KS3 WJEC PE: Formula & Theorem Quick Reference Handbook | KS3 WJEC 体育：公式定理速查手册

📚 KS3 WJEC PE: Formula & Theorem Quick Reference Handbook | KS3 WJEC 体育：公式定理速查手册

This quick-reference handbook brings together the essential formulas and theoretical principles you will encounter in KS3 WJEC Physical Education. Whether you are calculating your training zones, analysing lever systems, or interpreting fitness test data, these equations will help you understand how the body works and how to improve performance. Keep this guide handy for revision, practical sessions, and coursework.

本速查手册汇总了 KS3 WJEC 体育课程中你会遇到的核心公式与理论原理。无论你是在计算训练区间、分析杠杆系统，还是解读体适能测试数据，这些等式都将帮助你理解身体的运作方式以及如何提升运动表现。请将本指南放在手边，供复习、实操课和课程作业随时查阅。

---

1. Maximum Heart Rate (MHR) | 最大心率

Maximum Heart Rate (MHR) is the theoretical highest number of beats your heart can pump in one minute during all-out exercise. It provides a baseline for setting training intensities. The most widely used estimation is:

最大心率（MHR）是指心脏在极度运动时每分钟理论上所能泵血的最高搏动次数，为设定训练强度提供基准。最常用的估算方法是：

MHR = 220 − Age

For a 12-year-old student the predicted MHR would be 208 bpm, while for a 14-year-old it drops to 206 bpm. Remember that this is an estimate — individual variation exists, and true MHR can only be determined accurately through a maximal exercise test.

对于 12 岁的学生，预估最大心率为 208 bpm，而 14 岁时降至 206 bpm。请记住这只是一个估值——个体之间存在差异，真正的最大心率只能通过最大强度运动测试准确测得。

---

2. Heart Rate Reserve (HRR) and the Karvonen Formula | 心率储备与卡沃宁公式

Heart Rate Reserve (HRR) is the difference between your maximum heart rate and your resting heart rate (RHR). It represents the ‘usable’ range for training adaptations. The Karvonen formula uses HRR to calculate target heart rates more accurately than using MHR alone.

心率储备（HRR）是你的最大心率与安静心率（RHR）之间的差值，代表可用于产生训练适应的“可用”范围。卡沃宁公式利用 HRR 来计算目标心率，比仅使用最大心率更为精确。

HRR = MHR − RHR

Target HR = (HRR × %Intensity) + RHR

For example, if a student has an MHR of 205 bpm and an RHR of 65 bpm, HRR = 140 bpm. To work at 70% intensity, Target HR = (140 × 0.70) + 65 = 163 bpm. This method ensures the exercise intensity reflects the individual’s fitness level.

例如，某学生的最大心率为 205 bpm、安静心率为 65 bpm，则 HRR 为 140 bpm。若以 70% 强度训练，目标心率 = (140 × 0.70) + 65 = 163 bpm。该方法确保运动强度反映了个人的体适能水平。

---

3. Target Heart Rate Zones | 目标心率区间

Training zones are set as percentages of MHR or HRR to produce specific fitness benefits. The main zones taught at KS3 are:

训练区间通常按照最大心率或心率储备的百分比来设定，以获得特定的体适能收益。KS3 阶段学习的主要区间如下：

• Aerobic zone (60–80% MHR): Develops cardiovascular endurance; the body uses oxygen to break down fuels.
• 有氧区间（60–80% MHR）：发展心血管耐力；身体利用氧气分解燃料。
• Anaerobic zone (80–90% MHR): Builds speed and power; energy is produced without sufficient oxygen, leading to lactic acid accumulation.
• 无氧区间（80–90% MHR）：提升速度和爆发力；在没有充足氧气的情况下产生能量，导致乳酸堆积。

Aerobic Threshold ≈ 60% MHR   |   Anaerobic Threshold ≈ 80–85% MHR

Staying within the correct zone ensures the training stimulus matches the goal, whether it is burning fat, improving lactate tolerance, or building an aerobic base.

保持在正确的区间内可以确保训练刺激与目标相匹配，无论是燃烧脂肪、提高乳酸耐受能力，还是建立有氧基础。

---

4. 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, healthy weight, overweight, or obese. The formula is:

BMI 是一种简单的筛查工具，将体重与身高相关联，用于将人群划分为体重过轻、健康体重、超重或肥胖。计算公式为：

BMI = Weight (kg) ÷ Height² (m)

For a person weighing 50 kg with a height of 1.60 m, BMI = 50 ÷ (1.60 × 1.60) = 19.5 kg/m², which falls within the healthy range. In PE lessons you might use BMI alongside other measures such as waist circumference to get a fuller picture of health.

一个体重 50 公斤、身高 1.60 米的人，BMI = 50 ÷ (1.60 × 1.60) = 19.5 kg/m²，属于健康范围。在体育课上，你可以将 BMI 与腰围等其他指标结合使用，以更全面地了解健康状况。

---

5. Speed, Distance, and Time | 速度、距离与时间

The relationship between speed, distance and time is fundamental in many sports, from sprinting to swimming. The key equation is:

速度、距离和时间之间的关系是许多运动项目（从短跑到游泳）的基础。核心等式为：

Speed = Distance ÷ Time

If a runner covers 100 metres in 13 seconds, average speed = 100 ÷ 13 ≈ 7.69 m/s. In games you may also calculate pace (time per distance) or use the rearranged forms: Distance = Speed × Time and Time = Distance ÷ Speed. Understanding this formula helps you analyse performance and set realistic targets for improvement.

若一名跑步运动员用 13 秒跑完 100 米，平均速度 = 100 ÷ 13 ≈ 7.69 米/秒。在比赛中你还可以计算配速（单位距离所用时间）或使用变形式：距离 = 速度 × 时间，时间 = 距离 ÷ 速度。理解该公式有助于你分析运动表现并设定切实可行的进步目标。

---

6. Newton’s Second Law: Force = Mass × Acceleration | 牛顿第二定律：力 = 质量 × 加速度

Newton’s Second Law explains how the motion of an object changes when a force is applied. In PE, it helps you understand sprinting starts, throwing, and kicking. The law is written as:

牛顿第二定律解释了当力作用于物体时，物体的运动状态如何改变。在体育中，它帮助你理解起跑、投掷和踢球等动作。定律写作：

F = m × a

F is the net force (N), m is the mass (kg), and a is the acceleration (m/s²). To accelerate a football of mass 0.45 kg at 20 m/s², the player must apply a force of 9 N. A larger force produces greater acceleration for the same mass, which is why strong leg muscles are essential for explosive movements like jumping.

F 是合力（牛顿），m 是质量（千克），a 是加速度（米/秒²）。要使一个 0.45 kg 的足球获得 20 m/s² 的加速度，运动员需施加大约 9 N 的力。相同质量下，更大的力产生更大的加速度，这就是为什么强壮的下肢肌肉对于跳跃等爆发性动作至关重要。

---

7. Mechanical Advantage of Levers | 杠杆的机械利益

Levers are present in nearly every human movement. Mechanical advantage (MA) tells you whether a lever system favours speed and range of motion or force production. It is calculated by comparing the lengths of the effort arm and the load arm:

几乎每个人体动作都涉及杠杆。机械利益（MA）告诉你一个杠杆系统是有利于速度与活动度，还是有利于力量的产生。通过比较力臂和重臂的长度来计算：

MA = Effort arm ÷ Load arm

In a third-class lever such as the bicep curl, the effort arm (distance from elbow to bicep insertion) is shorter than the load arm (distance from elbow to hand), giving an MA less than 1. This means the lever sacrifices force for a large range of motion and speed at the hand. In contrast, a second-class lever like a calf raise gives an MA greater than 1, favouring force over speed.

在肱二头肌弯举这样的第三类杠杆中，力臂（肘关节到肱二头肌附着点的距离）短于重臂（肘关节到手部的距离），机械利益小于 1。这意味着该杠杆牺牲了力量，换取了手部较大的活动范围和速度。相反，提踵这样的第二类杠杆则机械利益大于 1，有利于产生更大的力量。

---

8. Power Output | 功率输出

Power is the rate at which work is done or energy is transferred. In sport, power is often the decisive factor in explosive events like jumps, throws, and short sprints. It can be expressed as:

功率是做功或能量转换的速率。在体育运动中，功率往往是跳跃、投掷和短距离冲刺等爆发性项目中的决定性因素。可表示为：

Power = Work ÷ Time   or   Power = Force × Velocity

If a weightlifter lifts a barbell doing 1500 J of work in 2 seconds, average power output is 750 W. Using the force–velocity form, a strong sprinter applying 400 N of force at a velocity of 8 m/s generates 3200 W. Improving either the force applied or the speed of movement can boost power — a key concept behind plyometric and resistance training.

如果一名举重运动员在 2 秒内将杠铃举起并做功 1500 J，平均功率输出为 750 W。利用力-速度形式，一名强壮短跑运动员在施加 400 N 力并以 8 m/s 速度奔跑时，可产生 3200 W。提升所施加的力或动作速度均可提高功率——这正是增强式训练和抗阻训练背后的关键理念。

---

9. Estimating Energy Expenditure Using METs | 利用梅脱估算能量消耗

Metabolic Equivalent (MET) is a unit that estimates how much energy an activity uses compared to resting. One MET equals the energy used at rest (approximately 1 kcal/kg/hour). The formula for estimating calories burned during exercise is:

代谢当量（MET）是估算某项活动相对于安静状态消耗多少能量的单位。1 MET 等于安静时的能量消耗（约 1 千卡/公斤/小时）。估算运动期间消耗热量的公式为：

Calories burned = METs × Weight (kg) × Time (hours)

For example, jogging at 8 km/h has a MET value of around 8. A student weighing 45 kg jogging for 30 minutes (0.5 hours) would burn approximately 8 × 45 × 0.5 = 180 kcal. Knowing MET values helps you compare the energy cost of different activities and design balanced exercise programmes.

例如，以 8 公里/小时速度慢跑的 MET 值约为 8。一名体重 45 公斤的学生慢跑 30 分钟（0.5 小时），大约消耗 8 × 45 × 0.5 = 180 千卡。了解 MET 值有助于你比较不同活动的能量消耗，并设计均衡的训练计划。

---

10. Planning Overload with the FITT Principle | 利用 FITT 原则规划超负荷

The FITT principle is a theorem-like framework used to manipulate training variables and ensure the body is progressively overloaded — that is, stressed beyond its current capacity to force adaptation. FITT stands for:

FITT 原则是一个类似定理的框架，用于调整训练变量，确保身体承受渐进超负荷——即超过当前能力水平的压力，以促使身体产生适应。FITT 代表：

• Frequency: How often you train (e.g., 3 sessions per week).
• 频率：多久训练一次（例如每周 3 次）。
• Intensity: How hard you work (e.g., 70% MHR).
• 强度：训练有多努力（例如 70% MHR）。
• Time: Duration of each session (e.g., 30 minutes).
• 时间：每次训练的持续时间（例如 30 分钟）。
• Type: The kind of exercise (e.g., cycling, running).
• 类型：运动种类（例如骑行、跑步）。

By increasing one or more of these variables over time — for instance, adding an extra training day or extending the session by 5 minutes — you maintain overload and continue to see gains in strength, endurance, or flexibility. The FITT principle is a practical tool that links the formulas above to real-world training plans.

通过逐步增加上述一个或多个变量——例如增加一个训练日，或将训练时长延长 5 分钟——你便能保持超负荷，持续看到力量、耐力或柔韧性的进步。FITT 原则是一个实用工具，将前文所述公式与实际训练计划连接起来。

---

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

更多咨询请联系16621398022（同微信）