📚 KS3 Edexcel PE: Quick Reference Guide to Formulas and Principles | KS3 Edexcel 体育：公式定理速查手册
This quick reference handbook compiles the essential formulas and principles for KS3 Edexcel Physical Education. Understanding these concepts will help you analyse performance, plan training, and improve your fitness efficiently. Use it alongside your practical sessions to make connections between theory and action.
这本速查手册汇编了 KS3 Edexcel 体育课程的核心公式与基本原理。掌握这些概念有助于你分析运动表现、制定训练计划并高效提升体能。在实践课中配合使用，将理论与行动联系起来。
1. Maximum Heart Rate & Target Heart Rate Zones | 最大心率与靶心率区间
Maximum heart rate (HRmax) is the highest number of beats your heart can achieve in one minute. The simplest estimation formula is:
HRmax = 220 – Age (years)
For example, a 13-year-old student has an estimated HRmax of 207 bpm.
最大心率是心脏在一分钟内能达到的最高跳动次数。最简单的估算公式为：220 减去年龄。例如，13 岁学生的预测最大心率为 207 次/分。
Training zones are defined as a percentage of your HRmax to achieve specific fitness goals. The two main zones are: Moderate intensity (50–70% HRmax) — improves general health and aerobic base; Vigorous intensity (70–85% HRmax) — develops cardiovascular fitness and endurance.
训练区间定义为最大心率的百分比，以实现特定体能目标。两个主要区间为：中等强度（50–70% 最大心率）——提高整体健康和有氧基础；高强度（70–85% 最大心率）——发展心血管健康和耐力。
2. Karvonen Formula for Target Heart Rate | 卡沃宁公式计算目标心率
The Karvonen formula provides a more personalised training heart rate because it includes your resting heart rate (RHR). RHR should be measured first thing in the morning while still lying down.
卡沃宁公式提供了更个性化的训练心率，因为它纳入了你的安静心率。安静心率应在早晨醒来后、仍躺着时测量。
Target HR = ((HRmax – RHR) × Intensity%) + RHR
For a 12-year-old with a resting heart rate of 70 bpm training at 60% intensity: Target HR = ((208 – 70) × 0.60) + 70 = 152.8 ≈ 153 bpm.
以一名安静心率为 70 次/分、训练强度为 60% 的 12 岁学生为例：目标心率 = ((208 – 70) × 0.60) + 70 = 152.8 ≈ 153 次/分。
3. Body Mass Index (BMI) | 身体质量指数
BMI is a screening tool that estimates body fatness based on weight and height. It does not directly measure body fat but is useful for assessing weight categories.
身体质量指数是一种根据体重和身高估算体脂的筛查工具。它不直接测量体脂，但有助于评估体重类别。
BMI = Weight (kg) ÷ Height² (m²)
A student weighing 45 kg and 1.55 m tall has a BMI = 45 ÷ (1.55 × 1.55) = 18.7 kg/m², which falls in the healthy weight range for children.
一名体重 45 公斤、身高 1.55 米的学生，身体质量指数 = 45 ÷ (1.55 × 1.55) = 18.7 公斤/平方米，属于儿童健康体重范围。
4. Speed, Acceleration and Velocity | 速度、加速度与速率
Speed calculates how fast an object is moving regardless of direction. It is a scalar quantity and uses the formula:
速度计算物体移动的快慢，不考虑方向。它是标量，公式为：
Speed = Distance ÷ Time
If a sprinter covers 100 m in 13 seconds, the average speed is 100 ÷ 13 ≈ 7.69 m/s.
若一名短跑运动员 13 秒跑完 100 米，平均速度 = 100 ÷ 13 ≈ 7.69 米/秒。
Acceleration measures how quickly the velocity of a body changes. It is a vector quantity and can involve speeding up, slowing down, or changing direction.
加速度衡量物体速度变化的快慢。它是矢量，可能涉及加速、减速或改变方向。
Acceleration (a) = (Final velocity – Initial velocity) ÷ Time
a = (v – u) ÷ t
例如，一名自行车手在 4 秒内从 2 m/s 加速到 10 m/s，加速度为 (10 – 2) ÷ 4 = 2 m/s²。
5. Force and Newton’s Second Law | 力与牛顿第二定律
Newton’s second law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This is the fundamental link between force, mass, and acceleration.
牛顿第二定律指出，物体的加速度与作用在它上面的净力成正比，与它的质量成反比。这是力、质量和加速度之间的基本联系。
Force = Mass × Acceleration
F = m × a
To accelerate a 1.5 kg hockey ball at 8 m/s², the player must apply a force of 1.5 × 8 = 12 N.
要使一个 1.5 公斤的曲棍球以 8 米/秒² 的加速度运动，球员需施加 1.5 × 8 = 12 牛顿的力。
6. Moment of Force and Levers | 力矩与杠杆
The moment of a force (torque) is the turning effect produced when a force is applied at a distance from a pivot. A lever amplifies an input force to provide a greater output force.
力矩是力作用在距支点一定距离处时产生的转动效应。杠杆能放大输入力从而提供更大的输出力。
Moment of force (M) = Force × Perpendicular distance from pivot
M = F × d
For a lever system in equilibrium, the principle of moments applies: the sum of clockwise moments equals the sum of anticlockwise moments.
在平衡的杠杆系统中，力矩原理适用：顺时针力矩之和等于逆时针力矩之和。
ΣM↻ = ΣM↺
7. Mechanical Advantage in Levers | 杠杆的机械优势
Mechanical advantage (MA) tells you how much a lever multiplies the effort force. A mechanical advantage greater than 1 means the lever makes it easier to move a load.
机械优势表示杠杆将输入力放大了多少。机械优势大于 1 意味着杠杆使移动负载更省力。
MA = Effort arm length ÷ Resistance arm length
MA = Load ÷ Effort
If the effort arm is 30 cm and the resistance arm is 10 cm, MA = 30 ÷ 10 = 3, so you only need one third of the force.
如果动力臂为 30 厘米、阻力臂为 10 厘米，则机械优势 = 30 ÷ 10 = 3，你只需用三分之一的力。
8. Work and Power | 功与功率
Work is done when a force causes an object to move in the direction of the force. It is measured in joules (J).
当力使物体沿力的方向移动时，就做了功。功的单位是焦耳。
Work (W) = Force × Distance moved in direction of force
W = F × d
Lifting a 50 N weight vertically 0.4 m requires work of 50 × 0.4 = 20 J.
将一个 50 牛顿的重物垂直提升 0.4 米，需做功 50 × 0.4 = 20 焦耳。
Power is the rate at which work is done. An athlete who completes the same amount of work in a shorter time is more powerful.
功率是做功的速率。在更短时间内完成相同功的运动员功率更大。
Power (P) = Work ÷ Time
P = W ÷ t
If 20 J of work is performed in 0.5 seconds, the power output is 20 ÷ 0.5 = 40 W.
如果 20 焦耳的功在 0.5 秒内完成，则输出功率为 20 ÷ 0.5 = 40 瓦。
9. FITT Principles of Training | FITT 训练原则
The FITT principle is a simple framework for designing an effective exercise programme. Each letter represents a variable that must be adjusted to achieve progressive overload.
FITT 原则是设计有效锻炼计划的简单框架。每一个字母代表一个必须调整以达成渐进超负荷的变量。
FITT: Frequency, Intensity, Time, Type
Frequency: how often you train per week. Intensity: how hard you work (e.g., % of HRmax). Time: duration of each session. Type: the kind of exercise (e.g., aerobic, strength).
频率：每周训练的次数。强度：训练的艰苦程度（如最大心率百分比）。时间：每次训练的持续时间。类型：运动种类（如有氧、力量）。
10. SPORT and Overload Principles | SPORT 与超负荷原则
SPORT is an extension of the training principles that helps prevent boredom and plateauing. Alongside the overload principle, it ensures continued improvement.
SPORT 是训练原则的延伸，有助于防止枯燥和平台期。它与超负荷原则一起确保持续进步。
SPORT: Specificity, Progression, Overload, Reversibility, Tedium
Specificity: training must match the demands of the sport. Progression: gradually increase difficulty. Overload: work beyond normal levels (use FITT to apply). Reversibility: fitness is lost when training stops. Tedium: variety prevents boredom and maintains motivation.
特异性：训练必须与运动需求匹配。进阶性：逐步增加难度。超负荷：超出正常水平进行训练（用 FITT 来实施）。可逆性：停止训练后体适能会消退。枯燥性：多样化训练可防止厌倦并维持动力。
The overload principle states that to improve fitness, the body must be stressed beyond its current capacity. This can be achieved by manipulating FITT variables.
超负荷原则指出，要提高体适能，必须让身体承受超出当前能力的负荷。这可以通过调整 FITT 变量来实现。
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