📚 Year 10 WJEC PE: Formula & Theorem Quick Reference Handbook | WJEC 十年级体育：公式定理速查手册
This revision booklet compiles the essential formulas and scientific principles you will meet in the WJEC GCSE Physical Education course. Each formula is presented with a worked example so you can apply it confidently during your studies and exam preparation.
本速查手册汇集了 WJEC GCSE 体育课程中的必备公式与科学原理，每个公式均配有应用示例，帮助你在学习和备考中自信运用。
1. Max Heart Rate & Training Zones | 最大心率与训练区间
Your maximum heart rate (HRmax) is the highest number of beats your heart can achieve in one minute during all‑out exercise. The simplest estimation is:
最大心率（HRmax）指的是在极限运动中你的心脏每分钟所能达到的最高跳动次数。最简单的估算公式为：
HRmax = 220 – age (years)
For a 15‑year‑old student, the estimated HRmax is 205 beats per minute (bpm). Training zones are then set as percentages of HRmax:
对于一名 15 岁的学生，预估最大心率约为 205 次/分（bpm）。训练区间则按最大心率的百分比划分：
Zone 1 – Very light: 50–60% of HRmax
区间 1 – 极低强度：50–60% 最大心率
Zone 2 – Light: 60–70% of HRmax
区间 2 – 低强度：60–70% 最大心率
Zone 3 – Moderate: 70–80% of HRmax
区间 3 – 中等强度：70–80% 最大心率
Zone 4 – Hard: 80–90% of HRmax
区间 4 – 高强度：80–90% 最大心率
Zone 5 – Maximum: 90–100% of HRmax
区间 5 – 极限强度：90–100% 最大心率
The 220‑minus‑age formula is an estimate; the Karvonen method (Section 2) gives a more personalised target when resting heart rate is known.
“220 减去年龄” 仅是估算公式；若知道安静心率，卡沃宁法（第 2 节）能给出更具个体化的目标心率。
2. Karvonen Formula (Heart Rate Reserve) | 卡沃宁公式（心率储备）
The Karvonen formula uses your resting heart rate (HRrest) and heart rate reserve (HRR) to calculate target training intensity. The key equations are:
卡沃宁公式借助你的安静心率（HRrest）和心率储备（HRR）来计算目标训练强度。关键方程式如下：
HRR = HRmax – HRrest
Target HR = (HRR × intensity %) + HRrest
Example: A 15‑year‑old with a resting HR of 62 bpm wants to train at 70% intensity.
示例：一名 15 岁学生安静心率为 62 bpm，希望以 70% 强度训练。
HRmax = 220 – 15 = 205 bpm. HRR = 205 – 62 = 143 bpm. Target HR = (143 × 0.70) + 62 = 100.1 + 62 = 162 bpm (rounded).
HRmax = 220 – 15 = 205 bpm。HRR = 205 – 62 = 143 bpm。目标心率 = (143 × 0.70) + 62 = 100.1 + 62 = 162 bpm（四舍五入）。
This method is widely used to set aerobic and anaerobic training intensities because it accounts for individual fitness levels.
该方法因顾及个人体能水平而被广泛用于设定有氧和无氧训练强度。
3. Body Mass Index (BMI) | 身体质量指数
BMI is a simple screening tool that relates weight to height. Although it does not measure body composition directly, it is required throughout the WJEC specification.
BMI 是一项将体重与身高关联的简单筛查工具。尽管它并不直接测量身体成分，却是 WJEC 考纲中的必学内容。
BMI = weight (kg) ÷ [height (m)]²
Worked example: A student weighs 64 kg and is 1.70 m tall.
计算示例：一名学生体重 64 kg，身高 1.70 m。
BMI = 64 ÷ (1.70 × 1.70) = 64 ÷ 2.89 ≈ 22.1 kg/m².
BMI = 64 ÷ (1.70 × 1.70) = 64 ÷ 2.89 ≈ 22.1 kg/m²。
According to standard classification, 18.5–24.9 kg/m² is considered healthy weight. Under 18.5 is underweight, 25–29.9 is overweight, and 30 or above is obese.
按照标准分类，BMI 在 18.5–24.9 kg/m² 为健康体重，低于 18.5 为偏瘦，25–29.9 为超重，30 及以上为肥胖。
4. Cardiac Output & Stroke Volume | 心输出量与每搏输出量
Cardiac output (Q) is the volume of blood pumped by the heart per minute. It is the product of heart rate (HR) and stroke volume (SV) – the amount of blood ejected with each beat.
心输出量（Q）是心脏每分钟泵出的血液总量，等于心率（HR）与每搏输出量（SV，每次心跳射出的血量）的乘积。
Q = HR × SV
SV = end‑diastolic volume – end‑systolic volume
might have HR = 72 bpm and SV = 70 mL/beat, giving Q = 72 × 70 = 5,040 mL/min (≈5 L/min).
静息时，一位久坐青少年的心率可能为 72 bpm，每搏输出量为 70 mL/beat，则 Q = 72 × 70 = 5,040 mL/min（约 5 L/min）。
During maximal exercise, trained athletes can increase both HR and SV, sometimes doubling or tripling resting cardiac output. This improvement occurs through cardiac hypertrophy and increased venous return.
在极限运动中，受过训练的运动员能同时提升心率和每搏输出量，有时能将静息心输出量提高到两倍或三倍。这一提升源于心肌增厚与静脉回流的增加。
5. Mechanical Advantage & Levers | 机械优势与杠杆
In sport, levers allow us to apply a small effort to overcome a larger resistance or to increase speed. The mechanical advantage (MA) of any lever system describes its efficiency.
在体育运动中，杠杆使我们能用较小的力克服较大的阻力，或增加运动速度。任何杠杆系统的机械优势（MA）描述了其效率。
Mechanical advantage = effort arm ÷ resistance arm
The effort arm is the distance from the effort force to the fulcrum (joint); the resistance arm is the distance from the resistance to the fulcrum.
力臂是动力作用点到支点（关节）的距离；阻力臂是阻力到支点的距离。
First‑ ., neck raising the head): fulcrum between effort and resistance. MA can be >1, =1, or <1.
第一类杠杆（如颈部抬头动作）：支点在动力与阻力之间，MA 可大于、等于或小于 1。
Second‑class lever (e.g., standing on tiptoes): resistance between fulcrum and effort. MA > 1, so a small effort lifts a large resistance.
第二类杠杆（如踮脚尖站姿）：阻力在支点与动力之间，MA > 1，可用较小的力抬起较大的阻力。
Third‑class lever (e.g., biceps curl): effort between fulcrum and resistance. MA < 1, allowing large range and speed of movement at the expense of force.
第三类杠杆（如肱二头肌弯举）：动力在支点与阻力之间，MA < 1，牺牲力量换取大幅度和快速动作。
Most human movement levers are third‑class, favouring speed over strength.
人体的运动杠杆多为第三类，以速度而非力量为优先。
6. Speed, Velocity & Acceleration | 速率、速度与加速度
Speed is the rate at which an object covers distance. Velocity is speed in a given direction. Acceleration measures how quickly velocity changes.
速率描述物体覆盖距离的快慢。速度是特定方向上的速率。加速度则衡量速度变化的快慢。
Speed = distance ÷ time
Velocity = displacement ÷ time
Acceleration = (final velocity – initial velocity) ÷ time taken
Using symbols: v = s / t and a = (v – 8.33 m/s. If she starts from rest and reaches 10 m/s in 3 seconds, her acceleration is (10 – 0) ÷ 3 ≈ 3.33 m/s².
用符号表示为：v = s / t，a = (v – u) / t。一位短跑运动员在 12 秒内跑完 100 m，平均速率为 100 ÷ 12 = 8.33 m/s。若她从静止开始，在 3 秒内达到 10 m/s，则加速度为 (10 – 0) ÷ 3 ≈ 3.33 m/s²。
Negative acceleration (deceleration) occurs when a player slows down; it is calculated in the same way but yields a negative value.
当运动员减速时，出现负加速度（减速度），其计算方法相同但结果为负值。
7. Force, Mass & Momentum | 力、质量与动量
Newton's second law links force, mass and acceleration. Momentum describes the quantity of motion an object possesses and is conserved during collisions.
牛顿第二定律将力、质量和加速度联系起来。动量描述物体的运动量，并在碰撞中满足守恒定律。
Force (N) = mass (kg) × acceleration (m/s²) → F = m × a
Momentum (kg·m/s) = mass × velocity → p = m × v
240 N. If the same player is sprinting at 7 m/s, her momentum is p = 80 × 7 = 560 kg·m/s.
示例：一名 80 kg 的橄榄球运动员以 3 m/s² 的加速度冲刺，所需的地面反作用力为 F = 80 × 3 = 240 N。若她以 7 m/s 的速度奔跑，其动量为 p = 80 × 7 = 560 kg·m/s。
ime) and momentum helps explain how to reduce injury risk and improve tackling techniques.
在对抗性运动中，理解冲量（力 × 时间）与动量有助于解释如何降低受伤风险并改进擒抱技术。
8. Work, Power & Energy in Sport | 体育中的功、功率与能量
Work is done when a force moves an object. Power is the rate of doing work. These concepts help evaluate athletic performance and movement efficiency.
力使物体移动时便做了功。功率是做功的速率。这些概念有助于评价运动表现和动作效率。
Work (J) = force (N) × distance moved in direction of force (m)
Power (W) = work done ÷ time taken or Power = force × velocity
2.2 = 2,156 J. If the lift takes 2.5 seconds, average power output = 2,156 ÷ 2.5 ≈ 862 W.
若举重运动员用 980 N 的力将杠铃上举 2.2 m，做功为 980 × 2.2 = 2,156 J。若完成动作用时 2.5 秒，则平均功率输出为 2,156 ÷ 2.5 ≈ 862 W。
During continuous exercise, aerobic energy production yields around 38–39 ATP per glucose molecule, whereas anaerobic glycolysis yields only 2 ATP – hence the difference in sustainable power.
在持续运动中，有氧供能每个葡萄糖分子产生约 38–39 个 ATP，而无氧糖酵解仅产生 2 个 ATP，这就是可持续功率存在差异的原因。
9. Training Load & FITT Principle | 训练负荷与 FITT 原则
Training load can be quantified to avoid overtraining and ensure progressive overload. The FITT principle (Frequency, Intensity, Time, Type) forms the foundation of programme design.
训练负荷可以量化，以避免过度训练并确保渐进超负荷。FITT 原则（频率、强度、时间、类型）是训练计划设计的基础。
Training load = session RPE (e.g., Borg scale 1–10) × duration (minutes)
For example, a 40‑ y units. Over a week, summing these session loads monitors whether workload is increasing too rapidly.
例如，一次 40 分钟的足球训练自感用力评分（RPE）为 7，负荷为 7 × 40 = 280 任意单位。每周汇总各次训练负荷可监控训练量是否增长过快。
The FITT guidelines suggest adapting variables: Frequency (days per week), Intensity (%HRmax or %1RM), Time (session duration), and Type (mode of exercise).
FITT 指导原则建议调整以下变量：频率（每周几天）、强度（%最大心率或 1RM 百分比）、时间（每次时长）和类型（运动模式）。
10. Fluid Dynamics & the Magnus Effect | 流体动力学与马格努斯效应
When a spinning ball travels through the air, the difference in airflow velocity on either side creates a pressure imbalance – the Magnus effect. This principle explains curved trajectories in football, tennis and cricket.
当旋转的球在空中飞行时，两侧气流速度的差异会产生压力差——这就是马格努斯效应。这一原理解释了足球、网球和板球中的弧线轨迹。
According to Bernoulli's principle, faster airflow reduces pressure. A clockwise spin on a ball moving left makes air travel faster over the top, creating lower pressure above and causing the ball to dip or swerve.
根据伯努利原理，气流越快则压强越小。向左飞行的球产生顺时针旋转，球顶部的气流速度更快，因而上部压强较小，球便下坠或拐弯。
spin → airflow difference → pressure gradient → lateral force → deviation in flight path.
虽然 GCSE 阶段不要求具体计算公式，但该效应可概括为：旋转 → 气流差异 → 压力梯度 → 侧向力 → 飞行轨迹偏离。
Coaches and athletes exploit the Magnus effect deliberately, for example a free‑kick specialist striking the ball with sidespin to bend it around a defensive wall.
教练和运动员会有意识地利用马格努斯效应，例如任意球专家通过侧旋使球绕过人墙。
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