FWIW, describing a baseball's arc is not a trivial calculation in the real world.

It really depends on what you are after and what accuracy you require.

If you are interested in how far the ball will fly, or how high up it will go, when tossed by a outfielder at a certain angle and initial speed then equations from high school physics will get you fairly close. If you want to know how the baseball moves when thrown by a knuckle ball pitcher then even a super computer will probably not get you an accurate answer.

When I talk about simple models for closed box and bass reflex enclosures then the results will be reasonably accurate for small signal inputs and using the rest of the assumptions that come with a Thiele/Small type of model/analysis. This is how I operate my stereo system most of the time. If you are talking about high input signals driving the driver into the nonlinear range then the simple model's accuracy will suffer.

However, in my opinion and within my experience the simple models do an excellent job of describing the behavior of a baseball's trajectory and a speaker's low frequency performance. Sometimes people overcomplicate problems and the result is they never get a decent usable answer. I had a manager that used to preach "Better is the enemy of good enough!". But there are always people (engineers in particular) who dive right into rocket science when it is really not required.

Martin

I know it's my personal prejudice, but when, for example, we calculate process temperatures and vapor fractions my answers are along the lines of "10 ppm methane at about 85F". My boss, asked the same question answers "9.879 ppm methane at 84.067F". It just drives me insane when the boundary conditions are about as well defined as a blob of whipped cream.

I blame computers; Colin probably didn't work in the era (I started at the tail-end)when you had to turn in your hand written calcs on quadrille paper for peer check. Not too many "9.8705 kips" solutions in those days.

From my perspective while extreme precision may well be a very good when working in deep sub-micron lithography, the application of that sort of precision to loudspeakers is fairly ridiculous - the whipped cream boundary condition problem again.

Today I see young engineers pointing and clicking as they analyze simple cantilever beams with 3D finite element models. They don't even get a course in programming anymore in some colleges. I even had one young engineer argue with me that his finite element analysis of a test set-up was correct even though the calculated result was not close to the measured value from the test, my simple calculation in MathCad was much closer. Did not matter to him, we (me and the test) were both wrong.

While computers have made good engineers even better, they have also masked understanding of a problem and thinking by the inexperienced engineers. You have to really understand to boil a problem down to something simple and elegant. I worked with another gray haired guy who used to say that if an engineer could not explain in simple terms what he/she was working on in five minutes, chances are they did not know what they were working on.

Martin

As an example, I've been having a discussion with some guys about heat transfer in loudspeaker motors. These are guys that work in prosound, where power levels are pretty high. But a lot of them have a complete lack of understanding on how heat transfer works. They have an almost sophomoric outlook, even those with some standing in the prosound field. Any mechanical engineer immediately grasps the issues, but the prosound guys talk from a seat-of-the-pants perspective, one that is almost completely wrong. They couldn't find the truth because they weren't willing to look. They reminded me of guys running flathead Fords at the racetrack even after overhead valve engines started cleaning their clocks. They had horse and buggys, and by God, they were going to stick by them, no newfangled motor carriages for them, no sir!

Another example, I was talking to an acoustical engineer a little while back that boasted proudly about his programming skills. He was going to write a script to do some analysis, and he was confident that his way was the only way. I couldn't help but think how arrogant he was, and frankly, undeservedly arrogant. He is a published author, and a very bright guy. That part I can respect. But the largest, most complex things he ever did were things that could be described with a month of mathematical analysis, tops. Most were just a few days work, at best. So to discount what others had done was offputting, to say the least. It made me realize that everything he said was from the perspective of a very narrow (and strongly biased) view and almost completely worthless. He wanted to promote his pet ideas from an ego-driven perspective more than he wanted to discover the truth.

A large software project is sometimes the result of tens, sometimes hundreds of man-years of work. We're getting to the point where some computing systems have thousands of man-years of work in tens of thousands of files. The complexity is mind-numbing and no one person can get their hands around the whole project. So specialization is required. You can see the system from a holistic view, sort of a top-down, birds-eye view. Or you can see it reductionistically, looking at machine level device drivers and code modules. But to see the whole thing is impossible; It would be like memorizing every book ever written and being expert in them all. In this environment, no one would ever get locked in a stubborn narrow-minded view, because then they would be completely lost, out of touch, and always embarrassed by their lack of understanding, being so isolated and out of the loop. This kind of complexity is a whole other level than the hardest problems in acoustics.

All that to say I agree with Martin about loudspeakers, and about acoustics in general. Loudspeakers are very simple machines having three or four moving parts, and that's it. They are very much like mass-spring systems. Sure, things like summing multiple point sources, reflections and diffraction are involved, but those aren't terribly difficult. Cone flex becomes chaotic and the motor becomes non-linear at some points. But mass-spring system have non-linearities too, the metal is elastic at some levels and then goes plastic at other levels. A speaker cabinet is a Helmholtz resonator or it is a tuned pipe or a horn, or a hybrid having some of each property. The crossover is reactive. Each has very simple, predictable behaviors for the most part. Then there is an element of non-linear behavior, but even that can be expressed to some degree, certainly it isn't hard to understand. More complex systems have these same behaviours, and they have more parts too.

So while I enjoy audio and making things as best as I can, I don't think even the most complex audio projects I've done come anywhere close to the complexity of say an large-scale integrated circuit, an operating system, a jet airplane or a nuclear reactor. I find the best acoustical engineers are usually physicists or mechanical or electrical engineers with a keen interest in audio. There are some very smart guys with acoustical engineering degrees too, some good talent working in sound fields. But I'd have to say that I think the best acoustical engineer is actually someone converted from another field, someone used to dealing with things of greater complexity. He isn't as likely to bullshit himself or try to bullshit others.