📚 Year 10 CCEA PE: Formula & Principle Quick Reference Handbook | 10年级 CCEA 体育：公式与定理速查手册
This quick reference handbook has been compiled to help Year 10 CCEA Physical Education students revise the essential formulas, biomechanical principles, and physiological thresholds that underpin the GCSE specification. Understanding these equations and concepts is vital for analysing human performance, designing safe and effective training programmes, and evaluating health-related fitness. Keep this guide close during lesson work, homework, and last-minute exam preparation.
这本速查手册专为10年级CCEA体育课程学生整理，涵盖了GCSE考纲所依据的关键公式、生物力学原理以及生理阈值。掌握这些方程式和概念，对于分析人体运动表现、设计安全有效的训练计划以及评估健康相关体能至关重要。请将本指南放在手边，用于课堂学习、课后作业和考前冲刺复习。
1. Maximum Heart Rate (MHR) | 最大心率 (MHR)
The maximum heart rate (MHR) is the highest number of beats per minute (bpm) your heart can achieve during maximal effort. Laboratory testing provides the most accurate individual value, but the age-predicted formula is widely accepted for setting exercise intensity in school and amateur sport.
最大心率 (MHR) 是指心脏在全力运动时每分钟所能达到的最高跳动次数 (bpm)。实验室测试能提供最精准的个人数值，但基于年龄的预测公式在学校和业余运动中已被广泛接受，常用于设定运动强度。
MHR = 220 − age (years)
5 bpm. This value forms the baseline for calculating all target heart rate zones and helps ensure training remains safe and progressive.
例如，一名15岁学生的估算最大心率为 220 − 15 = 205 bpm。该数值是计算所有目标心率区间的基准，有助于确保训练安全渐进地进行。
2. Karvonen Formula (Heart Rate Reserve) | 卡沃南公式 (心率储备)
The Karvonen formula refines target heart rate calculation by incorporating resting heart rate (RHR). It uses the concept of heart rate reserve (HRR), which represents the range between resting and maximum heart rate that can be utilised during exercise.
卡沃南公式通过加入静息心率 (RHR) 进一步精细化了目标心率的计算。它采用心率储备 (HRR) 的概念，即静息心率与最大心率之间可用于运动的区间。
Target HR = RHR + [Intensity % × (MHR − RHR)]
a resting heart rate of 70 bpm, a maximum heart rate of 200 bpm, and wants to train at 70% s for individual fitness differences and is particularly useful for aerobic endurance programming.
假如一名运动员的静息心率为70 bpm，最大心率为200 bpm，希望以70%的强度训练，则目标心率为：70 + [0.70 × (200 − 70)] = 70 + (0.70 × 130) = 161 bpm。该方法考虑了个体体能的差异，对有氧耐力训练计划的制定尤为有用。
3. Training Zones and Percentage Ranges | 训练区域与百分比区间
Training zones are based on percentages of maximum heart rate or heart rate reserve. Each zone corresponds to a distinct physiological adaptation and fuel source, making zone-based training a powerful tool for improving specific components of fitness.
训练区域基于最大心率或心率储备的百分比划分。每个区间对应不同的生理适应和能量来源，因此基于区间的训练是提升特定体能成分的有力工具。
| Zone / 区间 | %MHR | Main benefit / 主要效益 |
|---|---|---|
| Recovery / 恢复区 | 50–60% | Active recovery, improved blood flow / 积极恢复，促进血液循环 |
| Fat burning / 燃脂区 | 60–70% | Aerobic base, fat metabolism / 有氧基础，脂肪代谢 |
| Aerobic / 有氧区 | 70–80% | Cardiovascular endurance / 心血管耐力 |
| Anaerobic threshold / 无氧阈 | 80–90% | Lactate tolerance, speed endurance / 乳酸耐受，速度耐力 |
| Maximum effort / 最大努力 | 90–100% | Peak power, neuromuscular sprint / 峰值功率，神经肌肉冲刺 |
Using these zones, a student can plan a weekly training mix. For example, three sessions in the aerobic zone and one in the anaerobic zone can develop overall fitness safely.
利用这些区间，学生可以规划每周的训练组合。例如，每周三次有氧区训练加一次无氧阈区训练，即可安全地发展综合体能。
4. Body Mass Index (BMI) | 身体质量指数 (BMI)
Body Mass Index is a screening tool used to classify individuals into weight categories based on their height and mass. Although it does not differentiate between muscle and fat, it remains a useful starting point for population-level health assessment.
身体质量指数是一种筛查工具，根据身高和体质量将个体分为不同体重类别。尽管它无法区分肌肉和脂肪，但仍是群体健康评估的有用起点。
BMI = weight (kg) ÷ height² (m²)
of 1.70 m, BMI = 65 ÷ (1.70 × 1.70) = 22.5 kg/m². This is classified as a healthy weight.
一位体重65 kg、身高1.70 m的人，BMI = 65 ÷ (1.70 × 1.70) = 22.5 kg/m²，属于健康体重范围。
- Underweight / 体重过轻: BMI < 18.5
- Healthy weight / 健康体重: 18.5 – 24.9
- Overweight / 超重: 25.0 – 29.9
- Obese / 肥胖: ≥ 30.0
For youth athletes, BMI should be interpreted with caution because muscle hypertrophy can produce a high BMI without excess body fat. Always combine BMI with other fitness data.
对于青少年运动员，解读BMI需谨慎，因为肌肉增长可导致BMI偏高而并无过多体脂。请务必将BMI与其他体适能数据结合使用。
5. Speed, Distance and Time | 速度、距离与时间
The relationship between speed, distance and time is fundamental in biomechanics and performance analysis. Speed describes how quickly a body moves without considering direction.
速度、距离和时间的关系是生物力学和运动表现分析的基础。速度描述物体运动的快慢，不考虑方向。
Speed = Distance ÷ Time
peed. These are essential for calculating split times, race pacing, and tracking improvement.
若一名短跑选手在12秒内跑完100 m，则平均速度 = 100 ÷ 12 ≈ 8.33 m/s。该公式可变形为：距离 = 速度 × 时间，以及时间 = 距离 ÷ 速度。这些公式是计算分段计时、配速策略和追踪进步所必不可少的。
Always check that units are consistent—metres for distance and seconds for time. When analysing video footage or using GPS, you may need to convert units.
请始终确保单位统一——距离用米，时间用秒。在分析视频录像或使用GPS数据时，可能需要进行单位换算。
6. Acceleration | 加速度
Acceleration measures how quickly velocity changes over time. In sport, positive acceleration indicates speeding up, while negative acceleration (deceleration) shows slowing down.
加速度衡量速度随时间变化的快慢。在运动中，正的加速度表示加速，负的加速度（减速度）表示减速。
Acceleration = (Final velocity − Initial velocity) ÷ time or a = Δv ÷ t
seconds. Acceleration = (8 − 2) ÷ 3 = 6 ÷ 3 = 2 m/s². This value indicates that the player's speed increases by 2 m/s every second during the effort.
示例：一名曲棍球运动员在3秒内从2 m/s加速到8 m/s。加速度 = (8 − 2) ÷ 3 = 6 ÷ 3 = 2 m/s²。该数值表明，运动员的速度在此过程中每秒增加2 m/s。
Understanding acceleration helps coaches design resisted sprints or assisted overspeed drills. The same principle applies to braking forces and change-of-direction movements that require rapid deceleration.
理解加速度有助于教练设计抗阻冲刺或助力超速训练。这一原理同样适用于急停和需要快速减速的变向动作。
7. Newton's Second Law: Force, Mass and Acceleration | 牛顿第二定律：力、质量与加速度
Newton's Second Law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This principle governs all linear movements in sport.
牛顿第二定律指出，物体的加速度与作用于其上的合外力成正比，与其质量成反比。这一原理支配着体育运动中的所有线性运动。
F = m × a
f a 70 kg rugby player accelerates at 3 m/s², the net force applied is F = 70 × 3 = 210 N.
力的单位是牛顿 (N)，质量单位为千克 (kg)，加速度单位为米每二次方秒 (m/s²)。若一名70 kg的橄榄球运动员以3 m/s²加速，则所施加的合力为 F = 70 × 3 = 210 N。
To generate greater acceleration, athletes can either increase applied force through strength training or reduce body mass without sacrificing power. This trade-off is critical in sports where speed and agility determine success.
要产生更大的加速度，运动员可通过力量训练增加施加的力，或在不牺牲爆发力的前提下降低体重。这一权衡在速度和敏捷性决定成败的运动项目中至关重要。
8. Weight and Mass | 重量与质量
Weight and mass are often confused in everyday language, but in physics and physical education they are distinct concepts. Mass is the amount of matter in a body, while weight is the gravitational force acting on that mass.
重量和质量在日常用语中常被混淆，但在物理和体育学中它们是截然不同的概念。质量是物体所含物质的多少，而重量是作用在该质量上的重力。
Weight = mass × gravitational field strength (W = m g)
acts downwards through the centre of mass and affects balance, landing forces, and lift in jumps.
在地球上，g ≈ 9.8 m/s²（在GCSE计算中通常取10 m/s²）。因此，一名60 kg学生的重量约为60 × 9.8 = 588 N。这个重力垂直向下作用于质心，会影响平衡、落地冲击力以及跳跃中的腾空。
Understanding the difference helps when discussing reaction forces, buoyancy in water, and the effects of altitude training where g is slightly lower.
理解这一区别有助于讨论反作用力、水中浮力以及高海拔训练的影响（当地重力加速度略小）。
9. Work Done | 做功
Mechanical work is done whenever a force moves an object in the direction of the force. In sport, work quantifies the energy transferred during activities like lifting weights, kicking a ball, or pushing against a scrum.
当力使物体沿力的方向发生位移时，即做机械功。在体育运动中，功量化了举重、踢球或在争球中推挤等活动所传递的能量。
Work = Force × distance (W = F d)
n the shot is 200 × 1.5 = 300 J. This energy is transferred to the shot as kinetic energy.
功的单位是焦耳 (J)。若一名铅球运动员在出手阶段施加了200 N的平均力，并将铅球推出1.5 m的距离，则对铅球做的功为 200 × 1.5 = 300 J。这部分能量以动能的形式转移给了铅球。
Note that if the force is applied at an angle, only the component of force in the direction of movement does work. Coaches use this principle to optimise technique and avoid wasted effort.
注意，如果力以某个角度施加，只有沿运动方向的分力做功。教练员利用这一原理优化技术动作，避免无效做功。
10. Power (Performance) | 功率 (运动表现)
Power measures the rate at which work is done or energy is transferred. Explosive sporting actions such as sprint starts, vertical jumps, and punches depend on high power output rather than just strength or endurance alone.
功率衡量做功或能量转移的快慢。起跑冲刺、纵跳和出拳等爆发性运动动作依赖于高功率输出，而不仅仅是力量或耐力。
Power = Work done ÷ time or Power = (Force × distance) ÷ time
or 4 kilowatts. This explains why Olympic lifters generate enormous short-duration power.
功率的单位是瓦特 (W)。如果一名举重运动员在0.5秒内将1000 N的杠铃上举2米，则功率输出 = (1000 × 2) ÷ 0.5 = 4000 W，即4千瓦。这解释了为什么奥运举重选手能在短时间内产生巨大功率。
The same work performed over a longer time yields lower power. Interval training often targets improvements in both maximum power and the ability to sustain submaximal power.
相同的功若在较长时间内完成，输出功率则会较低。间歇训练通常旨在同时提高最大功率和维持次最大功率的能力。
11. Moment of Force (Torque) and Levers | 力矩 (扭矩) 与杠杆
A moment (or torque) is the turning effect of a force around a pivot point. In the human body, joints act as pivots, bones serve as levers, and muscles provide the effort force. Understanding moments explains why some joint actions feel easier or harder depending on limb position.
力矩 (或称扭矩) 是力使物体绕支点转动的效应。在人体中，关节充当支点，骨骼作为杠杆，肌肉提供动力。理解力矩可以帮助解释为什么某些关节动作在不同肢体位置时感觉更轻松或更费力。
Moment = Force × perpendicular distance from pivot (M = F d⊥)
anticlockwise moment to lift the forearm. If the weight is 5 N held at 0.3 m from the elbow, the moment = 5 × 0.3 = 1.5 N m. Moving the weight further from the joint increases the moment arm and demands more muscle force.
例如，做肱二头肌弯举时，手中的重物会对肘关节产生一个顺时针力矩。肱二头肌
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