📚 Year 11 OCR PE: Formula & Theorem Quick Reference Handbook | Year 11 OCR 体育：公式定理速查手册
Mastering the key formulas and theorems in OCR GCSE Physical Education is essential for analysing performance, understanding physiological responses, and applying training principles correctly. This quick reference handbook covers all the essential equations, laws, and theoretical models you need for both the written examination and practical coursework. Each section pairs an English explanation with a Chinese translation, enabling bilingual learners to consolidate their knowledge effectively.
掌握 OCR GCSE 体育中的关键公式和定理对于分析运动表现、理解生理反应以及正确应用训练原则至关重要。这本速查手册涵盖了笔试和实践课程所需的所有基本方程式、定律和理论模型。每个部分都提供中英对照，帮助双语学习者高效巩固知识。
1. Cardiovascular Formulas | 心血管公式
Cardiac output (Q) is the volume of blood pumped by the heart per minute. It is calculated as stroke volume multiplied by heart rate: Q = SV × HR.
心输出量 (Q) 是心脏每分钟泵出的血量。计算公式为每搏输出量乘以心率：Q = SV × HR。
Stroke volume is the amount of blood ejected per beat, and heart rate is beats per minute. A typical resting Q is around 5 L/min, rising to 20–25 L/min during maximal exercise.
每搏输出量是每次心跳泵出的血量，心率是每分钟心跳次数。静息时心输出量通常约为 5 升/分钟，最大运动时可升至 20–25 升/分钟。
Maximum heart rate can be estimated as 220 minus age. This is used to set training zones, though more accurate methods exist.
最大心率可用 220 减去年龄来估算。这用于设定训练区间，但也存在更精确的方法。
Blood pressure is expressed as systolic over diastolic pressure, e.g. 120/80 mmHg. Mean arterial pressure (MAP) can be approximated by: MAP ≈ diastolic + ⅓(systolic – diastolic).
血压以收缩压/舒张压表示，如 120/80 mmHg。平均动脉压 (MAP) 可近似为：MAP ≈ 舒张压 + ⅓(收缩压 – 舒张压)。
2. Respiratory Formulas | 呼吸公式
Minute ventilation (VE) is the total air moved in and out of the lungs per minute. It equals tidal volume multiplied by respiratory rate: VE = TV × f.
每分通气量 (VE) 是每分钟进出肺部的总空气量。等于潮气量乘以呼吸频率：VE = TV × f。
Tidal volume is the air per breath, and respiratory rate is breaths per minute. During exercise, both increase, dramatically raising VE.
潮气量是每次呼吸的空气量，呼吸频率是每分钟呼吸次数。运动时两者均增加，使每分通气量急剧上升。
Vital capacity is the maximum air exhaled after maximum inhalation; it can be predicted by formulas based on height, age, and sex, but OCR typically references lung volume changes in spirometer traces.
肺活量是最大吸气后能呼出的最大气量；可根据身高、年龄和性别用公式预测，但 OCR 通常通过肺活量计曲线考查肺容量的变化。
Alveolar ventilation takes dead space into account: VA = (TV – dead space) × f. Dead space is the air not reaching alveoli, approximately 150 mL.
肺泡通气量考虑了解剖无效腔：VA = (TV – 无效腔) × f。无效腔指未到达肺泡的空气，约为 150 mL。
3. Energy System Equations | 能量系统方程
ATP (adenosine triphosphate) is broken down to release energy: ATP → ADP + Pi + energy. The resynthesis of ATP uses different fuels depending on intensity and duration.
ATP（三磷酸腺苷）分解时释放能量：ATP → ADP + Pi + 能量。ATP 的再合成根据运动强度和持续时间使用不同燃料。
The ATP-PC system (phosphocreatine) resynthesises ATP rapidly: PC → Pi + creatine + energy to reform ATP. This system lasts up to 10 seconds.
ATP-PC 系统（磷酸肌酸）快速再合成 ATP：PC → Pi + 肌酸 + 能量，用于重新形成 ATP。此系统最多持续 10 秒。
Anaerobic glycolysis yields ATP quickly without oxygen: Glucose → 2 ATP + pyruvic acid → lactic acid (when oxygen is insufficient).
无氧糖酵解快速产生 ATP，无需氧气：葡萄糖 → 2 ATP + 丙酮酸 → 乳酸（当氧气不足时）。
Aerobic system summary: Glucose + Oxygen → Carbon dioxide + Water + 38 ATP. Fat oxidation: Fatty acids + Oxygen → CO₂ + H₂O + large ATP yield. The OCR exam often uses simplified versions.
有氧系统总结：葡萄糖 + 氧气 → 二氧化碳 + 水 + 38 ATP。脂肪氧化：脂肪酸 + 氧气 → CO₂ + H₂O + 大量 ATP。OCR 考试通常使用简化版本。
4. Biomechanical Principles: Newton’s Laws | 生物力学原理：牛顿定律
Newton’s First Law (Inertia): A body remains at rest or in uniform motion unless acted upon by a net external force. A football will stay still until kicked.
牛顿第一定律（惯性）：物体保持静止或匀速直线运动，直到受到净外力作用。足球在被踢之前保持静止。
Newton’s Second Law (Acceleration): F = m × a. Force equals mass times acceleration. The greater the force applied, the greater the acceleration for a constant mass.
牛顿第二定律（加速度）：F = m × a。力等于质量乘以加速度。在质量不变的情况下，施加的力越大，加速度越大。
Newton’s Third Law (Action-Reaction): For every action, there is an equal and opposite reaction. When a sprinter pushes back on the blocks, the blocks push the sprinter forward.
牛顿第三定律（作用与反作用）：每个作用力都有一个大小相等、方向相反的反作用力。短跑运动员向后蹬起跑器，起跑器给予运动员向前的推力。
5. Levers, Moments & Torque | 杠杆、力矩与扭矩
A lever consists of a fulcrum (axis), effort, and load. The mechanical advantage = effort arm ÷ load arm. In the body, bones are levers, joints are fulcrums, muscles apply effort.
杠杆由支点、力点和阻力点组成。机械利益 = 力臂 ÷ 阻力臂。在人体中，骨是杠杆，关节是支点，肌肉施加力。
Torque (moment of force) = Force × perpendicular distance from fulcrum. Units are Newton metres (Nm). A longer lever arm increases torque for the same force.
扭矩（力矩）= 力 × 力到支点的垂直距离。单位为牛顿米 (Nm)。在相同力下，较长的力臂产生更大的扭矩。
OCR exam requires identification of first, second, and third-class levers in sporting movements. Third-class levers (effort between fulcrum and load) are most common in the body, e.g. bicep curl.
OCR 考试要求识别体育动作中的一类、二类和三类杠杆。三类杠杆（力在支点和阻力之间）在人体中最常见，例如肱二头肌弯举。
6. Speed, Velocity & Acceleration | 速度、速度与加速度
Speed is a scalar quantity: speed = distance ÷ time. Typical units: m/s. Velocity = displacement ÷ time, and is a vector including direction.
速率是标量：速率 = 距离 ÷ 时间。常见单位：m/s。速度 = 位移 ÷ 时间，是具有方向的矢量。
Acceleration = change in velocity ÷ time taken: a = (v – u)/t. Negative acceleration is deceleration. The gradient of a velocity-time graph gives acceleration.
加速度 = 速度变化量 ÷ 所用时间：a = (v – u)/t。负加速度为减速。速度-时间图像的斜率即为加速度。
Equations of uniform motion are used in sports biomechanics: v = u + at; s = ut + ½at²; v² = u² + 2as, where u = initial velocity, v = final velocity, a = acceleration, s = displacement, t = time.
匀加速直线运动方程常用于运动生物力学：v = u + at；s = ut + ½at²；v² = u² + 2as，其中 u = 初速度，v = 末速度，a = 加速度，s = 位移，t = 时间。
7. Force, Mass, Weight & Momentum | 力、质量、重量与动量
Weight is a force due to gravity: Weight = mass × gravitational field strength (W = m × g). g ≈ 9.8 m/s² on Earth. Mass is constant; weight changes on the moon.
重力是一种由引力产生的力：重力 = 质量 × 重力场强度 (W = m × g)。地球上 g ≈ 9.8 m/s²。质量不变，重量在月球上会改变。
Momentum = mass × velocity (p = m × v). Conservation of momentum is observed in collisions. A rugby player tackling another illustrates momentum transfer.
动量 = 质量 × 速度 (p = m × v)。碰撞中动量守恒。橄榄球运动员擒抱对方时发生动量传递。
Impulse = force × time = change in momentum. To increase momentum change, apply force for a longer time (follow-through) or greater force.
冲量 = 力 × 时间 = 动量变化。要增大动量变化，可延长力的作用时间（随挥）或增大力量。
8. Training Zones & Heart Rate Formulas | 训练区间与心率公式
Maximum heart rate (HRmax) = 220 – age. This is an estimation; individual variation exists. Training zones are percentages of HRmax.
最大心率 (HRmax) = 220 – 年龄。这是估计值，存在个体差异。训练区间是最大心率的百分比。
Aerobic training zone typically 60–80% HRmax. Anaerobic zone 80–90% HRmax. The Karvonen formula uses heart rate reserve: Target HR = Resting HR + (desired % × (HRmax – Resting HR)).
有氧训练区间通常为 60–80% HRmax。无氧区间为 80–90% HRmax。卡氏公式使用储备心率：目标心率 = 静息心率 + (期望百分比 × (最大心率 – 静息心率))。
Borg’s Rating of Perceived Exertion (RPE) scale 6–20 correlates roughly with heart rate (RPE × 10 ≈ heart rate). Not a formula but a subjective measure linked to physiological strain.
博格自感用力程度 (RPE) 量表 6–20 大致与心率相关 (RPE × 10 ≈ 心率)。虽非公式，但它是与生理负荷相关的主观量度。
9. Body Composition & BMI | 身体成分与体重指数
Body Mass Index (BMI) = weight (kg) ÷ height² (m²). It is a simple screening tool but does not distinguish between muscle and fat mass.
体重指数 (BMI) = 体重 (kg) ÷ 身高² (m²)。这是一项简单的筛查工具，但不区分肌肉和脂肪质量。
BMI categories: underweight <18.5; normal 18.5–24.9; overweight 25–29.9; obese ≥30. Athletes with high muscle mass may be classified as overweight despite low body fat.
BMI 分类：过轻 <18.5；正常 18.5–24.9；超重 25–29.9；肥胖 ≥30。肌肉量高的运动员可能被归为超重，尽管体脂率低。
Body fat percentage can be estimated via skinfold measurements using formulas like Jackson-Pollock or Durnin-Womersley. No single OCR formula, but understanding measurement principles is essential.
体脂百分比可通过皮褶测量，使用杰克逊-波洛克或杜宁-沃姆斯利等公式估算。OCR 没有指定单一公式，但理解测量原理是必要的。
10. Measurement & Data: Scales of Measurement | 测量与数据：测量尺度
Nominal scale: categories without order, e.g. team positions (goalkeeper, defender). Ordinal scale: ordered but unequal intervals, e.g. ranking of finishers. Interval scale: equal intervals but no true zero, e.g. temperature in °C. Ratio scale: equal intervals and true zero, e.g. time, mass.
名义尺度：无顺序的类别，如团队位置（守门员、后卫）。有序尺度：有序但不等距，如比赛名次。等距尺度：等距但无绝对零点，如摄氏度。比率尺度：等距且有绝对零点，如时间、质量。
Mean, median, mode, and range are used to describe performance data. Standard deviation formula: σ = √(Σ(x – mean)² / n). This measures the spread of data around the mean.
平均数、中位数、众数和极差用于描述运动表现数据。标准差公式：σ = √(Σ(x – 平均)² / n)。这衡量数据围绕平均值的离散程度。
11. Nutrition & Energy Balance | 营养与能量平衡
Energy balance: Energy intake (kcal) – Energy expenditure (kcal) = net energy. Positive balance leads to weight gain; negative balance leads to weight loss.
能量平衡：能量摄入（千卡） – 能量消耗（千卡）= 净能量。正平衡导致体重增加，负平衡导致体重减少。
Basal metabolic rate (BMR) can be estimated using the Mifflin-St Jeor equation or, more simply, approx 1 kcal per kg body mass per hour. Physical activity level (PAL) multiplies BMR to find total energy expenditure.
基础代谢率 (BMR) 可用 Mifflin-St Jeor 方程估算，或简单记为约每小时每千克体重 1 千卡。身体活动水平 (PAL) 乘以 BMR 得出总能量消耗。
Carbohydrate and protein provide 4 kcal/g; fat provides 9 kcal/g; alcohol provides 7 kcal/g. Understanding ATP yield per gram is crucial for dietary planning in sport.
碳水化合物和蛋白质提供 4 千卡/克；脂肪提供 9 千卡/克；酒精提供 7 千卡/克。了解每克物质的 ATP 产量对运动膳食计划至关重要。
12. Recovery, Rest & Fluid Balance | 恢复、休息与液体平衡
Sweat rate = (body mass pre-exercise – body mass post-exercise + fluid consumed – urine excreted) ÷ exercise time. Used to guide rehydration strategies.
出汗率 = (运动前体重 – 运动后体重 + 摄入液体 – 排出尿液) ÷ 运动时间。用于指导补水策略。
Rehydration goal is to replace 150% of fluid lost within 4–6 hours post-exercise, including electrolytes. There is no single OCR formula but principles of fluid balance are examined.
补水目标是运动后 4–6 小时内补充 150% 的流失液体，并包含电解质。OCR 没有单一公式，但会考查液体平衡的原则。
Work-to-rest ratios for interval training are calculated based on energy system emphasis, e.g. 1:3 for ATP-PC, 1:2 for anaerobic glycolysis. The formula is simply the ratio of exercise duration to recovery duration.
间歇训练的运动-休息比根据目标供能系统计算，如 ATP-PC 为 1:3，无氧糖酵解为 1:2。公式就是运动时间与恢复时间之比。
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