4-2-1 exhaust pipe lengths

[Manifolds BGR13]

Hello

I'm lookimg for a formula to calculate the lengths of the 4-2-1 exhaust system.
I do have a formula for the primaries and secondaries (the 4-2 section).
My problem is to figure out how long should be the tail pipe, before it enters the silencer.

I have searched the forum, and the net, but all I've found were rough approximations, not an accurate formula.

Thanks

[Racer-X]

My understanding is that anything after the collector is just a duct to get the exhaust where you want it. All the resonant tuning is done. All I've ever worried about is if the exhaust has cooled down enough to not burn up the packing.

[penna]

If the tail pipe diameter is large enough then the rarefaction wave you get from it exiting the tail pipe should be negligible as the pressure differential between the tail pipe and atmosphere will be very small. If you have a small tail pipe the pressure differential will be larger hence creating a significant rarefaction wave. You should be able to use the same formula you used for the secondaries, remember this goes up all four pipes though

[Manifolds BGR13]

Originally posted by Racer-X:
My understanding is that anything after the collector is just a duct to get the exhaust where you want it. All the resonant tuning is done. All I've ever worried about is if the exhaust has cooled down enough to not burn up the packing.

That is what I was thinking as well.

The real question is, has it been implemented in a real automobile?
Has anyone used the 4-2-1 configuration, with the two scondaries converge to one, and going immediatly to the silencer?
If so, what were the effects on HP and torque?

[Freddie]

I used Blairs equations (from Design And Simulation Of Four Stroke Engines) for all pipe lengths for the car we're building. We're not using the exact measurements due to packaging issues, but if you want formulas you can find them there.

[Warpspeed]

A lot depends on the nature of the silencer.

If it is just usual straight through absorption type. with a perforated pipe, enclosed in a drum not much larger diameter than the pipe, then the whole exhaust pipe length will add it's own only slightly damped resonance.

If the silencer has a very large internal volume (compared with individual cylinder displacement) then the tuned section of pipe effectively ends at the silencer entry.

The large gas volume contained in the muffler effectively becomes "ambient pressure" that the tuned pipes empty into.

The way to think about all this is that exhaust reflections are produced by sudden step changes in velocity and flow area.
Stepping up suddenly into a collector or into huge muffler will create a point of strong reflection. A continuous pipe with a wimpy straight through muffler will not be very different to just a continuous bare pipe. The point of largest reflection then becomes the open end.