技术参考与公式
完整的数学实现
实现指南
本页面为所有游泳分析指标提供复制粘贴公式和分步计算方法。使用这些内容进行自定义实现、验证或深入理解。
⚠️ 实现注意事项
- 所有时间应转换为秒进行计算
- 游泳速度是反向的(较高的百分比 = 较慢的速度)
- 始终验证输入是否在合理范围内
- 处理边界情况(除以零、负值)
核心性能指标
临界游泳速度 (CSS)
公式:
CSS (m/s) = (D₂ - D₁) / (T₂ - T₁)
CSS Pace/100m (seconds) = (T₄₀₀ - T₂₀₀) / 2
🧪 交互式计算器 - 测试公式
CSS 每100米速度:
1:49
计算步骤:
CSS (m/s) = (400 - 200) / (368 - 150) = 0.917 m/s
Pace/100m = 100 / 0.917 = 109 seconds = 1:49
CSS (m/s) = (400 - 200) / (368 - 150) = 0.917 m/s
Pace/100m = 100 / 0.917 = 109 seconds = 1:49
JavaScript 实现:
function calculateCSS(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 CSS 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 = calculateCSS(200, 150, 400, 368);
// Returns: { css_ms: 0.917, pace_seconds: 109, pace_formatted: "1:49" }
游泳训练应力分数 (sTSS)
完整公式:
sTSS = (IF³) × Duration (hours) × 100
IF = NSS / FTP
NSS = Total Distance / Total Time (m/min)
🧪 交互式计算器 - 测试公式
计算的 sTSS:
55
计算步骤:
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 实现:
function calculateSTSS(distance, timeMinutes, ftpMetersPerMin) {
// Calculate Normalized Swim 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 CSS to FTP
function cssToFTP(cssPacePer100mSeconds) {
// FTP in m/min = 100m / (pace in minutes)
return 100 / (cssPacePer100mSeconds / 60);
}
// Example: CSS of 1:33 (93 seconds)
const ftp = cssToFTP(93); // Returns: 64.5 m/min
SWOLF
公式:
SWOLF = Lap Time (seconds) + Stroke Count
SWOLF₂₅ = (Time × 25/Pool Length) + (Strokes × 25/Pool Length)
🧪 交互式计算器 - 测试公式
SWOLF 分数:
35
计算:
SWOLF = 20s + 15 strokes = 35
SWOLF = 20s + 15 strokes = 35
JavaScript 实现:
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;
}
// Example:
const swolf = calculateSWOLF(20, 15);
// Returns: 35
const swolf50m = calculateNormalizedSWOLF(40, 30, 50);
// Returns: 35 (normalized to 25m)
划水机制
划水速率 (SR)
公式:
SR = 60 / 周期时间 (秒)
SR = (划水次数 / 时间(秒)) × 60
🧪 交互式计算器 - 测试公式
划水速率 (SPM):
72
计算:
SR = (30 / 25) × 60 = 72 SPM
SR = (30 / 25) × 60 = 72 SPM
JavaScript 实现:
function calculateStrokeRate(strokeCount, timeSeconds) {
return (strokeCount / timeSeconds) * 60;
}
// Example:
const sr = calculateStrokeRate(30, 25);
// Returns: 72 SPM
每划距离 (DPS)
公式:
DPS = 距离 / 划水次数
DPS = 距离 / (SR / 60)
JavaScript 实现:
function calculateDPS(distance, strokeCount, pushoffDistance = 0) {
const effectiveDistance = distance - pushoffDistance;
return effectiveDistance / strokeCount;
}
// Example (25m pool, 5m push-off):
const dps = calculateDPS(25, 12, 5);
// Returns: 1.67 m/stroke
// For multiple laps:
const dps100m = calculateDPS(100, 48, 4 * 5);
// Returns: 1.67 m/stroke (4 laps × 5m push-off)
从 SR 和 DPS 计算速度
公式:
速度 (m/s) = (SR / 60) × DPS
JavaScript 实现:
function calculateVelocity(strokeRate, dps) {
return (strokeRate / 60) * dps;
}
// Example:
const velocity = calculateVelocity(70, 1.6);
// Returns: 1.87 m/s
划水指数 (SI)
公式:
SI = 速度 (m/s) × DPS (m/划)
JavaScript 实现:
function calculateStrokeIndex(velocity, dps) {
return velocity * dps;
}
// Example:
const si = calculateStrokeIndex(1.5, 1.7);
// Returns: 2.55
性能管理图表 (PMC)
CTL、ATL、TSB 计算
公式:
CTL today = CTL yesterday + (TSS today - CTL yesterday) × (1/42)
ATL today = ATL yesterday + (TSS today - ATL yesterday) × (1/7)
TSB = CTL yesterday - ATL yesterday
JavaScript 实现:
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
高级计算
多距离的 CSS(回归方法)
JavaScript 实现:
function calculateCSSRegression(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 swimming 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 = calculateCSSRegression(distances, times);
// Returns: { css: 1.18, anaerobic_capacity: 15.3 }
从速度计算强度因子
JavaScript 实现:
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 (swimming at 84.5% of threshold)
速度一致性分析
JavaScript 实现:
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 ? "Excellent" :
coefficientOfVariation < 10 ? "Good" :
coefficientOfVariation < 15 ? "Moderate" : "Variable"
};
}
// Example:
const laps = [
{ distance: 100, time: 70 },
{ distance: 100, time: 72 },
{ distance: 100, time: 71 },
// ...
];
const analysis = analyzePaceConsistency(laps);
// Returns: { avgPace: 1.41, stdDev: 0.02, coefficientOfVariation: 1.4, consistency: "Excellent" }
从划水次数检测疲劳
JavaScript 实现:
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 ? "Moderate" :
strokeCountIncrease < 20 ? "Significant" : "Severe"
};
}
// Example:
const laps = [
{ strokeCount: 14 }, { strokeCount: 14 }, { strokeCount: 15 },
{ strokeCount: 15 }, { strokeCount: 16 }, { strokeCount: 16 },
{ strokeCount: 17 }, { strokeCount: 18 }, { strokeCount: 18 }
];
const fatigue = detectFatigue(laps);
// Returns: { firstThirdAvg: 14.3, lastThirdAvg: 17.7, percentIncrease: 23.8, fatigueLevel: "Severe" }
数据验证
训练数据质量检查
JavaScript 实现:
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(`Unusual average pace: ${Math.round(avgPace)}s per 100m`);
}
// Check for reasonable stroke counts (10-50 per 25m)
const avgStrokesPer25m = (workout.totalStrokes / workout.totalDistance) * 25;
if (avgStrokesPer25m < 10 || avgStrokesPer25m > 50) {
issues.push(`Unusual stroke count: ${Math.round(avgStrokesPer25m)} per 25m`);
}
// Check for reasonable stroke rate (30-150 SPM)
const avgSR = calculateStrokeRate(workout.totalStrokes, workout.totalTime);
if (avgSR < 30 || avgSR > 150) {
issues.push(`Unusual stroke rate: ${Math.round(avgSR)} SPM`);
}
// Check for missing laps (gaps in time)
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 minute gap
issues.push(`Large gap detected between laps ${i} and ${i+1}`);
}
}
}
return {
isValid: issues.length === 0,
issues
};
}
// Example:
const workout = {
totalDistance: 2000,
totalTime: 1800, // 30 minutes
totalStrokes: 800,
laps: [/* lap data */]
};
const validation = validateWorkoutData(workout);
// Returns: { isValid: true, issues: [] }
辅助函数
时间转换工具
JavaScript 实现:
// Convert mm:ss to seconds
function timeToSeconds(timeString) {
const parts = timeString.split(':');
return parseInt(parts[0]) * 60 + parseInt(parts[1]);
}
// Convert seconds to mm:ss
function secondsToTime(seconds) {
const minutes = Math.floor(seconds / 60);
const secs = Math.round(seconds % 60);
return `${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"