📚 Year 9 CIE Physical Education: Formulas & Principles Quick Reference Guide | Year 9 CIE 体育：公式定理速查手册
This quick reference guide brings together the essential formulas and principles you need to master Year 9 CIE Physical Education. From calculating heart rate zones and body composition to understanding levers, Newton's laws, and training principles, every key concept is presented with clear explanations in both English and Chinese. Use this handbook to support your revision, check your understanding, and build confidence before assessments.
这本速查手册汇集了 Year 9 CIE 体育课程必须掌握的核心公式与定理。从心率区间和身体成分的计算，到杠杆、牛顿定律和训练原则的理解，每个关键概念都用中英双语清晰解释。请利用本手册辅助复习、自查理解，并在测评前建立信心。
1. Heart Rate Formulas | 心率计算公式
ing intensity, the Karvonen formula uses heart rate reserve (HRR) to give a more personalised target. HRR is the difference between maximal and resting heart rate. Target heart rate is then calculated as (HRmax - HRrest) × desired intensity + HRrest. This method ensures that the training load is relative to the individual's fitness level.
心率监测是运动处方的基石。最常用的最大心率估算是 HRmax = 220 - 年龄。为了制定训练强度，卡氏公式借助心率储备提供更个性化的目标。心率储备是最大心率与安静心率之差。目标心率计算公式为：(最大心率 - 安静心率) × 目标强度 + 安静心率。这一方法确保训练负荷与个人体能水平相匹配。
HRmax = 220 - age
Heart Rate Reserve (HRR) = HRmax - HRrest
Target HR = (HRR × Intensity%) + HRrest
For a 14-year-old student with a resting HR of 70 bpm aiming to train at 70% = 136 bpm; Target = (136 × 0.7) + 70 = 165 bpm. Always round to the nearest whole number.
对于一名14岁、安静心率70 bpm的学生，若以70%强度训练，靶心率计算如下：最大心率 = 220 - 14 = 206 bpm；心率储备 = 206 - 70 = 136 bpm；靶心率 = (136 × 0.7) + 70 = 165 bpm。结果通常四舍五入至整数。
2. Body Mass Index (BMI) | 身体质量指数 (BMI)
BMI is a screening tool used to categorise individuals as underweight, healthy weight, overweight or obese. It is not a direct measure of body fat, but for most young people it provides a useful starting point for health-related discussions. The formula uses mass in kilograms and height in metres.
BMI 是一种筛查工具，用于将个体划分为消瘦、健康体重、超重或肥胖。它并非直接测量身体脂肪，但对多数青少年而言，可作为健康相关讨论的有效起点。公式使用以千克为单位的体重和以米为单位的身高。
BMI = weight (kg) / height² (m²)
h falls within the healthy weight range for adolescents. Remember that BMI cut-offs for young people also consider age and sex percentiles, but the raw calculation remains the same.
示例：一名 Year 9 学生体重 52 公斤，身高 1.62 米，其 BMI = 52 / (1.62 × 1.62) = 52 / 2.6244 ≈ 19.8 kg/m²，这属于青少年健康体重范围。请记住，青少年 BMI 界值还需参考年龄与性别百分位数，但原始计算方式不变。
3. Body Composition & Skinfold Equations | 身体成分与皮褶厚度公式
Skinfold measurements estimate body fat percentage by measuring subcutaneous fat at specific sites. The Siri equation is widely used to convert body density (BD) into fat percentage. Body density itself is often predicted from the sum of skinfolds using population-specific equations. For Year 9 PE, it is important to understand the relationship: a lower body density usually indicates a higher fat percentage.
皮褶厚度测量通过特定部位的皮下脂肪估算体脂百分比。Siri 公式被广泛用于将身体密度转换为脂肪比例。身体密度则常根据皮褶厚度总和，借助特定人群的回归方程预测。对 Year 9 体育而言，理解以下关系至关重要：身体密度越低，体脂率往往越高。
Body Fat % = (4.95 / BD - 4.50) × 100
+ subscapular + suprailiac skinfolds). For females, the coefficients differ. While you won' ula if given BD. A BD of 1.065 g/cm³, for example, yields (4.95/1.065 - 4.50) × 100 ≈ 14.8% body fat.
其中 BD 为身体密度 (g/cm³)。对于男性青少年，常用预测方程为：BD = 1.1533 - 0.0643 × log(肱三头肌 + 肩胛下 + 髂前上棘皮褶厚度之和)。女性系数不同。虽然无需死记回归方程，但若给出 BD，你应能应用 Siri 公式。例如 BD = 1.065 g/cm³，则体脂率 ≈ (4.95/1.065 - 4.50) × 100 ≈ 14.8%。
4. Levers, Moments and Mechanical Advantage | 杠杆、力矩与机械利益
The human body moves using three classes of levers. A moment (torque) is the turning effect produced by a force and is calculated as force multiplied by the perpendicular distance from the pivot. In biomechanics, this is used to analyse joint movements and muscular efforts. Mechanical advantage compares the effort arm to the load arm, telling us whether a lever system favours force or speed.
人体借助三类杠杆进行运动。力矩是力产生的转动效应，其值为力乘以力到支点的垂直距离。运动生物力学中，力矩用于分析关节活动与肌肉用力。机械利益比较力臂与阻力臂，表明杠杆系统是偏向省力还是偏向速度。
Moment (Torque) = Force × Perpendicular distance from pivot
Mechanical Advantage = Effort arm length / Load arm length
- First-class lever (e.g. neck extension): pivot between effort and load.
- 第一类杠杆（如颈部后伸）：支点在力点与阻力点之间。
- Second-class lever (e.g. standing calf raise): load between pivot and effort; mechanical advantage > 1.
- 第二类杠杆（如站立提踵）：阻力在支点与力点之间；机械利益 > 1。
- Third-class lever (e.g. biceps curl): effort between pivot and load; mechanical advantage < 1, favouring speed and range of motion.
- 第三类杠杆（如肱二头肌弯举）：力点在支点和阻力点之间；机械利益 < 1，利于速度与活动幅度。
5. Newton's Laws of Motion | 牛顿运动定律
Sir Isaac Newton's three laws explain the relationship between forces and motion, and they underpin all sporting actions. The first law (inertia) states that an object remains at rest or in uniform motion unless acted upon by an external force. The second law (acceleration) tells us that acceleration is directly proportional to net force and inversely proportional to mass. The third law (action-reaction) states that for every action there is an equal and opposite reaction. These laws help you understand sprint starts, swimming propulsion and collision sports.
牛顿三大定律阐释了力与运动的关系，是解释体育运动动作的基础。第一定律（惯性）指出，物体将保持静止或匀速直线运动，除非受到外力作用。第二定律（加速度）表明加速度与所受净力成正比、与质量成反比。第三定律（作用力与反作用力）指出，每个作用力都有一个大小相等、方向相反的反作用力。这些定律帮助你理解短跑起跑、游泳推进以及对抗性运动项目。
Force = mass × acceleration (F = ma)
pushes backwards against the blocks (action), and the blocks push the athlete forwards (reaction). The larger the force applied, the greater the acceleration, provided mass remains constant.
示例：一名 50 公斤运动员以 3 m/s² 加速，需要净力 50 × 3 = 150 牛。在短跑起跑中，运动员向后蹬起跑器（作用力），起跑器将运动员向前推（反作用力）。只要质量不变，施加的力越大，加速度就越大。
6. FITT Principle & Intensity Calculations | FITT 原则与强度计算
The FITT principle guides exercise programme design. Frequency refers to how often you train, Intensity to how hard, Time to session duration, and Type to the mode of exercise. Intensity is often quantified using heart rate or perceived exertion. Using the Karvonen method (see Heart Rate section) gives an accurate percentage of cardiovascular load, but a simpler method multiplies HRmax directly by the intensity fraction for an approximate zone.
FITT 原则指导着运动计划设计。F 代表训练频率（多久一次），I 代表强度（多辛苦），第一个 T 代表时间（持续多久），第二个 T 代表类型（练习模式）。强度常通过心率或主观用力感觉来量化。采用卡氏公式（见心率章节）可获得精准的心血管负荷百分比，而更简单的方法是直接用最大心率乘以强度分数来大致划分区间。
Intensity (%HRmax) ≈ Target HR / HRmax × 100
Simplified Target HR = HRmax × Intensity%
For a 13-year-old with HRmax of 207 bpm, a moderate intensity at 65% gives a target of about 135 bpm using the simplified method. FITT is often combined with SPORT principles for a complete training approach.
对一名 13 岁、最大心率 207 bpm 的学生，采用简化法，中等强度 65% 对应的目标心率约为 135 bpm。FITT 常与 SPORT 原则结合，形成完整的训练方案。
7. SPORT Training Principles | SPORT 训练原则
SPORT stands for Specificity, Progression, Overload, Reversibility and Tedium (or Variation). These principles ensure training is effective and safe. Specificity means training must match the demands of the sport. Progression requires gradual increase in load. Overload pushes the body beyond its comfort zone using the FITT variables. Reversibility warns that fitness gains are lost when training stops. Tedium (also called variety) reminds us to change training activities to maintain motivation. While mostly qualitative, these principles can be linked to formulas like the overload threshold and rate of progression (e.g. 10% increase per week).
SPORT 代表特异性、渐进性、超负荷、可逆性和单调（或称多样性）。这些原则保障训练有效且安全。特异性要求训练必须匹配专项需求。渐进性要求负荷逐步增加。超负荷则借助 FITT 变量让身体超越舒适区。可逆性警示，停止训练后体适能提升会消退。单调（也称多样性）提醒我们变换训练活动以保持动力。尽管多数是定性原则，但也能与公式关联，比如超负荷阈值和递增速率（如每周增加 10%）。
Progression rate (%) = (New load - Old load) / Old load × 100
- S: Specificity — 特异性
- P: Progression — 渐进性
- O: Overload — 超负荷
- R: Reversibility — 可逆性
- T: Tedium / Variation — 单调 / 多样性
8. Speed, Distance & Time | 速度、距离与时间
Speed is one of the simplest yet most important biomechanical quantities. In sport, it is often split into average speed over a whole event and instantaneous speed during phases. Distance–time graphs and speed calculations help evaluate performance in running, cycling and swimming.
速度是最简单却最重要的生物力学量之一。在体育运动中，它常分为全程平均速度和分阶段瞬时速度。距离 - 时间图和速度计算有助于评估跑步、自行车和游泳中的运动表现。
Average Speed = Total distance travelled / Total time taken
Distance = Speed × Time
00 / 4 = 50 s. These relationships are crucial for pacing strategies and analysing splits.
一名 100 米短跑选手以 12.5 秒完赛，平均速度为 100 / 12.5 = 8 m/s。若随后以 4 m/s 慢跑 200 米，所需时间为 200 / 4 = 50 秒。这些关系对于配速策略和分段分析至关重要。
9. Force, Work & Power | 力、功与功率
Work is done when a force moves an object through a distance in the direction of the force. Power measures how quickly work is performed, making it a key indicator of explosive ability in sports such as javelin throwing or vertical jumps. In linear motion, power can also be expressed as the product of force and velocity.
当力使物体沿力的方向移动一段距离时，即做功。功率衡量做功的快慢，因而成为标枪投掷或纵跳等项目中爆发力的关键指标。在直线运动中，功率也可表示为力与速度的乘积。
Work (J) = Force (N) × Distance (m)
Power (W) = Work / Time = Force × Velocity
1600 W. If the same lift were performed at a slower speed, the power output would be lower, even though the work remains constant.
示例：一名举重运动员在 0.5 秒内将 1000 牛的杠铃上举 0.8 米。做功 = 1000 × 0.8 = 800 焦。功率输出 = 800 / 0.5 = 1600 瓦。若以较慢速度完成同一动作，做功不变，但功率输出会降低。
10. Estimating 1RM & Training Volume | 1RM 估算与训练量
One-repetition maximum (1RM) is the heaviest load that can be lifted once with correct technique. Direct 1RM testing can be risky for younger athletes, so equations like the Epley formula allow safe estimation from submaximal repetitions. Training volume, on the other hand, quantifies the total load handled in a session and is essential for monitoring progressive overload.
一次最大重量 (1RM) 是指能以正确技术完整举起一次的最大负荷。对年轻运动员来说，直接测试 1RM 可能存在风险，因此像 Epley 公式这样的方法可以通过次最大重复次数安全估算。训练量则用于量化一堂课的总负荷，对监控渐进超负荷至关重要。
Estimated 1RM = Weight lifted × (1 + Reps / 30)
This Epley variant is reasonably accurate for 1– lifting 40 kg for 8 reps gives an estimated 1RM of 40 × (1 + 8/30) = 40 × 1.267 ≈ 50.7 kg.
该 Epley 变式对 1 - 10 次重复较为准确。例如，以 40 公斤完成 8 次，估算 1RM = 40 × (1 + 8/30) = 40 × 1.267 ≈ 50.7 kg。
Training Volume = Sets × Reps × Load (kg)
60 kg. Tracking volume helps coaches progressively increase training stress while avoiding overtraining.
若同一运动员完成 3 组 × 8 次、40 公斤的训练，训练量为 3 × 8 × 40 = 960 公斤。追踪训练量有助于教练渐进地增加训练刺激，同时避免过度训练。
11. Energy Systems & Their Thresholds | 能量系统及其阈值
The body uses three energy systems to resynthesise adenosine triphosphate (ATP). The ATP-PCr system provides immediate energy for up to about 10 seconds of maximal effort. The glycolytic system (anaerobic) takes over and sustains high-intensity activity for approximately 10–90 seconds, producing lactate. The oxidative (aerobic) system dominates during longer, submaximal exercise. Understanding these systems helps you design interval training and recovery.
人体通过三大能量系统再合成三磷酸腺苷 (ATP)。ATP-PCr 系统为时长约 10 秒的极限运动即刻供能。糖酵解系统（无氧）接手并维持约 10–90 秒的高强度活动，同时产生乳酸。氧化（有氧）系统则在长时间的次最大运动中占主导地位。理解这些系统有助于设计间歇训练和恢复。
| Energy System / 能量系统 | Duration / 时长 | Intensity / 强度 | Key Sport Example / 运动示例 |
|---|---|---|---|
| ATP-PCr | 0–10 s | Maximal | Shot put, 100 m start / 铅球、百米起跑 |
| Glycolytic (Anaerobic) / 糖酵解（无氧） | 10–90 s | Very high | 200 m sprint, 50 m swim / 200米跑、50米游泳 |
| Oxidative (Aerobic) / 氧化（有氧） | > 90 s | Moderate | 1500 m run, cycling / 1500米跑、自行车 |
or Year 9 it is enough to know that RER values near 1.0 indicate more carbohydrate metabolism (glycolytic), while values near 0.7 reflect fat oxidation (aerobic). EPOC (excess post-exercise oxygen consumption) is a physiological principle describing elevated oxygen uptake after intense exercise to restore the body.
一条相关公式将运动强度与主导供能系统联系起来。呼吸交换率 (RER) = VCO₂ / VO₂，可用于估算燃料利用，但对于 Year 9 只需知道 RER 接近 1.0 代表更多碳水化合物代谢（糖酵解），接近 0.7 则反映脂肪氧化（有氧）。运动后过量氧耗 (EPOC) 是指剧烈运动后身体为恢复而保持较高摄氧量的生理现象。
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