📚 KS3 OCR Physical Education: Formula and Principle Quick Reference Handbook | KS3 OCR 体育：公式定理速查手册
Physical Education at KS3 level is not only about playing sport; it also involves understanding the scientific principles and formulas that explain how the body works, how we train effectively, and how we measure performance. This quick reference handbook gathers all the essential formulas, principles and key facts you need to know for OCR Physical Education. Each topic is broken down with clear explanations in English and Chinese, helping you master the theory behind the practical.
KS3 阶段的体育不仅关乎运动本身，还需要理解解释身体如何运作、如何有效训练以及如何衡量表现的科学原理和公式。这本速查手册汇集了OCR体育课程所有必备的公式、原则和关键知识点。每个主题都配有清晰的中英文讲解，帮助你掌握实践背后的理论。
1. Heart Rate and Training Zones | 心率与训练区间
Heart rate is a vital measure of exercise intensity. The most basic formula used in PE is the estimation of Maximum Heart Rate (MHR), which depends on your age. Once you know your MHR, you can calculate target heart rate zones for different types of training, such as aerobic endurance or high-intensity interval work.
心率是衡量运动强度的重要指标。体育课中最基础的公式是根据年龄估算最大心率（MHR）。一旦知道了最大心率，你就可以计算出不同训练类型（如有氧耐力或高强度间歇训练）的目标心率区间。
Maximum Heart Rate (MHR) = 220 – age (in years)
This formula gives an approximate maximum number of times your heart can beat per minute during all-out exertion. For a 13-year-old student, MHR would be 220 – 13 = 207 beats per minute (bpm).
该公式给出了在全力运动时心脏每分钟大约最多能跳动的次数。对于13岁的学生，最大心率就是 220 – 13 = 207 次/分钟(bpm)。
Target heart rate zones are expressed as percentages of MHR. A common aerobic training zone is 60–80% of MHR. To find your target zone, multiply your MHR by the lower and upper percentages.
目标心率区间以最大心率的百分比表示。常见的有氧训练区间是最大心率的60–80%。要找到你的目标区间，用最大心率分别乘以下限和上限百分比即可。
Target Heart Rate = MHR × Intensity %
For example, if MHR is 207 bpm, the aerobic zone would be between 124 bpm (207 × 0.60) and 166 bpm (207 × 0.80). Working within this zone improves cardiovascular fitness safely.
例如，如果最大心率为207 bpm，有氧区间就在124 bpm (207 × 0.60) 和166 bpm (207 × 0.80) 之间。在这个区间内运动能安全地提升心血管健康。
| Training Zone 训练区间 | % of MHR 最大心率百分比 | Example for age 13 (MHR 207) 13岁示例 |
|---|---|---|
| Moderate activity 中等强度活动 | 50–60% | 104–124 bpm |
| Aerobic / fat-burning 有氧/燃脂 | 60–70% | 124–145 bpm |
| Cardio endurance 心肺耐力 | 70–80% | 145–166 bpm |
| High intensity 高强度 | 80–90% | 166–186 bpm |
2. Body Mass Index (BMI) | 身体质量指数 (BMI)
BMI is a simple indicator used to classify whether a person has a healthy body weight for their height. It is widely used in health-related fitness assessments, although it does not distinguish between muscle and fat mass.
BMI 是一个用于根据身高判断体重是否健康的简单指标。它广泛用于健康相关体能评估，但不能区分肌肉和脂肪重量。
BMI = weight (kg) ÷ height² (m²)
To calculate BMI, measure your body mass in kilograms and your height in metres, square the height, then divide. For instance, a student weighing 50 kg with a height of 1.60 m would have a BMI of 50 ÷ (1.60 × 1.60) = 19.5.
计算 BMI 时，用公斤测体重，用米测身高，将身高值平方，再用体重除以该数值。例如，一名学生重 50 kg，身高 1.60 m，其 BMI 为 50 ÷ (1.60 × 1.60) = 19.5。
| BMI Range BMI范围 | Classification 分类 |
|---|---|
| Below 18.5 低于18.5 | Underweight 体重过轻 |
| 18.5 – 24.9 | Healthy weight 健康体重 |
| 25 – 29.9 | Overweight 超重 |
| 30 and above 30及以上 | Obese 肥胖 |
While useful for populations, BMI is less accurate for athletes with large muscle mass, as muscle weighs more than fat. Therefore, it should be used alongside other measures such as waist-to-hip ratio and fitness tests.
虽然 BMI 对群体研究很有用，但对肌肉发达的运动者准确性较低，因为肌肉比脂肪重。因此，应结合腰臀比和体测结果等其他指标共同使用。
3. Speed, Distance and Time | 速度、距离与时间
The relationship between speed, distance and time is fundamental in many sports, from sprinting to cycling. Understanding this formula allows athletes to analyse performance and set goals.
速度、距离与时间的关系在短跑、自行车等众多运动中都是基础。理解这个公式能让运动员分析表现并设定目标。
Speed = Distance ÷ Time
Speed is usually measured in metres per second (m/s) or kilometres per hour (km/h). If a runner covers 100 metres in 12 seconds, her speed is 100 ÷ 12 ≈ 8.33 m/s. The same formula can be rearranged to find distance or time.
速度通常以米/秒(m/s)或千米/小时(km/h)为单位。如果一名跑者用12秒跑完100米，她的速度就是100 ÷ 12 ≈ 8.33 m/s。此公式可以变形，用来求距离或时间。
Distance = Speed × Time
Time = Distance ÷ Speed
These simple rearrangements are useful when planning training sessions. For example, if you want to know how far you can cycle in 30 minutes at a steady speed of 20 km/h, you calculate: Distance = 20 km/h × 0.5 h = 10 km.
这些简单的变形在制定训练计划时很有用。例如，若想知道以 20 km/h 的稳定速度骑行 30 分钟能走多远，计算方式为：距离 = 20 km/h × 0.5 h = 10 km。
4. Force, Work and Power | 力、功与功率
In PE we look at how forces move objects or the body. Force, work and power help explain why some movements are more explosive or tiring than others.
在体育中我们研究力如何移动物体或身体。力、功和功率有助于解释为什么有些动作爆发力更强或更费力。
Force = Mass × Acceleration (F = m × a)
Force is measured in newtons (N). When you kick a football, the force applied equals the mass of your leg/foot times the acceleration of the movement. Greater force leads to faster ball speed if technique is efficient.
力的单位是牛顿(N)。当你踢足球时，施加的力等于腿/脚的质量乘以动作加速度。如果技术有效，更大的力会让球速更快。
Work = Force × Distance (W = F × d)
Work is measured in joules (J). It represents the energy transferred when a force moves an object through a distance. Lifting a 10 kg weight upwards by 1 metre requires work of approximately 10 kg × 10 m/s² (gravity) × 1 m = 100 J.
功的单位是焦耳(J)。它表示力使物体移动一定距离所传递的能量。将 10 kg 的物体向上举起 1 米，做功约为 10 kg × 10 m/s² (重力加速度) × 1 m = 100 J。
Power = Work ÷ Time or Power = Force × Velocity
Power is the rate of doing work, measured in watts (W). An athlete who performs the same work in a shorter time generates more power, which is crucial for explosive sports like sprinting and jumping.
功率是做功的速率，单位是瓦特(W)。在更短时间内完成相同功的运动员能产生更大功率，这对于短跑、跳跃等爆发性运动至关重要。
5. Levers in the Human Body | 人体杠杆
Bones, joints and muscles act as lever systems to produce movement. Understanding the three classes of levers helps you analyse sporting techniques and efficiency.
骨、关节和肌肉构成杠杆系统来产生运动。理解三类杠杆有助于分析运动技术和效率。
- First class lever – the fulcrum is between the effort and the load. Example: nodding the head (neck joint). 第一类杠杆：支点在力点和阻力点之间。例如：点头（颈部关节）。
- Second class lever – the load is between the fulcrum and the effort. Example: standing on tiptoe (ball of foot as fulcrum). 第二类杠杆：阻力点在支点和力点之间。例如：踮脚站立（前脚掌为支点）。
- Third class lever – the effort is between the fulcrum and the load. Most body levers are third class, such as a bicep curl (elbow joint). 第三类杠杆：力点在支点和阻力点之间。人体多数杠杆属于此类，如肱二头肌弯举（肘关节）。
Third class levers allow a large range of movement and speed, but they require more effort to move a given load. This trade-off is an important principle of biomechanics.
第三类杠杆能提供大幅度的运动和速度，但移动给定负荷需要更多力。这种权衡是生物力学的一项重要原则。
6. METs and Energy Expenditure | 代谢当量与能量消耗
MET (Metabolic Equivalent of Task) is a way to describe the energy cost of physical activities. One MET is the energy you use while sitting quietly. Activities with higher MET values burn more calories.
MET（代谢当量）是一种描述身体活动能量消耗的方式。1 MET 代表静坐时的能量消耗。MET值越高的活动消耗的卡路里越多。
Calories burned ≈ MET × body mass (kg) × duration (hours)
This formula provides an estimate. For example, playing basketball has a MET value of approximately 6. A 50 kg student playing for 1 hour burns roughly 6 × 50 × 1 = 300 kcal. Actual values vary with intensity and fitness level.
这一公式可用于估算。例如，打篮球的 MET 值大约为6。一个50 kg的学生打1小时篮球大约消耗 6 × 50 × 1 = 300 千卡。实际消耗量因强度和个人体能而异。
| Activity 活动 | Approximate MET 近似MET |
|---|---|
| Sitting quietly 静坐 | 1.0 |
| Walking 5 km/h 步行5km/h | 3.5 |
| Cycling moderate 自行车中等强度 | 8.0 |
| Swimming laps 游泳连续游 | 8.0 |
| Running 8 km/h 跑步8km/h | 8.5 |
Knowing MET values helps you design balanced activity plans and understand nutritional energy needs.
了解MET值有助于设计均衡的活动计划，并理解营养能量需求。
7. Training Principles: FITT | 训练原则：FITT
The FITT principle is a framework for planning an effective training programme. It stands for Frequency, Intensity, Time and Type. Applying FITT ensures you overload the body correctly and avoid plateau or injury.
FITT 原则是制定有效训练计划的框架，分别代表频率、强度、时间和类型。运用 FITT 能确保对身体施加恰当的负荷，避免进入平台期或受伤。
- Frequency (F) – How often you train per week. 频率：每周训练多少次。
- Intensity (I) – How hard you train, measured by heart rate, weight lifted or perceived exertion. 强度：训练的难度，用心率、举起重量或主观疲劳感衡量。
- Time (T) – How long each session lasts. 时间：每次训练持续多久。
- Type (T) – The kind of exercise, e.g. continuous, interval, resistance. 类型：运动种类，如持续训练、间歇训练、抗阻训练。
To improve cardiovascular fitness, you might set FITT as: Frequency = 3 times per week, Intensity = 60–80% MHR, Time = 30 minutes, Type = continuous running or cycling.
为了提高心血管健康，你可以将 FITT 设定为：频率 = 每周3次，强度 = 60–80% 最大心率，时间 = 30分钟，类型 = 持续跑步或自行车。
8. Skill Classification | 技能分类
Skills in sport can be classified along different continua. This helps coaches and learners understand what makes a skill easy or difficult and how to practise it best.
运动技能可按不同连续体进行分类。这有助于教练和学习者理解一项技能难易的原因以及最佳练习方式。
- Open vs Closed skills – An open skill is affected by a changing environment (e.g., a pass in football). A closed skill is performed in a stable, predictable setting (e.g., a free throw in basketball). 开放式与封闭式技能：开放式技能受变化环境影响（如足球传球）；封闭式技能在稳定、可预测的环境中执行（如篮球罚球）。
- Gross vs Fine skills – Gross skills involve large muscle groups (e.g., running), while fine skills use smaller muscles for precision (e.g., dart throwing). 粗大与精细技能：粗大技能动用大肌肉群（如跑步）；精细技能运用小肌肉完成精准动作（如掷飞镖）。
- Discrete, Serial and Continuous skills – A discrete skill has a clear beginning and end (e.g., a golf swing). A serial skill links several discrete actions (e.g., a triple jump). A continuous skill has no obvious start or finish (e.g., swimming). 离散、序列与连续性技能：离散技能有明确起点与终点（如高尔夫挥杆）；序列技能串联多个离散动作（如三级跳远）；连续性技能无明显开始或结束（如游泳）。
Effective practice often starts with closed and discrete drills before progressing to open, serial game situations.
有效练习往往从封闭式、离散式训练开始，然后进阶到开放式、序列式的比赛情景。
9. Health-related Components of Fitness | 健康相关体能要素
These components are directly linked to general well-being and disease prevention. They are used to assess an individual’s overall physical fitness profile.
这些要素与整体健康和疾病预防直接相关，用于评估个人的综合体能状况。
- Cardiovascular endurance – ability of heart and lungs to deliver oxygen during sustained activity. 心血管耐力：心脏和肺部在持续运动中输送氧气的能力。
- Muscular strength – maximum force a muscle can exert in one effort. 肌肉力量：一块肌肉单次收缩能产生的最大力。
- Muscular endurance – ability of a muscle to sustain repeated contractions. 肌肉耐力：肌肉持续重复收缩的能力。
- Flexibility – range of motion around a joint. 柔韧性：关节的活动范围。
- Body composition – ratio of fat mass to lean mass. 身体成分：脂肪重量与去脂体重的比例。
All health-related components can be improved with appropriate training, and they form the basis of fitness testing in schools.
所有健康相关要素都能通过适当训练得到提升，它们构成了学校体质测试的基础。
10. Skill-related Components of Fitness | 技能相关体能要素
These components are more important for successful sports performance. They often depend on a person’s genetic potential as well as training.
这些要素对运动表现的成败更为重要，通常既依赖训练，也取决于个人先天潜力。
- Agility – ability to change direction quickly and under control. 敏捷性：快速且可控地改变方向的能力。
- Balance – maintaining the body’s centre of mass over its base of support. 平衡：维持身体重心在支撑面内。
- Coordination – using two or more body parts together smoothly. 协调性：流畅地同时运用两个或多个身体部位。
- Power – product of strength and speed (explosive actions). 爆发力：力量与速度的乘积（爆发性动作）。
- Reaction time – time taken to respond to a stimulus. 反应时：对刺激作出反应所需的时间。
- Speed – rate at which a movement or the whole body can travel. 速度：某一动作或整个身体移动的速率。
For instance, a tennis player requires agility, coordination and power for a successful serve, while a sprinter relies primarily on speed, power and reaction time.
例如，网球运动员发球需要敏捷性、协调性和爆发力，而短跑运动员主要依赖速度、爆发力和反应时。
11. Injury Prevention and Basic First Aid | 损伤预防与基本急救
Safety in PE is vital. Simple formulas and principles help you prevent injuries and respond correctly when they happen. The common RICE principle is used for soft tissue injuries such as sprains and strains.
体育课中的安全至关重要。简单的公式和原则可以帮助你预防损伤并正确处理。常见的RICE原则用于扭伤、拉伤等软组织损伤。
- R – Rest: Stop activity and protect the injured area. 休息：停止活动并保护受伤部位。
- I – Ice: Apply a cold pack to reduce swelling (wrap in cloth, 20 minutes on/off). 冰敷：用冷敷袋减轻肿胀（用布包裹，每敷20分钟间歇）。
- C – Compression: Use a bandage to limit swelling. 加压：用绷带包扎以限制肿胀。
- E – Elevation: Raise the injured limb above heart level. 抬高：将受伤肢体抬高至心脏水平以上。
Beyond RICE, proper warm-up and cool-down, using correct equipment, and following game rules can be expressed as a simple equation for safety:
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