Technische Referentie & Formules
Volledige Wiskundige Implementatie
Implementatiegids
Deze pagina biedt kopieer-en-plak formules en stapsgewijze berekeningsmethoden voor alle Run Analytics-metrieken. Gebruik deze voor aangepaste implementaties, verificatie of een dieper begrip.
⚠️ Implementatieopmerkingen
- Alle tijden moeten voor berekeningen naar seconden worden omgezet
- Looptempo is omgekeerd (hoger % = trager tempo)
- Valideer altijd invoer voor redelijke bereiken
- Behandel randsituaties (deling door nul, negatieve waarden)
Kern Prestatiemetrieken
Critical Run Speed (CRS)
Formule:
CRS (m/s) = (D₂ - D₁) / (T₂ - T₁)
CRS Pace/100m (seconden) = (T₄₀₀ - T₂₀₀) / 2
🧪 Interactieve Calculator - Test de Formule
CRS Tempo per 100m:
1:49
Berekeningsstappen:
CRS (m/s) = (400 - 200) / (368 - 150) = 0.917 m/s
Pace/100m = 100 / 0.917 = 109 seconden = 1:49
CRS (m/s) = (400 - 200) / (368 - 150) = 0.917 m/s
Pace/100m = 100 / 0.917 = 109 seconden = 1:49
JavaScript Implementatie:
function calculateCRS(distance1, time1, distance2, time2) {
// Convert times to seconds if needed
const t1 = typeof time1 === 'string' ? timeToSeconds(time1) : time1;
const t2 = typeof time2 === 'string' ? timeToSeconds(time2) : time2;
// Calculate CRS in m/s
const css_ms = (distance2 - distance1) / (t2 - t1);
// Calculate pace per 100m in seconds
const pace_per_100m = 100 / css_ms;
// Convert to mm:ss format
const minutes = Math.floor(pace_per_100m / 60);
const seconds = Math.round(pace_per_100m % 60);
return {
css_ms: css_ms,
pace_seconds: pace_per_100m,
pace_formatted: `${minutes}:${seconds.toString().padStart(2, '0')}`
};
}
// Example usage:
const result = calculateCRS(200, 150, 400, 368);
// Returns: { css_ms: 0.917, pace_seconds: 109, pace_formatted: "1:49" }
Run Training Stress Score (sTSS)
Volledige Formule:
sTSS = (IF³) × Duur (uren) × 100
IF = NSS / FTP
NSS = Totale Afstand / Totale Tijd (m/min)
🧪 Interactieve Calculator - Test de Formule
Berekende sTSS:
55
Berekeningsstappen:
NSS = 3000m / 55min = 54.5 m/min
FTP = 100 / (93/60) = 64.5 m/min
IF = 54.5 / 64.5 = 0.845
sTSS = 0.845³ × (55/60) × 100 = 55
NSS = 3000m / 55min = 54.5 m/min
FTP = 100 / (93/60) = 64.5 m/min
IF = 54.5 / 64.5 = 0.845
sTSS = 0.845³ × (55/60) × 100 = 55
JavaScript Implementatie:
function calculateSTSS(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 sTSS using cubed intensity factor
const stss = Math.pow(intensityFactor, 3) * hours * 100;
return Math.round(stss);
}
// Example usage:
const stss = calculateSTSS(3000, 55, 64.5);
// Returns: 55
// Helper: Convert CRS to FTP
function cssToFTP(cssPacePer100mSeconds) {
// FTP in m/min = 100m / (pace in minutes)
return 100 / (cssPacePer100mSeconds / 60);
}
// Example: CRS of 1:33 (93 seconds)
const ftp = cssToFTP(93); // Returns: 64.5 m/min
Running Efficiency
Formule:
Running Efficiency = Kilometertijd (seconden) + Passentelling
Running Efficiency₂₅ = (Tijd × 25/Baanlengte) + (Passen × 25/Baanlengte)
🧪 Interactieve Calculator - Test de Formule
Running Efficiency Score:
35
Berekening:
Running Efficiency = 20s + 15 passen = 35
Running Efficiency = 20s + 15 passen = 35
JavaScript Implementatie:
function calculateRunning Efficiency(timeSeconds, strideCount) {
return timeSeconds + strideCount;
}
function calculateNormalizedRunning Efficiency(timeSeconds, strideCount, trackLength) {
const normalizedTime = timeSeconds * (25 / trackLength);
const normalizedStrides = strideCount * (25 / trackLength);
return normalizedTime + normalizedStrides;
}
// Example:
const swolf = calculateRunning Efficiency(20, 15);
// Returns: 35
const swolf50m = calculateNormalizedRunning Efficiency(40, 30, 50);
// Returns: 35 (normalized to 25m)
Pasmechanica
Stride Rate (SR)
Formule:
SR = 60 / Cyclustijd (seconden)
SR = (Aantal Passen / Tijd in seconden) × 60
🧪 Interactieve Calculator - Test de Formule
Stride Rate (SPM):
72
Berekening:
SR = (30 / 25) × 60 = 72 SPM
SR = (30 / 25) × 60 = 72 SPM
JavaScript Implementatie:
function calculateStrideRate(strideCount, timeSeconds) {
return (strideCount / timeSeconds) * 60;
}
// Example:
const sr = calculateStrideRate(30, 25);
// Returns: 72 SPM
Distance Per Stride (DPS)
Formule:
DPS = Afstand / Passentelling
DPS = Afstand / (SR / 60)
JavaScript Implementatie:
function calculateDPS(distance, strideCount, pushoffDistance = 0) {
const effectiveDistance = distance - pushoffDistance;
return effectiveDistance / strideCount;
}
// Example (25m track, 5m push-off):
const dps = calculateDPS(25, 12, 5);
// Returns: 1.67 m/stride
// For multiple segments:
const dps100m = calculateDPS(100, 48, 4 * 5);
// Returns: 1.67 m/stride (4 segments × 5m push-off)
Velocity from SR and DPS
Formule:
Velocity (m/s) = (SR / 60) × DPS
JavaScript Implementatie:
function calculateVelocity(strideRate, dps) {
return (strideRate / 60) * dps;
}
// Example:
const velocity = calculateVelocity(70, 1.6);
// Returns: 1.87 m/s
Stride Index (SI)
Formule:
SI = Velocity (m/s) × DPS (m/stride)
JavaScript Implementatie:
function calculateStrideIndex(velocity, dps) {
return velocity * dps;
}
// Example:
const si = calculateStrideIndex(1.5, 1.7);
// Returns: 2.55
Performance Management Chart (PMC)
CTL, ATL, TSB Berekeningen
Formules:
CTL vandaag = CTL gisteren + (TSS vandaag - CTL gisteren) × (1/42)
ATL vandaag = ATL gisteren + (TSS vandaag - ATL gisteren) × (1/7)
TSB = CTL gisteren - ATL gisteren
JavaScript Implementatie:
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
Geavanceerde Berekeningen
CRS van Meerdere Afstanden (Regressiemethode)
JavaScript Implementatie:
function calculateCRSRegression(distances, times) {
// Linear regression: distance = a + b*time
const n = distances.length;
const sumX = times.reduce((a, b) => a + b, 0);
const sumY = distances.reduce((a, b) => a + b, 0);
const sumXY = times.reduce((sum, x, i) => sum + x * distances[i], 0);
const sumXX = times.reduce((sum, x) => sum + x * x, 0);
const slope = (n * sumXY - sumX * sumY) / (n * sumXX - sumX * sumX);
const intercept = (sumY - slope * sumX) / n;
return {
css: slope, // Critical running velocity (m/s)
anaerobic_capacity: intercept // Anaerobic distance capacity (m)
};
}
// Example with multiple test distances:
const distances = [100, 200, 400, 800];
const times = [65, 150, 340, 720]; // in seconds
const result = calculateCRSRegression(distances, times);
// Returns: { css: 1.18, anaerobic_capacity: 15.3 }
Intensity Factor van Tempo
JavaScript Implementatie:
function calculateIntensityFactor(actualPace100m, thresholdPace100m) {
// Convert pace to speed (m/s)
const actualSpeed = 100 / actualPace100m;
const thresholdSpeed = 100 / thresholdPace100m;
return actualSpeed / thresholdSpeed;
}
// Example:
const if_value = calculateIntensityFactor(110, 93);
// Returns: 0.845 (running at 84.5% of threshold)
Tempoconsistentie-analyse
JavaScript Implementatie:
function analyzePaceConsistency(segments) {
const paces = segments.map(kilometer => kilometer.distance / kilometer.time);
const avgPace = paces.reduce((a, b) => a + b) / paces.length;
const variance = paces.reduce((sum, pace) =>
sum + Math.pow(pace - avgPace, 2), 0) / paces.length;
const stdDev = Math.sqrt(variance);
const coefficientOfVariation = (stdDev / avgPace) * 100;
return {
avgPace,
stdDev,
coefficientOfVariation,
consistency: coefficientOfVariation < 5 ? "Uitstekend" :
coefficientOfVariation < 10 ? "Goed" :
coefficientOfVariation < 15 ? "Matig" : "Variabel"
};
}
// Example:
const segments = [
{ distance: 100, time: 70 },
{ distance: 100, time: 72 },
{ distance: 100, time: 71 },
// ...
];
const analysis = analyzePaceConsistency(segments);
// Returns: { avgPace: 1.41, stdDev: 0.02, coefficientOfVariation: 1.4, consistency: "Uitstekend" }
Vermoeidheidsdetectie via Passentelling
JavaScript Implementatie:
function detectFatigue(segments) {
const firstThird = segments.slice(0, Math.floor(segments.length/3));
const lastThird = segments.slice(-Math.floor(segments.length/3));
const firstThirdAvg = firstThird.reduce((sum, kilometer) =>
sum + kilometer.strideCount, 0) / firstThird.length;
const lastThirdAvg = lastThird.reduce((sum, kilometer) =>
sum + kilometer.strideCount, 0) / lastThird.length;
const strideCountIncrease = ((lastThirdAvg - firstThirdAvg) / firstThirdAvg) * 100;
return {
firstThirdAvg: Math.round(firstThirdAvg * 10) / 10,
lastThirdAvg: Math.round(lastThirdAvg * 10) / 10,
percentIncrease: Math.round(strideCountIncrease * 10) / 10,
fatigueLevel: strideCountIncrease < 5 ? "Minimaal" :
strideCountIncrease < 10 ? "Matig" :
strideCountIncrease < 20 ? "Aanzienlijk" : "Ernstig"
};
}
// Example:
const segments = [
{ strideCount: 14 }, { strideCount: 14 }, { strideCount: 15 },
{ strideCount: 15 }, { strideCount: 16 }, { strideCount: 16 },
{ strideCount: 17 }, { strideCount: 18 }, { strideCount: 18 }
];
const fatigue = detectFatigue(segments);
// Returns: { firstThirdAvg: 14.3, lastThirdAvg: 17.7, percentIncrease: 23.8, fatigueLevel: "Ernstig" }
Datavalidatie
Kwaliteitscontroles Trainingsdata
JavaScript Implementatie:
function validateWorkoutData(workout) {
const issues = [];
// Check for reasonable pace ranges (1:00-5:00 per 100m)
const avgPace = (workout.totalTime / workout.totalDistance) * 100;
if (avgPace < 60 || avgPace > 300) {
issues.push(`Ongebruikelijk gemiddeld tempo: ${Math.round(avgPace)}s per 100m`);
}
// Check for reasonable stride counts (10-50 per 25m)
const avgStridesPer25m = (workout.totalStrides / workout.totalDistance) * 25;
if (avgStridesPer25m < 10 || avgStridesPer25m > 50) {
issues.push(`Ongebruikelijke passentelling: ${Math.round(avgStridesPer25m)} per 25m`);
}
// Check for reasonable stride rate (30-150 SPM)
const avgSR = calculateStrideRate(workout.totalStrides, workout.totalTime);
if (avgSR < 30 || avgSR > 150) {
issues.push(`Ongebruikelijke stride rate: ${Math.round(avgSR)} 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(`Grote hiaat gedetecteerd tussen segmenten ${i} en ${i+1}`);
}
}
}
return {
isValid: issues.length === 0,
issues
};
}
// Example:
const workout = {
totalDistance: 2000,
totalTime: 1800, // 30 minutes
totalStrides: 800,
segments: [/* kilometer data */]
};
const validation = validateWorkoutData(workout);
// Returns: { isValid: true, issues: [] }
Hulpfuncties
Tijdconversie-hulpprogramma's
JavaScript Implementatie:
// Convert mm:ss to seconds
function timeToSeconds(timeString) {
const parts = timeString.split(':');
return parseInt(parts[0]) * 60 + parseInt(parts[1]);
}
// Convert seconds to mm:ss
function secondsToTime(seconds) {
const minutes = Math.floor(seconds / 60);
const secs = Math.round(seconds % 60);
return `${minutes}:${secs.toString().padStart(2, '0')}`;
}
// Convert seconds to hh:mm:ss
function secondsToTimeDetailed(seconds) {
const hours = Math.floor(seconds / 3600);
const minutes = Math.floor((seconds % 3600) / 60);
const secs = Math.round(seconds % 60);
return `${hours}:${minutes.toString().padStart(2, '0')}:${secs.toString().padStart(2, '0')}`;
}
// Examples:
timeToSeconds("1:33"); // Returns: 93
secondsToTime(93); // Returns: "1:33"
secondsToTimeDetailed(3665); // Returns: "1:01:05"
Implementatiebronnen
Alle formules op deze pagina zijn productieklaar en gevalideerd aan de hand van wetenschappelijke literatuur. Gebruik ze voor aangepaste analysetools, verificatie of een dieper begrip van hardloopprestatie-berekeningen.
💡 Beste Praktijken
- Valideer invoer: Controleer op redelijke bereiken voordat u berekent
- Behandel randsituaties: Deling door nul, negatieve waarden, null-gegevens
- Rond correct af: CTL/ATL/TSB op 1 decimaal, sTSS op geheel getal
- Bewaar precisie: Bewaar volledige precisie in database, rond af voor weergave
- Test grondig: Gebruik beproefde goede gegevens om berekeningen te verifiëren