📚 Year 8 SQA Physical Education: Quick Reference Handbook of Formulas & Principles | Year 8 SQA 体育：公式定理速查手册
This handbook brings together the key formulas, numerical principles, and applied science concepts that underpin your Year 8 SQA Physical Education course. Whether you are calculating your target heart rate, estimating energy expenditure, or applying the principles of training, these tools will sharpen your understanding of how the body responds to exercise and how performance can be measured and improved.
本手册汇集了 Year 8 SQA 体育课程中核心的公式、数值原理及应用科学概念。无论你是在计算目标心率、估算能量消耗，还是应用训练原则，这些工具都将加深你对身体如何应对运动以及如何衡量和提升运动表现的理解。
1. Maximum Heart Rate (MHR) Formula | 最大心率 (MHR) 公式
Your Maximum Heart Rate is the highest number of beats per minute your heart can achieve during all‑out effort. A simple age‑based estimation is used worldwide.
最大心率是你在全力运动中每分钟心跳能达到的最高次数。全球通用一个基于年龄的简易估算公式。
MHR = 220 - age
For a Year 8 student typically aged 12‑13, the estimated MHR is 208‑207 bpm. This formula gives a baseline, but actual MHR can vary with genetics and fitness level.
对于通常 12‑13 岁的 Year 8 学生，估算最大心率为 208‑207 次/分。该公式提供了一个基准，但实际最大心率会因遗传和体能水平而异。
Remember to use this number only for exercise planning; never push yourself to MHR without qualified supervision.
谨记，这个数值仅用于运动计划；未经专业指导，切勿强迫自己达到最大心率。
2. Target Heart Rate Zone (Karvonen Formula) | 目标心率区间（卡沃宁公式）
The Karvonen method uses your resting heart rate (RHR) to personalise training intensity. It calculates a heart rate reserve, then adds a percentage of it back to RHR.
卡沃宁方法利用你的静息心率 (RHR) 来个性化训练强度。它先计算心率储备，然后按百分比加回到静息心率上。
Target HR = RHR + (Intensity % × (MHR - RHR))
Example for a 13‑year‑old with RHR 70 bpm and 65% intensity: MHR = 220‑13 = 207; reserve = 207‑70 = 137; target = 70 + (0.65 × 137) ≈ 159 bpm.
以一名 13 岁、静息心率 70 次/分、强度 65% 为例：MHR = 220‑13 = 207；储备 = 207‑70 = 137；目标心率 = 70 + (0.65 × 137) ≈ 159 次/分。
Typical zones: moderate 50‑65%, vigorous 65‑85%. Using this formula helps you train in the correct energy system.
典型区间：中等强度 50‑65%，高强度 65‑85%。使用此公式可确保你在正确的能量系统中训练。
3. Body Mass Index (BMI) | 身体质量指数 (BMI)
BMI is a screening tool that compares weight to height. It does not measure body fat directly but is used in school fitness assessments to classify underweight, healthy weight, overweight, and obesity.
BMI 是一种比较体重与身高的筛查工具。它不能直接测量体脂，但在学校体质评估中用于划分过轻、健康体重、超重和肥胖。
BMI = weight (kg) ÷ height² (m²)
For example, a student weighing 45 kg with height 1.55 m: BMI = 45 ÷ (1.55 × 1.55) = 45 ÷ 2.4025 ≈ 18.7 kg/m², which is within the healthy range for children (consult age‑specific centile charts).
例如，一名学生体重 45 kg，身高 1.55 m：BMI = 45 ÷ (1.55 × 1.55) = 45 ÷ 2.4025 ≈ 18.7 kg/m²，这在儿童健康范围内（需参考年龄别百分位图表）。
Because muscle weighs more than fat, athletic youngsters may have a higher BMI without excess body fat. Always interpret BMI alongside other fitness measures.
由于肌肉比脂肪重，爱运动的青少年可能 BMI 偏高但并无过多体脂。务必结合其他体质指标来解读 BMI。
4. Speed, Distance, Time Relationship | 速度、距离、时间关系
In many PE activities, you will measure how fast you run, swim, or cycle. These three variables are linked by a straightforward formula.
在许多体育活动中，你将测量跑步、游泳或骑行的速度。这三个变量由一个简单的公式连接。
Speed = Distance ÷ Time
Units must match. If you run 100 metres in 14 seconds, speed = 100 ÷ 14 ≈ 7.14 m/s. To convert m/s to km/h, multiply by 3.6: 7.14 m/s × 3.6 ≈ 25.7 km/h.
单位必须匹配。如果你在 14 秒内跑完 100 米，速度 = 100 ÷ 14 ≈ 7.14 米/秒。要将米/秒转换为公里/小时，乘以 3.6：7.14 米/秒 × 3.6 ≈ 25.7 公里/小时。
= Distance ÷ Speed. Practice these rearrangements so you can calculate splits and pacing.
变形公式：距离 = 速度 × 时间；时间 = 距离 ÷ 速度。练习这些变形，以便计算分段用时和配速。
5. Force, Mass, and Acceleration (Newton's Second Law) | 力、质量与加速度（牛顿第二定律）
Every time you sprint, jump, or kick a ball, you apply force. The relationship is fundamental to biomechanics.
每次冲刺、跳跃或踢球时，你都在施加力。这个关系是生物力学的基础。
Force = Mass × Acceleration (F = m a)
omentum. To jump higher, you push against the ground with greater force over a short time.
在体育中，我们常讨论冲量：力 × 时间 = 动量的变化。要想跳得更高，你需要在短时间内以更大的力蹬地。
Mass is measured in kilograms (kg), acceleration in metres per second squared (m/s²), and force in newtons (N). A student with mass 50 kg accelerating at 3 m/s² experiences a net force of 150 N.
质量以千克 (kg) 计，加速度以米每二次方秒 (m/s²) 计，力以牛顿 (N) 计。一名 50 kg 的学生以 3 m/s² 加速时，所受净力为 150 N。
6. Work and Power in Physical Activity | 体育活动中的功与功率
Work measures energy transfer when a force moves an object. Power tells you how quickly that work is done – crucial for explosive sports.
功衡量力使物体移动时的能量转移。功率则表示做功的快慢——对爆发性运动至关重要。
Work = Force × Distance moved in direction of force
Power = Work ÷ Time
If you lift a 20 kg weight (≈200 N) through 0.5 m, work = 200 × 0.5 = 100 J. If you do this in 0.8 s, power = 100 ÷ 0.8 = 125 W.
若将 20 kg 的重物（≈200 N）举起 0.5 m，功 = 200 × 0.5 = 100 J。若在 0.8 s 内完成，功率 = 100 ÷ 0.8 = 125 W。
In running or cycling, power output relates directly to speed and can be improved through strength and technique.
在跑步或骑行中，输出功率与速度直接相关，并可通过力量和技术加以提升。
7. Estimating Energy Expenditure (METs) | 能量消耗估算 (METs)
Physical activities are often graded by Metabolic Equivalent of Task (MET). 1 MET is the energy you use while sitting quietly.
体育活动常用代谢当量 (MET) 来分级。1 MET 即静坐时的能量消耗水平。
Calories burned per minute ≈ METs × (weight in kg ÷ 60)
For example, brisk walking at 5 km/h is about 3.8 METs. For a 45 kg student, calories per minute ≈ 3.8 × (45 ÷ 60) ≈ 2.85 kcal/min.
例如，以 5 km/h 快走约为 3.8 METs。对一名 45 kg 的学生，每分钟消耗 ≈ 3.8 × (45 ÷ 60) ≈ 2.85 千卡/分。
More vigorous activities (e.g. basketball 6.5 METs, running at 8 km/h 8.0 METs) burn proportionally more. This formula helps you understand energy balance in health‑related fitness.
更剧烈的活动（如篮球 6.5 METs，以 8 km/h 跑步 8.0 METs）消耗能量成比例增加。该公式有助于理解健康体适能中的能量平衡。
8. The FITT Principle of Training | 训练的 FITT 原则
The FITT principle is not a numerical equation but a set of four variables you manipulate to design an effective exercise programme. Every formula above plugs into one of its components.
FITT 原则不是数学公式，而是你用来设计有效锻炼计划的四个可调控变量。上述所有公式都对应其中的某个组成部分。
- Frequency: how often you train per week.
- 频率：每周训练的次数。
- Intensity: how hard you work (measured by HR, %1RM, or METs).
- 强度：训练的努力程度（用心率、%1RM 或 METs 衡量）。
- Time: duration of each session.
- 时间：每次训练的时长。
- Type: the kind of exercise (aerobic, anaerobic, flexibility, etc.).
- 类型：运动种类（有氧、无氧、柔韧性等）。
Applying FITT alongside your target heart rate calculations creates a personalised, progressive training plan.
将 FITT 与目标心率计算结合运用，就能制定出个性化、循序渐进的训练计划。
9. Agility and Reaction Time | 敏捷性与反应时间
Agility combines speed, balance, and coordination. While no single formula defines it, you can measure improvement using time in shuttle runs or Illinois agility test.
敏捷性是速度、平衡和协调的结合。虽然没有单一公式可以定义它，但你可以通过折返跑或伊利诺伊敏捷性测试的时间来衡量进步。
Reaction time is the interval between a stimulus and your first movement. Average simple reaction time for visual stimuli is ~0.2 s for trained youth.
反应时间是从刺激出现到你开始动作的间隔。对于受过训练的青少年，视觉简单反应时间平均约为 0.2 秒。
Agility index = (fastest trial time − slowest trial time) ÷ average time
Tracking this index over weeks shows how consistency and speed improve. Lower values indicate more reliable performance.
连续数周追踪该指数，可反映速度与稳定性的提升。数值越低表示表现越可靠。
10. Balance and Centre of Mass | 平衡与质心
Stability depends on the position of your centre of mass (CoM) relative to your base of support. The lower your CoM and the wider your base, the more stable you are.
稳定性取决于你的质心 (CoM) 相对于支撑面的位置。质心越低、支撑面越宽，你就越稳定。
In gymnastics or rugby, you instinctively lower your stance to resist being tackled. In biomechanics, the moment of a force causing rotation is torque:
在体操或橄榄球中，你会本能地降低站姿以抵抗擒抱。在生物力学中，使身体旋转的力的力矩称为扭矩：
Torque = Force × perpendicular distance from pivot
When you hold a plank, your CoM must stay within your hands and feet. Understanding torque helps you adjust body levers for better balance.
做平板支撑时，你的质心必须保持在手和脚的范围之内。理解扭矩有助于你调整身体杠杆以获得更好的平衡。
11. Aerobic and Anaerobic Thresholds | 有氧与无氧阈值
Your body switches energy systems as exercise intensity increases. The aerobic threshold is the point where lactate begins to accumulate slightly; the anaerobic threshold is where it rises sharply.
随着运动强度增加，你的身体会切换供能系统。有氧阈值是乳酸开始轻度积累的点；无氧阈值则是乳酸急剧上升的点。
You can estimate anaerobic threshold heart rate roughly at 80‑90% of MHR. For a 13‑year‑old, that is about 166‑186 bpm. Training near this threshold improves lactate clearance and endurance.
你可以粗略地将无氧阈值心率估计为最大心率的 80‑90%。对 13 岁学生而言，大约在 166‑186 次/分。在该阈值附近训练可提升乳酸清除能力和耐力。
Use the talk test: at aerobic threshold you can speak comfortably; at anaerobic threshold you can manage only a few words.
使用说话测试：在有氧阈值，你可以自如交谈；在无氧阈值，你只能说几个词。
12. Hydration and Body Water Loss | 水分补充与身体失水
Fluid loss through sweat can impair performance and concentration. Weighing yourself before and after exercise provides a practical formula.
通过汗液流失水分会损害运动表现和注意力。运动前后称重提供了一个实用的公式。
Fluid loss (L) = (pre‑exercise weight − post‑exercise weight) kg
Rehydration volume = fluid loss × 1.5
For every kg lost, you should drink approximately 1.5 litres over the next few hours. This replaces ongoing fluid turnover and offsets dehydration.
每减轻 1 kg 体重，应在接下来的几小时内补充约 1.5 升液体。这补偿了持续的液体周转并纠正脱水。
Monitor urine colour: pale straw indicates good hydration; dark yellow suggests you need more fluids.
观察尿液颜色：淡稻草色表示水分充足；深黄色提示需要补充更多水分。
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