It’s still an overly complicated explanation.
On a Torque vs RPM curve, the mechanical “power” delivered is best referred to by its definition: Speed (eg RPM) * Torque.
Sure, that can be construed as the same as the “area”, but the way you explained it, someone (even you?) might construe that the power at any point is found by integrating the area under the curve from zero to the point of interest. And that is wrong.
Let’s keep it simple if we can.
-MT
From: electricboats@yahoogroups.com [mailto:electricboats@yahoogroups.com] On Behalf Of jim_ranger_26
Sent: Thursday, August 18, 2011 11:08 PM
To: electricboats@yahoogroups.com
Subject: Re: [Electric Boats] power requirements - predicted vs observed
Hi again,
Fortunately, I posted my previous message late on a Friday evening after everyone had finished digesting dinner, fallen asleep in front of the boob tube, or otherwise enjoyed what should be a time to relax for normal people with actual lives. I may have left out an important point that the mechanically-oriented engineers (and maybe physicists) will likely spot right away (and the electrically-oriented engineers will probably be right behind), but, which may confuse others.
The _power_ delivered at any point on the discussed curves is actually represented by the _area_ under the curve from zero to the RPM of interest (i.e., the integral(s) of the function(s) represented by the curve(s)). The torque value at any point corresponding to an RPM on either curve is the _incremental_ torque (and therefore, incremental power) available at that RPM. In other words, the values on the curves represent the ability of the power plant to _accelerate_ the craft at those RPMs. That's why engines are generally able to provide their maximum ability to accelerate somewhere around 70 ~ 80% of maximum RPM, while electric motors can do so at zero RPM, and have exponentially-decreasing ability to accelerate with increasing RPM. If this weren't the case, it would appear that the total power delivered by an electric motor declines with RPM (and the same for engines above the point of maximum incremental torque), which is obviously not true to even the most casual of observers, as it would mean the craft would slow down with increasing RPM (some of us have props that actually make that true above certain RPMs, but, I won't open that can of worms ... here ;)
Sorry for any confusion this lack of specificity may have caused, but, the rest of my diatribe should still be valid, at least until I or someone else wakes up long enough to discover yet-another glitch in my verbosity.
We now return you to your life, already in progress!
All the Best,
Jim
--- In electricboats@yahoogroups.com, "jim_ranger_26" <jim_manley@...> wrote:
>
> Hi guys,
>
> Not to confuse things even more (oh, what the hell, everyone else is having too much fun :) but, please bear with me while I get a bit pedantic/pedestrian/Neanderthal and bring things back to first principles (I'm trying to make this approachable to the lurkers we all know are out there, who are too afraid to ask the experts what are actually not-so-dumb questions).
>
> There are only two ways to measure shaft horsepower directly, and that's by either:
>
> - connecting the prop end of the prop shaft to a dynamometer (basically, a cylinder filled with an oil having precisely-known characteristics, and equipped with a calibrated friction-creating mechanism; or a calibrated generator/alternator connected to a calibrated and adjustable load)
>
> - putting differential rotational strain gauges on the prop shaft, just forward of the prop, and on the output side of the engine/motor shaft (obviously, with some means of transmitting strain data remotely while the shaft is turning). For the non-engineers, rotational strain is the measured number of degrees of twisting of the shaft as torque is applied along the length of the shaft, between the engine/electric motor and the prop. Strain should not be confused with stress, which you can consider as being directly related to the torque, so, we'll bundle stress into the torque, and not worry about it any more here.
>
> These allow direct measurement of the instantaneous torque (and therefore, work, and, over time, power, in horsepower, watts, Newton-meters-per-second, or whatever), being applied along the length of the shaft for any given RPM, taking all of the other variables out of the equation, for now.
>
> Of course, we already know that the engine torque(power)/RPM curve will increase exponentially initially, go somewhat linear for a while, then start decreasing in slope sort of parabolically until the peak of the curve is reached, then pretty rapidly fall off at some high-exponential rate (until certain failure at a high-enough RPM).
>
> We also expect that the electric motor torque(power)/RPM curve will have something like an inverse exponential curve, offset to the left such that the maximum torque is available where the curve touches the positive Y axis (i.e., 0 RPM), and gradually petering out as RPM on the X axis increases until the RPM of certain failure is reached.
>
> I suspect Eric now knows where I'm going with this - the two curves are _completely_ different shapes, and that's why Gerr's equations for engines don't hold well for electric drives _ACROSS_SOME/MUCH_OF_THE_RPM_RANGE_ (sorry, I'm not yelling, I'm just trying to emphasize the important stuff). Shaft horsepower _DELIVERED_ is _NOT_ the same for engines as electric drives _FOR_ANY_PARTICULAR_RPM_ (it's not even identical for different engines, and especially different engine technologies, e.g., piston/Wankel-rotary/etc.). In fact, if it weren't for the roughly fourth-power increase in friction (Friction ~= k*(Speed^4) ) of a displacement hull as you get anywhere above about half of hull speed (it's closer to second-power below that, and the curve goes essentially vertical near/at hull speed - you start planing, not necessarily prettily, above that point, and the curve changes radically up there), Gerr's systemic curves (fuel or electrical power consumed vs. speed achieved) would have absolutely nothing in common with each other for the two kinds of power sources. The only reason you are seeing any concordance at all is because of that severe increase in friction with speed - the good ol' Second Law of Thermodynamics is seeing to that (it states that, not only is there no free lunch, but, you can't even get anywhere close to break-even, especially as energy expended is increased - entropy/disorder/chaos increases much faster across the entire system).
>
> What I'm basically saying is that, unless you do the torque/RPM measurements described above and adjust Gerr's formulae for them, you're going to be comparing pineapples to tennis balls, if not outright McIntosh/Delicious/Fuji/etc. to igneous/sedimentary/metamorphic objects.
>
> Tossing of over-ripe fruit, vegetable, and other metaphors now heartily welcome - please try to avoid actual mineral-based objects, but, if you must, be advised that I can duck and run pretty well for someone of my advanced senility! ;)
>
> All the Best,
> Another Jim
>
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