📚 Year 8 Edexcel PE: Quick-Reference Formulas & Theorems Handbook | Year 8 Edexcel 体育：公式定理速查手册
This handbook gathers the essential formulas, equations and fundamental principles you will encounter in Year 8 Edexcel Physical Education. Use it as a quick revision tool to understand how your body works during exercise, how to analyse movement and how to apply core training concepts.
本手册汇总了 Year 8 Edexcel 体育课程中你将遇到的基本公式、方程与核心原理。你可以把它当作快速复习工具，理解身体在运动中的工作机制，学会分析动作并运用关键训练概念。
1. Estimating Maximum Heart Rate (HRmax) | 估算最大心率
The simplest way to estimate your maximum heart rate is to subtract your age from 220. This value is used as a baseline for setting training intensities.
估算最大心率最简单的方法是用 220 减去你的年龄。该数值可作为设定训练强度的基线。
HRmax = 220 − age
最大心率 = 220 − 年龄
2. Target Heart Rate (Karvonen Formula) | 目标心率（卡尔沃宁公式）
The Karvonen formula gives a more personalised training heart rate by including your resting heart rate (HRrest). You multiply the heart rate reserve by the desired intensity percentage and then add your resting heart rate.
卡尔沃宁公式纳入了安静心率，能给出更个性化的训练心率。先将储备心率乘以目标强度百分比，再加上安静心率即可。
Target HR = ((HRmax − HRrest) × % intensity) + HRrest
目标心率 = （（最大心率 − 安静心率）× 强度 %）+ 安静心率
For example, if HRmax is 200 bpm, HRrest is 60 bpm and you want to work at 70% intensity, target HR = ((200 − 60) × 0.7) + 60 = 158 bpm.
举例来说，若最大心率为 200 bpm，安静心率为 60 bpm，你想以 70% 强度运动，目标心率 = ((200 − 60) × 0.7) + 60 = 158 bpm。
3. Common Training Zones Based on HRmax | 基于最大心率的常用训练区间
Training zones are often defined as percentages of your HRmax. Different zones target different fitness components.
训练区间通常按最大心率的百分比来划分。不同区间对应不同的体能目标。
| Zone / 区间 | % HRmax | Typical benefit / 主要收益 |
|---|---|---|
| Recovery / 恢复 | 50–60% | Active recovery, warm-up / 主动恢复、热身 |
| Aerobic / 有氧 | 60–70% | Improves basic endurance / 提高基础耐力 |
| Aerobic threshold / 有氧阈值 | 70–80% | Enhances cardiovascular fitness / 增强心血管功能 |
| Anaerobic threshold / 无氧阈值 | 80–90% | Lactic acid tolerance / 乳酸耐受 |
| Maximum effort / 极限输出 | 90–100% | Sprint speed, maximum power / 冲刺速度、最大功率 |
4. Body Mass Index (BMI) | 身体质量指数
BMI provides a quick estimate of whether a person has a healthy body weight for their height. It is widely used in health and fitness screening.
BMI 能快速判断一个人的体重相对于身高是否处于健康范围，广泛用于健康体适能筛查。
BMI = weight (kg) ÷ height² (m)
BMI = 体重（kg）÷ 身高²（m）
For example, a person weighing 50 kg with a height of 1.60 m: BMI = 50 ÷ (1.60 × 1.60) = 19.5 kg/m², which falls in the healthy range.
例如，某人体重 50 kg，身高 1.60 m：BMI = 50 ÷ (1.60 × 1.60) = 19.5 kg/m²，处于健康范围。
5. Speed, Distance and Time | 速度、距离与时间
Speed is the distance travelled per unit of time. This formula is fundamental for analysing running, swimming, cycling and many other activities.
速度是单位时间内移动的距离。该公式是分析跑步、游泳、骑行等项目的基础。
Speed = Distance ÷ Time
速度 = 距离 ÷ 时间
Rearranged forms: Distance = Speed × Time, Time = Distance ÷ Speed. Units are typically metres per second (m/s) or kilometres per hour (km/h).
变形公式：距离 = 速度 × 时间，时间 = 距离 ÷ 速度。常用单位是米/秒 (m/s) 或千米/小时 (km/h)。
6. Acceleration | 加速度
Acceleration describes how quickly velocity changes. It is especially important when looking at sprint starts or changes of direction in sport.
加速度描述速度变化的快慢，在冲刺起跑或变向动作中尤为重要。
Acceleration = (Final velocity − Initial velocity) ÷ Time
加速度 = （末速度 − 初速度）÷ 时间
If a sprinter increases velocity from 0 m/s to 8 m/s in 2 seconds, acceleration = (8 − 0) ÷ 2 = 4 m/s².
若短跑运动员在 2 秒内速度从 0 m/s 提升到 8 m/s，加速度 = (8 − 0) ÷ 2 = 4 m/s²。
7. Work Done | 做功
In physics, work is done when a force moves an object. In PE, understanding work helps explain energy transfer during exercise, such as lifting weights or jumping.
物理中，力使物体移动便做了功。在体育中，理解做功有助于解释举重或跳跃等运动中的能量转换。
Work = Force × Distance
功 = 力 × 距离
Force is measured in newtons (N), distance in metres (m), so work is measured in joules (J).
力以牛顿 (N) 为单位，距离以米 (m) 为单位，因此功的单位是焦耳 (J)。
8. Power | 功率
Power is the rate at which work is done. Athletes with high power output can sprint faster, jump higher or strike harder.
功率是做功的快慢。高输出功率的运动员冲刺更快、跳得更高、击打更有力。
Power = Work ÷ Time
功率 = 功 ÷ 时间
An alternative useful form: Power = Force × Velocity. Power is measured in watts (W).
另一种常用形式：功率 = 力 × 速度。功率的单位是瓦特 (W)。
9. Moments and Levers | 力矩与杠杆
A moment is the turning effect of a force around a pivot. Levers in the human body work on this principle; muscles pull on bones to overcome resistance.
力矩是力绕支点转动的效应。人体内的杠杆便基于此原理运行；肌肉拉动骨骼克服阻力。
Moment = Force × Distance from pivot
力矩 = 力 × 力臂（支点距离）
In a first-class lever (e.g., neck extension), pivot lies between effort and resistance. In a second-class lever (e.g., calf raise), resistance is between pivot and effort. In a third-class lever (e.g., biceps curl), effort is between pivot and resistance.
第一类杠杆（如颈部后仰）支点在动力与阻力之间。第二类杠杆（如提踵）阻力在支点与动力之间。第三类杠杆（如肱二头肌弯举）动力在支点与阻力之间。
10. Force, Mass and Acceleration | 力、质量与加速度
Newton’s Second Law explains the relationship between the force applied to an object, its mass and the acceleration it experiences. This is useful when analysing striking, throwing or starting a sprint.
牛顿第二定律解释了施加于物体的力、其质量以及所产生加速度之间的关系。这对分析击球、投掷或起跑加速很有用。
Force = Mass × Acceleration
力 = 质量 × 加速度
Mass is in kilograms (kg), acceleration in m/s², and force in newtons (N). To accelerate a 5 kg shot put at 3 m/s², you need 15 N of force.
质量单位为千克 (kg)，加速度单位为 m/s²，力的单位为牛顿 (N)。要让 5 kg 的铅球以 3 m/s² 加速，需要 15 N 的力。
11. Energy Expenditure and Simple Calorie Estimation | 能量消耗与简易卡路里估算
One way to estimate energy used during physical activity is the MET formula. MET stands for Metabolic Equivalent and can be used to approximate calories burned.
估算身体活动能量消耗的一种方法是使用 MET 公式。MET（代谢当量）可用来近似计算热量消耗。
Calories burned ≈ MET × weight (kg) × duration (hours)
消耗卡路里 ≈ MET × 体重（kg）× 时长（小时）
Walking at 5 km/h has a MET of about 3.5. A 45 kg student walking for 1 hour would burn approximately 3.5 × 45 × 1 = 157.5 kcal.
以 5 km/h 步行的 MET 约 3.5。一名 45 kg 的学生步行 1 小时，大约消耗 3.5 × 45 × 1 = 157.5 千卡。
12. Key Training Principles | 关键训练原则
Beyond formulas, the following principles guide how to plan effective and safe training programmes. They are the ‘theorems’ of training adaptation.
除公式外，以下原则指导着如何制定有效且安全的训练计划。它们是训练适应的“法则”。
- FITT principle / FITT 原则
Frequency / 频率：How often / 训练次数；
Intensity / 强度：How hard / 训练强度；
Time / 时间：Duration of session / 每次持续时长；
Type / 类型：Kind of exercise / 运动方式。 - Overload / 超负荷
To improve, the body must work harder than it is used to. This can be achieved by adjusting FITT variables progressively.
要提高，身体必须承受比平时更大的负荷。可通过逐步调整 FITT 变量来实现。 - Specificity / 专项性
Training must match the demands of the sport or goal. A sprinter trains differently from a long-distance runner.
训练必须与项目或目标的需求相匹配。短跑选手与长跑选手的训练截然不同。 - Reversibility / 可逆性
Fitness gains are lost when training stops or decreases significantly. ‘Use it or lose it.’
停止或大幅减少训练后，体能提升会消退。“用进废退”。
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