📚 Handbook of Key Formulas and Principles | 公式定理速查手册
This quick-reference guide draws together the essential formulas and scientific principles you will meet in Year 10 CCEA Physical Education. Whether you are calculating training zones, analysing lever systems or revising Newton's laws, having these at your fingertips will strengthen both your written answers and your practical understanding.
这本速查手册汇集了 Year 10 CCEA 体育学科中必须掌握的关键公式与科学原理。无论是计算训练区域、分析杠杆系统，还是复习牛顿定律，随时翻阅这些内容都能帮助你巩固书面答题能力和实践理解。
1. Maximum Heart Rate (HRmax) | 最大心率
The simplest and most widely used estimate of maximum heart rate is derived from age alone. It gives a foundation for setting aerobic and anaerobic training intensities.
最大心率的最简单、最常用估算方法仅基于年龄，它是设定有氧与无氧训练强度的基础。
HRmax = 220 - age
- HRmax is expressed in beats per minute (bpm).
- HRmax 以每分钟心跳次数（bpm）表示。
- A 15-year-old performer would have an estimated HRmax of 220 - 15 = 205 bpm.
- 一名 15 岁的运动者估算最大心率为 220 - 15 = 205 bpm。
2. Heart Rate Reserve (HRR) & Target Heart Rate | 心率储备与目标心率
The Karvonen formula incorporates resting heart rate (RHR) to give a more personalised training intensity. It is widely used to prescribe target heart rate zones.
卡沃宁公式引入静息心率（RHR），提供更个性化的训练强度，广泛用于设定目标心率区域。
HRR = HRmax - RHR
Target HR = (HRR × desired intensity %) + RHR
- Resting heart rate is best measured first thing in the morning.
- 静息心率最好在清晨刚醒来时测量。
- For moderate-intensity exercise, use 60-70% of HRR; for vigorous, use 70-85%.
- 中等强度运动使用 HRR 的 60-70%；大强度运动使用 70-85%。
3. Body Mass Index (BMI) | 身体质量指数
BMI is a simple screening tool that relates body mass to height. It helps classify individuals as underweight, normal weight, overweight or obese.
BMI 是一种将体重与身高关联的简易筛查工具，可用于将个体分类为偏瘦、正常、超重或肥胖。
BMI = body mass (kg) ÷ height² (m²)
- Mass must be in kilograms and height in metres.
- 质量必须以千克为单位，身高以米为单位。
- A performer who is 1.65 m tall and weighs 58 kg: BMI = 58 ÷ (1.65 × 1.65) ≈ 21.3 kg/m².
- 一名身高 1.65 m、体重 58 kg 的运动员：BMI = 58 ÷ (1.65 × 1.65) ≈ 21.3 kg/m²。
- Note that BMI does not distinguish between muscle and fat; very muscular individuals may be misclassified.
- 注意，BMI 不区分肌肉与脂肪，肌肉量极高者可能被误判。
4. Speed Calculation | 速度计算
Speed is a scalar quantity describing how quickly a body moves. It is fundamental to many fitness tests and performance analyses.
速度是描述物体运动快慢的标量，是许多体能测试和运动表现分析的基础。
Speed = distance ÷ time
- Units are typically metres per second (m/s) or kilometres per hour (km/h).
- 单位通常为米/秒（m/s）或千米/小时（km/h）。
- A 100 m sprinter runs the distance in 12.5 s: speed = 100 ÷ 12.5 = 8.0 m/s.
- 一名 100 m 短跑运动员用 12.5 秒跑完全程：速度 = 100 ÷ 12.5 = 8.0 m/s。
- In team games, average speed is often less informative than changes in speed (acceleration and deceleration).
- 在团队运动中，平均速度的信息往往不如速度变化（加速与减速）重要。
5. Levers & Moments | 杠杆与力矩
In the human body, bones act as levers, joints as fulcrums and muscles provide the effort. Understanding lever classes helps analyse movement efficiency and mechanical advantage.
在人体中，骨骼充当杠杆，关节充当支点，肌肉提供动力。理解杠杆类别有助于分析动作效率和机械效益。
Moment of a force = force × perpendicular distance from fulcrum
- First-class lever: fulcrum between effort and load (e.g., nodding the head).
- 第一类杠杆：支点在动力和阻力之间（如点头动作）。
- Second-class lever: load between fulcrum and effort (e.g., standing on tiptoes).
- 第二类杠杆：阻力在支点和动力之间（如提踵站立）。
- Third-class lever: effort between fulcrum and load (e.g., biceps curl). Most body levers are third class, favouring speed and range of movement over force.
- 第三类杠杆：动力在支点和阻力之间（如肱二头肌弯举）。人体大部分杠杆属于第三类，以牺牲力量换取速度和活动范围。
6. Newton’s Laws of Motion | 牛顿运动定律
Newton’s three laws explain how forces create, alter and interact to produce motion. They are essential for describing sprint starts, tackles and projectile motion in sport.
牛顿三大定律解释了力如何产生、改变和相互作用以形成运动，是描述短跑起跑、擒抱动作和抛射体运动的重要理论。
- First Law (Inertia): A body remains at rest or in uniform motion unless acted upon by an external force. A football will stay still until kicked.
- 第一定律（惯性）：物体将保持静止或匀速直线运动，除非受到外力作用。足球会静止，直到被踢动。
- he acceleration of a body is proportional to the net force and inversely proportional to its mass. A lighter athlete can accelerate faster with the same force.
- 第二定律（加速度）：F = m × a。物体的加速度与所受合外力成正比，与质量成反比。施加相同力量时，体重较轻的运动员加速更快。
- Third Law (Action-Reaction): For every action, there is an equal and opposite reaction. When a swimmer pushes water backward, the water pushes the swimmer forward.
- 第三定律（作用与反作用）：每一个作用力都有一个大小相等、方向相反的反作用力。游泳者向后推水，水便向前推动游泳者。
7. The FITT Principle | FITT 训练原则
FITT is the classic tool for designing and adjusting an exercise programme. It stands for Frequency, Intensity, Time and Type.
FITT 是设计和调整运动计划的经典工具，分别代表频率、强度、时间和类型。
| Element 要素 | Definition 定义 | Example 示例 |
|---|---|---|
| Frequency | How often you train | 3-5 sessions per week |
| Intensity | How hard you exercise | 60-80% HRR |
| Time | Duration of each session | 20-60 minutes of continuous activity |
| Type | Mode of exercise | Cycling, running, swimming |
- Applying FITT helps ensure progressive overload without risking overtraining.
- 运用 FITT 原则有助于实现渐进超负荷，同时避免过度训练的风险。
8. Training Intensity using RPE | 使用 RPE 衡量训练强度
The Rate of Perceived Exertion (RPE) scale is a subjective method of monitoring exercise intensity, typically ranging from 6 to 20 on the original Borg scale.
自感用力度（RPE）量表是监测运动强度的主观方法，原始 Borg 量表通常从 6 到 20 级。
- RPE 6 means no exertion at all; RPE 20 means maximal exertion.
- RPE 6 表示完全不用力，RPE 20 表示最大用力。
- To estimate heart rate, multiply the RPE by 10: a rating of 13 corresponds roughly to 130 bpm. While not exact, it provides a useful field guide.
- 估算心率时，可将 RPE 乘以 10：评级 13 大致对应 130 bpm。虽不精确，但提供了实用的现场指导。
- RPE is valuable when heart rate monitors are unavailable or when certain medications affect heart rate.
- 在无法使用心率监测或某些药物影响心率时，RPE 非常有用。
9. Aerobic and Anaerobic Training Zones | 有氧与无氧训练区
Training zones based on HRmax help target specific energy systems. The aerobic zone develops cardiovascular endurance, while the anaerobic zone improves high-intensity performance.
基于最大心率的训练区域有助于针对特定能量系统进行训练。有氧区域发展心血管耐力，无氧区域提高高强度表现。
- Aerobic zone: typically 60-80% of HRmax. The body uses oxygen to produce energy, burning fat and carbohydrate. Fatigue is delayed.
- 有氧区域：通常为 HRmax 的 60-80%。身体利用氧气产生能量，燃烧脂肪和碳水化合物，疲劳出现较晚。
- Anaerobic zone: 80-90% of HRmax. The body works without sufficient oxygen, relying on stored glycogen and producing lactate. Fatigue occurs rapidly.
- 无氧区域：HRmax 的 80-90%。身体在没有足够氧气的条件下工作，依赖储存的糖原并产生乳酸，疲劳出现迅速。
- For a 15-year-old with HRmax 205 bpm, the aerobic zone is 123-164 bpm, and anaerobic zone 164-184 bpm.
- 对于一名 HRmax 为 205 bpm 的 15 岁运动者，有氧区域为 123-164 bpm，无氧区域为 164-184 bpm。
10. Force, Mass and Acceleration | 力、质量与加速度
Newton' n explains how changing force or mass affects the rate at which an athlete or object speeds up.
牛顿第二定律的定量表达式为 F = m × a。在体育运动中，该公式解释了改变力或质量如何影响运动员或物体的加速速率。
F = m × a
- Force is measured in newtons (N), mass in kilograms (kg), acceleration in metres per second squared (m/s²).
- 力的单位为牛顿（N），质量单位为千克（kg），加速度单位为米每二次方秒（m/s²）。
- To increase acceleration for a given force, reduce mass (e.g., lighter sprinting spikes, lower body fat).
- 要在给定力下增加加速度，可减少质量（例如更轻的短跑钉鞋、降低体脂）。
- In contact sports, greater mass at the same acceleration produces greater force, aiding tackles and scrums.
- 在身体接触类运动中，同样加速度下更大的质量会产生更大的力，有助于擒抱和争球。
11. Mechanical Advantage of Levers | 杠杆的机械效益
Mechanical advantage (MA) describes how effectively a lever amplifies the effort force. It depends on the relative lengths of the effort arm and resistance arm.
机械效益（MA）描述杠杆放大动力的有效程度，取决于动力臂和阻力臂的相对长度。
Mechanical Advantage = effort arm ÷ resistance arm
- Effort arm: distance from fulcrum to the point where effort is applied.
- 动力臂：支点到动力作用点的距离。
- Resistance arm: distance from fulcrum to the load.
- 阻力臂：支点到阻力作用点的距离。
- MA > 1 means the lever multiplies force (second-class levers, e.g., calf raise). A small effort can lift a large load, but over a shorter range.
- MA > 1 表示杠杆放大了力（第二类杠杆，如提踵）。较小的动力即可举起较大负荷，但活动范围较小。
- MA < 1 (most body levers) favours speed and range of movement at the expense of force (third-class levers).
- MA < 1（人体大部分杠杆）以牺牲力量为代价换取速度和活动范围（第三类杠杆）。
12. SPORT Principles of Training | SPORT 训练原则
Beyond FITT, the SPORT acronym reminds coaches and performers of broader training principles that underpin effective programme design.
在 FITT 之外，SPORT 这一缩写提醒教练和运动员关注支撑有效训练计划设计的更广泛原则。
- Specificity: training must be relevant to the sport, energy system and muscle groups used.
- 专项性（Specificity）：训练必须与运动项目、能量系统及所用肌群相关。
- Progression: overload should be increased gradually as the body adapts.
- 渐进性（Progression）：随着身体适应，应逐步增加超负荷。
- Overload: the body must be stressed beyond its current capacity for improvement to occur (achieved via FITT).
- 超负荷（Overload）：身体必须承受超过当前能力的压力才能进步（通过 FITT 实现）。
- Reversibility: fitness gains are lost when training stops or reduces ('use it or lose it').
- 可逆性（Reversibility）：停止或减少训练后，体能增长会消退（“用进废退”）。
- Tedium: variety prevents boredom and maintains motivation.
- 多样性（Tedium）：训练多样化可防止枯燥、保持动机。
Published by TutorHao | CCEA GCSE Physical Education Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图