BTW my speed of sound was based on a rough guess of 600 MPH.
The speed of sound varies with temperature so corrections must
be made for the actual speed of sound in the pipes.
I could be off by a lot. I'll have to look it up for 1500 degrees
or so.
Paul Lamar
Perry Casson wrote:
For what it's worth I discussed some of this acoustic velocity stuff with
a guy who's spends his days designing sonar arrays for Lockheed Martin
and his evenings putting a Soob in Cozy so I suspect he might know
a bit about this. He had the acoustic velocity for the Soob exhaust
at 1200 ft/sec from that I did the following to get a 1310 ft/sec
velociy for a 1400 F EGT. Here's a link to Phil's web site if you want to read his
theory on what's going on in an exhaust pipe.
<http://www.geocities.com/plmjohnson/exhaust.htm>
I assumed an average exhaust temp of 1100 F for the soob and 1400F for the 13B.
Unfortunatly I never did learn how he got the 1200 ft/sec acoustic velocity
which this whole house of card relies on.
1100F = 866K
1400F = 1033K
1200 ft/sec = 365.76 m/sec
// solve for rR/M at 1100F and 1200 ft/sec
c = sqrt(rRT/M) // formula for acoustic velocity
c*c/(rR/M) = T
133780/(rR/M) = 866
rR/M = 154.48
// For 1400F from a rotary
c = sqrt(154.48 * 1033)
c = 399.47 m/sec = 1310.3 ft/sec
Excerpt from <http://www.geocities.com/plmjohnson/exhaust.htm>
***************************************************************************************
If we start using simple numbers: An engine spinning at 6000 rpm emits exhaust pulses at a rate of
50 pulses per second from each pipe. For the pressure wave to be transmitted out to the end of the
pipe and be reflected back to the exhaust valve ready for the next opening the pulse must have
accomplished a journey of 2 x (pipe length) within 20 milli seconds. At 1200 ft per second, 20 milli
seconds covers a round trip distance of 24 ft which requires a pipe length of 12 ft. Clearly 12 ft
exhaust pipes are not acceptable on aircraft in a pusher
configuration. Reducing the engine speed to 2700 rpm ( certified engines) results in a pipe length
requirement of 26 feet to benefit fully from a tuned exhaust length.
*********************************************************************************
That is a very well written explanation of what goes on inside the pipe.
He is missing one thing however. Here is an example: If you have
some one on a child's swing and give them a small push every third time they
will still swing back and fourth unabated. In other words to keep a resonant system
going you only need to reinforce it once in a while with a little
push. All that matters is the pushes occur at some integral multiple
of the resonant frequency.
I can believe the 1200 feet per second for the pressure wave
as others have mentioned. Velocity of sound being a strong function of
the gas temperature. I also think we can calculate the flow
velocity in the pipe knowing the air consumption of the engine
and the pipe diameter. I suspect that will affect the speed
of the pressure wave but not the time required to make the round
trip much. Head verses tail wind.
Of course each pipe on a rotary emits 100 pulses per second
which equals every .01 seconds or every 10 milliseconds.
Paul Lamar
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