📚 Year 11 Edexcel PE: Formula & Theorem Quick Reference Guide | 爱德思体育公式定理速查手册
This guide brings together every essential formula, equation and principle you need to master for Year 11 Edexcel GCSE Physical Education. Whether you are calculating training zones, analysing movement or interpreting physiological data, having a quick reference to the key quantitative relationships will sharpen your exam performance and deepen your understanding of how the body and its movements work.
本手册汇集了 Year 11 爱德思 GCSE 体育课程中的每一个核心公式、方程与原理。无论你是在计算训练区间、分析运动动作，还是解读生理数据，一本囊括关键数量关系的速查手册都能提升你的考试成绩，并加深你对身体及其运动方式的理解。
1. Cardiac Output & Stroke Volume | 心输出量与每搏输出量
Cardiac Output (Q) = Stroke Volume (SV) × Heart Rate (HR)
Cardiac output is the volume of blood pumped out of the left ventricle in one minute. It is measured in litres per minute (L/min). Stroke volume is the amount of blood ejected per beat, and heart rate is the number of beats per minute. An increase in either SV or HR will raise Q, provided the other factor does not drop too far. Endurance training typically increases SV, allowing a lower resting HR while maintaining the same Q at rest.
心输出量是指左心室每分钟泵出的血量，单位为升/分钟。每搏输出量是每次心跳泵出的血液量，心率是每分钟心跳次数。只要其中一个因素不下降过多，SV 或 HR 的任何增加都会提高 Q。耐力训练通常会增大 SV，从而在维持相同静息 Q 的情况下降低静息心率。
Stroke Volume (SV) = EDV – ESV
Stroke volume can also be calculated as end-diastolic volume (EDV) minus end-systolic volume (ESV). EDV is the volume of blood in the ventricle just before contraction; ESV is the volume remaining after contraction. A stronger heart muscle pumps more blood out, reducing ESV and increasing SV.
每搏输出量也可通过舒张末期容积 (EDV) 减去收缩末期容积 (ESV) 计算得出。EDV 是心室收缩前的血液容积，ESV 是收缩后残留的血液容积。心肌越有力，泵出的血液越多，ESV 越小，SV 越大。
2. Minute Ventilation | 每分钟通气量
Minute Ventilation (VE) = Tidal Volume (TV) × Respiratory Rate (RR)
Minute ventilation is the total volume of air entering or leaving the lungs per minute, expressed in litres per minute. Tidal volume is the amount of air breathed in or out during a normal breath. Respiratory rate is the number of breaths taken per minute. During exercise, both TV and RR increase, causing a sharp rise in VE to meet the greater oxygen demand and remove carbon dioxide.
每分钟通气量是指每分钟进出肺部的空气总量，单位为升/分钟。潮气量是一次正常呼吸中吸入或呼出的空气量。呼吸频率是每分钟的呼吸次数。运动时，TV 和 RR 均会增加，使 VE 大幅上升，以满足更大的氧气需求并排出二氧化碳。
3. Maximum Heart Rate & Training Zones | 最大心率与训练区间
Maximum Heart Rate (MHR) ≈ 220 − age
bpm between individuals. It is used to set exercise intensity zones based on percentages.
最简单估算 MHR 的方法是 220 减去年龄。该数值仅为平均值，个体间可能存在约 ±10 次/分的差异。它被用来根据百分比设定运动强度区间。
Target Heart Rate = desired % × MHR
Using a fixed percentage of MHR: moderate aerobic training typically uses 60–80% MHR, while high-intensity anaerobic training uses 80–90% MHR. This method is quick but does not account for fitness level or resting heart rate.
使用 MHR 的固定百分比：中等有氧训练通常使用 60–80% MHR，高强度无氧训练使用 80–90% MHR。这种方法简便快捷，但未考虑体能水平或安静心率。
Karvonen Formula: Target HR = Resting HR + (desired % × (MHR − Resting HR))
The Karvonen formula uses heart rate reserve (HRR) for a more individualised training zone. Heart rate reserve is the difference between MHR and resting HR. This method better reflects changes in fitness: as resting HR decreases with training, the target zone automatically adjusts.
卡沃宁公式利用心率储备 (HRR) 制定更个性化的训练区间。心率储备是 MHR 与安静心率的差值。这一方法更能反映体能变化：随着训练导致安静心率下降，目标区间会自动调整。
4. Body Mass Index (BMI) | 身体质量指数
BMI = body mass (kg) ÷ (height in metres)²
BMI is a simple ratio used to classify individuals as underweight, normal weight, overweight or obese. It is widely used in epidemiological studies and by fitness professionals. However, it does not distinguish between muscle and fat mass, so a very muscular athlete may be misclassified as overweight.
BMI 是一个用于划分体重过轻、正常、超重或肥胖的简单比值，广泛用于流行病学研究和健身领域。但它不能区分肌肉与脂肪质量，因此肌肉发达的运动员可能被误判为超重。
Example: mass = 70 kg, height = 1.75 m → BMI = 70 ÷ (1.75²) ≈ 22.9 kg/m²
You must be able to calculate BMI and interpret the result against standard classification tables. In an exam, always square the height first, then divide the mass by that squared value.
你必须能够计算 BMI 并对照标准分类表解读结果。考试时务必先对身高平方，再用体重除以该平方值。
5. Speed, Velocity & Acceleration | 速率、速度与加速度
Speed = distance ÷ time
Speed is a scalar quantity describing how fast something moves, without regard to direction. It is usually expressed in metres per second (m/s). In sport, sprint speed is often calculated over a known distance, e.g. 100 m.
速率是标量，描述物体移动的快慢而不涉及方向，单位通常为米/秒 (m/s)。在体育中，冲刺速度常通过已知距离（如 100 米）来计算。
Velocity = displacement ÷ time
Velocity is a vector quantity; it includes direction. Displacement is the straight-line distance between start and finish points. In a 400 m lap where the athlete returns to the start, displacement is 0 m, so average velocity is 0 m/s despite a high speed.
速度是矢量，包含方向。位移是起点到终点的直线距离。在 400 米绕圈跑中，运动员回到起点，位移为 0 米，因此尽管速率很高，平均速度仍为 0 m/s。
Acceleration = change in velocity ÷ time taken
initial velocity) ÷ time, measured in m/s². Positive acceleration means speeding up; negative acceleration (deceleration) means slowing down. Explosive starts and rapid changes of direction rely on high acceleration.
加速度 a = (末速度 − 初速度) ÷ 时间，单位为 m/s²。正加速度表示加速，负加速度（减速）表示变慢。爆发式起跑和快速变向都依赖高加速度。
6. Force, Mass & Weight | 力、质量与重量
Force (F) = mass (m) × acceleration (a)
Newton's second law tells us that the net force acting on an object is equal to its mass multiplied by its acceleration. In sport, the force generated by muscles accelerates limbs, implements or the whole body. Force is measured in newtons (N).
牛顿第二定律指出物体所受合力等于其质量乘以加速度。在体育运动中，肌肉产生的力使四肢、器械或整个身体加速。力的单位是牛顿 (N)。
Weight = mass × gravitational field strength (g)
in newtons, while mass is measured in kilograms. An athlete with a mass of 65 kg has a weight of approximately 650 N. Weight acts downwards through the centre of mass.
重量是由于重力产生的力。地球表面的 g ≈ 10 N/kg。重量以牛顿为单位，质量以千克为单位。一名 65 kg 的运动员重量约为 650 N。重量通过重心竖直向下作用。
7. Work, Power & Energy | 功、功率与能量
Work done (W) = force (F) × distance (d)
Work is done when a force moves an object. It is measured in joules (J). In the context of sport, lifting a weight against gravity or pushing a sled both involve work. The direction of force and movement must be aligned for work to be done.
当力使物体移动时即做功，单位为焦耳 (J)。在体育中，克服重力举起重物或推动雪橇都涉及做功。力的方向与移动方向必须一致才做功。
Power = work done ÷ time
Power is the rate at which work is performed, measured in watts (W). An athlete who can produce more power can complete the same work in less time, which is critical for explosive events such as sprinting, jumping and throwing.
功率是做功的速率，单位为瓦特 (W)。能够产生更大功率的运动员可在更短时间内完成相同工作，这对冲刺、跳跃和投掷等爆发性项目至关重要。
Power = force × velocity
When constant velocity is maintained, power can also be calculated as force multiplied by velocity. This is useful in cycling or rowing, where athletes sustain a certain force at a given speed.
当保持匀速时，功率也可表示为力乘以速度。这在自行车或划船运动中非常实用，运动员在某个速度下维持一定的力。
Kinetic Energy (KE) = ½ m v²
Kinetic energy is the energy of motion. Doubling the speed quadruples the kinetic energy, which explains why fast bowlers in cricket or fast serves in tennis have such a powerful impact.
动能是运动的能量。速度加倍会使动能增至四倍，这解释了板球快速投球手或网球大力发球为何冲击力如此之大。
Gravitational Potential Energy (GPE) = m × g × h
GPE depends on mass, gravity and height. When a gymnast lifts their body vertically or a high jumper clears the bar, chemical energy is converted into GPE, which can be estimated using this formula.
重力势能取决于质量、重力加速度和高度。当体操运动员垂直提升身体或跳高运动员越过横杆时，化学能转化为重力势能，可用该公式估算。
8. Mechanical Advantage & Lever Systems | 机械优势与杠杆系统
Mechanical Advantage (MA) = effort arm ÷ resistance arm
Mechanical advantage describes the ratio of the load force to the effort force in a lever system. The effort arm is the distance from the effort to the fulcrum; the resistance arm is the distance from the resistance to the fulcrum. A mechanical advantage greater than 1 means the lever multiplies the effort force, making it easier to move a heavy load but through a smaller range of motion.
机械优势描述杠杆系统中负荷力与作用力的比值。动力臂是作用力到支点的距离，阻力臂是阻力到支点的距离。机械优势大于 1 表示杠杆放大了作用力，能更省力地移动重物，但运动幅度较小。
Example: second-class lever (e.g. calf raise) – effort arm > resistance arm → MA > 1
In the human body, a second-class lever system such as the foot during plantar flexion has the load between the fulcrum and the effort, giving a mechanical advantage that favours force production. First-class levers can have MA greater or less than 1 depending on fulcrum position; third-class levers (most common in the body) always have MA < 1, favouring speed and range of motion over force.
在人体中，第二类杠杆系统（如跖屈时的足部）负荷位于支点与作用力之间，机械优势大于 1，有利于产生力量。第一类杠杆的 MA 可大于或小于 1，取决于支点位置；第三类杠杆（人体中最常见）的 MA 始终小于 1，以牺牲力量为代价换取速度和运动幅度。
9. Moments & Equilibrium | 力矩与平衡
Moment (turning effect) = force × perpendicular distance from the pivot
A moment is the turning effect of a force measured in newton-metres (Nm). In sport, moments are crucial for understanding balance, rotation and leverage. The greater the force or the distance from the pivot, the larger the moment.
力矩是力的转动效应，单位为牛顿·米 (Nm)。在体育中，力矩对于理解平衡、旋转和杠杆作用至关重要。力越大或离支点的垂直距离越远，力矩就越大。
Principle of moments: total clockwise moments = total anticlockwise moments at equilibrium
When an object is balanced, the sum of clockwise moments equals the sum of anticlockwise moments. This principle explains how gymnasts maintain poses on a beam or how a rugby player adjusts their centre of mass to resist a tackle.
当物体平衡时，顺时针力矩之和等于逆时针力矩之和。这一原理解释了体操运动员如何在平衡木上保持姿势，或者橄榄球运动员如何调整重心来抵抗擒抱。
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