Naked Science Forum
Non Life Sciences => Technology => Topic started by: peppercorn on 31/03/2009 18:21:30
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...bit of a mathematical thought experiment here:
I was trying to picture what the pressure wave in a car exhaust at its ideal (most efficient) RPM.
With four-stroke on four cylinders I reckon the exhaust pressure would be pretty close to a saw-tooth wave.
If this is so, would theoretically a perfect exhaust be an infinite number of tuned pipes (one for each sinusoidal component) - as described by the Fourier transform
http://mathworld.wolfram.com/FourierSeriesSawtoothWave.html (http://mathworld.wolfram.com/FourierSeriesSawtoothWave.html)
mmmm?
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If you use a set of resonators, they will 'talk to each other' and the result will be a broader but lower peak in performance. Useful but not 'peaky'.
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If you use a set of resonators, they will 'talk to each other' and the result will be a broader but lower peak in performance. Useful but not 'peaky'.
So your saying having a set up like this - I guess it would look a bit like a church organ - would result in a wider, flatter power curve, yes?
Although, interesting, its not really what I wanted to know, but thinking about how the Fourier Transform works out - here my maths is real rusty, but I think each sine component should have be a frequency multiple of the first wave (ie. harmonics of n=0). On this bases at fixed RPM all waves should be tuned to one length (if the sawtooth model is valid)...
What I was considering was if say the sinusoidal components can be separated then pipes with (super-fast) valves in could be tuned to derive useful work without causing back pressure (as a turbo does for example).
It would be almost unimaginably complex, but as a theory is it correct?
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Which part of the theory are you trying to invoke?
The time function of the pressure (or the gas flow) variation can be expressed as a sum of harmonics by using the DFT. That will be in addition to (or around) the constant factor - which is the through flow of the gas.
To obtain the maximum gas flow, you have to produce a resonance at the frequency of the exhaust pulses so that the gas can shift out of the cylinder against a low (appropriate) impedance. It seems that you are also thinking in terms of resonating at some of the higher harmonics too (?).
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Two stroke engines use tuned exhasts in order to improve the performance.
http://en.wikipedia.org/wiki/Expansion_chamber (http://en.wikipedia.org/wiki/Expansion_chamber)
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peppercorn
I think I see what you are proposing - a temporal filter.
To achieve that, you'd need a set of ports along the exhaust pipe, with valves, operated in sync with the camshaft. Definitely not trivial!!
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Uh! You would do a little better if you properly comprehended a few more things well.
E.g. how 4 stroke and two stroke operate relating revolutions of engine,
360° degrees in two stroke, and 720° degrees in a four stroke.
What a cylinder firing order is e.g. [ 1 5 3 6 2 4 ].
What an exhaust Manifold is, and thus
an extractor or a "hot dog".
Finally with a camshaft, racing and standard,
and the number of degrees the exhaust valve is open during the exhaust stroke.
Venturi effect to the "expansion chamber", alike that for the air through the carburetor.
Are these shapes some sort of threat from picking up the wrong bag of chips from the counter at McDonalds one saturday night??? How much gas you'll.... e.t.c.????
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What is all that about?
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Tis Greek to me!!
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Regardless the wave, you do not get engine performance from tuned exhaust, you get effective extraction of exhaust fumes only, and the only benefit to the intake side of accessing fuel is the inertia generated by vacum from the drag of the expelled exhaust.
Performance finally comes from the fuel type and its air to fuel ratio balanced properly for the quantity of air taken in at the RPM(lagging intake from inertia and obstruction by the shape of the manifold).
Square wave sounds about right if you want to quibble the only two effective pressures that are ever present massive high pressure or one atmosphere - vacum(around the same).
Also the resonation from the travel along the pipe.