📚 Year 8 CIE Physical Education: Formula & Principle Quick Reference Handbook | Year 8 CIE 体育：公式定理速查手册
In Year 8 CIE Physical Education, a firm grasp of key formulas and scientific principles helps you analyse human performance, measure fitness and understand how the body responds to exercise. This quick reference handbook brings together the essential equations for body composition, cardiovascular training, biomechanics and respiratory function. Each entry includes a clear definition, the standard formula with units and a practical example, so you can apply the maths directly to your sport and health activities. Use it to check your understanding, complete coursework and prepare confidently for assessments.
在 Year 8 CIE 体育课程中，牢固掌握关键公式和科学原理有助于你分析运动表现、测量体能并理解身体对锻炼的反应。这本速查手册汇集了身体成分、心血管训练、生物力学和呼吸功能的基本方程。每个条目都包含清晰的定义、带单位的标准公式和实际示例，让你可以将数学直接应用到运动与健康活动中。用它来检验你的理解、完成课程作业并为评估做好充分准备。
1. Body Mass Index (BMI) | 体重指数
Body Mass Index is a simple screening tool that estimates whether a person's weight is appropriate for their height. It helps PE students understand the link between body composition and health. The formula divides mass in kilograms by the square of height in metres.
体重指数是一个简单的筛查工具，用于估计一个人的体重与身高是否相称。它帮助体育学生理解身体成分与健康之间的联系。该公式用体重（千克）除以身高（米）的平方。
BMI = mass (kg) / height² (m²)
For a 13‑year‑ .3 kg/m². According to standard adult categories, this falls within the normal range (18.5–24.9), but for adolescents, age‑ and sex‑ l Education you are expected to calculate BMI and discuss its limitations, such as the fact that it does not distinguish between muscle and fat.
对于一个体重 52 千克、身高 1.60 米的 13 岁少年：52 ÷ (1.60²) = 52 ÷ 2.56 ≈ 20.3 千克/米²。依据成人标准属于正常范围（18.5–24.9），但青少年需使用年龄与性别特定的百分位图表以考虑生长因素。在 CIE 体育中，你需要计算 BMI 并讨论其局限性，例如它无法区分肌肉与脂肪。
| BMI Range (kg/m²) | Classification | 分类 |
|---|---|---|
| Below 18.5 | Underweight | 偏瘦 |
| 18.5 – 24.9 | Normal weight | 正常 |
| 25.0 – 29.9 | Overweight | 超重 |
| 30.0 and above | Obese | 肥胖 |
2. Maximum Heart Rate (MHR) | 最大心率
Maximum heart rate is the highest number of beats per minute your heart can achieve during all‑out exercise. It is used to set safe and effective training intensities. The standard estimation formula, often cited in CIE syllabi, is 220 minus your age.
最大心率是指你在全力运动时心脏每分钟能够达到的最高搏动次数。它用于设定安全有效的训练强度。CIE 课程中常引用的标准估算公式为 220 减去你的年龄。
MHR = 220 – age (years)
For a Year 8 student aged 13, MHR ≈ 220 – al MHR can be measured in a laboratory, but the formula gives a safe starting point for designing aerobic and anaerobic sessions. When writing about exercise intensity, always refer back to MHR as a baseline.
对于一名 13 岁的 Year 8 学生，MHR ≈ 220 – 13 = 207 次/分钟（bpm）。请注意这只是估算值；个体差异受遗传、体能水平和体型影响。实际最大心率可在实验室测得，但公式为设计有氧与无氧训练课提供了一个安全起点。在描述运动强度时，务必以 MHR 作为基准进行说明。
3. Target Heart Rate Zones | 目标心率区
Training within specific heart rate zones helps you develop different fitness components, such as aerobic endurance or anaerobic power. The simplest method applies a percentage directly to your MHR, while the more precise Karvonen formula also considers your resting heart rate (RHR). Both approaches appear in CIE Physical Education coursework.
在特定心率区内训练有助于发展不同的体能要素，如有氧耐力或无氧爆发力。最简单的方法是直接对 MHR 应用百分比，而更精确的 Karvonen 公式还会考虑你的安静心率（RHR）。两种方法都会出现在 CIE 体育课程作业中。
Percentage of MHR method:
MHR 百分比法：
Target HR = MHR × Intensity %
Karvonen formula:
Karvonen 公式：
Target HR = RHR + [Intensity % × (MHR – RHR)]
Example using Karvonen: a 13‑year‑old with RHR = 65 bpm and MHR = 207 bpm wants to train at 70% intensity. Heart rate reserve = 207 – e, which typically improves cardiovascular fitness without accumulating excessive lactate.
以 Karvonen 公式为例：一名 13 岁学生 RHR = 65 bpm，MHR = 207 bpm，想以 70% 强度训练。心率储备 = 207 – 65 = 142 bpm。目标心率 = 65 + (0.70 × 142) = 65 + 99.4 ≈ 164 bpm。这属于有氧区，通常可提升心血管适能而不堆积过多乳酸。
| Zone | Intensity (%MHR) | Primary Benefit | 主要效益 |
|---|---|---|---|
| Moderate | 50–60% | Warm‑up, recovery | 热身与恢复 |
| Aerobic (fat‑burning) | 60–70% | Endurance base, fat oxidation | 耐力基础与脂肪氧化 |
| Aerobic (cardiovascular) | 70–80% | Aerobic capacity, stroke volume | 有氧能力与每搏输出量 |
| Anaerobic threshold | 80–90% | Lactate tolerance, speed | 乳酸耐受与速度 |
| Maximal | 90–100% | Peak power, sprinting | 峰值爆发力与短跑 |
4. Speed and Velocity | 速率与速度
Speed and velocity are fundamental concepts in movement analysis. Speed is a scalar quantity that measures how fast an object moves, while velocity is a vector quantity that also specifies direction. Both are calculated as the ratio of distance (or displacement) to time.
速率和速度是动作分析中的基本概念。速率是标量，衡量物体运动的快慢；速度是矢量，还需指明方向。两者均用距离（或位移）与时间的比值计算。
Speed = distance / time
Velocity = displacement / time
ge speed is 100 / 12.5 = 8 m/s. However, velocity after 100 m in a straight line with no change of direction is also 8 m/s forward. When an athlete runs around a bend, displacement is less than distance, so average velocity differs. Remember: speed answers 'how fast?'; velocity answers 'how fast and in which direction?'.
在考题中单位通常为米每秒（m/s），长距离项目也可能使用千米每小时（km/h）。若一名 100 米短跑选手以 12.5 秒完赛，其平均速率为 100 / 12.5 = 8 m/s。由于沿直线奔跑无方向改变，这 100 米的平均速度也是向前 8 m/s。当运动员绕弯跑时，位移小于路程，因此平均速度不同。记住：速率回答“多快？”；速度回答“多快并朝哪个方向？”。
5. Force, Mass and Acceleration | 力、质量与加速度
Newton's Second Law of Motion explains how a resultant force changes an object's motion. In physical education, this relationship governs sprint starts, throwing actions and tackling. The equation links force (F), mass (m) and acceleration (a).
牛顿第二运动定律解释了合力如何改变物体的运动状态。在体育中，这一关系支配着起跑加速、投掷动作和擒抱动作。该方程将力（F）、质量（m）和加速度（a）联系起来。
F = m × a
pplied by the legs is 60 × 3 = 180 N. For a given force, a smaller mass accelerates faster – he ground pushes back with an equal and opposite reaction force, propelling the athlete forward.
力以牛顿（N）为单位。若一名 60 千克的橄榄球运动员以 3 m/s² 加速，腿部施加的合力为 60 × 3 = 180 N。在给定力的情况下，质量越小加速度越大——这就是为何体重较轻的运动员变向更快。你还须理解，当身体对地面施加作用力时，地面会以等大反向的反作用力回推，推动运动员前进。
6. Work Done | 做功
Work done measures the energy transferred when a force moves an object through a distance. In sport, this helps quantify the muscular effort required to lift, push or pull. The formula only counts the distance moved in the direction of the applied force.
做功衡量力使物体移动一段距离时所传递的能量。在运动中，这有助于量化举、推或拉所需的肌肉用力。该公式仅计算沿着力方向移动的距离。
Work = Force × distance (in the direction of the force)
W = F × d
weight motionless above the head does zero mechanical work because distance moved is zero – distinction is important for explaining energy demands in static versus dynamic exercises.
单位为焦耳（J）。若举重运动员向上施加 800 N 的力将杠铃举起 1.5 米，所做的功为 800 × 1.5 = 1200 J。将重量静止举在头上时机械功为零，因为移动距离为零——尽管肌肉在等长收缩中感到疲劳。这一区别对解释静态与动态练习的能量需求十分重要。
7. Power | 功率
Power describes the rate at which work is performed or energy is transferred. Explosive activities such as jumping, sprinting and throwing demand high power output. The formula relates work done (or energy converted) to the time taken.
功率描述做功或能量传递的速率。爆发性活动如跳跃、冲刺和投掷需要较高的功率输出。该公式将做功（或能量转换）与所用时间联系起来。
Power = work done / time taken
P = W / t
0 / 0.5 = 1200 W. Power can also be calculated as force × velocity when the force is constant and direction of motion aligns with the force. In training, a Wingate test or vertical jump test is often used to estimate peak anaerobic power.
国际单位是瓦特（W），1 W = 1 J/s。若篮球运动员在垂直跳跃中耗时 0.5 秒做了 600 J 的功，则平均功率为 600 / 0.5 = 1200 W。当力恒定且运动方向与力一致时，功率也可用力×速度计算。在训练中，常利用温盖特测试或纵跳测试来估算峰值无氧功率。
8. Levers and Mechanical Advantage | 杠杆与机械效益
The human skeleton acts as a system of levers, with joints as pivots, muscles applying effort and body segments or external objects providing the load. Understanding lever classes helps you explain movement efficiency and force production in sport. Mechanical advantage (MA) indicates how effectively a lever multiplies the effort force.
人体骨骼相当于一个杠杆系统，关节是支点，肌肉施加动力，身体环节或外部物体提供阻力。理解杠杆类别有助于解释运动中的动作效率和力的产生。机械效益（MA）表示杠杆放大动力力的有效程度。
Mechanical Advantage = Load / Effort
Alternatively, for a rigid lever: MA = Length of effort arm / Length of load arm. A lever with MA > 1 multiplies force (e.g. a wheelbarrow‑style second‑class lever like the calf raise); MA < 1 sacrifices force for speed and range of motion (e.g. a third‑class lever like the biceps curl). Most body levers are third‑class, favouring speed over force – an excellent design for throwing and kicking. In coursework, sketch a lever system, label effort, load and fulcrum, and calculate MA to justify your analysis.
或者，对于刚性杠杆：机械效益 = 动力臂长 / 阻力臂长。MA > 1 的杠杆可以省力（如二类杠杆的提踵动作，类似独轮车）；MA < 1 的杠杆牺牲力来换取速度与活动范围（如三类杠杆的肱二头肌弯举）。人体大多数杠杆为三类杠杆，以力换速度——这非常适合投掷与踢击动作。在课程作业中，画出杠杆系统，标出动力、阻力与支点，并计算机械效益来支持你的分析。
| Lever Class | Arrangement (Fulcrum‑Effort‑Load) | Mechanical Advantage | Sporting Example |
|---|---|---|---|
| First‑class | Fulcrum in middle | Can be >1, =1 or <1 | Neck during heading a football |
| Second‑class | Load in middle | Always >1 (force multiplier) | Ankle during calf raise (plantar flexion) |
| Third‑class | Effort in middle | Always <1 (speed multiplier) | Biceps curl, knee extension in kicking |
9. Cardiac Output (Q) | 心输出量
Cardiac output is the volume of blood pumped by the heart in one minute. It reflects the delivery of oxygen and nutrients to working muscles and is a central concept in cardiovascular fitness. The equation shows how heart rate and stroke volume work together.
心输出量是心脏每分钟泵出的血液体积。它反映了向工作肌肉输送氧气与营养物质的能力，是心血管适能的核心概念。该方程显示了心率与每搏输出量如何协同工作。
Cardiac Output (Q) = Heart Rate (HR) × Stroke Volume (SV)
Units: Q is expressed in litres per minute (L/min). At rest, a typical 13‑year‑ L/min or more in trained youths. Regular endurance training increases stroke volume, which means the heart pumps more blood per beat and does not need to beat as fast at submaximal intensities – an important adaptation to explain in exam answers.
单位：心输出量以
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