📚 SQA PE Formula & Theorem Quick Reference Handbook | SQA 体育公式定理速查手册
This quick reference handbook covers the essential formulas and theorems you need for SQA Physical Education at Year 9 level. Whether you are calculating your target heart rate, estimating VO₂max from a Cooper test, or applying biomechanical principles, these key equations will support your learning and exam preparation.
本速查手册涵盖了Year 9级别SQA体育课程所需的基本公式和定理。无论是计算靶心率、通过库珀测试估算最大摄氧量，还是应用生物力学原理，这些关键方程都将支持你的学习和考试准备。
1. Maximum Heart Rate (MHR) Formula | 最大心率公式
The simplest and most commonly used method to estimate maximum heart rate is: MHR = 220 − age er minute (bpm). While individual variations exist, this formula provides a practical starting point for setting exercise intensity.
估算最大心率最简单且最常用的方法是：MHR = 220 − 年龄。对于一名14岁的学生，预测的最大心率为220 − 14 = 206次/分钟(bpm)。虽然存在个体差异，但此公式为设定运动强度提供了一个实用的起点。
2. Karvonen Formula (Heart Rate Reserve) | 卡沃宁公式（心率储备）
The Karvonen formula calculates target heart rate (THR) using heart rate reserve (HRR): THR = ((HRmax − HRrest) × %intensity) + HRrest the morning. For example, if HRmax = 206 bpm, HRrest = 60 bpm, and you want to train at 70% + 60 = 162 bpm. This method is more personalised than using a straight percentage of MHR.
卡沃宁公式利用心率储备(HRR)计算靶心率(THR)：THR = ((最大心率 − 安静心率) × 强度百分比) + 安静心率。安静心率通常是一大早测量的心率。例如，如果最大心率=206 bpm，安静心率=60 bpm，你想以70%的强度训练，你的靶心率 = ((206 − 60) × 0.70) + 60 = 162 bpm。这种方法比直接使用最大心率的百分比更加个性化。
3. Target Heart Rate Zones | 靶心率区间
Using the Karvonen formula, different training zones can be defined. Typical zones include a moderate-intensity zone (50–70% HRR) and a vigorous-intensity zone (70–85% HRR). The table below summarises common training zones and their associated percentage ranges.
使用卡沃宁公式，可以定义不同的训练区间。典型的区间包括中等强度（50–70% HRR）和高强度（70–85% HRR）。下表总结了常见的训练区间及其对应的百分比范围。
| Zone / 区间 | %HRR / 心率储备百分比 | Typical Use / 典型用途 |
|---|---|---|
| Moderate / 中等 | 50–70% | Aerobic base, warm-up / 有氧基础，热身 |
| Vigorous / 高强度 | 70–85% | Improving cardiovascular fitness / 改善心血管适能 |
| Near-maximal / 接近最大 | 85–95% | Interval training, speed / 间歇训练，速度 |
Always warm up before entering higher-intensity zones and monitor how you feel alongside heart rate data. / 在进入更高强度区间之前务必热身，并结合心率数据关注自身感觉。
4. Body Mass Index (BMI) | 身体质量指数
BMI is a simple measure used to classify underweight, normal weight, overweight, and obesity. The formula is: BMI = weight (kg) ÷ height² (m²) /m². While BMI does not distinguish between fat and muscle mass, it is a widely used screening tool.
BMI是用于分类偏瘦、正常体重、超重和肥胖的简单指标。公式为：BMI = 体重(kg) ÷ 身高²(m²)。对于一名体重55 kg、身高1.65 m的学生，BMI = 55 ÷ (1.65 × 1.65) ≈ 20.2 kg/m²。虽然BMI无法区分脂肪和肌肉质量，但仍是一个广泛使用的筛查工具。
5. Work to Rest Ratio | 训练与休息比率
Work to rest ratios are critical for designing interval training sessions. They determine how long you exercise compared to how long you recover. The ratio is expressed as work time : rest time. For example, a 1:3 ratio means that for every 10 seconds of intense effort, you rest for 30 seconds. Different ratios target different energy systems.
训练与休息比率对设计间歇训练课至关重要。它们决定了运动时间与恢复时间的长短。该比率表示为运动时间：休息时间。例如，1:3的比率意味着每进行10秒的高强度运动，你就休息30秒。不同的比率针对不同的能量系统。
| Work:Rest Ratio / 运动:休息比率 | Primary Energy System / 主要能量系统 | Example / 示例 |
|---|---|---|
| 1:3 or higher / 1:3或更高 | ATP-PC (alactic) / ATP-PC（无乳酸） | 10 s sprint, 30 s rest / 10秒冲刺，30秒休息 |
| 1:2 to 1:1 | Anaerobic lactic / 乳酸无氧 | 30 s hard run, 30 s rest / 30秒快速跑，30秒休息 |
| 1:1 to 1:0.5 or continuous / 1:1至1:0.5或持续 | Aerobic / 有氧 | 3 min run, 2 min jog recovery / 3分钟跑，2分钟慢跑恢复 |
6. Training Load Formula (Session RPE) | 训练负荷公式（课次RPE）
Training load can be quantified using the Session RPE (Rate of Perceived Exertion) method: Training Load = RPE × duration (minutes). After a session, an athlete rates their overall effort on a scale (e.g. 1– f 7 × 45 = 315 arbitrary units. This helps monitor training stress and avoid overtraining.
训练负荷可通过课次RPE（主观体力感觉等级）方法来量化：训练负荷 = RPE × 持续时间（分钟）。训练课后，运动员在一个量表（如1–10）上评定整体努力程度，并将其乘以课次持续时间（分钟）。例如，一个45分钟的训练课被评为RPE 7，则训练负荷为7 × 45 = 315个任意单位。这有助于监控训练压力，避免过度训练。
7. Rate of Perceived Exertion (RPE) Scales | 主观体力感觉等级量表
There are two widely used RPE scales: the original Borg 6–20 scale and a simpler 0– equals heart rate. For instance, an RPE of 12 corresponds to approximately 120 bpm. The 0–10 scale is more intuitive, with 0 being rest and 10 being maximal effort.
有两种广泛使用的RPE量表：原始的博格6–20量表和更简单的0–10量表。博格量表的设计使RPE × 10大致等于心率。例如，RPE 12约对应120次/分钟。0–10量表更直观，0表示休息，10表示最大努力。
| Borg 6–20 Scale / 博格6–20量表 | Perceived Exertion / 主观感觉 | 0–10 Scale / 0–10量表 |
|---|---|---|
| 6 | No exertion / 毫不费力 | 0 – Rest / 休息 |
| 11 | Light / 轻松 | 3 – Moderate / 中等 |
| 15 | Hard / 吃力 | 7 – Very hard / 非常吃力 |
| 20 | Maximal exertion / 精疲力竭 | 10 – Maximum / 最大 |
8. Moment (Torque) in Levers | 杠杆力矩
In biomechanics, the moment (or torque) of a force about a joint is calculated as: Moment = Force × Perpendicular distance from the fulcrum (d⊥). In the human body, muscles create forces that act on bones (levers) around joints (fulcrums). For example, during a bicep curl, the biceps muscle applies a force at a small distance from the elbow joint, generating a moment that lifts the weight. Increasing the weight or the distance increases the moment, requiring greater muscular effort.
在生物力学中，力绕关节的力矩计算方式为：力矩 = 力 × 到支点的垂直距离 (d⊥)。在人体中，肌肉产生的力作用于骨（杠杆）并围绕关节（支点）运动。例如，在进行二头弯举时，肱二头肌在距肘关节一小段距离处施加力，产生力矩以举起重量。增加负重或距离都会增大力矩，从而需要更大的肌肉用力。
M = F × d⊥
Understanding this principle helps explain why third-class levers (the most common in the body) favour speed and range of motion over force production. / 理解这一原理有助于解释为什么第三类杠杆（身体中最常见）更利于速度和运动幅度，而非力量输出。
9. Speed
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