<p>Has anyone used mathematical models to help you solve problems?</p>
<p>Can they make you more effective in the engineering field or only certain fields?</p>
<p>What place does modeling have in Aerospace and Chem.E?</p>
<p>I haven’t seen this brought to attention, so I wondering if modeling was beneficial in anyway.</p>
<p>Modeling is very important at the design stage for ChemEs, without some of the programs that do this for us out there it would be very difficult to design a process.</p>
<p>Think of a simple distillation process, for example, in which you want to capture and reuse fusel draws, collect and process side draws, maintain a certain temperature and pressure differential, as well as a constant feed rate. What size/duty heat exchanger will I need? Pump duty? Vacuum pump duty? What if I have a solids build up? What effect will the recycling of the noncondensables have on the efficiency of my tower? What if I controlled the rate of recycling? How little of a change in vacuum will effect my tower performance? Is that worth it seeing as it might be cheaper to supply energy than to remove it? Do I have enough trays?</p>
<p>All these things, and more, need to be considered before you decide to spend the 10s of millions on the equipment and labor to set it up. Engineering design firms usually have guarantees on yields and caps on costs, so if the are wrong in their estimates it can cost them big money and possibly the company. While there are programs that help with this modeling there is still field know-how that must be added to mix and tweaks will be made after the construction to yield a successful project, but it all starts with the model.</p>
<p>From an Chem. E perspective modeling sounds like factory job or something similar to industrial engineering. I’m guessing Aerospace modeling goes for less of a hands on approach and uses computers. Modeling seem to be more on the maintenance/sustain cost advantage side, while being a scaffold for creating designs/processes.</p>
<p>Mathematical models would be used extensively in aerospace considering a lot of the design is done with finite element analysis programs (FEA’s) these days. FEA’s essentially break up objects into a cloud of points connected in some way and between these points certain conditions have to hold (e.g. sum of electrical current entering/leaving at each point is 0) so that the solutions to equations that describe complex systems may be approximated. Using these conditions, a huge matrix is built and through solving this matrix you can find various properties at each point to determine things like structural weakness.</p>
<p>A FEA program sounds matlab esque and look of it reminds me of the armature 3d animation I used to do, only in wire frame. Structural weakness could also be failure analysis, which what Material engineers use. Well now I have a better appreciation for matlab and were it comes from. Thanks for explaining modeling to me guys.</p>
<p>What do you mean by “mathematical model”?</p>
<p>F = ma is a “mathematical model”.</p>
<p>Well going by this thread a mathematical model means how to apply textbook stuff effectively in the real world, rather it be hands on or computer aided.</p>
<p>I learned F=ma from a “textbook” and I assume engineers use that at some point in their careers… explicitly or implicitly…</p>
<p>As far as computational models go, there’s CFD, computational molecular dynamics, etc…</p>
<p>In CS, complexity of algorithms is a “model” that is fairly useful. I’m not really sure what the OP is asking… whenever anyone does anything with “math” in the real world, it’s a “mathematical model”. If it happens to involve using computers, it falls into the realm of numerical analysis/numerical methods/computational models.</p>
<p>I think knowing why you’re asking… sort of what you’re driving at… would help us a little. I’d guess that most of us in engineering, upon reading your thread title, think, “WOW. Everything!” I mean, there’s very little that I do right now that <em>doesn’t</em> draw on mathematics in some way, shape, or form.</p>
<p>So… are you trying to justify to yourself that it’s just flat-out ridiculous that you have to learn point-slope formulas in math class, because who’s ever gonna use these again? The answer would unfortunately be “engineers.” Engineers use point-slope formulas. I’ve used all sorts of random math that I thought I’d never, ever have to use again, because after all, I’m not a farmer who is trying to build a fence around his sheep and I don’t care how much grass they need to graze on, and I don’t want to know the cheapest fence I can build around them.</p>
<p>So… what’s your background? Are you a high schooler? Why are you asking this question, so that we can get a better idea of how to answer it?</p>
<p>I’m a junior in college and of course I know we all use math everyday rather intimately. I just want to know the values behind these models in different fields and how they can relate to real life. Maybe I need to do a little investigative reporting since I’m curious about it. Anyway sorry if my question was to broad, I was trying to get a gasp of things.</p>
<p>Mathematical models are what make the difference between natural philosophy and science.</p>
<p>In that case, in structural engineering, my field, we try to find accurate mathematical models of how everything behaves… What are our variables? Can we use our engineering judgment to determine these variables? How is one thing related to another mathematically?.. so that we can predict how materials will behave, so that we can design predictably-behaving structures.</p>
<p>We try to analyze soils the same way, and analyze wind, and analyze snow loads, and analyze the weather, and analyze earthquakes… Try and fit everything in nice, neat equations so that we can apply those equations to our real-life situations and determine predictable responses.</p>
<p>In fact, most of academic engineering (at least in my field) is devoted to coming up with and testing mathematical models of natural phenomena. These mathematical models may be very complex and very iterative, and that’s where the use of computers comes into play. Or we may try and divide things up into very small, regular bits and apply very simple equations to them, and have the computer add up all those very small, regular bits to come up with how complex forces affect complex shapes (that’s what finite element analysis is), and that also requires a lot of computing horsepower, too.</p>
<p>But yeah, it’s all about the mathematical model in most fields of engineering.</p>
<p>absolutely nothing . . . say it again . . .</p>
<p>
</p>
<p>i thought the difference was hypothesis & experiment . . .</p>
<p>I know some kid in my CS department who interns for the department of defense helping build math models for various things…i would assume many things cost a lot less if you do proper sophisticated planning which would involve such things.</p>
<p>but as someone stated, math models can be applied in most area, partly because the phrase math model is so broad.</p>
<p>Engineers need to “predict” how their design will work under a wide variety of conditions. That prediction is the “modeling” of the design’s expected behavior, and can range from a simple equation like F=ma (as auburnmathtutor pointed out) to computer simulations that can take days to execute.</p>
<p>Models, both math models and other kinds, are abstractions of reality that are “wrong but useful”, to paraphrase George Box, a noted statistician. They simplify and integrate knowledge about a system of interrelating factors. With “reality” there are many factors that affect outcomes that are sometimes difficult to know completely, but at least with a model, one can know what is consciously put in the model and how well it predicts.</p>
<p>In Engineering and science, models are helpful in gaining understanding and predicting how things, people, systems, etc. “work”. Math is the language of science, so it is the way of universally explaining our understanding.</p>
<p>I personally find developing models rewarding because it is fun to be able to predict what will happen.</p>