Do engineers working on high-tech applications make approximations?

[EddiePhys]

I'll start by saying I'm not an engineer. If I understand correctly, analytical models engineers create for their systems or machines generally involve some degree of approximation or simplification. Factors that are deemed sufficiently small when it comes to determining how the system works are ignored

1. I wanted to know if what I said is accurate
2. Is the same true for high-tech applications? Obviously at the minimum the accuracy of the models here will be greater, but are there high-tech applications where we apply the laws of physics exactly? (Ignoring the fact that the laws themselves might have some degree of approximation)

 

[PeroK]

Everything in physics and engineering is an approximation.

 

[EddiePhys]

Everything in physics and engineering is an approximation.

At least for the physics part of this — isn't this a matter of opinion? Remember reading at some point that we simply do not know (at least for modern physics theories, not classical) if they are approximations or are fundamental and that physicists may have differing views about this

 

[Chestermiller]

At least for the physics part of this — isn't this a matter of opinion? Remember reading at some point that we simply do not know (at least for modern physics theories, not classical) if they are approximations or are fundamental and that physicists may have differing views about this

The physical parameters involved in describing the system behavior in both physics and engineering (applied physics) cannot even be measured exactly. Do you think you can even measure length exactly (or is there an extra atom at the end of the object you are measuring)? Name one thing you can measure exactly.

Even if you could measure things exactly (which you can't), the physical laws themselves are not exact. We have not yet even resolved the inconsistencies between relativistic physics and quantum mechanics.

So, in short, nothing is exact.

 

[Filip Larsen]

In both physics and engineering (and other fields that use applied mathematics to describe the real world) we use (mathematical) models that approximate the real world phenomenon in a way that is useful for us. The approximations primarily express that we want to keep the models as simple as possible and that we do not have infinite knowledge of the actual state of the particular part of the world the system models. Quite often even very simple models can be very useful for specific purposes and there are also often techniques to cope with approximations. For instance, in control theory the dynamics of a system is often described using a approximate linear model but is then coupled with feed-back control that allows the controlled system to cope with (unknown) variations in its state.

And in general in physics and engineering a statistical approach is very often used to describe the effect and limits of approximations meaning we often are able to establish fairly good idea of how accurate a particular model is for a particular purpose.

 

[Dullard]

I'm wondering what 'high-tech' means. I agree that Engineering involves a lot of approximation, but that's a feature - not a bug. Engineering (Design) is about optimizing on specific axes. It might be cost, weight, energy consumption, temperature range, etc., or some combination of those; There are always trade-offs. Depending on what you're up to, some approximations need to be as accurate as possible; Others: not so much. As an old guy (I can fly a slide-rule), I notice that my junior co-workers are much better at running elaborate simulations than they are at determining if it's necessary to do so. Many struggle with the difference between precision and accuracy. I just realized: I sound like every old guy, ever.

 

[PeroK]

At least for the physics part of this — isn't this a matter of opinion? Remember reading at some point that we simply do not know (at least for modern physics theories, not classical) if they are approximations or are fundamental and that physicists may have differing views about this

Classical theories are exact, although generally an approximation to modern theories. Modern theories are generally messier with approximations build in: like renormalization in QFT (Quantum Field Theory).

For example, in the classical theory of the scattering of charged particles, we have an exact law of nature (Coulomb's law) and can model the scattering as a precise classical trajectory. This can be done by any competent undergraduate student.

In modern QFT, the scattering is approximated theoretically by a scattering matrix (which looks at the initial and final states, with the scattering itself as something of a black-box). Then the scattering probabilities (cross-section) are calculated to whatever level of precision you need. This entails calculations of excrutiating complexity. Even so, you are calculating the approximate numerical answer to an approximate theoretical model!

I'm not sure in what sense QFT could be described as an exact theory, in the way that Maxwell's electrodynamics is theoretically exact.

 

[jack action]

Any specification will be a value±deviation, whether this deviation is specified or implied. The "high-tech applications" just have smaller deviations.

A perfect example is comparing fasteners for the aerospace industry versus those for general purposes. They both look the same, but the ones for the aerospace industry are manufactured in such a controlled environment, allowing for greater precision of the expected results (but never exact).

 

[russ_watters]

You can specify a problem in such a way that the math gives an exact value, but there are always simplifying assumptions constraining the problem. As Jack said, answering 'how exact does this need to be?' is part of the problem.

 

[Baluncore]

Perfection is the enemy of progress.

 

[DaveE]

My favorite quote from one of my EE profs:
"Engineering is the art of approximation" - R. D. Middlebrook

It's not just that you can't be perfect in engineering, it's that you probably shouldn't even try to get too close to perfect. That's not what you are being paid to do. Part of the job is always to determine the level of modelling accuracy required. And yes, even for the highest of high tech. In my case satellite power supplies and some of the best lasers you can buy.

 

[EddiePhys]

The physical parameters involved in describing the system behavior in both physics and engineering (applied physics) cannot even be measured exactly. Do you think you can even measure length exactly (or is there an extra atom at the end of the object you are measuring)? Name one thing you can measure exactly.

Even if you could measure things exactly (which you can't), the physical laws themselves are not exact. We have not yet even resolved the inconsistencies between relativistic physics and quantum mechanics.

So, in short, nothing is exact.

Okay, fair enough. I suppose I should've been clearer in my question, but what I wanted to know is: Leaving aside the issue of approximations inherent in the laws of physics and measurement uncertainty, do you, in your work as an engineer usually make additional approximations from your end as you analyze the system you are working on, and if this is the case even for high-tech applications.

 

[EddiePhys]

Classical theories are exact, although generally an approximation to modern theories. Modern theories are generally messier with approximations build in: like renormalization in QFT (Quantum Field Theory).

For example, in the classical theory of the scattering of charged particles, we have an exact law of nature (Coulomb's law) and can model the scattering as a precise classical trajectory. This can be done by any competent undergraduate student.

In modern QFT, the scattering is approximated theoretically by a scattering matrix (which looks at the initial and final states, with the scattering itself as something of a black-box). Then the scattering probabilities (cross-section) are calculated to whatever level of precision you need. This entails calculations of excrutiating complexity. Even so, you are calculating the approximate numerical answer to an approximate theoretical model!

I'm not sure in what sense QFT could be described as an exact theory, in the way that Maxwell's electrodynamics is theoretically exact.

Hmm, okay. I should've been a bit clearer in my question about this, but what I wanted to know is: Leaving aside the issue of approximations inherent in the laws of physics, do you, in your work as an engineer usually make additional approximations from your end as you analyze the system you are working on, and if this is the case even for high-tech applications.

 

[EddiePhys]

Any specification will be a value±deviation, whether this deviation is specified or implied. The "high-tech applications" just have smaller deviations.

A perfect example is comparing fasteners for the aerospace industry versus those for general purposes. They both look the same, but the ones for the aerospace industry are manufactured in such a controlled environment, allowing for greater precision of the expected results (but never exact).

Understood that there's measurement uncertainty. What I wanted to know is: Leaving aside this issue, do you, in your work as an engineer usually make additional approximations from your end as you analyze the system you are working on, and if this is the case even for high-tech applications.

 

[EddiePhys]

In both physics and engineering (and other fields that use applied mathematics to describe the real world) we use (mathematical) models that approximate the real world phenomenon in a way that is useful for us. The approximations primarily express that we want to keep the models as simple as possible and that we do not have infinite knowledge of the actual state of the particular part of the world the system models. Quite often even very simple models can be very useful for specific purposes and there are also often techniques to cope with approximations. For instance, in control theory the dynamics of a system is often described using a approximate linear model but is then coupled with feed-back control that allows the controlled system to cope with (unknown) variations in its state.

And in general in physics and engineering a statistical approach is very often used to describe the effect and limits of approximations meaning we often are able to establish fairly good idea of how accurate a particular model is for a particular purpose.

In the context of which field of engineering are you talking about? You mention control theory so I'm guessing EE right.. I wanted to know if this is the case for mechanical engineering as well, and whether mechanical engineers usually make approximations when studying their systems and designing machines

 

[EddiePhys]

I'm wondering what 'high-tech' means. I agree that Engineering involves a lot of approximation, but that's a feature - not a bug. Engineering (Design) is about optimizing on specific axes. It might be cost, weight, energy consumption, temperature range, etc., or some combination of those; There are always trade-offs. Depending on what you're up to, some approximations need to be as accurate as possible; Others: not so much. As an old guy (I can fly a slide-rule), I notice that my junior co-workers are much better at running elaborate simulations than they are at determining if it's necessary to do so. Many struggle with the difference between precision and accuracy. I just realized: I sound like every old guy, ever.

Would it be fair to say though that in your work as a mechanical engineer (I'm guessing mechanical because of those tradeoffs you mentioned) you need to make some degree of approximations (beyond those inherent in the laws of physics) in your analysis of your machines and systems

 

[EddiePhys]

You can specify a problem in such a way that the math gives an exact value, but there are always simplifying assumptions constraining the problem. As Jack said, answering 'how exact does this need to be?' is part of the problem.

Within the context of which branch of engineering are you talking? To clarify my initial question a bit: In your work as an engineer, when you're analysing your system, do you usually introduce additional simplifications beyond those inherent in the laws of physics?

 

[The Fez]

There will always bee approximations in any engineering application, no matter how "high tech" it is. For instance, starting with the material you are working with, whether simple mass-produced steel beams, to aluminum, to titanium to some exotic nickel super alloy, you can't even know the actual strength of the material to any great accuracy, so you're using established minimum values, often 20% or more lower than the actual strength. Then you have actual loads on whatever, which also need to be approximated. Building a bridge? How much does a car weigh? How many cars are on the bridge at any given time? What is the wind? Did it snow and now there's a foot on the bridge, and you have to account for that. So many different things you have to approximate.

Now maybe what you mean by high-tech, there are different levels of how approximate you are, depending on a lot of factors. In the bridge example, you can't test every beam and every load, so maybe you make things 2x bigger than it needs to be, or 5x, or 10x. Something that can be rigorously tested and controlled might only need to be 1.1x bigger.

 

[Baluncore]

To clarify my initial question a bit: In your work as an engineer, when you're analysing your system, do you usually introduce additional simplifications beyond those inherent in the laws of physics?

Yes, always.

There is usually a design code, that is a set of tables or simplified equations that will give reliable solutions. Engineers follow the code because it is too expensive to analyse every case and carry the liability of a failure.

The design must be on the safe side of the computations. Great accuracy is unimportant since the safety margins allowed, are greater than the error in the analysis, the computational model, or the material quality.

 

[gmax137]

There's another kind of approximation that shows up in specification "interface requirements." Suppose my calculations use the weight of some components, and one of those components is to be provided by another company. I don't know how much their piece will weigh (in fact, I might not know who will be providing it yet). So I can assume a limiting value (say 5 tons) and use that in my calculation. Then I create an interface requirement: "component X must weigh less than 5 tons."

This doesn't have to be weight, it could be anything:
"pump X must deliver at least 600 gpm at 1000 psi"
"the ambient temperature in room XYZ must be maintained below 104 F"

The subsequent calculations are "conservative" - they assume limiting values for all of the inputs. The whole thing is an approximation that may not look anything like the final "real world" scenario.

 

[DaveE]

Even if you do want to be precise in engineering, you will quickly find that it's impossible. No, not Heisenberg, lack of knowledge about the components you are using.

- Exactly what is the yield strength of that aluminum strut?
- How much pressure will your pump produce after 10kHrs of service in only partially predictable conditions?
- How much ESR does the 573rd capacitor on the assembly line have?
- How will o-ring compliance affect the seal in a rocket engine after it's been sitting in cold, but unpredictable, temperatures?

Honestly, sometimes I think engineers are paid to guess. But they have to guess really well.
Key phrases: "worst case analysis", "failure modes and effects analysis", "return on investment", "non-recuring engineering costs", "time to market".
This is the real world, where safe and good enough are the goals.

Plus, when the specifications of the machine you bought say <40^oC ambient, you might not read it or care, but the design engineers do. Things can be borderline and sketchy beyond the specs; all bets are off.

 

[EddiePhys]

Yes, always.

There is usually a design code, that is a set of tables or simplified equations that will give reliable solutions. Engineers follow the code because it is too expensive to analyse every case and carry the liability of a failure.

The design must be on the safe side of the computations. Great accuracy is unimportant since the safety margins allowed, are greater than the error in the analysis, the computational model, or the material quality.

Okay. You're a mechanical engineer?

 

[Baluncore]

Okay. You're a mechanical engineer?

Sometimes, but often an electronics engineer, microprogrammer, or a geologist. What difference does it make, these days, there is a code for everything, with a tolerance or a safety factor, that allows us to ignore the irrelevant minor influences.

 

[EddiePhys]

Sometimes, but often an electronics engineer, microprogrammer, or a geologist. What difference does it make, these days, there is a code for everything, with a tolerance or a safety factor, that allows us to ignore the irrelevant minor influences.

Interesting. But what you said is applicable even for the projects you've taken on that are purely mechanical as well right?

 

[EddiePhys]

My favorite quote from one of my EE profs:
"Engineering is the art of approximation" - R. D. Middlebrook

It's not just that you can't be perfect in engineering, it's that you probably shouldn't even try to get too close to perfect. That's not what you are being paid to do. Part of the job is always to determine the level of modelling accuracy required. And yes, even for the highest of high tech. In my case satellite power supplies and some of the best lasers you can buy.

Alright, so it is true in EE. I wonder if this holds for mechanical engineering as well

 

[Baluncore]

Interesting. But what you said is applicable even for the projects you've taken on that are purely mechanical as well right?

Welcome to the "cult of the imperfect".
Everything mechanical that is available, is only ever the third best.

We are working on an improved version, the second best, but you will have to make do with third best, until the new version becomes available.

The very best is perfect, and perfection is impossible.

This is a continuous process of improvement. It guarantees that you will always be working with a compromise, the third best.

 

[EddiePhys]

Welcome to the "cult of the imperfect".
Everything mechanical that is available, is only ever the third best.

We are working on an improved version, the second best, but you will have to make do with third best, until the new version becomes available.

The very best is perfect, and perfection is impossible.

This is a continuous process of improvement. It guarantees that you will always be working with a compromise, the third best.

Hmm, okay

 

[DaveE]

Hmm, are we done here?
You asked a simple question and got a bunch of very similar answers from experienced engineers. What's the point? You don't have to believe us, do it your way.

 

[Frabjous]

Every theory has a set of assumptions or approximations. When you choose to apply a certain theory, you are making those assumptions.

 

[boneh3ad]

"...truth ... is much too complicated to allow anything but approximations..."
- John von Neumann, 1947

 

[EddiePhys]

Hmm, are we done here?
You asked a simple question and got a bunch of very similar answers from experienced engineers. What's the point? You don't have to believe us, do it your way.

I didn't question whether what you wrote was true. I said in my post "Alright, so it is true in EE. I wonder if this holds for mechanical engineering as well" since you mentioned you're an EE

 

[Baluncore]

@EddiePhys
Have you considered the study of pure mathematics, or maybe entering a monastery?

 

[DaveE]

I didn't question whether what you wrote was true. I said in my post "Alright, so it is true in EE. I wonder if this holds for mechanical engineering as well" since you mentioned you're an EE

It's true for all engineering disciplines. Also most of science.
The question "do we approximate things" is too simple to be interesting. It's time to graduate to how, when, and why we make approximations.
I'm done.