📚 OCR GCSE Physical Education: Quick Reference Formulas & Principles | 公式定理速查手册
This reference handbook brings together the essential quantitative relationships and key principles you will encounter in Year 10 OCR GCSE Physical Education. From heart rate calculations to levers and mechanical advantage, each formula is presented with its definition, typical units, and a brief application example. Use this guide to support your revision, data analysis questions, and exam preparation in the Applied Anatomy and Physiology, Physical Training, and Movement Analysis topics.
本速查手册集中整理了 Year 10 OCR GCSE 体育学科中会遇到的重要定量关系和关键原理。从心率计算到杠杆与机械利益，每个公式都配有定义、常用单位和简要应用示例。将该指南用于辅助复习、数据分析题型以及应用解剖与生理学、身体训练和运动分析模块的备考。
1. Heart Rate & Training Zones | 心率与训练区间
Estimating maximum heart rate (MHR) is the first step in setting aerobic training intensity. The simplest equation, commonly used at GCSE, subtracts age from 220. More accurate population‑specific formulas exist, but the version below is the one required by OCR.
估计最大心率 (MHR) 是设定有氧训练强度的第一步。GCSE 阶段最常用的简单公式为 220 减去年龄。虽然存在更精准的特定人群公式，但 OCR 要求掌握的是下面这个版本。
MHR = 220 – age
To prescribe a target heart rate zone, use the Karvonen formula, which takes resting heart rate (RHR) into account. You calculate heart rate reserve first.
要给出目标心率区间，需使用卡氏公式（Karvonen formula），该公式考虑了安静心率 (RHR)。首先计算心率储备。
Heart Rate Reserve (HRR) = MHR – RHR
Target HR = (HRR × intensity %) + RHR
For a performer aiming at 70% intensity, intensity % is 0.70. This method relates training effort directly to the individual's fitness level, making it more personalised than using MHR alone.
若运动员希望以 70% 强度训练，强度百分数取 0.70。此方法将训练负荷直接与个人体能水平挂钩，比单独使用最大心率更加个性化。
2. Cardiac Output & Stroke Volume | 心输出量与每搏输出量
Cardiac output (Q) is the volume of blood pumped by the heart per minute. It is the product of heart rate and stroke volume. Understanding this relationship helps explain how the cardiovascular system adapts during exercise.
心输出量 (Q) 是心脏每分钟泵出的血量，由心率与每搏输出量相乘得到。理解这一关系有助于解释心血管系统在运动中的适应机制。
Q = HR × SV
Stroke volume is the amount of blood ejected by the left ventricle in one beat (ml/beat). During endurance training, stroke volume increases, allowing the same cardiac output to be achieved at a lower heart rate – a sign of improved fitness.
每搏输出量是左心室每次搏动射出的血量 (毫升/次)。经过耐力训练，每搏输出量增大，从而可在较低的心率下达到同等心输出量——这是体适能提升的标志。
3. Respiratory Calculations | 呼吸计算
Minute ventilation (VE) describes the total volume of air moved into and out of the lungs per minute. It rises sharply as exercise intensity increases, because both breathing rate and tidal volume increase.
分钟通气量 (VE) 表示每分钟进出肺部的空气总量。随着运动强度增加，呼吸频率和潮气量均上升，分钟通气量也会急剧升高。
VE = breathing rate × tidal volume
For analysing energy systems, the respiratory exchange ratio (RER) is used. It indicates the ratio of carbon dioxide produced to oxygen consumed at the lungs and suggests which fuel (carbohydrate or fat) is predominantly being metabolised.
在分析能量系统时，会用到呼吸交换率 (RER)。它表示肺部产生的二氧化碳与消耗的氧气之比，可提示身体主要代谢的燃料是碳水化合物还是脂肪。
RER = VCO₂ / VO₂
An RER of 1.0 typically indicates carbohydrate‑dominated metabolism, while a value of 0.7 points towards fat utilisation. This is often discussed in the context of aerobic and anaerobic thresholds.
RER 值为 1.0 通常表明以碳水化合物代谢为主，0.7 则指向脂肪利用。该知识点常常放在有氧阈与无氧阈的情境中讨论。
4. Force, Mass, and Weight | 力、质量与重量
The relationship between net force, mass, and acceleration is given by Newton’s Second Law. It explains how a player’s mass affects the acceleration they can achieve when a force is applied – for example, when pushing off the blocks in a sprint start.
合力、质量和加速度之间的关系可由牛顿第二定律描述。它解释了运动员的质量如何影响在受力时所能达到的加速度——例如短跑起跑蹬离起跑器时。
F = m × a
Weight is a specific force caused by gravity acting on a mass. On Earth, the gravitational field strength g is taken as 9.8 m/s². Weight is measured in newtons (N), distinct from mass measured in kilograms (kg).
重量是由重力作用于质量而产生的特定力。在地球表面，重力场强度 g 取 9.8 米/秒²。重量的单位是牛顿 (N)，区别于以千克 (kg) 为单位的质量。
W = m × g
5. Speed, Velocity & Acceleration | 速率、速度与加速度
Speed is a scalar quantity describing how fast an object moves, while velocity is a vector that also includes direction. In many sports, calculating average speed from split times provides feedback on pacing.
速率是标量，描述物体运动的快慢；速度是矢量，还包含方向。在许多运动中，通过分段计时计算平均速率可为配速提供反馈。
speed = distance ÷ time
velocity = displacement ÷ time
Acceleration measures how quickly velocity changes. A sprinter who dramatically increases velocity out of the blocks has a high positive acceleration; deceleration is negative acceleration.
加速度衡量速度变化的快慢。短跑运动员起跑后若速度急剧提升，则具有较大的正加速度；减速即为负加速度。
a = (v – u) / t
Here u is initial velocity, v is final velocity, and t is the time taken for the change. This formula is frequently used when interpreting velocity‑time graphs.
式中 u 为初速度，v 为末速度，t 为变化所用时间。这个公式常用于解读速度–时间图。
6. Momentum & Impulse | 动量与冲量
Momentum depends on both mass and velocity. A rugby forward with large mass moving at speed possesses high momentum, which makes them difficult to tackle.
动量取决于质量和速度。一名质量大且速度快的橄榄球前锋拥有高动量，因而很难被擒抱停下。
p = m × v
Impulse is the effect of a force applied over a time interval. It equals the change in momentum. In long jump take‑off, applying force over a slightly longer time can increase the take‑off velocity and thus the jump distance.
冲量是力在一段时间内作用的效果，等于动量的变化量。在跳远起跳中，稍微延长力作用时间可增加起跳速度，从而增长跳跃距离。
Impulse = F × t = Δp
Athletes use this principle in follow‑through actions to maximise the time of force application and control momentum transfer.
运动员在随挥动作中应用该原理，以最大化力作用时间并控制动量传递。
7. Work, Power & Energy | 功、功率与能量
In biomechanics, work is done when a force causes displacement in the direction of the force. Lifting a barbell vertically against gravity performs mechanical work.
在运动生物力学中，力使物体沿力的方向发生位移时，即做了功。竖直向上举杠铃抵抗重力便是做机械功。
W = F × d
Power is the rate of doing work. A weightlifter who completes the same lift in a shorter time generates greater power, which is a vital component of explosive strength.
功率是做功的速率。在更短时间内完成同一举重的举重运动员产生了更大的功率，这是爆发力的重要组成部分。
P = W / t
energy (KE = ½mv²), but at GCSE the focus is primarily on work and power as defined above.
分析运动效率时可能会遇到动能公式 (KE = ½mv²)，但 GCSE 阶段主要聚焦于上述功与功率的定义。
8. Moments, Levers & Mechanical Advantage | 力矩、杠杆与机械利益
A moment is the turning effect produced by a force. In sport, moments help explain how levers operate around joints. The moment is calculated by multiplying the force by the perpendicular distance from the pivot.
力矩是力产生的转动效应。在运动中，力矩帮助解释杠杆如何围绕关节运作。力矩等于力乘以力到支点的垂直距离。
Moment = force × perpendicular distance from pivot
The principle of moments states that for a lever in equilibrium, the clockwise moment equals the anticlockwise moment. This concept is used to analyse balance and stability in starting positions.
力矩原理指出，杠杆平衡时顺时针力矩等于逆时针力矩。这一概念用于分析起跑姿势的平衡与稳定性。
Mechanical advantage (MA) indicates how effectively a lever multiplies the effort force. It can be expressed using either the effort arm and resistance arm, or the load and effort forces.
机械利益 (MA) 表示杠杆放大施力的有效程度。可以用力臂和阻力臂，或者负荷与施力来表示。
MA = effort arm / resistance arm
MA = load / effort
Second‑class levers (e.g. standing on tiptoes) always have a mechanical advantage greater than 1, meaning they can move large loads with a smaller effort. First‑class and third‑class levers can have MA less than, equal to, or greater than 1 depending on their arrangement, though most third‑class levers in the body favour speed and range of motion over force.
第二类杠杆（如踮脚站立）的机械利益始终大于 1，意味着能用较小的施力移动较大的负荷。第一类和第三类杠杆的 MA 可小于、等于或大于 1，具体取决于结构布局，不过人体内的第三类杠杆大多为速度与活动范围而舍弃了力量。
9. Body Mass Index (BMI) | 身体质量指数
BMI is a simple screening tool used to categorise individuals as underweight, normal weight, overweight or obese. While it does not distinguish between muscle and fat, it is widely used in epidemiological studies and GCSE data tasks.
身体质量指数是一种简易的筛查工具，用于将个体划分为体重过轻、正常、超重或肥胖。虽然 BMI 不区分肌肉和脂肪，但仍广泛用于流行病学研究和 GCSE 数据处理题目。
BMI = weight (kg) / height² (m)
in the normal range. However, heavily muscled performers may have a misleadingly high BMI.
例如，一名体重 70 公斤、身高 1.75 米的运动员其 BMI 为 70 ÷ (1.75 × 1.75) ≈ 22.9，属于正常范围。但肌肉发达的运动者可能出现偏高的误导性 BMI 值。
10. Rating of Perceived Exertion (RPE) | 自感劳累评级
The Borg Rating of Perceived Exertion scale is a subjective method of monitoring exercise intensity. The original scale runs from 6 to 20, where 6 means no exertion at all and 20 means maximal exertion. The numbers roughly correlate with heart rate (e.g. RPE 12 suggests a heart rate of around 120 bpm for many individuals).
博格自感劳累评级量表是一种主观监控运动强度的方法。原始量表分为 6–20 级，其中 6 表示毫不费力，20 表示最大极限用力。这些数字大致与心率对应（如 RPE 12 对很多人意味着心率约为 120 次/分）。
Estimated HR ≈ RPE × 10
Coaches often use the modified 0–10 scale (Category Ratio Scale), but the 6–20 version is the one linked to exam data‑handling questions. Combining RPE with heart rate monitors helps performers learn to interpret internal sensations of effort.
教练常使用修改版的 0–10 级量表（类别比率量表），但 6–20 级版本才是与考试数据处理题关联的。将 RPE 与心率监测结合可帮助运动员学会解读自身内部用力感觉。
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