Teknisk referens & formler
Komplett matematisk implementering
Implementeringsguide
Den här sidan tillhandahåller kopiera-och-klistra-formler och steg-för-steg-beräkningsmetoder för alla Run Analytics-mätvärden. Använd dessa för anpassade implementeringar, verifiering eller djupare förståelse.
⚠️ Implementeringsnoteringar
- Alla tider ska konverteras till sekunder för beräkningar
- Löptempo är inverterat (högre % = långsammare tempo)
- Validera alltid indata för rimliga intervall
- Hantera kantfall (division med noll, negativa värden)
Grundläggande prestationsmått
Kritisk löphastighet (CRS)
Formel:
CRS (m/s) = (D₂ - D₁) / (T₂ - T₁)
CRS Tempo/100m (sekunder) = (T₄₀₀ - T₂₀₀) / 2
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CRS-tempo per 100m:
1:49
Beräkningssteg:
CRS (m/s) = (400 - 200) / (368 - 150) = 0.917 m/s
Tempo/100m = 100 / 0.917 = 109 sekunder = 1:49
CRS (m/s) = (400 - 200) / (368 - 150) = 0.917 m/s
Tempo/100m = 100 / 0.917 = 109 sekunder = 1:49
JavaScript-implementering:
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" }
Löpningsträningsbelastning (sTSS)
Komplett formel:
sTSS = (IF³) × Varaktighet (timmar) × 100
IF = NSS / FTP
NSS = Total distans / Total tid (m/min)
🧪 Interaktiv kalkylator - Testa formeln
Beräknad sTSS:
55
Beräkningssteg:
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-implementering:
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
Löpeffektivitet
Formel:
Löpeffektivitet = Kilometertid (sekunder) + Stegräkning
Löpeffektivitet₂₅ = (Tid × 25/Banlängd) + (Steg × 25/Banlängd)
🧪 Interaktiv kalkylator - Testa formeln
Löpeffektivitetspoäng:
35
Beräkning:
Löpeffektivitet = 20s + 15 steg = 35
Löpeffektivitet = 20s + 15 steg = 35
JavaScript-implementering:
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)
Stegmekanik
Stegfrekvens (SR)
Formel:
SR = 60 / Cykeltid (sekunder)
SR = (Antal steg / Tid i sekunder) × 60
🧪 Interaktiv kalkylator - Testa formeln
Stegfrekvens (SPM):
72
Beräkning:
SR = (30 / 25) × 60 = 72 SPM
SR = (30 / 25) × 60 = 72 SPM
JavaScript-implementering:
function calculateStrideRate(strideCount, timeSeconds) {
return (strideCount / timeSeconds) * 60;
}
// Example:
const sr = calculateStrideRate(30, 25);
// Returns: 72 SPM
Sträcka per steg (DPS)
Formel:
DPS = Distans / Stegräkning
DPS = Distans / (SR / 60)
JavaScript-implementering:
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)
Hastighet från SR och DPS
Formel:
Hastighet (m/s) = (SR / 60) × DPS
JavaScript-implementering:
function calculateVelocity(strideRate, dps) {
return (strideRate / 60) * dps;
}
// Example:
const velocity = calculateVelocity(70, 1.6);
// Returns: 1.87 m/s
Stegindex (SI)
Formel:
SI = Hastighet (m/s) × DPS (m/steg)
JavaScript-implementering:
function calculateStrideIndex(velocity, dps) {
return velocity * dps;
}
// Example:
const si = calculateStrideIndex(1.5, 1.7);
// Returns: 2.55
Prestationshanteringsdiagram (PMC)
CTL-, ATL-, TSB-beräkningar
Formler:
CTL idag = CTL igår + (TSS idag - CTL igår) × (1/42)
ATL idag = ATL igår + (TSS idag - ATL igår) × (1/7)
TSB = CTL igår - ATL igår
JavaScript-implementering:
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
Avancerade beräkningar
CRS från flera distanser (regressionsmetod)
JavaScript-implementering:
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 }
Intensitetsfaktor från tempo
JavaScript-implementering:
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)
Tempokonsistensanalys
JavaScript-implementering:
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 ? "Utmärkt" :
coefficientOfVariation < 10 ? "Bra" :
coefficientOfVariation < 15 ? "Måttlig" : "Varierande"
};
}
// 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: "Utmärkt" }
Trötthetsdetektion från stegräkning
JavaScript-implementering:
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 ? "Minimal" :
strideCountIncrease < 10 ? "Måttlig" :
strideCountIncrease < 20 ? "Betydande" : "Svår"
};
}
// 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: "Svår" }
Datavalidering
Kvalitetskontroller för träningsdata
JavaScript-implementering:
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(`Ovanligt genomsnittligt 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(`Ovanlig stegräkning: ${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(`Ovanlig stegfrekvens: ${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(`Stort gap upptäckt mellan segment ${i} och ${i+1}`);
}
}
}
return {
isValid: issues.length === 0,
issues
};
}
// Example:
const workout = {
totalDistance: 2000,
totalTime: 1800, // 30 minutes
totalStrides: 800,
segments: [/* kilometer data */]
};
const validation = validateWorkoutData(workout);
// Returns: { isValid: true, issues: [] }
Hjälpfunktioner
Tidskonverteringsverktyg
JavaScript-implementering:
// Convert mm:ss to seconds
function timeToSeconds(timeString) {
const parts = timeString.split(':');
return parseInt(parts[0]) * 60 + parseInt(parts[1]);
}
// Convert seconds to mm:ss
function secondsToTime(seconds) {
const minutes = Math.floor(seconds / 60);
const secs = Math.round(seconds % 60);
return `${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"
Implementeringsresurser
Alla formler på denna sida är produktionsklara och validerade mot vetenskaplig litteratur. Använd dem för anpassade analysverktyg, verifiering eller djupare förståelse av löpprestationsberäkningar.
💡 Bästa praxis
- Validera indata: Kontrollera rimliga intervall innan beräkning
- Hantera kantfall: Division med noll, negativa värden, null-data
- Avrunda lämpligt: CTL/ATL/TSB till 1 decimal, sTSS till heltal
- Lagra precision: Behåll full precision i databasen, avrunda för visning
- Testa noggrant: Använd känd god data för att verifiera beräkningar