  const crs_ms = (distance2 - distance1) / (t2 - t1);

  // Calculate pace per km in seconds
  const pace_per_km = 1000 / crs_ms;

  // Convert to mm:ss format
  const minutes = Math.floor(pace_per_km / 60);
  const seconds = Math.round(pace_per_km % 60);

  return {
    velocity_ms: crs_ms,
    pace_seconds: pace_per_km,
    pace_formatted: `${minutes}:${seconds.toString().padStart(2, '0')}`
  };
}

Complete Formula:

JavaScript Implementation:

function calculateRTSS(distance, timeMinutes, ftpMetersPerMin) {
  // Calculate Normalized Run Speed
  const nss = distance / timeMinutes;

  // Calculate Intensity Factor
  const intensityFactor = nss / ftpMetersPerMin;

  // Calculate hours
  const hours = timeMinutes / 60;

  // Calculate rTSS using quadratic intensity factor
  const rtss = Math.pow(intensityFactor, 2) * hours * 100;

  return Math.round(rtss);
}

// Example usage:
const rtss = calculateRTSS(3000, 55, 64.5);
// Returns: 65

// Helper: Convert CRS Pace to Running Speed (m/min)
function crsPaceToSpeed(crsPacePerKmSeconds) {
  // Speed in m/min = 1000m / (pace in minutes)
  return 1000 / (crsPacePerKmSeconds / 60);
}

// Example: CRS of 4:15 (255 seconds)
const speed = crsPaceToSpeed(255); // Returns: 235.3 m/min

Formula:

JavaScript Implementation:

function calculateVerticalRatio(oscillationCm, strideLengthCm) {
  return (oscillationCm / strideLengthCm) * 100;
}

function calculateEfficiencyFactor(paceMetersPerMin, avgHeartRate) {
  return paceMetersPerMin / avgHeartRate;
}

Formulas:

JavaScript Implementation:

function updateCTL(previousCTL, todayTSS) {
  return previousCTL + (todayTSS - previousCTL) * (1/42);
}

function updateATL(previousATL, todayTSS) {
  return previousATL + (todayTSS - previousATL) * (1/7);
}

function calculateTSB(yesterdayCTL, yesterdayATL) {
  return yesterdayCTL - yesterdayATL;
}

// Calculate PMC for series of workouts
function calculatePMC(workouts) {
  let ctl = 0, atl = 0;
  const results = [];

  workouts.forEach(workout => {
    ctl = updateCTL(ctl, workout.tss);
    atl = updateATL(atl, workout.tss);
    const tsb = calculateTSB(ctl, atl);

    results.push({
      date: workout.date,
      tss: workout.tss,
      ctl: Math.round(ctl * 10) / 10,
      atl: Math.round(atl * 10) / 10,
      tsb: Math.round(tsb * 10) / 10
    });
  });

  return results;
}

// Example usage:
const workouts = [
  { date: '2025-01-01', tss: 50 },
  { date: '2025-01-02', tss: 60 },
  { date: '2025-01-03', tss: 45 },
  // ... more workouts
];

const pmc = calculatePMC(workouts);
// Returns array with CTL, ATL, TSB for each day

JavaScript Implementation:

function validateWorkoutData(workout) {
  const issues = [];

  // Check for reasonable pace ranges (3:00-8:00 per km)
  const avgPaceSecs = workout.totalTime / (workout.totalDistance / 1000);
  if (avgPaceSecs < 180 || avgPaceSecs > 480) {
    issues.push(`Unusual average pace: ${Math.round(avgPaceSecs)}s per km`);
  }

  // Check for reasonable Vertical Ratio (4% - 15%)
  if (workout.avgVerticalRatio < 4 || workout.avgVerticalRatio > 15) {
    issues.push(`Unusual Vertical Ratio: ${workout.avgVerticalRatio}%`);
  }

  // Check for reasonable cadence (120-220 SPM)
  const avgCadence = calculateCadence(workout.totalSteps, workout.totalTime);
  if (avgCadence < 120 || avgCadence > 220) {
    issues.push(`Unusual cadence: ${Math.round(avgCadence)} SPM`);
  }

  // Check for missing segments (gaps in time)
  if (workout.segments && workout.segments.length > 1) {
    for (let i = 1; i < workout.segments.length; i++) {
      const gap = workout.segments[i].startTime -
                  (workout.segments[i-1].startTime + workout.segments[i-1].duration);
      if (gap > 300) { // 5 minute gap
        issues.push(`Large gap detected between segments ${i} and ${i+1}`);
      }
    }
  }

  return {
    isValid: issues.length === 0,
    issues
  };
}

// Example:
const workout = {
  totalDistance: 2000,
  totalTime: 1800, // 30 minutes
  totalStrides: 800,
  segments: [/* kilometer data */]
};
const validation = validateWorkoutData(workout);
// Returns: { isValid: true, issues: [] }