Teknisk Reference & Formler

Komplet Matematisk Implementering

Implementeringsguide

Denne side indeholder kopierbare formler og trin-for-trin beregningsmetoder for alle Swim Analytics metrikker. Brug disse til tilpassede implementeringer, verifikation eller dybere forståelse.

⚠️ Implementeringsnoter

  • Alle tider skal konverteres til sekunder for beregninger
  • Svømmetempo er omvendt (højere % = langsommere tempo)
  • Valider altid inputs for rimelige intervaller
  • Håndter kanttilfælde (division med nul, negative værdier)

Kerne Performance Metrikker

Kritisk Svømmehastighed (CSS)

Formel:

CSS (m/s) = (D₂ - D₁) / (T₂ - T₁)
CSS Tempo/100m (sekunder) = (T₄₀₀ - T₂₀₀) / 2

🧪 Interaktiv Lommeregner - Test Formlen

CSS Tempo pr. 100m:
1:49
Beregningstrin:
CSS (m/s) = (400 - 200) / (368 - 150) = 0.917 m/s
Tempo/100m = 100 / 0.917 = 109 sekunder = 1:49

JavaScript Implementering:

function calculateCSS(distance1, time1, distance2, time2) {
  // Konverter tider til sekunder om nødvendigt
  const t1 = typeof time1 === 'string' ? timeToSeconds(time1) : time1;
  const t2 = typeof time2 === 'string' ? timeToSeconds(time2) : time2;

  // Beregn CSS i m/s
  const css_ms = (distance2 - distance1) / (t2 - t1);

  // Beregn tempo pr. 100m i sekunder
  const pace_per_100m = 100 / css_ms;

  // Konverter til 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')}`
  };
}

// Eksempel på brug:
const result = calculateCSS(200, 150, 400, 368);
// Returnerer: { css_ms: 0.917, pace_seconds: 109, pace_formatted: "1:49" }

Swim Training Stress Score (sTSS)

Komplet Formel:

sTSS = (IF³) × Varighed (timer) × 100
IF = NSS / FTP
NSS = Total Distance / Total Tid (m/min)

🧪 Interaktiv Lommeregner - Test Formlen

Beregnet sTSS:
55
Beregningstrin:
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) {
  // Beregn Normalized Swim Speed (NSS)
  const nss = distance / timeMinutes;

  // Beregn Intensity Factor (IF)
  const intensityFactor = nss / ftpMetersPerMin;

  // Beregn timer
  const hours = timeMinutes / 60;

  // Beregn sTSS ved brug af kubisk intensitetsfaktor
  const stss = Math.pow(intensityFactor, 3) * hours * 100;

  return Math.round(stss);
}

// Eksempel på brug:
const stss = calculateSTSS(3000, 55, 64.5);
// Returnerer: 55

// Hjælper: Konverter CSS til FTP
function cssToFTP(cssPacePer100mSeconds) {
  // FTP i m/min = 100m / (tempo i minutter)
  return 100 / (cssPacePer100mSeconds / 60);
}

// Eksempel: CSS på 1:33 (93 sekunder)
const ftp = cssToFTP(93); // Returnerer: 64.5 m/min

SWOLF

Formel:

SWOLF = Omgangstid (sekunder) + Antal Slag
SWOLF₂₅ = (Tid × 25/Pool Længde) + (Slag × 25/Pool Længde)

🧪 Interaktiv Lommeregner - Test Formlen

SWOLF Score:
35
Beregning:
SWOLF = 20s + 15 slag = 35

JavaScript Implementering:

function calculateSWOLF(timeSeconds, strokeCount) {
  return timeSeconds + strokeCount;
}

function calculateNormalizedSWOLF(timeSeconds, strokeCount, poolLength) {
  const normalizedTime = timeSeconds * (25 / poolLength);
  const normalizedStrokes = strokeCount * (25 / poolLength);
  return normalizedTime + normalizedStrokes;
}

// Eksempel:
const swolf = calculateSWOLF(20, 15);
// Returnerer: 35

const swolf50m = calculateNormalizedSWOLF(40, 30, 50);
// Returnerer: 35 (normaliseret til 25m)

Svømmemekanik

Slagfrekvens (SR)

Formel:

SR = 60 / Cyklus Tid (sekunder)
SR = (Antal Slag / Tid i sekunder) × 60

🧪 Interaktiv Lommeregner - Test Formlen

Slagfrekvens (SPM):
72
Beregning:
SR = (30 / 25) × 60 = 72 SPM

JavaScript Implementering:

function calculateStrokeRate(strokeCount, timeSeconds) {
  return (strokeCount / timeSeconds) * 60;
}

// Eksempel:
const sr = calculateStrokeRate(30, 25);
// Returnerer: 72 SPM

Distance Pr. Slag (DPS)

Formel:

DPS = Distance / Antal Slag
DPS = Distance / (SR / 60)

JavaScript Implementering:

function calculateDPS(distance, strokeCount, pushoffDistance = 0) {
  const effectiveDistance = distance - pushoffDistance;
  return effectiveDistance / strokeCount;
}

// Eksempel (25m pool, 5m push-off):
const dps = calculateDPS(25, 12, 5);
// Returnerer: 1.67 m/slag

// For flere omgange:
const dps100m = calculateDPS(100, 48, 4 * 5);
// Returnerer: 1.67 m/slag (4 omgange × 5m push-off)

Hastighed fra SR og DPS

Formel:

Hastighed (m/s) = (SR / 60) × DPS

JavaScript Implementering:

function calculateVelocity(strokeRate, dps) {
  return (strokeRate / 60) * dps;
}

// Eksempel:
const velocity = calculateVelocity(70, 1.6);
// Returnerer: 1.87 m/s

Slagindeks (SI)

Formel:

SI = Hastighed (m/s) × DPS (m/slag)

JavaScript Implementering:

function calculateStrokeIndex(velocity, dps) {
  return velocity * dps;
}

// Eksempel:
const si = calculateStrokeIndex(1.5, 1.7);
// Returnerer: 2.55

Performance Management Chart (PMC)

CTL, ATL, TSB Beregninger

Formler:

CTL i dag = CTL i går + (TSS i dag - CTL i går) × (1/42)
ATL i dag = ATL i går + (TSS i dag - ATL i går) × (1/7)
TSB = CTL i går - ATL i går

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;
}

// Beregn PMC for en række træningspas
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;
}

// Eksempel på brug:
const workouts = [
  { date: '2025-01-01', tss: 50 },
  { date: '2025-01-02', tss: 60 },
  { date: '2025-01-03', tss: 45 },
  // ... flere træningspas
];

const pmc = calculatePMC(workouts);
// Returnerer array med CTL, ATL, TSB for hver dag

Avancerede Beregninger

CSS fra Flere Distancer (Regressionsmetode)

JavaScript Implementering:

function calculateCSSRegression(distances, times) {
  // Lineær 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, // Kritisk svømmehastighed (m/s)
    anaerobic_capacity: intercept // Anaerob kapacitet (m)
  };
}

// Eksempel med flere testdistancer:
const distances = [100, 200, 400, 800];
const times = [65, 150, 340, 720]; // i sekunder
const result = calculateCSSRegression(distances, times);
// Returnerer: { css: 1.18, anaerobic_capacity: 15.3 }

Intensitetsfaktor fra Tempo

JavaScript Implementering:

function calculateIntensityFactor(actualPace100m, thresholdPace100m) {
  // Konverter tempo til hastighed (m/s)
  const actualSpeed = 100 / actualPace100m;
  const thresholdSpeed = 100 / thresholdPace100m;
  return actualSpeed / thresholdSpeed;
}

// Eksempel:
const if_value = calculateIntensityFactor(110, 93);
// Returnerer: 0.845 (svømmer ved 84.5% af tærskel)

Tempo Konsistens Analyse

JavaScript Implementering:

function analyzePaceConsistency(laps) {
  const paces = laps.map(lap => lap.distance / lap.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 ? "Fremragende" :
                 coefficientOfVariation < 10 ? "God" :
                 coefficientOfVariation < 15 ? "Moderat" : "Variabel"
  };
}

// Eksempel:
const laps = [
  { distance: 100, time: 70 },
  { distance: 100, time: 72 },
  { distance: 100, time: 71 },
  // ...
];
const analysis = analyzePaceConsistency(laps);
// Returnerer: { avgPace: 1.41, stdDev: 0.02, coefficientOfVariation: 1.4, consistency: "Fremragende" }

Træthedsdetektion fra Slagtælling

JavaScript Implementering:

function detectFatigue(laps) {
  const firstThird = laps.slice(0, Math.floor(laps.length/3));
  const lastThird = laps.slice(-Math.floor(laps.length/3));

  const firstThirdAvg = firstThird.reduce((sum, lap) =>
    sum + lap.strokeCount, 0) / firstThird.length;
  const lastThirdAvg = lastThird.reduce((sum, lap) =>
    sum + lap.strokeCount, 0) / lastThird.length;

  const strokeCountIncrease = ((lastThirdAvg - firstThirdAvg) / firstThirdAvg) * 100;

  return {
    firstThirdAvg: Math.round(firstThirdAvg * 10) / 10,
    lastThirdAvg: Math.round(lastThirdAvg * 10) / 10,
    percentIncrease: Math.round(strokeCountIncrease * 10) / 10,
    fatigueLevel: strokeCountIncrease < 5 ? "Minimal" :
                  strokeCountIncrease < 10 ? "Moderat" :
                  strokeCountIncrease < 20 ? "Signifikant" : "Alvorlig"
  };
}

// Eksempel:
const laps = [
  { strokeCount: 14 }, { strokeCount: 14 }, { strokeCount: 15 },
  { strokeCount: 15 }, { strokeCount: 16 }, { strokeCount: 16 },
  { strokeCount: 17 }, { strokeCount: 18 }, { strokeCount: 18 }
];
const fatigue = detectFatigue(laps);
// Returnerer: { firstThirdAvg: 14.3, lastThirdAvg: 17.7, percentIncrease: 23.8, fatigueLevel: "Alvorlig" }

Data Validering

Træningsdata Kvalitetstjek

JavaScript Implementering:

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

  // Tjek for rimelige tempointervaller (1:00-5:00 pr. 100m)
  const avgPace = (workout.totalTime / workout.totalDistance) * 100;
  if (avgPace < 60 || avgPace > 300) {
    issues.push(`Usædvanligt gennemsnitstempo: ${Math.round(avgPace)}s pr. 100m`);
  }

  // Tjek for rimelige slagtal (10-50 pr. 25m)
  const avgStrokesPer25m = (workout.totalStrokes / workout.totalDistance) * 25;
  if (avgStrokesPer25m < 10 || avgStrokesPer25m > 50) {
    issues.push(`Usædvanligt slagtal: ${Math.round(avgStrokesPer25m)} pr. 25m`);
  }

  // Tjek for rimelig slagfrekvens (30-150 SPM)
  const avgSR = calculateStrokeRate(workout.totalStrokes, workout.totalTime);
  if (avgSR < 30 || avgSR > 150) {
    issues.push(`Usædvanlig slagfrekvens: ${Math.round(avgSR)} SPM`);
  }

  // Tjek for manglende omgange (huller i tid)
  if (workout.laps && workout.laps.length > 1) {
    for (let i = 1; i < workout.laps.length; i++) {
      const gap = workout.laps[i].startTime -
                  (workout.laps[i-1].startTime + workout.laps[i-1].duration);
      if (gap > 300) { // 5 minutters hul
        issues.push(`Stort hul opdaget mellem omgang ${i} og ${i+1}`);
      }
    }
  }

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