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This may sound rather vague on its own so I will explain with examples.

The solid booster rockets used by NASA space shuttle used a central bore design because it had a certain characteristic on burn rate and thrust.

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If this data was to be acquired only form experimentation like burning test rockets and not deriving any mathematical relation between bore design and thrust then would it be considered sound engineering?

Are any designs based solely on data from trial and error used in critical mainstream engineering?

Like we use it just because it works and do not investigate why it works like that because it's very complex to understand but still easier to implement.

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  • $\begingroup$ Often as not, your complete theoretical understanding can be thrown out the window because you still have to do what the regs say. And the regs on things like building fishing boats and bridges are mostly based on when things went wrong. Look at the early power grid. We had electrified cities and designed and built hundreds of different types of electrical machines and none of those involved had a clue as to what electricity was. $\endgroup$ – Phil Sweet Mar 30 '18 at 18:45
  • $\begingroup$ They built some beautiful buildings with trial and error, the mathematics had to be invented so the theory could catch up. One example of how theory catches up with the real world is the relatively « new » science of fatigue analysis after a series of serious plane crashes... $\endgroup$ – Solar Mike Mar 30 '18 at 19:43
  • $\begingroup$ Depends, not all things need to be optimozed the hell out. However, theories help when you need to do optimisation. So if you launch rockets then it does help. Manny things are not like that so they dont need this. $\endgroup$ – joojaa Mar 30 '18 at 20:27
  • $\begingroup$ this is really overly broad. Th simple answer is "of course" plenty of sound engineering design relies on empirical data. Are you seeking cases where we literally have no clue what the underlying physics is and don't care to even bother to investigate what that physics might be? $\endgroup$ – agentp Mar 30 '18 at 21:46
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    $\begingroup$ As one of my lecturers said many years ago, "if the maths doesn't fit reality, the maths is wrong". Experimentation will always be a part of engineering. We are not that intelligent, individually or as a group, to be able to devise theory & engineering systems without experimentation. As others have commented here, sometimes the theory is developed after experimentation & observation of what actually happens. $\endgroup$ – Fred Mar 31 '18 at 8:03
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Are any designs based solely on data from trial and error used in critical mainstream engineering?

Usually not. And the reason is that trial and error is expensive and time consuming. As engineers, we are always working on projects with a budget and a deadline. Take your rocket example. Rockets are expensive. For sake of argument, let's just say it's $1 million per rocket test. You can't afford to build rocket after rocket after rocket solely by trial and error. You'll go through your budget very quickly.

Does every engineering design needs to have a complete theoretical backing?

Again, usually not. And the reason is that developing complete theoretical understanding is also expensive. You could hire army of PhD researchers to come up with an incredibly detailed model and buy giant supercomputers to simulate it. But an engineer with a PhD will cost $100k/year just in salary. If your model is so detailed that you need a team of 20 researchers working for years to come up with the model, it would be cheaper to just run a test.

So there is a balance. You try to come up with a model that is sophisticated enough that it explains the majority of the behavior, but simple enough that you don't break the bank coming up with it. Your model won't be perfect, so you run a few experiments to fill in the holes in the theory, but not so many that you kill the budget. The key decision is deciding the tradeoff between model and experiments.

In fact, if I had to describe what engineers do in exactly one word, that word is "tradeoffs". In every engineering decision, there is always a balance between multiple competing objectives, and the engineers job is to make the best tradeoff.

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  • $\begingroup$ excellent exposition. $\endgroup$ – niels nielsen May 17 at 6:08
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For complex and expensive systems you usually want to have an understanding of its behavior, cast in models. To model a system (or part of it), a complete theoretical understanding is usually not required.

You should, however, have a complete knowledge of the phenomena that act on your system. Then you identify the key phenomena and, if it does not yet exist, a theoretical understanding of those phenomena to a degree required to describe your system accurately enough.

The actual work is in finding out which phenomena are important and which are not, what effects to include, what effects to neglect, what depth of understading is actually required, which effects need to be understood, which effects are too expensive to understand now but can be compensated by overly conservative design decisions, etc. Those are some of the tradeoffs that @DanielKiracofe mentions in his answer.

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