📚 Case Study in Engineering: Practical Analysis of a Simple Catapult | 工程案例分析实战演练：简易弹射器设计分析
Engineering case studies give you the chance to put scientific ideas into practice. In this case study, you will follow the process of designing, building and refining a simple catapult made from everyday materials. By working through the steps, you will see how forces, energy and materials all come together in a real engineering challenge.
工程案例分析让你有机会将科学概念付诸实践。本案例学习中，你将跟着一个利用日常材料设计、制作和改进简易弹射器的全过程。通过一步步分析，你会看到力、能量和材料如何在一个真实的工程挑战中协同作用。
1. Introduction to the Engineering Design Challenge | 工程设计挑战简介
Engineers often start with a clear design brief. The challenge here is to construct a catapult that can launch a small projectile, such as a ping-pong ball or a scrunched-up paper ball, over a distance of at least 2 metres. The catapult must be stable, reusable and made without specialist tools.
工程师通常从一份明确的设计说明书开始。这里的挑战是制作一台能把乒乓球或纸团等小型抛射物发射到至少 2 米外的弹射器。该弹射器必须稳定、可重复使用，并且不用专业工具就能制作。
This project mimics the kind of problem a product designer might face when creating a simple mechanical toy with limited resources. It tests your understanding of levers, energy storage and structure.
这个项目模拟了产品设计师在资源有限条件下设计简单机械玩具时可能遇到的问题。它考验你对杠杆、能量存储和结构的理解。
All engineering case studies require you to document your process — that way you can explain why you made each decision and how you improved the outcome.
所有的工程案例分析都要求你记录过程 —— 这样你就能解释为什么做出每个决定，以及你是如何改善结果的。
2. Understanding the Problem and Setting Specifications | 理解问题与设定规格
Before building anything, you need to know exactly what the device must do. The main requirement is to reach a minimum launch distance, but you should also think about accuracy, portability and cost. A good specification might state: the catapult must weigh under 200 g, fit on an A4 sheet, and fire at least 10 times without breaking.
在动手制作之前，你需要确切知道这个装置必须做什么。主要需求是达到最低射程，但你还要考虑精度、便携性和成本。一份好的规格说明可能会写明：弹射器重量不得超过 200 克，能放在一张 A4 纸上，并且至少能连续发射 10 次而不会损坏。
Setting measurable targets helps you judge whether your design is successful later. For example, instead of saying “it should fire far”, you can aim for “90% of shots must land within a 50 cm diameter circle at 2 m distance”.
设定可测量的目标有助于你日后判断设计是否成功。例如，与其说“它应该射得远”，你可以设定“90% 的发射必须落在 2 米外直径 50 厘米的圆圈内”。
Specifications also force you to consider the user. If a younger student were to operate the catapult, the trigger mechanism must be simple and safe.
规格说明还迫使你考虑用户。如果一个年龄较小的学生操作弹射器，触发装置必须简单且安全。
3. Research and Initial Design Ideas | 调研与初步设计想法
Good engineers look at existing solutions before inventing their own. A quick search reveals that most simple catapults use a lever arm pulled back against a rubber band’s tension. Some designs have a fixed pivot, while others use a moving arm that swings forward to hit a stop, launching the projectile from a cup or spoon.
优秀的工程师在发明自己的方案之前会先研究现有的解决方案。快速查阅资料可以发现，大多数简易弹射器利用一根杠杆臂向后拉，对抗橡皮筋的张力。有些设计采用固定支点，另一些则使用一个活动臂向前摆动并撞击挡块，从而将抛射物从杯或勺子中发射出去。
Sketching three different initial ideas opens up possibilities. One idea might use a long spoon as the throwing arm and a stack of lollipop sticks for the base. Another could use a plastic bottle as the frame, but that might be less stable. A third idea might use a cardboard box to hold everything, reducing weight but risking weakness.
画出三种不同的初步构思可以打开思路。一个构想可能用长柄勺做投掷臂，用一叠冰棍棒做底座。另一个可能用塑料瓶做框架，但可能不够稳定。第三个想法可能用纸板箱容纳所有部件，虽然减轻重量但可能强度不足。
Always weigh the pros and cons of each idea against your specification before moving forward.
在进入下一步之前，始终要对照规格说明权衡每个想法的利弊。
4. Material Selection and Properties | 材料选择与特性
The materials available for the catapult are typical classroom items: wooden lollipop sticks, plastic spoons, rubber bands, masking tape, string and hot glue. Each material has different properties that affect the design.
可用于制作弹射器的材料是典型的课堂物品：木制冰棍棒、塑料勺、橡皮筋、美纹纸胶带、绳子和热熔胶。每种材料都有不同的特性，对设计产生影响。
Wooden sticks are strong in bending but can snap if overloaded. They have low density, which keeps the catapult light. Plastic spoons are flexible and can store a small amount of strain energy, but they are not as stiff as wood.
木制棍棒抗弯强度好，但过载时会折断。它们密度低，使弹射器保持轻便。塑料勺有弹性，能储存少量应变能，但刚度不如木材。
| Material | Key Property | Effect on Catapult |
|---|---|---|
| Lollipop stick (wood) | High stiffness, low density | Good for frames, resists bending |
| Plastic spoon | Moderate flexibility, tough | Acts as throwing arm and cup |
| Rubber band | High elasticity, returns to shape | Stores and releases energy |
| Masking tape / hot glue | Adhesion, easy to use | Joins parts together |
材料选择与特性
Rubber bands are the most critical component because they store the elastic potential energy. Choosing a band that is too thin might not give enough force, while an overly thick band could be hard to stretch.
橡皮筋是最关键的部件，因为它们储存弹性势能。选择太细的橡皮筋可能无法提供足够的力量，而过粗的橡皮筋则可能很难拉伸。
Engineers always consider how materials will fail. In a catapult, the glued joints where the spoon meets the base can be a weak point, so reinforcing them with tape or extra sticks improves durability.
工程师总是考虑材料会如何失效。在弹射器中，勺子和底座连接的胶合处可能是薄弱点，因此用胶带或额外的棍棒加固可以提高耐用性。
5. Forces and Energy in a Catapult | 弹射器中的力与能量
The catapult works as a lever. When you pull back the spoon, you apply an effort force at one end, the pivot acts as the fulcrum, and the projectile (load) sits at the other end. The principle of moments tells you that for the catapult to launch, the clockwise moment caused by the rubber band’s pull about the pivot must be large enough.
弹射器的工作原理类似杠杆。当你向后拉勺子时，你在一端施加一个作用力，支点充当杠杆的支点，抛射物（负载）位于另一端。力矩原理告诉我们，要使弹射器发射，橡皮筋对支点产生的顺时针力矩必须足够大。
Moment = Force × Perpendicular distance from pivot
力矩 = 力 × 到支点的垂直距离
Once released, the elastic potential energy stored in the stretched rubber band is converted into kinetic energy of the arm and the projectile. The larger the stretch (extension x), the more energy stored, as given by:
一旦释放，拉伸的橡皮筋中储存的弹性势能就会转化为弹射臂和抛射物的动能。拉伸量（伸长量 x）越大，储存的能量就越多，如下式所示：
Elastic potential energy = ½ k x²
弹性势能 = ½ k x²
where k is the spring constant of the rubber band. In practice, not all this energy goes into the projectile — some is lost as heat and sound.
其中 k 是橡皮筋的弹性系数。实际上，这些能量不会全部转移到抛射物上——部分会以热和声音的形式散失。
Understanding these energy changes helps you tune the catapult: increasing the pull-back distance or using two rubber bands in parallel raises the stored energy, giving a longer range.
理解这些能量转换有助于你调校弹射器：增加回拉距离或并联使用两根橡皮筋可提高储存能量，从而增加射程。
6. Developing a Stable Structure: Base and Frame | 开发稳定结构：底座与框架
A common problem with rubber band catapults is that the base lifts off the table when launching. This wastes energy and ruins accuracy. To prevent this, the base must be wide and heavy enough to resist the moment created by the throwing arm.
橡皮筋弹射器的一个常见问题是在发射时底座会翘离桌面。这会浪费能量并严重影响精度。为了防止这种情况，底座必须足够宽和足够重，以抵抗投掷臂产生的力矩。
Using a triangular frame made from lollipop sticks is an effective solution. Triangles are naturally rigid shapes that do not change shape when loaded — this is why they are used in bridges and roof trusses. A rectangular frame without diagonals would easily twist.
用冰棍棒制作三角形框架是一种有效的解决方案。三角形是天然刚性的形状，受力时不会变形——这就是它们在桥梁和屋顶桁架中被使用的原因。没有对角支撑的矩形框架很容易扭曲。
To make the structure even more stable, you can stick a wooden block or a heavy eraser onto the base to lower the centre of gravity. A lower centre of gravity makes the catapult harder to tip over.
为使结构更加稳固，你可以在底座上粘一块木块或一块沉重的橡皮来降低重心。重心越低，弹射器就越难倾覆。
The connection between the throwing arm and the base is the pivot. A loose pivot causes inaccurate launches, so using a split pin through drilled holes or tightly wrapping wire creates a reliable hinge.
投掷臂与底座之间的连接就是支点。松动的支点会导致发射不准，因此通过钻孔使用开口销或者紧紧缠绕金属丝可以形成一个可靠的铰链。
7. Prototyping and Gathering Data | 制作原型与收集数据
Building a first prototype lets you test whether your design actually works. Don’t expect it to be perfect — the purpose is to learn as much as possible. Make notes on how easily you can pull the spoon back, whether the rubber band slips, and where the base moves.
制作第一个原型可以检验你的设计是否真的有效。不要期望它十全十美——目的是尽可能多地获取信息。记录下拉动勺子的难易程度，橡皮筋是否滑脱，以及底座哪里会移动。
To collect useful data, plan a fair test. Choose a fixed pull-back distance, say 5 cm, and launch the same projectile ten times. Measure the distance from the front of the catapult to where the ball first lands. Record all results in a table.
要收集有用的数据，就要规划一个公平的测试。选择一个固定的回拉距离，比如 5 厘米，将同一个抛射物发射十次。测量从弹射器前端到球第一次落地的距离。将所有结果记录在表格中。
| Trial | Distance (cm) |
|---|---|
| 1 | 215 |
| 2 | 208 |
| 3 | 222 |
| 4 | 198 |
| 5 | 210 |
| 6 | 225 |
| 7 | 200 |
| 8 | 218 |
| 9 | 205 |
| 10 | 212 |
原型测试数据表
From this data you can calculate the mean distance and see the spread. If the range varies a lot, that indicates a problem with consistency, perhaps because the pull-back length varies or the projectile sits differently each time.
从这些数据可以计算出平均距离并看出离散程度。如果射程变化很大，那就表明一致性有问题，可能是因为回拉长度每次不同，或抛射物每次放置的姿势不一样。
8. Analysing Performance: Range and Precision | 性能分析：射程与精度
m. This exceeds the 2 m specification, so the prototype meets the basic range requirement.
平均射程能告诉你典型性能。根据上述数据，平均值为 (215+208+222+198+210+225+200+218+205+212) ÷ 10 = 211.3 厘米。这超过了 2 米的规格要求，因此原型满足了基本的射程要求。
Precision is about consistency. You can work out the range by subtracting the smallest value (198 cm) from the largest (225 cm), giving a spread of 27 cm. A small spread means high precision. In engineering, a device with high precision is more reliable, especially if you want to hit a target.
精度关乎一致性。你可以通过用最大值（225 厘米）减去最小值（198 厘米）来求极差，得到 27 厘米的离散范围。极差小意味着精度高。在工程中，高精度的装置更可靠，尤其在你想要击中目标时。
If the spread is too big, you can examine variables that might cause variation. Is the rubber band being stretched to exactly the same mark each time? Does the spoon release smoothly? Identifying these factors leads to design improvements.
如果离散范围太大，你可以检查可能导致变化的因素。橡皮筋每次是否拉伸到完全相同的标记处？勺子释放是否顺畅？识别这些因素有助于改进设计。
Angle of launch also affects range: theoretically, 45° gives maximum range if there is no air resistance, but in a catapult the release angle is set by when the arm hits its stop. You can adjust the stop position to control launch angle.
发射角度也会影响射程：理论上，若无空气阻力，45° 能获得最大射程，但在弹射器中，释放角度是由弹射臂撞击挡块的那一刻决定的。你可以通过调整挡块位置来控制发射角度。
9. Iterating the Design: Troubleshooting and Improvements | 设计迭代：故障排除与改进
No engineering solution is perfect on the first go. Based on test results, you can make targeted changes. If the base wobbles, add cross braces to form triangles. If the rubber band snaps, use a thicker one or pre-stretch it gradually to condition it.
没有任何工程方案能够一次就完美无缺。根据测试结果，你可以进行有针对性的修改。如果底座晃动，就添加斜撑构成三角形结构。如果橡皮筋断裂，就换一根更粗的，或者通过逐步预拉伸来“训练”它。
If the range is too short, increasing the number of rubber bands or shifting the pivot point to change the lever ratio can increase the force on the projectile. Changing the lever ratio might involve moving the spoon further through the pivot so that the effort arm is longer.
如果射程太短，增加橡皮筋的数量或移动支点以改变杠杆比，可以增大施加在抛射物上的力。改变杠杆比可能需要让勺子更深入地穿过支点，使得动力臂更长。
Keep a log of every change and its effect. For instance, “added a second rubber band parallel to the first — mean range increased to 267 cm but spread rose to 40 cm”. This evidence-based approach is at the heart of good engineering.
记录每一次改动及其效果。例如，“在第一根橡皮筋旁并联了第二根——平均射程增至 267 厘米但极差升到 40 厘米”。这种基于证据的方法正是优秀工程的核心所在。
Testing a small change at a time makes it clear which factor is responsible for any improvement, avoiding confusion from changing too many things at once.
每次只测试一项小的改动，可以清晰地看出是哪个因素带来了改善，避免同时改动太多而引起混淆。
10. Final Evaluation and Conclusion | 最终评估与结论
After several iterations, you should have a catapult that meets the specification. The final evaluation should compare the end product to the original design brief, commenting on how well each target was met. Did it reach 2 m? Was it portable? How consistent was it?
经过几次迭代，你应该拥有一台符合规格的弹射器。最终评估应该将成品与原设计说明书进行比较，评论每项目标达成得如何。它达到 2 米了吗？便携吗？一致性如何？
You also reflect on what you would do differently next time. Perhaps investing more time in strengthening the pivot would have improved accuracy, or using a stiffer material for the base would have reduced wasted energy.
你还要反思下次会做哪些不同的尝试。也许在加固支点上投入更多时间会提高精度，或者使用更硬的材料做底座会减少能量浪费。
This case study shows that engineering is more than just building — it is a cycle of defining problems, generating ideas, modelling, testing and refining. The skills you practised — selecting materials, analysing forces, collecting data and redesigning — are the same skills used by professional engineers every day.
本案例研究表明，工程不仅仅是建造——它是一个定义问题、产生创意、建模、测试和改进的循环。你所练习的技能——选择材料、分析受力、收集数据和重新设计——正是专业工程师每天使用的技能。
Presenting your findings clearly, with labelled sketches and data tables, completes the professional engineering process.
清晰展示你的发现，并附上带标注的草图和数据表格，就完成了完整的专业工程过程。
Published by TutorHao | Engineering Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图