KS3 CAIE Physical Education: Formula & Principles Quick Reference Handbook | KS3 CAIE 体育：公式定理速查手册

📚 KS3 CAIE Physical Education: Formula & Principles Quick Reference Handbook | KS3 CAIE 体育：公式定理速查手册

This quick reference handbook is designed for KS3 CAIE Physical Education students. It brings together the essential formulas, biomechanical principles, training calculations, and physiological constants you need to analyse performance, plan training, and understand the science behind movement. Keep it handy for homework, tests, and practical application.

这本速查手册专为 KS3 CAIE 体育课程的学生编写。它汇集了分析运动表现、制定训练计划和理解运动科学所需的关键公式、生物力学原理、训练计算公式和生理常数。请将此手册放在手边，用于完成作业、准备考试和指导实践。

1. Maximum Heart Rate (MHR) Estimation | 最大心率 (MHR) 估算

The simplest and most widely used formula to estimate maximum heart rate is MHR = 220 – age. This gives a baseline for calculating training zones, although individual variation exists. At KS3, you will use it to set aerobic and anaerobic intensity targets.

最简单且使用最广的最大心率估算公式是 MHR = 220 – 年龄。它为计算训练区间提供了基准，但个体间存在差异。在 KS3 阶段，你将用它来设定有氧和无氧训练的强度目标。

MHR = 220 – age

Example: For a 13‑year‑old student, estimated MHR = 220 – 13 = 207 beats per minute (bpm). This value is then used to determine training percentages.

示例：对一名 13 岁的学生，估算最大心率 = 220 – 13 = 207 次/分 (bpm)。此数值随后用于确定训练百分比区间。

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2. Karvonen Formula for Target Heart Rate | 卡沃内目标心率公式

The Karvonen formula gives a more personalised target heart rate by including resting heart rate (RHR). It calculates heart rate reserve (HRR): HRR = MHR – RHR, then applies desired intensity.

卡沃内公式纳入了安静心率 (RHR)，从而提供更个性化的目标心率。先计算心率储备 (HRR)：HRR = MHR – RHR，再乘以期望的训练强度。

Target HR = (HRR × intensity %) + RHR

Measure your RHR first thing in the morning while lying quietly. For a 13‑year‑old with MHR 207 bpm and RHR 65 bpm, HRR = 207 – 65 = 142 bpm. To train at 70% intensity, target HR = (142 × 0.70) + 65 = 99.4 + 65 ≈ 164 bpm. This method reflects oxygen delivery potential more accurately than a simple percentage of MHR.

请于清晨安静平躺时测量安静心率。对上文 13 岁学生（MHR 207 bpm，RHR 65 bpm），HRR = 207 – 65 = 142 bpm。若要达到 70% 强度训练，目标心率 = (142 × 0.70) + 65 = 99.4 + 65 ≈ 164 bpm。该方法比简单采用最大心率百分比更能准确反映氧气输送潜力。

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3. Body Mass Index (BMI) Calculation | 身体质量指数 (BMI) 计算

BMI is a simple screening tool that relates weight to height. It helps categorise individuals as underweight, healthy weight, overweight or obese, though it does not distinguish between muscle and fat.

BMI 是一种将体重与身高相关联的简易筛查工具，可用于将个体划分为体重不足、健康体重、超重或肥胖，但它无法区分肌肉与脂肪。

BMI = weight (kg) ÷ (height (m))²

Worked example: A young athlete weighs 50 kg and is 1.60 m tall. BMI = 50 ÷ (1.60 × 1.60) = 50 ÷ 2.56 = 19.5 kg/m². This falls within the healthy weight range for adolescents. Remember, sporty students often have higher muscle mass, so BMI alone should be interpreted with caution.

计算实例：一名年轻运动员体重 50 kg，身高 1.60 m。BMI = 50 ÷ (1.60 × 1.60) = 50 ÷ 2.56 = 19.5 kg/m²，这属于青少年的健康体重范围。请记住，经常运动的学生肌肉含量较高，所以单独依据 BMI 进行解读时需谨慎。

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4. Newton’s First Law of Motion (Inertia) | 牛顿第一运动定律（惯性）

Newton’s First Law states that an object will remain at rest or move with constant velocity unless acted upon by an external resultant force. In sport, this explains why a stationary football stays still until kicked, and why a sprinting runner continues moving forward unless friction or another force slows them down.

牛顿第一定律指出，除非受到外部的合外力作用，否则物体将保持静止或匀速直线运动状态。在体育运动中，这解释了为什么静止的足球在被踢之前会保持不动，以及为何短跑运动员会继续向前移动，直到摩擦力或其他力使其减速。

Key applications: a hockey ball sliding on ice eventually stops due to friction; a gymnast’s body will rotate uniformly in the air until they change their body shape to alter angular velocity. This principle underlies balance and stability analysis.

关键应用：冰上滑动的冰球最终因摩擦而停下；体操运动员在空中将保持匀速转动，直到他们改变身体姿态来改变角速度。这一原理是平衡与稳定性分析的基础。

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5. Newton’s Second Law (Acceleration & Force) | 牛顿第二定律（加速度与力）

The Second Law defines the relationship between force, mass and acceleration. It predicts how quickly a player can accelerate when a force is applied.

牛顿第二定律界定了力、质量与加速度之间的关系。它可以预测运动员在受力时的加速快慢。

Force = mass × acceleration (F = m a)

For a given force, a smaller mass results in greater acceleration. This is why lighter athletes can often change direction more quickly. For example, if a 60 kg rugby player generates a net force of 300 N, his acceleration is a = F ÷ m = 300 ÷ 60 = 5 m/s². Please note that the force here refers to the resultant force, and mass is measured in kilograms, acceleration in metres per second squared.

施加一定大小的力时，质量越小，加速度越大。这就是体重较轻的运动员往往能更快改变方向的原因。例如，一名 60 kg 的橄榄球运动员产生 300 N 的净力，他获得的加速度 a = F ÷ m = 300 ÷ 60 = 5 m/s²。请注意，这里的力是指合外力，质量单位为千克，加速度单位为米每二次方秒。

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6. Newton’s Third Law (Action‑Reaction) | 牛顿第三定律（作用力与反作用力）

For every action force, there is an equal and opposite reaction force. These pairs act on different objects and never cancel each other within the same body. In swimming, the swimmer pushes water backwards (action), and the water pushes the swimmer forwards (reaction).

每个作用力都有一个大小相等、方向相反的反作用力。这对力作用在不同物体上，绝不会在同一个物体上相互抵消。在游泳中，游泳者向后推水（作用力），水则将游泳者向前推（反作用力）。

The starting block push‑off in athletics is another perfect example: the athlete applies a force against the block, and the block provides an equal and opposite force that propels the sprinter forward. This law is fundamental to understanding propulsion in all sports.

田径中的起跑器蹬伸是另一个绝佳例子：运动员对起跑器施加力，起跑器提供大小相等、方向相反的力推动短跑选手前进。这一定律是理解所有运动中推进力的基础。

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7. Levers and Mechanical Advantage | 杠杆与机械效益

Levers in the human body consist of a bone (lever), a joint (fulcrum), muscular force (effort), and the weight to be moved (load). The arrangement determines mechanical advantage. A third‑class lever, where the effort lies between the fulcrum and load, is most common in the body (e.g., biceps curl). It favours speed and range of movement over force.

人体中的杠杆由骨（杠杆）、关节（支点）、肌肉力（动力）和待移动的重量（阻力）构成。它们的排列方式决定了机械效益。第三类杠杆（动力在支点和阻力之间）在人体中最常见（例如肱二头肌弯举），它偏重于速度和运动幅度而非力量。

For a simple lever, Mechanical Advantage (MA) = Effort arm ÷ Load arm. When MA > 1, the lever amplifies force; when MA < 1, it amplifies speed. In most sporting actions, the body uses third‑class levers to maximise throwing, kicking or running speed, sacrificing force amplification.

对简单杠杆而言，机械效益 (MA) = 动力臂 ÷ 阻力臂。当 MA > 1 时，杠杆省力；当 MA < 1 时，杠杆增速。在大多数运动动作中，人体利用第三类杠杆来最大化投掷、踢击或奔跑的速度，而牺牲了力的放大效果。

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8. Work, Power and Energy | 功、功率与能量

When a force moves an object through a distance in the direction of the force, work is done. Power is the rate at which work is performed. These concepts explain why explosive athletes generate high power outputs.

当力使物体沿力的方向移动一段距离时，就做了功。功率是指做功的快慢。这些概念解释了为什么具有爆发力的运动员能产生很高的输出功率。

Work = force × distance (W = F d)

Power = work ÷ time (P = W / t)

In the weight room, lifting a 200 N barbell vertically by 1.5 m requires 300 J of work. If the lift takes 2 seconds, power output is 150 watts. In sprinting, a high power‑to‑weight ratio is a key predictor of acceleration. Understanding work and power helps you compare the physical demands of different activities.

在力量房中，将一根 200 N 的杠铃垂直上举 1.5 m 需要做 300 J 的功。如果完成该动作耗时 2 秒，则功率输出为 150 瓦。在短跑中，高功重比是预测加速度的关键指标。理解功和功率有助于你比较不同活动的身体负荷。

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9. Speed, Distance and Time Relationship | 速度、距离与时间的关系

The fundamental kinematics equation links speed, distance and time. This allows you to calculate average speed during a race or a training interval, and to predict time splits.

这一基础运动学方程将速度、距离和时间联系起来。你可以用它来计算比赛或训练间歇中的平均速度，并预测分段用时。

Speed = distance ÷ time

If a 100‑metre sprinter completes the race in 12.5 seconds, the average speed is 100 ÷ 12.5 = 8 m/s. For longer events, average speed is often expressed in km/h. Note that during a sprint, speed is not constant; the athlete accelerates, reaches maximum velocity and then may slightly decelerate. Therefore, the formula gives an average, not instantaneous velocity.

如果一名 100 米短跑选手以 12.5 秒完成比赛，其平均速度为 100 ÷ 12.5 = 8 米/秒。对于长距离项目，平均速度常以公里/小时表示。请注意，在短跑中，速度并非恒定；运动员会加速、达到最大速度，随后可能略微减速。因此，该公式给出的是平均速度，而非瞬时速度。

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10. FITT Principle for Training Design | 训练设计中的 FITT 原则

FITT stands for Frequency, Intensity, Time and Type. This principle provides a framework for designing safe and effective training programmes, regardless of the fitness component being developed.

FITT 分别代表频率（Frequency）、强度（Intensity）、时间（Time）和类型（Type）。该原则为设计安全有效的训练计划提供了框架，无论你要发展哪项体能要素。

• Frequency – How often you train (e.g., 3 sessions per week). | 频率 – 你多久训练一次（例如每周 3 次）。
• Intensity – How hard you work (can be measured via heart rate, %1RM, perceived exertion). | 强度 – 你练得有多努力（可通过心率、1RM 百分比或主观疲劳感来衡量）。
• Time – Duration of the session or interval (e.g., 30 minutes steady run). | 时间 – 每次训练或间歇的持续时间（例如 30 分钟匀速跑）。
• Type – The mode of exercise (continuous, interval, resistance, plyometric). | 类型 – 运动方式（持续训练、间歇训练、抗阻训练、超等长训练等）。

For aerobic improvement, a KS3 student might apply FITT as: F = 3‑4 times/week, I = 60‑80% MHR, T = 20‑40 min, Type = running, cycling or swimming. Progression should be gradual to avoid overtraining.

对有氧能力提升而言，一名 KS3 学生可如此应用 FITT：频率 = 每周 3‑4 次，强度 = 60‑80% MHR，时间 = 20‑40 分钟，类型 = 跑步、骑行或游泳。应循序渐进地增加负荷，以避免过度训练。

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11. Aerobic and Anaerobic Training Zones | 有氧与无氧训练区间

Training zones are usually defined as percentages of MHR or VO₂ max. The aerobic zone improves cardiovascular endurance, while the anaerobic zone develops speed and tolerance to lactic acid. Accurate heart rate monitoring ensures you are training the correct energy system.

训练区间通常以 MHR 或最大摄氧量 (VO₂ max) 的百分比来界定。有氧区用于改善心血管耐力，而无氧区则发展速度和乳酸耐受能力。准确的心率监测能确保你正在训练正确的能量系统。

Zone	% MHR	Main Fuel	Typical Use
Recovery / Light	50‑60%	Fat	Warm‑up, cool‑down
Aerobic / Endurance	60‑80%	Fat + CHO	Long steady runs, cycling
Anaerobic / High Intensity	80‑90%	CHO	Interval training, sprints
Maximal / Speed	90‑100%	ATP‑PCr, CHO	Short sprints, plyometrics

Use these zones in conjunction with the Karvonen formula to personalise your training. For a 13‑year‑old with MHR 207 bpm who wishes to train aerobically at 70%, target heart rate would be approximately 164 bpm, which falls perfectly into the aerobic zone.

请将这些区间与卡沃内公式结合使用，实现个性化的训练。对于上文 MHR 207 bpm 的 13 岁学生而言，若想以 70% 强度进行有氧训练，目标心率约为 164 bpm，恰好落在有氧区内。

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12. Energy Balance and Hydration Guidelines | 能量平衡与补水指南

Energy balance is the relationship between energy intake (kilocalories from food) and energy expenditure (basal metabolism + physical activity). A positive balance leads to weight gain; a negative balance results in weight loss. For young athletes, maintaining a slight positive balance during growth spurts can support development.

能量平衡是指能量摄入（来自食物的千卡）与能量消耗（基础代谢 + 身体活动）之间的关系。正平衡导致体重增加；负平衡导致体重减轻。对于青少年运动员，在快速生长期保持轻微的正平衡有助于生长发育。

Approximate daily energy expenditure can be estimated, but at KS3 the emphasis is on understanding the importance of carbohydrate for high‑intensity activity, protein for repair, and hydration. A simple rule for hydration: drink 400‑600 ml of water 2‑3 hours before exercise and 150‑300 ml every 15‑20 minutes during prolonged activity.

每日能量消耗虽然可以估算，但 KS3 阶段的教学重点在于理解碳水化合物对高强度活动的重要性、蛋白质对组织修复的作用以及补水原则。一条简单的补水规则是：运动前 2‑3 小时饮用 400‑600 ml 水，长时间活动中每 15‑20 分钟补充 150‑300 ml 水。

One gram of carbohydrate or protein provides approximately 4 kilocalories, while one gram of fat provides 9 kilocalories. This knowledge helps you interpret food labels and plan balanced meals to fuel training and recovery.

每克碳水化合物或蛋白质提供约 4 千卡热量，每克脂肪提供约 9 千卡热量。这些知识可帮助你学会看懂食品标签，并合理安排均衡膳食，为训练和恢复提供燃料。

Published by TutorHao | Physical Education Revision Series | aleveler.com

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