AS AQA PE Formula & Theorem Quick Reference | AS AQA 体育：公式定理速查手册

📚 AS AQA PE Formula & Theorem Quick Reference | AS AQA 体育：公式定理速查手册

This quick reference handbook compiles the essential formulas and theorems that you need to master for the AS AQA Physical Education specification. It covers cardiovascular dynamics, respiratory mechanics, Newton’s laws, momentum, work and power, efficiency of energy systems, and training prescription formulas. Use it as a last-minute revision tool to reinforce your understanding and nail those calculation questions in the exam.

本速查手册汇总了 AS AQA 体育课程中必须掌握的关键公式与定理，涵盖心血管动力学、呼吸力学、牛顿定律、动量、功与功率、能量系统效率以及训练强度计算公式。可作为考前快速回顾的工具，帮助你巩固理解并在考试中精准应对计算类题目。

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1. Cardiac Output (Q = HR × SV) | 心输出量 (Q = 心率 × 每搏输出量)

Q = HR × SV

Cardiac output (Q) is the volume of blood ejected from the left ventricle per minute. It is calculated as the product of heart rate (HR) and stroke volume (SV). HR is the number of heart beats per minute (bpm). SV is the volume of blood ejected per beat (ml). Typical resting values: HR = 60-80 bpm, SV = 70 ml, thus Q ≈ 5 L/min. During exercise, HR increases linearly with intensity, and SV also increases due to enhanced venous return and myocardial contractility, raising Q to 20-40 L/min in trained individuals.

心输出量 (Q) 是指左心室每分钟泵出的血量，等于心率 (HR) 与每搏输出量 (SV) 的乘积：Q = HR × SV。心率是每分钟心跳次数（次/分），每搏量是每次心跳泵出的血量（毫升）。静息时典型值为 HR = 60~80 次/分，SV = 70 毫升，因此 Q 约为 5 升/分。运动时，心率随强度线性升高，每搏量也因静脉回流增强与心肌收缩力提升而增加，训练有素者的心输出量可达 20~40 升/分。

It is vital to understand the relationship: for a given SV, a higher HR gives a higher Q; conversely, if HR drops, a larger SV can help maintain Q. This interplay is central to cardiovascular drift, where HR gradually rises during prolonged exercise to compensate for a declining SV caused by dehydration and reduced plasma volume.

理解这一关系至关重要：在每搏量一定时，心率越高心输出量越大；反之，若心率下降，更大的每搏量可帮助维持心输出量。这种相互作用是心血管漂移的核心——长时间运动中因脱水和血浆量减少导致每搏量下降，心率会逐步升高以代偿。

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2. Mean Arterial Pressure (MAP = Q × TPR) | 平均动脉压 (MAP = 心输出量 × 总外周阻力)

MAP = Q × TPR

Mean arterial pressure (MAP) is the average pressure in the arteries during one cardiac cycle. It depends on cardiac output (Q) and total peripheral resistance (TPR) – the resistance offered by arterioles. MAP = Q × TPR. At rest, TPR is relatively high to maintain diastolic pressure. During aerobic exercise, active muscles trigger local vasodilation, reducing TPR. However, the dramatic rise in Q outweighs the drop in TPR, so MAP increases moderately to enhance blood flow to working muscles.

平均动脉压 (MAP) 是一个心动周期中动脉内的平均压力，取决于心输出量 (Q) 和总外周阻力 (TPR) —— 小动脉所造成的阻力。MAP = Q × TPR。静息时 TPR 较高以维持舒张压。有氧运动时，活动肌群触发局部血管舒张，降低 TPR，但 Q 的大幅升高超过 TPR 的下降，因此 MAP 适度上升，增加工作肌的血流灌注。

Blood pressure can also be expressed as systolic pressure over diastolic pressure. MAP may be estimated using the formula: MAP = DBP + ⅓ (SBP – DBP), where SBP is systolic and DBP is diastolic pressure. Both formulations help explain how vascular changes during exercise protect the cardiovascular system while still meeting oxygen demand.

血压也可用收缩压与舒张压表示。MAP 可近似计算为：MAP = 舒张压 + ⅓ (收缩压 – 舒张压)。以上两个公式都有助于解释运动中的血管变化如何在满足氧供的同时保护心血管系统。

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3. Starling’s Law of the Heart | 心脏的斯塔林定律

Starling’s law states that the force of myocardial contraction is proportional to the initial length of the cardiac muscle fibres (preload). An increased venous return stretches the ventricular walls, leading to a stronger contraction and a higher stroke volume – the heart ‘pumps what it receives’. This intrinsic mechanism matches cardiac output to venous return without immediate neural input, and is particularly important during the transition from rest to steady-state exercise.

斯塔林定律指出，心肌收缩力与心肌纤维的初始长度（前负荷）成正比。静脉回流量增加会拉伸心室壁，使收缩更有力，搏出量更大——心脏“泵出它所接收的血液”。这一内在机制无需即刻的神经调节即可使心输出量与静脉回流量匹配，在从安静过渡到稳定运动状态时尤为重要。

Venous return is enhanced by the muscle pump, respiratory pump, and venoconstriction. As these mechanisms elevate preload, Starling’s law ensures the left ventricle ejects a larger SV, thereby maximising oxygen delivery with every heartbeat.

肌肉泵、呼吸泵和静脉收缩均能增加静脉回流。这些机制提高前负荷后，斯塔林定律确保左心室搏出更大的每搏量，使每次心跳都能充分运送氧气。

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4. Minute Ventilation (VE = TV × f) | 每分通气量 (VE = 潮气量 × 呼吸频率)

VE = TV × f

Minute ventilation (VE) is the volume of air moved into and out of the lungs per minute. It is the product of tidal volume (TV) – air per breath – and breathing frequency (f). At rest, TV is about 0.5 L and f is 12-15 breaths/min, giving a VE of 6-7.5 L/min. During maximal exercise, TV can reach 2-3 L and f 40-60 breaths/min, driving VE up to 120-180 L/min in elite athletes.

每分通气量 (VE) 是每分钟进出肺的气体总量，等于潮气量 (TV) 与呼吸频率 (f) 的乘积。静息时 TV 约 0.5 升，f 12~15 次/分，VE 约为 6~7.5 升/分。最大运动时，TV 可升至 2~3 升，f 达 40~60 次/分，优秀运动员的 VE 可高达 120~180 升/分。

TV rarely exceeds 60% of vital capacity because of mechanical limitations. Thus, large increases in VE at high intensities rely mainly on rising frequency. The respiratory centres in the medulla control this response, integrating feedback from chemoreceptors and proprioceptors to match ventilation to metabolic demand.

由于机械限制，TV 很少超过肺活量的 60%，因此高强度运动时 VE 的大幅提升主要依靠呼吸频率的加快。延髓的呼吸中枢整合化学感受器和本体感受器的反馈，使通气量与代谢需求相匹配。

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5. Newton’s Laws of Motion | 牛顿运动定律

First Law: Law of Inertia

A body remains at rest or in uniform motion in a straight line unless acted upon by a net external force. In sport, a hockey puck continues sliding on ice until friction or a stick intervenes; a stationary rugby ball does not move until a force is applied.

任何物体都保持静止或匀速直线运动状态，直到有净外力迫使它改变。运动中，冰上曲棍球会持续滑行直到摩擦力或球杆干预；静止的橄榄球只有在受力后才会移动。

Second Law: F = ma

The acceleration of an object is directly proportional to the net force applied and inversely proportional to its mass: F = ma. A greater force results in a larger acceleration; a heavier shot put requires much more force to achieve the same acceleration as a lighter implement.

物体的加速度与所受合外力成正比，与质量成反比：F = ma。力量越大加速度越大；投掷更重的铅球需要更大的力才能获得与轻器械相同的加速度。

Third Law: Action-Reaction

For every action, there is an equal and opposite reaction. When a swimmer pushes water backwards, the water pushes the swimmer forwards. Similarly, a sprinter drives against the blocks and the blocks exert an equal forward force.

每一个作用力都有一个大小相等、方向相反的反作用力。游泳者向后推水，水则向前推游泳者；短跑运动员蹬离起跑器时，起跑器施加同样大小的向前的力。

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6. Impulse-Momentum Relationship | 冲量–动量关系

Impulse (Ft) = Change in Momentum (Δp) = m(v – u)

Impulse is the product of force (F) and the time (t) for which it acts. It equals the change in momentum of an object. Increasing the time over which a force is applied, or applying a larger force, produces a greater change in velocity. In a tennis serve, the player applies a large force over a short time to create high racket-head speed and ball velocity. In a follow-through, the impulse is extended to control the direction and spin.

冲量是力 (F) 与其作用时间 (t) 的乘积，等于物体动量的变化量：Ft = m(v – u)。延长力的作用时间或施加更大的力都能产生更大的速度变化。网球发球时，运动员在短时间内施加大力以产生高拍头速度和球速；随挥动作中延长冲量时间以控制方向和旋转。

Momentum (p) is the product of mass and velocity (p = mv). A rugby player with greater mass and speed has more momentum, making them harder to tackle. The impulse-momentum principle explains why a tackling technique that increases contact time (rolling with the hit) reduces the impact force on the ball carrier.

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