📚 Year 8 Edexcel PE Formula & Theorem Quick Reference Handbook | 公式定理速查手册
This handbook provides a quick reference for the essential formulas, theorems, and principles you will encounter in Year 8 Edexcel Physical Education. Understanding these calculations and concepts will help you analyse fitness levels, design training programmes, and evaluate performance effectively. Keep this guide handy for revision and practical application.
本手册为 Year 8 Edexcel 体育课程中涉及的核心公式、定理和原理提供快速参考。掌握这些计算和概念，将帮助你有效分析体能水平、设计训练计划并评估运动表现。请将此指南放在手边，便于复习和实际应用。
1. Maximum Heart Rate (MHR) | 最大心率 (MHR)
The Maximum Heart Rate is the highest number of beats per minute your heart can reach during maximal exercise. The most common estimation formula is MHR = 220 − age. For a 12-year-old, MHR = 220 − 12 = 208 bpm.
最大心率是你在最大强度运动时心脏每分钟能跳动的最高次数。最常用的估算公式是：最大心率 = 220 − 年龄。对于一个 12 岁的学生，最大心率 = 220 − 12 = 208 次/分。
MHR = 220 − Age
Remember that this is an estimate; individual variation exists, and more precise tests require laboratory conditions.
请记住这只是估算；个体之间存在差异，更精确的测量需要在实验室条件下进行。
2. Karvonen Formula (Heart Rate Reserve) | 卡沃宁公式 (心率储备)
The Karvonen Formula uses your resting heart rate (RHR) to calculate a more personalised target heart rate zone. It first calculates Heart Rate Reserve (HRR), then applies the desired intensity percentage.
卡沃宁公式利用你的安静心率 (RHR) 来计算更个性化的靶心率区间。它首先计算心率储备 (HRR)，然后乘以所需强度百分比。
HRR = MHR − RHR
Target Heart Rate = (HRR × Intensity %) + RHR
Example: For a 13-year-old with RHR = 65 bpm, MHR = 207 bpm. HRR = 207 − 65 = 142 bpm. Target at 60% intensity = (142 × 0.6) + 65 = 150 bpm. This formula is valuable because it considers individual fitness levels.
示例：一名 13 岁学生安静心率为 65 次/分，最大心率 207 次/分。心率储备 = 207 − 65 = 142 次/分。60% 强度时的靶心率 = (142 × 0.6) + 65 = 150 次/分。这个公式之所以有价值，是因为它考虑了个人的体能水平。
3. Target Heart Rate Zones for Aerobic Training | 有氧训练的靶心率区间
To improve cardiovascular fitness, you should exercise within a target zone ranging 60–85% of your Maximum Heart Rate. Two common zones are the aerobic zone (60–80% MHR) and the anaerobic zone (80–90% MHR).
要提高心血管适能，你应在最大心率的 60–85% 的靶心率区间内运动。两个常见区间为有氧区间（60–80% 最大心率）和 无氧区间（80–90% 最大心率）。
| Training Zone / 训练区间 | % MHR | Perceived Exertion / 主观感觉 |
|---|---|---|
| Warm-up & Recovery / 热身与恢复 | 50–60% | Very light / 非常轻松 |
| Aerobic/Fat-burning / 有氧/燃脂 | 60–70% | Light to moderate / 轻松到中等 |
| Aerobic/Cardio / 有氧/心肺 | 70–80% | Moderate to hard / 中等偏累 |
| Anaerobic/Performance / 无氧/极限 | 80–90% | Hard to very hard / 很累 |
| Maximal effort / 最大努力 | 90–100% | Maximum effort / 最大努力 |
Applying these zones ensures you exercise at an appropriate intensity for your fitness goals.
运用这些区间可确保你根据健身目标选择适当的运动强度。
4. Body Mass Index (BMI) | 身体质量指数 (BMI)
BMI is a simple method to classify body weight relative to height. The formula is weight in kilograms divided by height in metres squared.
BMI 是衡量体重与身高关系的一种简单方法。公式为体重（千克）除以身高（米）的平方。
BMI = Weight (kg) ÷ Height² (m²)
Example: A student weighs 50 kg and is 1.55 m tall. BMI = 50 ÷ (1.55 × 1.55) = 50 ÷ 2.4025 ≈ 20.8. This falls within the healthy weight range. Remember that BMI does not distinguish muscle from fat; athletes may be incorrectly classified as overweight.
示例：一名学生体重 50 千克，身高 1.55 米。BMI = 50 ÷ (1.55 × 1.55) = 50 ÷ 2.4025 ≈ 20.8，属健康体重范围。请记住 BMI 无法区分肌肉和脂肪；运动员可能被误判为超重。
- Underweight / 体重过轻：＜18.5
- Healthy weight / 健康体重：18.5–24.9
- Overweight / 超重：25–29.9
- Obese / 肥胖：≥30
5. Training Load and Volume | 训练负荷与训练量
Training load measures the amount of stress placed on the body during a session. It can be calculated using the formula: Training Load = Frequency × Intensity × Time (FIT). Sometimes sets × reps × weight is used for resistance training.
训练负荷衡量一次训练课对身体施加的压力大小。可用公式计算：训练负荷 = 频率 × 强度 × 时间 (FIT)。有时，在抗阻训练中用 组数 × 次数 × 重量 来计算。
Training Load = Frequency × Intensity × Time
Resistance Load = Sets × Reps × Weight (kg)
Example: A student does 3 sets of 12 reps bench press with 20 kg. Load = 3 × 12 × 20 = 720 kg lifted in total. This helps track progressive overload over weeks.
示例：一名学生用 20 千克做卧推 3 组，每组 12 次。负荷 = 3 × 12 × 20 = 720 千克总推举重量。这有助于追踪数周内的渐进超负荷。
6. Energy Balance Equation | 能量平衡公式
Body weight is determined by the balance between energy intake (calories consumed) and energy expenditure (calories burned). This is the fundamental theorem of weight management.
体重由能量摄入（摄入的热量）与能量消耗（消耗的热量）之间的平衡决定。这是体重管理的基本定理。
Energy Balance = Energy Intake − Energy Expenditure
- If Intake > Expenditure → Weight gain / 体重增加
- If Intake < Expenditure → Weight loss / 体重减轻
- If Intake = Expenditure → Weight stable / 体重稳定
Physical activity, basal metabolic rate (BMR), and the thermic effect of food all contribute to energy expenditure.
体力活动、基础代谢率 (BMR) 和食物热效应都是能量消耗的组成部分。
7. Rating of Perceived Exertion (Borg RPE Scale) | 自感劳累分级 (Borg RPE 量表)
The Borg Scale (6–20) allows individuals to rate how hard they feel they are working. It correlates strongly with heart rate (RPE × 10 ≈ Heart Rate). A rating of 12–14 corresponds to moderate intensity (120–140 bpm).
Borg 量表（6–20 级）让个体对自我感觉的运动强度进行评分。该评分与心率高度相关（RPE × 10 ≈ 心率）。12–14 级相当于中等强度（120–140 次/分）。
| RPE / 评分 | Perceived Effort / 主观感觉 |
|---|---|
| 6 | No exertion / 毫不费力 |
| 7–8 | Extremely light / 极其轻松 |
| 9–10 | Very light / 非常轻松 |
| 11–12 | Light / 轻松 |
| 13–14 | Somewhat hard / 有点累 |
| 15–16 | Hard / 累 |
| 17–18 | Very hard / 很累 |
| 19 | Extremely hard / 极其累 |
| 20 | Maximal exertion / 最大努力 |
Use this scale when you cannot measure heart rate; it provides a subjective yet reliable method to gauge intensity.
当无法测量心率时，可使用此量表；它提供了一种主观但可靠的强度评估方法。
8. FITT Principle | FITT 原则
The FITT principle is the fundamental theorem for designing an effective exercise programme. FITT stands for Frequency, Intensity, Time, and Type. Adjusting these variables ensures progression and prevents plateaus.
FITT 原则是制定有效锻炼计划的基本定理。FITT 分别代表频率、强度、时间和类型。调整这些变量可确保持续进步并避免瓶颈期。
| Component / 要素 | Definition / 定义 | Example (Aerobic) / 示例 (有氧) |
|---|---|---|
| Frequency / 频率 | How often / 多久一次 | 3–5 days per week / 每周 3–5 天 |
| Intensity / 强度 | How hard / 多用力 | 60–85% MHR / 最大心率 60–85% |
| Time / 时间 | How long / 多长时间 | 20–60 minutes / 20–60 分钟 |
| Type / 类型 | Kind of exercise / 运动种类 | Running, cycling, swimming / 跑步、骑车、游泳 |
For resistance training, the Type component includes specific exercises (e.g., squats, press-ups) and the order in which they are performed.
对于抗阻训练，类型要素包括特定练习（如深蹲、俯卧撑）及其执行顺序。
9. Progressive Overload Theorem | 渐进超负荷原理
Progressive overload states that for fitness gains to occur, the body must be subjected to a greater load than it is accustomed to. This is achieved by gradually increasing one or more FITT variables. Overload is a key principle of training adaptation.
渐进超负荷原理指出，要实现体能进步，身体必须承受比平时更大的负荷。这通过逐步增加一个或多个 FITT 变量来实现。超负荷是训练适应的关键原则。
New Load = Previous Load + Incremental Increase
Example: If you can currently run 3 km in 15 minutes, continuously apply overload by increasing distance to 3.5 km or reducing time to 14 minutes. Avoid increasing load by more than 10% per week to minimise injury risk.
示例：如果你目前能在 15 分钟内跑完 3 公里，可通过将距离增加到 3.5 公里或将用时缩短到 14 分钟来持续施加超负荷。为避免受伤，每周增加的负荷最好不要超过 10%。
10. Hydration and Sweat Loss Estimation | 水合作用与流汗失水估算
During exercise, the body loses water and electrolytes through sweat. A simple theorem helps estimate fluid needs: for every hour of exercise, drink 400–800 ml of fluid additional to normal daily intake. The exact amount depends on intensity, environment, and individual sweat rates.
运动中身体会通过汗水流失水分和电解质。一个简单定理有助于估算补水需求：每运动 1 小时，除日常饮水量外，额外补充 400–800 毫升液体。具体量取决于强度、环境和个人出汗率。
Fluid Replacement (ml per hour) ≈ Sweat Rate (ml per hour)
Sweat Rate = (Pre-exercise Weight − Post-exercise Weight) ÷ Duration (hours)
A 1 kg weight loss represents approximately 1 litre of fluid lost. Rehydrate by consuming 1.2–1.5 times the fluid deficit.
体重每下降 1 千克约代表流失 1 升液体。应补充失液量 1.2–1.5 倍的水量进行补水。
11. VO₂max Concept and Estimation | 最大摄氧量 (VO₂max) 概念与估算
VO₂max is the maximum amount of oxygen the body can utilise during intense exercise, measured in ml/kg/min. It is a key indicator of cardiovascular endurance. While direct measurement requires lab testing, field tests like the Multi-Stage Fitness Test (bleep test) provide estimates using conversion tables.
最大摄氧量是身体在剧烈运动时所能利用的最大氧气量，单位为 ml/kg/min。它是衡量心血管耐力的关键指标。虽然直接测量需要实验室测试，但像多阶段体能测试（哔哔声测试）这样的现场测试可通过转换表提供估算值。
VO₂max ≈ (Distance covered in m − 504.9) ÷ 44.73
(Based on the Cooper 12-minute run test)
Higher VO₂max values indicate a greater capacity for sustained aerobic activity. A typical untrained Year 8 boy might have a VO₂max around 42 ml/kg/min, while a trained peer might reach 55 ml/kg/min.
最大摄氧量值越高，进行持续有氧活动的能力就越强。一个未经训练的 Year 8 男生最大摄氧量可能在 42 ml/kg/min 左右，而一名训练有素的同龄人可达 55 ml/kg/min。
12. Recovery and Reversibility Principles | 恢复与可逆性原则
Adaptation occurs during rest, not during training. The principle of recovery states that adequate rest between sessions is essential to allow the body to repair and grow stronger. The reversibility principle (or ‘detraining’) warns that fitness gains are lost when training stops or decreases significantly.
适应发生在休息期间，而非训练期间。恢复原则表明，练习之间充分的休息对于身体修复并变得更强至关重要。可逆性原则（或“失训”）警告说，当训练停止或显著减少时，已获得的体能将会丧失。
Fitness loss can begin within 1–2 weeks of inactivity. The rate of loss varies: cardiovascular endurance declines faster than strength. This is why maintaining a consistent training rhythm is crucial.
在停止活动的 1–2 周内，体能便开始下降。下降速度因项目而异：心血管耐力比力量下降得更快。这就是保持持续训练节奏至关重要的原因。
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