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Year 9 CCEA PE: Quick Formula & Principles Handbook | Year 9 CCEA 体育：公式定理速查手册

2026-07-18 20:35 · 本文部分内容由AI辅助创作

📚 Year 9 CCEA PE: Quick Formula & Principles Handbook | Year 9 CCEA 体育：公式定理速查手册

This quick reference handbook compiles essential formulae and principles for Year 9 CCEA Physical Education. Mastering these tools will help you analyse performance, design training programmes, and understand the biomechanics of human movement. Keep it handy during revision and practical sessions to solidify your understanding of the science behind sport.

本快速参考手册汇集了 Year 9 CCEA 体育学科的基本公式与原理。掌握这些工具将有助于你分析运动表现、设计训练计划以及理解人体运动的生物力学。在复习和实践课中随时查阅，以巩固你对运动科学基础的理解。

1. Maximum Heart Rate (HRmax) Estimation | 最大心率估算

Your maximum heart rate (HRmax) is the highest number of beats per minute (bpm) your heart can achieve during maximal exercise. The most widely used age-predicted formula gives a simple baseline for setting training intensities.

最大心率（HRmax）是你在极限运动中心脏每分钟能达到的最高心跳次数（bpm）。最常用的年龄预测公式为设定训练强度提供了一个简单的基准。

HRₘₐₓ = 220 − age

t, HRmax = 220 − 14 = 206 bpm. In practical application, individual variation exists; a laboratory maximal test or field test can provide a more accurate value. Nevertheless, the 220 − age formula remains the starting point for designing safe aerobic and anaerobic training zones in school PE.

该估算假定从出生时理论上的 220 bpm 开始，每年约下降一次心跳。对于 14 岁学生，HRmax = 220 − 14 = 206 bpm。在实际应用中，存在个体差异；实验室最大测试或场地测试可提供更准确的值。尽管如此，220 − 年龄公式仍然是学校体育中设计安全的有氧和无氧训练区间的起点。

2. Target Heart Rate Zones | 目标心率区间

Once you have estimated HRmax, you can calculate target heart rate zones by multiplying HRmax by the desired intensity percentage. This helps you train at the correct effort level for specific fitness goals.

估算出 HRmax 后，你可以将 HRmax 乘以期望的强度百分比来计算目标心率区间。这有助于你根据特定的体能目标，在正确的努力水平下进行训练。

Target HR = HRₘₐₓ × Intensity %

Intensity (% HRmax)Training ZoneTypical Use
50–60%Very LightWarm-up, cool-down, recovery
60–70%ModerateFat burning, base endurance
70–80%AerobicCardiovascular improvement
80–90%AnaerobicLactate threshold, high-intensity intervals
90–100%MaximalSprint, peak power development

For a 14-year-old with an estimated HRmax of 206 bpm, a moderate zone (60–70%) would be 124–144 bpm. Monitoring heart rate during exercise ensures you stay in the intended zone and avoid over-training. These zones are fundamental to applying the FITT principle effectively in any training programme.

对于一个估计 HRmax 为 206 bpm 的 14 岁学生，中等强度区间（60–70%）为 124–144 bpm。运动时监测心率可确保你保持在预定的区间内，避免过度训练。这些区间对于在任何训练计划中有效应用 FITT 原则至关重要。

3. Body Mass Index (BMI) | 身体质量指数

Body Mass Index is a screening tool used to categorise weight status relative to height. Although it does not directly measure body fat, it provides a quick and useful health indicator for populations.

身体质量指数（BMI）是一种根据身高来划分体重状态的筛查工具。虽然它不能直接测量身体脂肪，但它为人群提供了一个快速且有用的健康指标。

BMI = weight (kg) ÷ [height (m)]²

as BMI = 50 ÷ (1.60 × 1.60) = 50 ÷ 2.56 ≈ 19.5 kg/m². According to standard charts, this falls within the healthy weight range (18.5– ues and discuss their limitations, such as not distinguishing between muscle and fat mass.

计算 BMI 时，用体重（千克）除以身高（米）的平方。例如，一名体重 50 kg、身高 1.60 m 的学生，BMI = 50 ÷ (1.60 × 1.60) = 50 ÷ 2.56 ≈ 19.5 kg/m²。根据标准图表，这属于健康体重范围（18.5–24.9）。在 GCSE 体育中，你可能需要解读 BMI 值并讨论其局限性，例如无法区分肌肉和脂肪质量。

4. Speed Calculation | 速度计算

Speed, often used interchangeably with velocity in school physics, describes how quickly an object or athlete covers distance. It is a scalar quantity, meaning it has magnitude but no direction.

速度（在学校物理中常与速率互换）描述物体或运动员通过距离的快慢。它是一个标量，即有大小而无方向。

v = d ÷ t

fundamental equation underpins performance analysis in athletics and many team sports. Coaches use split times to calculate average speed over given segments and identify where a performer accelerates or fatigues.

式中 v 为速度（m/s），d 为距离（m），t 为时间（s）。如果一名短跑运动员在 12.5 秒内跑完 100 m，速度 = 100 ÷ 12.5 = 8 m/s。这个基本公式支撑着田径和诸多团体运动中的表现分析。教练利用分段计时来计算特定阶段的平均速度，并判断运动员何时加速或疲劳。

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5. Acceleration | 加速度

Acceleration measures the rate at which velocity changes. It is highly relevant in sports requiring explosive starts, changes of direction, or rapid deceleration.

加速度衡量速度变化的快慢。在需要爆发式起跑、变向或快速减速的运动中，它极为重要。

a = (v − u) ÷ t

aller accelerates from a stationary position (u = 0) to 6 m/s in 1.5 seconds, acceleration = (6 − 0) ÷ 1.5 = 4 m/s². A negative value indicates deceleration (e.g., slowing down before a tackle in rugby). Understanding acceleration helps in analysing sprint mechanics and reaction time.

式中 a 为加速度（m/s²），v 为最终速度（m/s），u 为初速度（m/s），t 为所用时间（s）。如果一名足球运动员从静止状态（u = 0）在 1.5 秒内加速到 6 m/s，加速度 = (6 − 0) ÷ 1.5 = 4 m/s²。负值则表示减速（例如在橄榄球抢断前的减速）。理解加速度有助于分析冲刺力学和反应时间。

6. Force and Newton's Second Law | 力与牛顿第二定律

Newton's Second Law states that the acceleration of an object is directly proportional to the net force acting upon it and inversely proportional to its mass. This law explains the relationship between force, mass, and motion in every sporting action.

牛顿第二定律指出，物体的加速度与作用在其上的净力成正比，与物体的质量成反比。该定律解释了每一项体育动作中力、质量与运动之间的关系。

F = m × a

Force (F) is measured in newtons (N), mass (m) in kilograms (kg), and acceleration (a) in m/s². One newton is the force needed to accelerate 1 kg at 1 m/s². If a PE teacher pushes a 50 kg tackle shield causing an acceleration of 2 m/s², the applied force is 100 N. This principle helps students appreciate how increasing force or reducing mass can improve performance in events like shot put or sprinting.

力（F）的单位是牛顿（N），质量（m）的单位是千克（kg），加速度（a）的单位是 m/s²。1 牛顿是使 1 kg 质量产生 1 m/s² 加速度所需的力。如果体育老师推动一个 50 kg 的撞垫并产生 2 m/s² 的加速度，施加的力就是 100 N。该原理有助于学生理解如何通过增加力量或减小质量来提升推铅球或短跑等项目的运动表现。

7. Momentum | 动量

Momentum is the product of a body's mass and its velocity. It is a vector quantity, so direction matters. In collision sports, momentum plays a key role in tackling and impact absorption.

动量是物体质量与其速度的乘积。它是一个矢量，因此方向至关重要。在碰撞类运动中，动量在抢断和冲击吸收中起着关键作用。

p = m × v

Momentum (p) is expressed in kilogram metres per second (kg·m/s). A 70 kg rugby player running at 5 m/s has a momentum of 350 kg·m/s. According to the law of conservation of momentum, total momentum before a collision equals total momentum after, assuming no external forces. This concept explains why a lighter but faster player can still deliver a powerful tackle if they generate enough velocity.

动量（p）的单位是千克·米/秒（kg·m/s）。一名 70 kg 的橄榄球运动员以 5 m/s 的速度奔跑，其动量为 350 kg·m/s。根据动量守恒定律，在没有外力作用的情况下，碰撞前的总动量等于碰撞后的总动量。这一概念解释了为什么体重较轻但速度较快的球员，只要产生足够的速度，仍能做出有力的擒抱。

8. Moment of Force (Torque) | 力矩

The moment of a force, or torque, describes the turning effect produced when a force is applied at a distance from a pivot or joint. It is central to understanding human leverage and rotational movements in sport.

力矩，也称转矩，描述了在距离支点或关节一定距离处施加力时所产生的转动效应。它是理解人体杠杆作用和运动中旋转动作的核心。

M = F × d

Where M is moment (in newton-metres, Nm), F is the applied force (N), and d is the perpendicular distance from the pivot to the line of action of the force (m). To maximise the moment – for instance, when opening a door or kicking a ball – increase the force or apply it further from the pivot. In the body, longer levers (limbs) can generate greater torque, which is why tall athletes often have an advantage in throwing events.

式中 M 为力矩（牛顿·米，Nm），F 为施加的力（N），d 为从支点到力作用线的垂直距离（m）。要最大化力矩——例如开门或踢球时——可以增大力量或将力施加在离支点更远处。在人体中，较长的杠杆（四肢）能产生更大的力矩，这也就是身材高大的运动员在投掷项目中往往占优势的原因。

9. Lever Systems and Mechanical Advantage | 杠杆系统与机械优势

A lever system consists of a rigid bar (bone), a pivot (joint), an effort force (muscle contraction) and a resistance (weight or external load). The arrangement determines whether the lever amplifies force, speed, or range of motion.

杠杆系统由刚性杆（骨）、支点（关节）、动力（肌肉收缩）和阻力（体重或外部负荷）组成。其配置决定了杠杆是增大力量、速度还是运动幅度。

E × dE = R × dR

Mechanical Advantage (MA) = dE ÷ dR = R ÷ E

Here, E is effort, dE is effort arm length, R is resistance, and dR is resistance arm. First-class levers (e.g., neck extension) can have MA greater than, less than or equal to 1. Second-class levers (e.g., plantar flexion when standing on tiptoes) always have MA > 1, meaning they multiply force but reduce speed. Third-class levers (e.g., elbow flexion during a bicep curl) have MA < 1; they favour speed and range of motion at the expense of force – the most common arrangement in the human body.

式中 E 为动力，dE 为动力臂长度，R 为阻力，dR 为阻力臂。第一类杠杆（如颈部后伸）的 MA 可大于、等于或小于 1。第二类杠杆（如站立时提踵的跖屈）MA 始终大于 1，这意味着它们能省力但降低速度。第三类杠杆（如肱二头肌弯举时的肘屈）MA < 1；它们以牺牲力为代价换取速度和活动范围——这是人体中最常见的配置。

10. FITT Principle | FITT 原则

The FITT principle is a framework used to design and monitor training programmes. By manipulating each component, you can ensure progression and avoid plateaus.

FITT 原则是用于设计和监控训练计划的框架。通过调整每个要素，你可以确保持续进步并避免停滞不前。