t/s specs and theoretical comparisons

I agree with what that paper is pointing out, it makes sense. That said, there was one point glossed over that I want talk about some. That paper points out that current is proportional to acceleration. Not equal, proportional. Acceleration "is strictly a function of the current through the driver". To show the math: a = i(Bl/m) That function states that acceleration equals the current times the Bl divided by mass. Efficiency is not a time-dependent problem, so you cannot substitute C in place of the variables when using the formula. Therefore as mass increases, efficiency decreases because it takes more current to keep acceleration the same. which is what I thought in the beginning: Heavy woofers are less efficient. The paper is focusing on "does mass affect speed" and therefore transient response, a time-dependent measure, so they can replace Bl and m with C in the paper, which helps show the proportionality, however, it leads you to believe that efficiency remains the same regardless of mass, which is, as far as I can tell, wrong.

No, efficiency is affected by the total mass of the system.  If I said anything differently I must have misunderstood you.Support the12volt.com

SPL is determined by rate-of-change. What that literally means is this: How fast a woofer can change direction, to make the atmospheric high-pressure to atmospheric low-pressure gradients happen as fast as possible. Short time-frame, large-scale pressure changes (in millibars) are what determines SPL. The faster the peak pressure (in positive millibars) changes to the trough pressure (in negative millibars), the greater the SPL. The lower the inductance of the voice coil, the faster the rise time of the current THROUGH the voice coil, thus affecting the acceleration OF the voice coil. With this being said, you could now see that it should be possible to have a high efficiency, long-throw woofer (they are just EXCEPTIONALLY expensive to produce) but it has nothing to do specifically with the throw of the woofer, or the frequency being produced; i.e. a long-throw woofer DOES NOT MEAN a "loud" woofer. (I hope that made sense... I will have to re-read (with potential edits) after the LARGE bottle of Blue Moon Grand Crü wears off...)It all reminds me of something that Molière once said to Guy de Maupassant at a café in Vienna: "That's nice. You should write it down."

Gotcha. So in theory, to achieve maximum SPL with lowest power requirements, you want the fastest, lightest, largest, longest throw woofer possible. Fast so that it moves peak-to-peak quickly Light so it is highly efficient and uses less power Large and long throw so that the woofer generates higher peak and lower trough pressures. New question: Why wouldn't all woofers have extremely low inductance since it's so advantageous? Cost?

Long throw ONLY APPLIES when looking for low-frequency extension! It does NOTHING in the overall scheme of SPL! SPL competitions are one-note applications. 60Hz is EASY to make in abundance, which is exactly why you see so many RF and CV wins in the SPL arena. Those systems will NOT go deep. To address the inductance, you either have to widen the voice coil (re-tooling), add a shorting ring to the pole piece (re-tooling AND additional materials), or reduce the number of turns in the coil (lower power handling). Either expense or claims go out the window for any of the above solutions.It all reminds me of something that Molière once said to Guy de Maupassant at a café in Vienna: "That's nice. You should write it down."

What I stated came directly from what you told me... Here's how I came to those conclusions: I'm using your own words... "SPL is determined by rate-of-change. What that literally means is this: How fast a woofer can change direction, to make the atmospheric high-pressure to atmospheric low-pressure gradients happen as fast as possible." Lets say that the low-peak-pressure=p1 and the high-peak-pressure=p2. Now lets say the low-peak happens at time=t0 and the high-peak happens at time=t1. Rate-of-change is how much pressure changes during the timeframe of t0 to t1. So in this case: Rate-of-Change=(p2-p1)/(t1-t0) Now, going from nothing but how you defined SPL, it appears that SPL will increase because the rate-of-change increases. Say we make the low-pressure lower and the high-pressure higher WHILE keeping the low-peak at t0 and the high-peak at t1. The top of the fraction in the formula would increase, thus the Rate-Of-Change increases, thus SPL increases. If this is wrong, please explain why.

Perhaps I am wrong in using that phrase... The one regarding the "nothing to do with"... It DOES have something to do with it: It usuall impacts it negatively. Look into the Eta null numbers, that one represented by "n0". That number is the representative figure, indicating how much electrical power (in percentage) is converted to acoustic power. Less than 1% is typical, and WELL less than 1% is fairly common. You will start to notice that the drivers typically described as "Long Throw", i.e. Eclipse Ti, TCSounds, Rockford T1's... Their Eta null numbers will be very low, comparatively speaking. If you examine the numbers of drivers from JBL, Cerwin Vega, they'll be quite high in the range. Now... Conversely, many long-throw woofers will have outrageous power handling capabilites. These capabilities are enhanced (or maybe provided) by their amazing motor structures - HUGE magnets and giant, (high-inductance...) multi-layer voice-coils, low Fs... These capabilities and structures directly affect one another. The giant moving mass DEMANDS monster power to get the output levels that people are willing to pay for. Short throw, light, high Fs cones, smaller, lower-inductance single layer voice coils seen in many "lesser" woofers provide better SPL per watt... I say "lesser", because that's how people see them today. They'll ask themselves: Is it a fat surround? Is it 1500WRMS power handling? Those questions have all been influenced by cheap, multi-kilowatt amplifiers that cost $300.00. Big power is cheap to make now. Big power SINKS (the woofer) becomes the norm, and certainly ANY woofer being driven by 1.5 horsepower will be loud, right? There's the confusion. Short throw woofers are generally preferred for SPL, using reasonable power. They just are more efficient, as a GENERAL rule.It all reminds me of something that Molière once said to Guy de Maupassant at a café in Vienna: "That's nice. You should write it down."

Exactly, then we are in agreement... I didn't say so in my post 2 posts ago but I did recognize that woofer efficiency was far more important than Xmax. Basically what I meant is that if you have 2 woofers with everything identical except Xmax, then take the one with the larger Xmax because it could reach higher SPL... And of course in reality, that never happens, so we have to weigh the options, and what you are saying is that longer throw woofers loose a lot of efficiency, and there goes the SPL for a given power level.

KyferEz wrote: for a given power level.

is the key.  If you are not power limited, the longer Xmax woofer will displace more air and therefor produce higher dbSPL.

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DYohn wrote: KyferEz wrote: for a given power level. is the key.  If you are not power limited, the longer Xmax woofer will displace more air and therefor produce higher dbSPL.

^^COULD^^ produce higher SPL. And if it does, it's most likely JUST because of the enhanced power input, and NOT because of the enhanced throw. In the same alignment, a short-throw CV woofer will ALWAYS output more SPL than a long-throw Eclipse Ti in the same alignment, even though the CV might be rated 250 watts, and the Eclipse rated at 1000. Even if run at rated power, there is still no guarantee that the Eclipse will produce higher SPL than would the CV, and I'd even bet cash that with 1/4 the input power, the CV will spank hands DOWN the Eclipse. With 4 times the power, there SHOULD be a 6dB benefit to the Eclipse, right? If it's EQUAL in output, I'd be surprised. This is what I am trying to say. Long throw, in no way, ensures output superiority. At lower frequencies, to be sure, there will be advantages, but broad spectrum output, the longer theow woofer is actually handicapped.It all reminds me of something that Molière once said to Guy de Maupassant at a café in Vienna: "That's nice. You should write it down."