📚 Quick Reference Guide to Formulas and Principles | 公式定理速查手册
This quick reference guide brings together the essential formulas, calculation methods, and key principles you will meet in Year 9 SQA Physical Education. Being confident with these tools helps you monitor fitness, plan safe and effective training, and understand how the body responds to exercise.
本速查手册汇集了 Year 9 SQA 体育课程中必须掌握的公式、计算方法和核心原则。熟练运用这些工具，能够帮助你监测体适能、设计安全高效的训练计划，并理解身体对运动的反应。
1. Maximum Heart Rate (MHR) | 最大心率
Your maximum heart rate is the highest number of beats per minute your heart can achieve during all‑out effort. It is estimated using a simple age‑based formula.
最大心率是你在全力运动中每分钟心跳的最高次数，可以通过一个简单的年龄公式来估算。
MHR = 220 − Age
For a 14‑year‑old student, MHR ≈ 220 − 14 = 206 bpm. This estimate gives a safe reference point for setting training zones.
以一名 14 岁学生为例，最大心率 ≈ 220 − 14 = 206 次/分。该估算值为设定训练区间提供了一个安全参照点。
Some resources also use the slightly more accurate Tanaka formula: MHR = 208 − (0.7 × Age). In Year 9, the 220 − Age method is the standard expectation.
某些资料也会使用更精确的 Tanaka 公式：MHR = 208 − (0.7 × 年龄)。在 Year 9 阶段，220 − 年龄的方法为标准要求。
2. Karvonen Formula (Target Heart Rate) | 卡沃宁公式（靶心率）
The Karvonen formula calculates a target heart rate that takes your resting heart rate (RHR) into account, giving a more personalised training intensity.
卡沃宁公式在计算靶心率时引入了安静心率（RHR），能够提供更加个性化的训练强度。
Target HR = RHR + [Intensity% × (MHR − RHR)]
Worked example: RHR = 65 bpm, MHR = 206 bpm, desired intensity = 70%.
计算示例：安静心率 = 65 次/分，最大心率 = 206 次/分，目标强度 = 70%。
(MHR − RHR) = 206 − 65 = 141 bpm.
70% of 141 = 0.70 × 141 = 98.7 ≈ 99 bpm.
Target HR = 65 + 99 = 164 bpm.
（最大心率 − 安静心率）= 206 − 65 = 141 次/分。
141 的 70% = 0.70 × 141 = 98.7 ≈ 99 次/分。
靶心率 = 65 + 99 = 164 次/分。
Using Karvonen gives a more realistic working heart rate, especially for athletes with a low resting pulse.
使用卡沃宁公式能够得出更贴合实际的工作心率，尤其适用于安静脉搏较低的运动员。
3. Heart Rate Training Zones | 心率训练区间
Training zones group intensity levels into bands based on your maximum heart rate or heart rate reserve. They help you target specific fitness gains.
训练区间根据最大心率或储备心率将强度划分成不同的区间，帮助你针对性地获得特定的体适能效益。
| Zone | %MHR | Typical purpose |
|---|---|---|
| Very light | 50–60% | Warm‑up, recovery |
| Light | 60–70% | Basic endurance, fat burning |
| Moderate | 70–80% | Aerobic fitness, cardiovascular gain |
| Hard | 80–90% | Lactate threshold, high‑intensity work |
| Maximum | 90–100% | Speed, sprint training |
中文对照：非常轻松（50–60%，热身与恢复），轻松（60–70%，基础耐力与燃脂），中等（70–80%，有氧能力与心血管获益），高强度（80–90%，乳酸阈与高强度训练），极限（90–100%，速度与冲刺训练）。
In SQA discussions, the aerobic training zone is typically 60–80% MHR, while the anaerobic zone is above 80% MHR.
在 SQA 讨论中，有氧训练区间通常取 60–80% MHR，无氧区间则高于 80% MHR。
4. Body Mass Index (BMI) | 身体质量指数
BMI is a quick screening tool that relates your body mass to your height. It helps identify whether you are underweight, a healthy weight, overweight, or obese.
BMI 是一种将体重与身高关联的快速筛查工具，用于判断体重不足、健康体重、超重或肥胖。
BMI = Weight (kg) / Height² (m)
Example: a student weighing 55 kg with a height of 1.65 m.
Height² = 1.65 × 1.65 = 2.7225 m².
BMI = 55 / 2.7225 ≈ 20.2 kg/m² (healthy range).
示例：一名学生体重 55 kg，身高 1.65 m。
身高² = 1.65 × 1.65 = 2.7225 m²。
BMI = 55 / 2.7225 ≈ 20.2 kg/m²（健康范围）。
- Underweight: below 18.5
- Healthy weight: 18.5 – 24.9
- Overweight: 25 – 29.9
- Obese: 30 and above
中文分类：体重不足（低于 18.5）、健康体重（18.5–24.9）、超重（25–29.9）、肥胖（30 及以上）。
BMI does not distinguish between muscle and fat, so very muscular individuals may be classified as overweight even with low body fat.
BMI 无法区分肌肉与脂肪，因此肌肉发达的人即使体脂很低也可能被划为超重。
5. Speed, Distance and Time | 速度、距离与时间
The relationship between speed, distance and time is fundamental in many performance analyses and fitness tests.
速度、距离和时间之间的关系是许多运动表现分析和体适能测试的基础。
Speed = Distance / Time
If you complete a 1500 m run in 360 seconds, your average speed = 1500 / 360 ≈ 4.17 m/s.
如果你用 360 秒跑完 1500 米，平均速度 = 1500 / 360 ≈ 4.17 米/秒。
Rearranging the formula gives:
Distance = Speed × Time and Time = Distance / Speed.
变换公式可得：距离 = 速度 × 时间，时间 = 距离 / 速度。
Coaches use these equations to set pacing strategies, estimate finish times, and design interval training accurately.
教练利用这些公式来制定配速策略、预估完赛时间，并精准设计间歇训练。
6. Caloric Expenditure Using METs | 用代谢当量（MET）计算热量消耗
Metabolic Equivalent of Task (MET) expresses the energy cost of physical activities. One MET is the energy used while sitting quietly (≈1 kcal/kg/hour).
代谢当量（MET）表示身体活动的能量消耗。1 MET 相当于安静坐着时的能量消耗（约 1 千卡/公斤/小时）。
Calories burned ≈ MET × Body mass (kg) × Time (hours)
Example: jogging at 7 MET for 30 minutes by a 55 kg student.
Time = 0.5 hours.
Calories burned = 7 × 55 × 0.5 = 192.5 kcal.
示例：一名 55 公斤的学生以 7 MET 慢跑 30 分钟。
时间 = 0.5 小时。
热量消耗 = 7 × 55 × 0.5 = 192.5 千卡。
- Walking (5 km/h): ~3.5 MET
- Jogging (8 km/h): ~8 MET
- Cycling (moderate): ~6 MET
- Swimming (freestyle, moderate): ~7 MET
- Football (casual): ~7 MET
中文常见活动 MET 值：步行（5 km/h）约 3.5，慢跑（8 km/h）约 8，中等强度骑行约 6，自由泳中等速度约 7，休闲足球约 7。
This method helps you compare energy demands across activities and understand why some exercises burn more energy.
该方法有助于对比不同活动的能量需求，并理解为什么某些运动消耗更多能量。
7. FITT Principle | FITT 原则
The FITT principle provides a simple framework for planning an exercise programme. Each letter describes a variable you can adjust to keep training safe and effective.
FITT 原则为制定锻炼计划提供了一个简单的框架，每个字母代表一个你可以调整的变量，以确保训练安全有效。
- Frequency – how often you exercise (e.g. 3 times per week).
- Intensity – how hard you work (e.g. heart rate zone, RPE).
- Time – how long a session lasts (e.g. 30 minutes).
- Type – the kind of activity (e.g. running, cycling, team games).
中文释义：频率——锻炼频次（如每周 3 次）；强度——运动难度（如靶心率区间、自觉用力程度）；时间——每次时长（如 30 分钟）；类型——活动方式（如跑步、骑行、团队项目）。
Applying FITT ensures you gradually match the activity to your current fitness level and personal goals.
运用 FITT 原则可确保你逐步将活动与当前体适能水平和个人目标相匹配。
8. SPORT Principles of Training | 训练的 SPORT 原则
The SPORT acronym is widely used in SQA Physical Education to remember the key principles that make training effective and safe.
在 SQA 体育课程中，SPORT 这一首字母缩写被广泛用来记忆那些使训练高效且安全的核心原则。
- Specificity – training must match the demands of the sport or goal.
- Progression – gradually increase workload as fitness improves.
- Overload – work above your normal level to stimulate adaptation (use FITT to apply overload).
- Reversibility – fitness gains are lost when you stop training (‘use it or lose it’).
- Tedium – introduce variety to avoid boredom and maintain motivation.
中文释义：针对性——训练必须符合运动项目或个人目标的要求；渐进性——随着体适能提高逐步增加负荷；超负荷——在高于常态的水平下训练以激发适应（可运用 FITT 实现超负荷）；可逆性——停训后体适能水平的提升会消退（“用进废退”）；趣味性——增加变化避免枯燥，保持训练动机。
Understanding SPORT helps you design a balanced, long‑term training plan and explain why athletes need rest and variety.
理解 SPORT 原则有助于你设计平衡的长期训练计划，并解释为什么运动员需要休息和多样化训练。
9. Rating of Perceived Exertion (RPE) | 自觉用力程度分级（RPE）
RPE is a subjective scale that lets you rate how hard you feel the exercise is. It is a simple, equipment‑free way to monitor intensity.
RPE 是一种主观量表，让你可以评价自己感觉运动有多费力，是无需设备即可监测强度的简便方法。
The original Borg scale runs from 6 (no exertion at all) to 20 (maximal exertion). A quick estimation links RPE to heart rate.
最初的 Borg 量表范围为 6（完全不费力）至 20（最大努力程度）。有一种快速估算法将 RPE 与心率关联。
Estimated HR ≈ RPE × 10
If you rate an effort as 13 (somewhat hard), your estimated HR ≈ 13 × 10 = 130 bpm. This works reasonably well for many individuals.
如果你将运动感觉评为 13（稍费力），那么估算心率 ≈ 13 × 10 = 130 次/分。对很多人来说，这一估计相当符合。
A simplified CR‑10 scale (0–10) is also used, where 0 is nothing at all and 10 is very, very hard. In SQA practical work, both scales help you listen to your body.
还有一种简化的 CR‑10 量表（0–10），0 表示毫无感觉，10 表示极度费力。在 SQA 实践操作中，这两种量表都可以帮助你倾听身体的反馈。
10. Daily Fluid Intake Estimation | 每日液体摄入量估算
Staying hydrated is vital for performance, concentration, and recovery. A simple formula estimates baseline daily needs.
保持充足水分对运动表现、注意力和恢复至关重要。一个简单的公式可以估算每日基础需求。
Daily fluid (ml) ≈ Body mass (kg) × 30 to 40 ml
A 55 kg student: minimum ≈ 55 × 30 = 1650 ml; upper limit ≈ 55 × 40 = 2200 ml. Activity, heat, and sweat loss increase this requirement significantly.
一名 55 公斤的学生：最小值 ≈ 55 × 30 = 1650 毫升；上限 ≈ 55 × 40 = 2200 毫升。运动、高温和出汗会显著增加这一需求量。
During intense exercise you may lose 0.5–2+ litres of sweat per hour. Weighing yourself before and after a session helps personalise replacement: drink 1.2–1.5 litres for every 1 kg of body mass lost.
剧烈运动时每小时可流失 0.5–2 升以上汗液。训练前后称体重有助于个性化补水：每丢失 1 公斤体重，应补充 1.2–1.5 升液体。
Using a hydration plan built on these numbers reduces the risk of dehydration and supports decision‑making in training and competition.
根据以上数字制定补水方案，可以降低脱水风险，并在训练和比赛中为决策提供支持。
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