技术参考和公式
完整的数学实现
实现指南
本页面为所有Run Analytics指标提供即插即用的公式和分步计算方法。使用它们进行自定义实现、验证或更深入的理解。
⚠️ 实现说明
- 所有时间应转换为秒进行计算
- 跑步配速是反比关系(更高% = 更慢配速)
- 始终验证输入在合理范围内
- 处理边界情况(除以零、负值)
核心性能指标
临界跑步速度 (CRS)
公式:
CRS (m/s) = (D₂ - D₁) / (T₂ - T₁)
CRS Pace/100m (秒) = (T₄₀₀ - T₂₀₀) / 2
🧪 交互式计算器 - 测试公式
每 100m 的 CRS 配速:
1:49
计算步骤:
CRS (m/s) = (400 - 200) / (368 - 150) = 0.917 m/s
Pace/100m = 100 / 0.917 = 109 秒 = 1:49
CRS (m/s) = (400 - 200) / (368 - 150) = 0.917 m/s
Pace/100m = 100 / 0.917 = 109 秒 = 1:49
JavaScript Implementation:
function calculateCRS(distance1, time1, distance2, time2) {
// Convert times to 秒 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 配速 per 100m in 秒
const 配速_per_100m = 100 / css_ms;
// Convert to mm:ss format
const 分钟 = Math.floor(配速_per_100m / 60);
const 秒 = Math.round(配速_per_100m % 60);
return {
css_ms: css_ms,
配速_秒: 配速_per_100m,
配速_formatted: `${分钟}:${秒.toString().padStart(2, '0')}`
};
}
// Example usage:
const result = calculateCRS(200, 150, 400, 368);
// Returns: { css_ms: 0.917, 配速_秒: 109, 配速_formatted: "1:49" }
Run 训练压力评分 (sTSS)
Complete Formula:
sTSS = (IF³) × Duration (小时) × 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 Implementation:
function calculateSTSS(distance, timeMinutes, ftpMetersPerMin) {
// Calculate Normalized Run Speed
const nss = distance / timeMinutes;
// Calculate Intensity Factor
const intensityFactor = nss / ftpMetersPerMin;
// Calculate 小时
const 小时 = timeMinutes / 60;
// Calculate sTSS using cubed intensity factor
const stss = Math.pow(intensityFactor, 3) * 小时 * 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 / (配速 in 分钟)
return 100 / (cssPacePer100mSeconds / 60);
}
// Example: CRS of 1:33 (93 秒)
const ftp = cssToFTP(93); // Returns: 64.5 m/min
跑步效率
Formula:
跑步效率 = Kilometer Time (秒) + Stride Count
Running Efficiency₂₅ = (Time × 25/Track Length) + (Strides × 25/Track Length)
🧪 交互式计算器 - 测试公式
跑步效率分数:
35
计算:
跑步效率 = 20s + 15 strides = 35
跑步效率 = 20s + 15 strides = 35
JavaScript Implementation:
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)
步幅力学
步幅频率 (SR)
公式:
SR = 60 / Cycle Time (秒)
SR = (Number of Strides / Time in 秒) × 60
🧪 交互式计算器 - 测试公式
步幅频率 (SPM):
72
计算:
SR = (30 / 25) × 60 = 72 SPM
SR = (30 / 25) × 60 = 72 SPM
JavaScript Implementation:
function calculateStrideRate(strideCount, timeSeconds) {
return (strideCount / timeSeconds) * 60;
}
// Example:
const sr = calculateStrideRate(30, 25);
// Returns: 72 SPM
每步距离 (DPS)
公式:
DPS = Distance / Stride Count
DPS = Distance / (SR / 60)
JavaScript 实现:
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)
从 SR 和 DPS 计算速度
公式:
Velocity (m/s) = (SR / 60) × DPS
JavaScript Implementation:
function calculateVelocity(strideRate, dps) {
return (strideRate / 60) * dps;
}
// Example:
const velocity = calculateVelocity(70, 1.6);
// Returns: 1.87 m/s
步幅指数 (SI)
公式:
SI = Velocity (m/s) × DPS (m/stride)
JavaScript Implementation:
function calculateStrideIndex(velocity, dps) {
return velocity * dps;
}
// Example:
const si = calculateStrideIndex(1.5, 1.7);
// Returns: 2.55
表现管理图表 (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 训练s
function calculatePMC(训练s) {
let CTL = 0, ATL = 0;
const results = [];
训练s.forEach(训练 => {
CTL = updateCTL(CTL, 训练.TSS);
ATL = updateATL(ATL, 训练.TSS);
const TSB = calculateTSB(CTL, ATL);
results.push({
date: 训练.date,
TSS: 训练.TSS,
CTL: Math.round(CTL * 10) / 10,
ATL: Math.round(ATL * 10) / 10,
TSB: Math.round(TSB * 10) / 10
});
});
return results;
}
// Example usage:
const 训练s = [
{ date: '2025-01-01', TSS: 50 },
{ date: '2025-01-02', TSS: 60 },
{ date: '2025-01-03', TSS: 45 },
// ... more 训练s
];
const pmc = calculatePMC(训练s);
// Returns array with CTL, ATL, TSB for each day
高级计算
从多个距离计算 CRS (回归方法)
JavaScript 实现:
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 秒
const result = calculateCRSRegression(distances, times);
// Returns: { css: 1.18, anaerobic_capacity: 15.3 }
从配速计算强度因子
JavaScript 实现:
function calculateIntensityFactor(actualPace100m, thresholdPace100m) {
// Convert 配速 to 速度 (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)
配速一致性分析
JavaScript 实现:
function analyzePaceConsistency(segments) {
const 配速s = segments.map(kilometer => kilometer.distance / kilometer.time);
const avgPace = 配速s.reduce((a, b) => a + b) / 配速s.length;
const variance = 配速s.reduce((sum, 配速) =>
sum + Math.pow(配速 - avgPace, 2), 0) / 配速s.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 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: "Excellent" }
从步幅数检测疲劳
JavaScript 实现:
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,
疲劳Level: strideCountIncrease < 5 ? "Minimal" :
strideCountIncrease < 10 ? "Moderate" :
strideCountIncrease < 20 ? "Significant" : "Severe"
};
}
// Example:
const segments = [
{ strideCount: 14 }, { strideCount: 14 }, { strideCount: 15 },
{ strideCount: 15 }, { strideCount: 16 }, { strideCount: 16 },
{ strideCount: 17 }, { strideCount: 18 }, { strideCount: 18 }
];
const 疲劳 = detectFatigue(segments);
// Returns: { firstThirdAvg: 14.3, lastThirdAvg: 17.7, percentIncrease: 23.8, 疲劳Level: "Severe" }
数据验证
训练数据质量检查
JavaScript 实现:
function validateWorkoutData(训练) {
const issues = [];
// Check for reasonable 配速 ranges (1:00-5:00 per 100m)
const avgPace = (训练.totalTime / 训练.totalDistance) * 100;
if (avgPace < 60 || avgPace > 300) {
issues.push(`Unusual average 配速: ${Math.round(avgPace)}s per 100m`);
}
// Check for reasonable stride counts (10-50 per 25m)
const avgStridesPer25m = (训练.totalStrides / 训练.totalDistance) * 25;
if (avgStridesPer25m < 10 || avgStridesPer25m > 50) {
issues.push(`Unusual stride count: ${Math.round(avgStridesPer25m)} per 25m`);
}
// Check for reasonable stride rate (30-150 SPM)
const avgSR = calculateStrideRate(训练.totalStrides, 训练.totalTime);
if (avgSR < 30 || avgSR > 150) {
issues.push(`Unusual stride rate: ${Math.round(avgSR)} SPM`);
}
// Check for missing segments (gaps in time)
if (训练.segments && 训练.segments.length > 1) {
for (let i = 1; i < 训练.segments.length; i++) {
const gap = 训练.segments[i].startTime -
(训练.segments[i-1].startTime + 训练.segments[i-1].duration);
if (gap > 300) { // 5 minute gap
issues.push(`Large gap detected between segments ${i} and ${i+1}`);
}
}
}
return {
isValid: issues.length === 0,
issues
};
}
// Example:
const 训练 = {
totalDistance: 2000,
totalTime: 1800, // 30 分钟
totalStrides: 800,
segments: [/* kilometer data */]
};
const validation = validateWorkoutData(训练);
// Returns: { isValid: true, issues: [] }
辅助函数
时间转换工具
JavaScript 实现:
// Convert mm:ss to 秒
function timeToSeconds(timeString) {
const parts = timeString.split(':');
return parseInt(parts[0]) * 60 + parseInt(parts[1]);
}
// Convert 秒 to mm:ss
function 秒ToTime(秒) {
const 分钟 = Math.floor(秒 / 60);
const secs = Math.round(秒 % 60);
return `${分钟}:${secs.toString().padStart(2, '0')}`;
}
// Convert 秒 to hh:mm:ss
function 秒ToTimeDetailed(秒) {
const 小时 = Math.floor(秒 / 3600);
const 分钟 = Math.floor((秒 % 3600) / 60);
const secs = Math.round(秒 % 60);
return `${小时}:${分钟.toString().padStart(2, '0')}:${secs.toString().padStart(2, '0')}`;
}
// Examples:
timeToSeconds("1:33"); // Returns: 93
秒ToTime(93); // Returns: "1:33"
秒ToTimeDetailed(3665); // Returns: "1:01:05"