Formula & Theorem Quick Reference | 公式定理速查手册

📚 Formula & Theorem Quick Reference | 公式定理速查手册

Understanding key formulas and principles in physical education helps you monitor fitness, set training targets and stay safe during exercise. This quick reference handbook covers the essential calculations and models you will meet in KS3 AQA PE, from heart rate to BMI, speed to power. Each entry includes a clear formula where applicable, an explanation of how to use it, and real-life examples to make the numbers meaningful.

理解体育中的关键公式和原理有助于监测体能、设定训练目标并在运动中保持安全。这本速查手册涵盖 KS3 AQA 体育中你会遇到的核心计算和模型，从心率到 BMI，从速度到功率。每个条目包含清晰的公式（如适用）、使用说明以及让数字变得有意义的实际例子。

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

Your maximum heart rate is the highest number of times your heart can beat in one minute. While laboratory tests give the most accurate value, a simple estimation formula is widely used in schools.

最大心率是心脏一分钟能跳动的最高次数。虽然实验室测试能给出最精确的数值，但一个简单的估算公式在学校中被广泛使用。

MHR = 220 – age

For a student aged 13, approximate MHR = 220 – 13 = 207 bpm. This number serves as a reference for calculating training zones and should never be treated as an absolute limit.

若学生年龄为 13 岁，估算最大心率 = 220 – 13 = 207 次/分钟。这个数字是计算训练区的参考值，不应被视为绝对极限。

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2. Target Heart Rate Zone | 目标心率区

To improve cardiovascular fitness safely, you need to exercise within specific heart rate ranges. The target zone is usually expressed as a percentage of MHR.

为安全地提升心血管健康，你需要在特定的心率区间内运动。目标区通常以最大心率的百分比表示。

Training goal / 训练目标	% of MHR / 最大心率百分比	Example for a 13-year-old (207 bpm) / 13岁示例 (207 bpm)
Moderate activity (健康促进) / 中等强度	50–65%	104–135 bpm
Vigorous aerobic training / 高强度有氧训练	65–85%	135–176 bpm
High-intensity intervals / 极限间歇	85–95%	176–197 bpm

Staying in the right zone ensures you work hard enough to gain fitness but not so hard that you risk injury. Use a heart rate monitor or count your pulse for 15 seconds and multiply by 4 to check your bpm.

保持在合适的区间内能保证你练得足够刻苦以提升体能，但又不至于过度而受伤。可使用心率监测器或数 15 秒脉搏再乘以 4 来检查每分钟心跳次数。

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

BMI is a simple screening tool that relates weight to height. It helps identify whether a person is underweight, healthy weight, overweight or obese, although it does not measure body fat directly.

BMI 是将体重与身高关联的简单筛查工具。它有助于判断体重不足、健康、超重或肥胖，但不直接测量体脂。

BMI = weight (kg) ÷ (height (m))²

For example, a student weighing 50 kg with a height of 1.60 m has BMI = 50 ÷ (1.60 × 1.60) = 50 ÷ 2.56 ≈ 19.5 kg/m². This falls within the healthy range for children and adolescents when plotted on age-specific centile charts.

例如，一个体重 50 公斤、身高 1.60 米的学生，BMI = 50 ÷ (1.60 × 1.60) = 50 ÷ 2.56 ≈ 19.5 公斤/米²。在儿童青少年专属百分位图中，该值处于健康范围内。

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4. Speed Calculation | 速度计算

Speed measures how quickly an object or person moves from one place to another. It is one of the fundamental concepts in biomechanics and sports analysis.

速度衡量物体或人从一处移动到另一处的快慢，是生物力学和运动分析的基本概念之一。

Speed = distance ÷ time

If a sprinter covers 100 metres in 13 seconds, average speed = 100 ÷ 13 ≈ 7.69 m/s. Remember to keep units consistent: metres and seconds give m/s; kilometres and hours give km/h. To convert m/s to km/h, multiply by 3.6.

如果一名短跑运动员 13 秒跑完 100 米，平均速度 = 100 ÷ 13 ≈ 7.69 米/秒。请注意单位一致：米和秒得出米/秒；公里和小时得出公里/小时。将米/秒转换为公里/小时乘以 3.6 即可。

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5. Power Calculation | 功率计算

Power combines strength and speed; it is the rate at which work is done. Sports that involve explosive movements, such as jumping and throwing, rely heavily on power.

功率将力量与速度结合在一起，是做功的速率。涉及爆发性动作的运动，如跳跃和投掷，在很大程度上依赖功率。

Power = work done ÷ time taken

In many physical education contexts, a simplified version can be used when force and velocity are known: Power = force × velocity. For instance, if a student exerts a force of 400 N to push a sled at 1.5 m/s, the power output is approximately 600 W. Improving power often involves both resistance training and plyometric exercises.

在许多体育情境中，若已知力和速度，可以使用简化版本：功率 = 力 × 速度。例如，一名学生用 400 牛的力以 1.5 米/秒的速度推雪橇，输出的功率约为 600 瓦。提升功率通常需要结合抗阻训练和增强式练习。

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6. Rate of Perceived Exertion (RPE) | 主观疲劳感觉等级 (RPE)

RPE is a subjective scale that allows you to rate how hard you feel your body is working during exercise. A common version is the 1–10 scale, where 1 represents ‘very light’ effort and 10 represents ‘maximal’ effort.

RPE 是一个主观量表，可让你在运动中评价身体感觉的费力程度。常用版本是 1–10 级量表，1 代表“非常轻松”，10 代表“极限”。

RPE / 等级	Description / 描述	Example activity / 活动示例
1–3	Light / 轻松	Walking / 步行
4–6	Moderate / 中等	Jogging / 慢跑
7–8	Hard / 费力	Running fast / 快速跑
9–10	Maximum / 极限	Sprinting all-out / 全力冲刺

RPE helps link subjective feeling with objective data like heart rate. Many athletes aim to train around RPE 5–7 for aerobic sessions and RPE 8–9 for high-intensity intervals.

RPE 有助于将主观感受与心率等客观数据联系起来。许多运动员将有氧训练的目标定为 RPE 5–7，高强度间歇训练定为 RPE 8–9。

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7. Karvonen Formula for Heart Rate Reserve | 心率储备卡氏公式

The Karvonen formula uses resting heart rate (RHR) and heart rate reserve to give a more personalised training intensity. It is particularly useful for students who have a lower or higher resting heart rate than average.

卡氏公式使用静息心率 (RHR) 和心率储备，提供更个性化的训练强度。对于静息心率低于或高于平均水平的学生尤其有用。

Target HR = [(MHR – RHR) × % intensity] + RHR

Steps: first find heart rate reserve (MHR – RHR); next multiply by the desired intensity (e.g., 0.70 for 70%); then add RHR. For a 13-year-old with RHR = 70 bpm, MHR ≈ 207 bpm, heart rate reserve = 207 – 70 = 137 bpm. At 70% intensity: (137 × 0.70) + 70 = 95.9 + 70 ≈ 166 bpm. This approach accounts for individual fitness levels.

计算步骤：首先得到心率储备 (MHR – RHR)；然后乘以目标强度（如 70% 用 0.70）；最后加上 RHR。若 13 岁学生 RHR = 70 次/分钟，MHR ≈ 207 次/分钟，心率储备 = 207 – 70 = 137 次/分钟。70% 强度下目标心率 = (137 × 0.70) + 70 = 95.9 + 70 ≈ 166 次/分钟。该方法考虑了个体体能差异。

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8. One-Rep Max Estimation | 单次最大重量估算

The one-repetition maximum (1RM) is the heaviest weight you can lift for one complete repetition of an exercise. Direct testing can be risky for young people, so estimation formulas are used to predict 1RM from sub-maximal lifts.

单次最大重量 (1RM) 是你在一项练习中完整完成一次动作所能举起的最大重量。对青少年来说直接测试有风险，因此使用估算公式通过次最大重量预测 1RM。

Estimated 1RM = weight lifted ÷ (1.0278 – 0.0278 × reps)

If a student performs 8 repetitions of a bench press with 30 kg, the estimated 1RM = 30 ÷ (1.0278 – 0.0278 × 8) = 30 ÷ (1.0278 – 0.2224) = 30 ÷ 0.8054 ≈ 37.2 kg. This formula works best when repetitions are between 2 and 10, and technique remains controlled. Always prioritise safety and proper form.

若一名学生用 30 公斤做 8 次卧推，估算 1RM = 30 ÷ (1.0278 – 0.0278 × 8) = 30 ÷ (1.0278 – 0.2224) = 30 ÷ 0.8054 ≈ 37.2 公斤。该公式在重复次数为 2 到 10 次且动作控制良好时效果最佳。始终将安全和规范动作放在首位。

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9. Calories Burned during Exercise | 运动热量消耗估算

Estimating energy expenditure helps you understand how different activities contribute to overall energy balance. While precise measurement requires laboratory equipment, approximate formulas use METs (Metabolic Equivalents).

估算能量消耗有助于理解不同活动如何影响整体能量平衡。虽然精确测量需要实验室设备，但近似公式可使用 MET（代谢当量）。

Calories burned per minute = MET × body weight (kg) ÷ 60

For example, jogging at 5 mph has a MET value of about 8. For a student weighing 50 kg, calories burned per minute = 8 × 50 ÷ 60 = 400 ÷ 60 ≈ 6.7 kcal. Over a 20-minute jog, total ≈ 134 kcal. Common MET values: walking (3 METs), cycling moderate (6 METs), running 6 mph (10 METs). Remember these are estimates; actual values vary with fitness and technique.

例如，以 5 英里/小时慢跑的 MET 值约为 8。对于体重 50 公斤的学生，每分钟热量消耗 = 8 × 50 ÷ 60 = 400 ÷ 60 ≈ 6.7 千卡。慢跑 20 分钟总消耗约 134 千卡。常见 MET 值：步行 (3 METs)、中等强度骑车 (6 METs)、跑步 6 英里/小时 (10 METs)。请记住这些是估算值，实际消耗因体能与技术而异。

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10. Recovery Heart Rate | 心率恢复

Recovery heart rate measures how quickly your heart returns to a resting state after exercise. A faster recovery is generally a sign of better cardiovascular fitness. It can be recorded as the drop in heart rate after a set period, typically 1 minute or 2 minutes post-exercise.

心率恢复衡量运动后心脏恢复到静息状态的速度。恢复更快通常意味着心血管健康更好。它可以记录为运动后固定时间段（通常为 1 或 2 分钟）内心率的下降值。

Recovery HR = peak exercise HR – HR after 1 (or 2) minute(s)

If your heart rate immediately after a run is 180 bpm and after 1 minute of rest it drops to 140 bpm, your 1-minute recovery is 40 bpm. A drop of 20 bpm or more in the first minute is often considered a good response. Tracking recovery over weeks can show improvements in fitness levels and helps prevent overtraining.

如果跑步结束时即刻心率为 180 次/分钟，休息 1 分钟后降至 140 次/分钟，那么 1 分钟心率恢复值为 40 次/分钟。第一分钟下降 20 次/分钟或以上通常视为反应良好。数周内追踪恢复情况可显示体能水平的提升，并有助于防止过度训练。

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11. FITT Principle | FITT 原则

The FITT principle is a framework for designing exercise programmes. It reminds you to consider Frequency, Intensity, Time and Type when planning training sessions. Each component can be adjusted to meet different fitness goals.

FITT 原则是设计运动计划的框架。它提醒你在规划训练课时考虑频率 (Frequency)、强度 (Intensity)、时间 (Time) 和类型 (Type)。每个要素均可调整以满足不同的健身目标。

Element / 要素	Definition / 定义	Example for improving aerobic fitness / 提高有氧能力的示例
Frequency	How often you exercise / 运动的频率	3–5 times per week / 每周 3–5 次
Intensity	How hard you work / 运动强度	65–85% of MHR / 最大心率的 65–85%
Time	Duration of session / 持续时间	20–60 minutes / 20–60 分钟
Type	Mode of exercise / 运动方式	Running, cycling, swimming / 跑步、骑车、游泳

Applying FITT helps create balanced training plans and reduces the risk of boredom or plateau. Students can use it to evaluate their own activity logs and set personal targets.

应用 FITT 原则有助于制定平衡的训练计划，并降低枯燥或平台期的风险。学生可用它来评估自己的活动日志并设定个人目标。

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12. Levers and Mechanical Advantage in the Body | 人体中的杠杆与机械效益

Your skeleton forms lever systems that produce movement. A basic lever consists of a rigid bar (bone), a fulcrum (joint), an effort (muscle force) and a load (resistance). The mechanical advantage tells you whether the lever favours speed or strength.

你的骨骼构成了产生运动的杠杆系统。基本杠杆由刚性杆（骨）、支点（关节）、动力（肌力）和负载（阻力）组成。机械效益表明杠杆更有利于速度还是力量。

Mechanical advantage = effort arm length ÷ load arm length

When the effort arm is longer than the load arm (mechanical advantage > 1), the lever can move a large load with relatively little effort – a strength advantage, as seen in the calf raising the body during walking. When the effort arm is shorter (mechanical advantage < 1), the lever sacrifices force for speed and range of motion – most limb levers fall into this category. Understanding lever classes helps explain why certain muscles need to generate large forces.

当动力臂长于负载臂（机械效益 > 1）时，杠杆可以用较小的力量移动较大负载——这是一种力学优势，比如行走时小腿提起身体的例子。当动力臂较短（机械效益 < 1）时，杠杆牺牲力量换取速度和运动幅度——大多数四肢杠杆属于这一类。理解杠杆类别有助于解释为什么某些肌肉需要产生很大的力。

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

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