📚 Year 8 Cambridge PE: Formula & Theorem Quick Reference Guide | 剑桥八年级体育：公式定理速查手册
In Year 8 Cambridge Physical Education, understanding key formulas and principles helps you analyse performance, monitor fitness and plan training effectively. This quick reference handbook brings together essential equations and theorems from exercise physiology, biomechanics and health science, presented in a clear bilingual format for easy revision.
在剑桥八年级体育课程中，理解关键公式和定理有助于你分析运动表现、监测体能状况并有效制定训练计划。这本速查手册汇集了运动生理学、生物力学和健康科学中的基本方程与原理，以清晰的双语对照形式呈现，便于复习。
1. Maximum Heart Rate (HRmax) | 最大心率
The simplest method to estimate your maximum heart rate is the age-predicted formula. This value is crucial for setting safe and effective exercise intensity zones.
HRmax = 220 − age
For a typical Year 8 student aged 12–13, the HRmax would be approximately 207–208 beats per minute (bpm). Bear in mind that individual variation exists, and this is only an estimation.
最简便的最大心率估算方法是用年龄预测公式。该数值对于设定安全有效的运动强度区间至关重要。
HRmax = 220 − 年龄
对于12–13岁的八年级学生，最大心率约为207–208次/分（bpm）。请注意存在个体差异，这只是估算值。
2. Karvonen Formula (Target Heart Rate Zone) | 卡沃宁公式（靶心率区间）
The Karvonen formula uses heart rate reserve (HRR) to calculate a personalised target heart rate range. You need your resting heart rate (HRrest) and your desired intensity percentage.
Target HR = HRrest + (HRmax − HRrest) × Intensity%
For example, if a student has HRrest = 70 bpm and HRmax = 208 bpm, a moderate zone of 60–80% intensity would be calculated as:
Lower limit: 70 + (208 − 70) × 0.60 = 152.8 bpm
Upper limit: 70 + (208 − 70) × 0.80 = 180.4 bpm
卡沃宁公式利用心率储备（HRR）计算个性化靶心率范围。你需要知道自己的静息心率（HRrest）以及期望的训练强度百分比。
靶心率 = 静息心率 + (最大心率 − 静息心率) × 强度%
例如，某学生静息心率为70 bpm，最大心率为208 bpm，若进行60–80%的中等强度训练，计算如下：
下限：70 + (208 − 70) × 0.60 = 152.8 bpm
上限：70 + (208 − 70) × 0.80 = 180.4 bpm
3. Body Mass Index (BMI) | 身体质量指数
BMI is a simple screening tool to assess whether an individual has a healthy body weight for their height. It is widely used in school fitness assessments.
BMI = weight (kg) ÷ height² (m)
have a BMI of 50 ÷ (1.55)² ≈ 20.8 kg/m². Classification: underweight < 18.5, healthy 18.5–24.9, overweight 25–29.9, obese ≥ 30.
BMI是衡量个体体重是否相对于身高处于健康范围的简易筛查工具，在学校体质测评中广泛使用。
BMI = 体重（kg）÷ 身高²（m）
例如，一名学生体重50 kg，身高1.55 m，其BMI = 50 ÷ (1.55)² ≈ 20.8 kg/m²。分类标准：偏瘦 < 18.5，正常 18.5–24.9，超重 25–29.9，肥胖 ≥ 30。
4. Speed and Velocity | 速度与速率
Speed is a scalar quantity measuring how fast an object moves, while velocity includes direction. In sport, both are used to analyse running, swimming or cycling performance.
Speed = distance ÷ time
÷ 5.0 = 8 m/s. Velocity would be stated as 8 m/s in the specific direction of the sprint.
速率是标量，衡量物体运动的快慢；速度则包含方向，为矢量。在体育运动中，两者都用于分析跑动、游泳或骑行等表现。
速率 = 距离 ÷ 时间
若一名足球运动员在5.0秒内冲刺40米，其平均速率为 40 ÷ 5.0 = 8 m/s。若指明方向，则速度为朝该方向8 m/s。
5. Newton's Second Law of Motion | 牛顿第二运动定律
Newton's second law explains the relationship between force, mass and acceleration. It is fundamental to understanding how athletes generate and control movement.
F = m × a
yer pushing a 0.16 kg ball with an acceleration of 20 m/s² applies a force of 0.16 × 20 = 3.2 N.
牛顿第二定律阐释了力、质量与加速度之间的关系，是理解运动员如何产生和控制动作的基础。
F = m × a
其中 F 为净力，单位牛顿（N）；m 为质量，单位千克（kg）；a 为加速度，单位米每二次方秒（m/s²）。一名曲棍球运动员以 20 m/s² 的加速度推动一个 0.16 kg 的球时，施加的力为 0.16 × 20 = 3.2 N。
6. Work and Power | 功和功率
Work is done when a force moves an object over a distance. Power measures the rate at which work is performed, indicating how explosive or sustained an action is.
Work (W) = Force (F) × distance (d)
Power (P) = Work (W) ÷ time (t)
Units: work is in joules (J), power in watts (W). Lifting a 200 N barbell through 1.5 m requires 300 J of work. If the lift takes 2 seconds, the power output is 150 W.
当力使物体沿力的方向移动一段距离时，就做了功。功率衡量做功的速率，反映动作的爆发性或持续性。
功（W）= 力（F）× 距离（d）
功率（P）= 功（W）÷ 时间（t）
单位：功为焦耳（J），功率为瓦特（W）。将200 N的杠铃上举1.5 m需要做300 J的功。如果上举耗时2秒，则功率输出为150 W。
7. Energy Expenditure (METs) | 能量消耗（代谢当量）
Metabolic Equivalent of Task (MET) helps estimate energy cost of physical activities. One MET equals the energy used at rest (approximately 1 kcal per kg of body weight per hour).
Energy (kcal) = MET × weight (kg) × time (h)
= 472.5 kcal. This formula is handy for planning energy intake and expenditure in sports.
代谢当量（MET）用于估算体力活动的能量消耗。1 MET 相当于静息时的能量消耗（约为每千克体重每小时1千卡）。
能量（千卡）= MET × 体重（kg）× 时间（小时）
例如，一名45 kg的学生以7 METs的强度踢足球1.5小时，消耗热量约为 7 × 45 × 1.5 = 472.5 千卡。该公式便于体育活动中安排能量摄入与消耗。
8. Session RPE (Training Load) | 训练课主观疲劳评分（训练负荷）
Foster's session RPE method provides a simple way to quantify internal training load by multiplying the session's RPE (Borg 6–20 scale) by the duration in minutes.
Training Load = RPE × duration (min)
The Borg Rating of Perceived Exertion scale is commonly used to assess how hard an athlete feels they are working:
| RPE | Perceived Exertion / 主观感觉 |
|---|---|
| 6 | No exertion at all / 完全不费力 |
| 7 | Extremely light / 极轻 |
| 8 | Very light / 很轻 |
| 9 | Very light / 很轻 |
| 10 | Light / 轻 |
| 11 | Light / 轻 |
| 12 | Moderate / 中等 |
| 13 | Somewhat hard / 有些吃力 |
| 14 | Somewhat hard / 有些吃力 |
| 15 | Hard / 吃力 |
| 16 | Hard / 吃力 |
| 17 | Very hard / 很吃力 |
| 18 | Very hard / 很吃力 |
| 19 | Extremely hard / 极吃力 |
| 20 | Maximal exertion / 精疲力竭 |
If a student rates a 45‑ PE lesson as 13 on the RPE scale, the training load is 13 × 45 = 585 arbitrary units (AU).
福斯特的训练课主观疲劳评分法通过将整堂课的自感劳累评分（博格6–20量表）乘以持续时间（分钟），简便地量化内部训练负荷。
训练负荷 = RPE × 持续时间（分钟）
博格主观疲劳感觉量表常被用于评估运动员对训练强度的自我感知：
| RPE | Perceived Exertion / 主观感觉 |
|---|---|
| 6 | No exertion at all / 完全不费力 |
| 7 | Extremely light / 极轻 |
| 8 | Very light / 很轻 |
| 9 | Very light / 很轻 |
| 10 | Light / 轻 |
| 11 | Light / 轻 |
| 12 | Moderate / 中等 |
| 13 | Somewhat hard / 有些吃力 |
| 14 | Somewhat hard / 有些吃力 |
| 15 | Hard / 吃力 |
| 16 | Hard / 吃力 |
| 17 | Very hard / 很吃力 |
| 18 | Very hard / 很吃力 |
| 19 | Extremely hard / 极吃力 |
| 20 | Maximal exertion / 精疲力竭 |
如果一名学生将一节45分钟的体育课评为RPE 13，则训练负荷为 13 × 45 = 585 任意单位（AU）。
9. Sweat Rate and Hydration | 出汗率与补水
Monitoring sweat loss helps athletes avoid dehydration and maintain performance. A simple way to estimate sweat rate is by measuring body mass change during exercise.
Sweat loss (L) ≈ body
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