4-2-1 Exhaust calculations

[Wanyama67]

I am designing a 4-2-1 exhaust for a fsae car and am struggling with the calcualtions for the pipe diameter and length for my project. Would anyone be able to help me with the equations etc that i need?

[tgman]

I am feeling nice so rather than rant about using the search function I will actually be mildly helpful(DO IT NEXT TIME!!!!!!)

1. If possible get hold of some engine simulation programs, Ricardo wave is the first one that comes to mind but there are many others.

2. Get a book on the subject and read it

3. Bent sections and steel pipe do not come in every imaginable size so have a look at some suppliers and see what they have available. That should quickly sort out your diameter.

4. Do you know what sort of back pressure your engine needs. If not this is something to find out very quickly, but as a dodgy method just calculate the pipe losses in the stock system and build a new one with the same numbers.

5. Look up transmission line theory, I know you will probably start with Wikipedia and the article there is about mostly about electrical stuff but read through it properly. This should also at least partly explain why you would choose 4-2-1 or 4-1 or 4-3-1 or whatever you actually do.

That could be good advice or that new beer from Holland I got could have a bit of a kick in it.

Either way good luck

[RenM]

just something to add:

point 1 should be the last point http://fsae.com/groupee_common/emoticons/icon_wink.gif
There is nothing to gain from a simulation if you dont understand the physics behind it. And without plenty of measuring data for calibration, your simulation results will be questionable.

Unlike a 2-Stroke back pressure is not needed to properly run the engine. In Fact less back pressure is better for your power development.

For a start you should stick with the stock diameters. If wanted the diameters can be reduced a bit, since you wont see as much massflow because of the restrictor.

Be sure to not tune your exhaust lengths to the same rev as your intake.

[Wanyama67]

Thanks for giving me some feedback.

I did search previous discussion but there was no definite answer.

I have read Gordon P. BLairs books on design and simulation of four stroke engnes and there is calculations for exhaust in there but doesn't say anything for secondary pipe diameter or length.

Should the diamter of exhaust pipe stay the same throughout or should it change when it goes from the 4 to 2 then 1?

Also is it best for the pipes to be as straight as possible or is it better for them to curve throughout?


Any reply is appreciated

[Luniz]

Things to consider in this respect: In the first length you are transporting a certain amount of gas through a certain cross section of tubing. If you now combine two or four of those tubes and don't encrease the cross section, the gas will need to speed up. Is that good or bad?

Also, the gas has some mass, therefor inertia, and if the pipe has a bend, there is a change in direction, which means it needs to be accelerated. What does this mean in terms of engine tuning?

[Owen Thomas]

This has been discussed at length a number of times. Here (http://fsae.com/eve/forums/a/tpc/f/125607348/m/49320447151?r=75220187151#75220187151) is one such example where I explain pressure wave tuning, which is the dominant effect in small NA engines. Another major contributor to exhaust performance is inertia tuning, and Lutz gave some good insight on that.

A little bit of time on the Google searching for something like "exhaust pipe diameter" will yield a wealth of resources in this area. There are loads of papers, tech tips, and etcetera; you just have to figure out how to apply them.

For steps and collectors, think about what is happening. Surely you can come up with some correlation between pressure, area, and velocity to apply here. You can also look at commercially available collectors and observe trends.

If you have read Blairs book, you should already know the answers to most of your questions. Again, you just have to apply what you read, and add in a dash of common sense.

[Mbirt]

I'll agree that Blair doesn't seem to touch on stepped ducts or 4-2-1 systems. You should check out Bell's "Four-Stroke Performance Tuning". It's more basic than Blair, but contains lots of tasty old racer wisdom. In my opinion, it's the "To Win" book to the RCVD that is "Design and Simulation".

[Warpspeed]

Another good resource is "Pipemax" very low cost software.
It will give you exact diameters and lengths for many different exhaust layouts, including 4-2-1.

It also includes induction diameters and lengths.

[Wanyama67]

I have found a website that is basically an online calculator for exhaust lenghts and diameters.You only have to put in Exhaust Open BBDC. Exh close ATDC. Engine R.P.M CC of one "Cylinder and it calculates everything for you

The formulas are taken from "Four-stroke Performance Tuning by A Graham Bell" and i would recommend people check it out

[Mbirt]

You would truly benefit more by just getting your hands on the book. As Blair warns in his writing, straight numerical empiricism can be dangerous without the story behind the derivation. Bell also shows lots of helpful back-to-back dyno tests in each chapter.

I do not wish to condone piracy, but you might even be able to find a .pdf online if you search hard enough.

[Freddie]

I'd recommend that you look into Blair more than Bell, since I believe that Bell's equations aren't really suited for those engines that we are working with here.

I had the same exact problem a couple of months ago trying to design our exhaust. As you say Blair gives you primary and tail-pipe length fairly easily while the secondary pipes are never mentioned, if I remember it correctly. I had a discussion with an expert, and I think my approach is at least somewhat correct:

If you think of the exhaust as a digital pulse (since this will make it easier to think about than a real exhaust pulse), will the pulses interfere with each other in your design? This will depend mostly on cam timing and how you connect the pipes. If they don't interfere, can you watch the secondary pipes as a "second primary pipe", and how will that affect your calculations?

One thing I did was also to measure the original exhaust and reverse enginer it with my formulas, just to reality-check them. I did this with both Bell and Blair, and while I don't remember the exact figures Blair made the exhaust system seem reasonable while my Bell equations went through the roof. I might have misinterpred them, but my theory is that Bell had V8 tuners in mind when writing his book, and engines a tenth in size revving the double may make the equations somewhat distorted.

[Wanyama67]

Thanks for your reply freddie

Blairs equations seemed based on an 'ITC engine'. how does that compare to the 4 cylinder engines we are using and how does it effect the calculations?

Would you mind messaging we the equations that you used for your exhaust calculations. It feels as though im hitting my head against a brick wall at the moment


Also how did you test your exhaust for flow,noice and heat loss etc?


Again any feedback much appreciated

[Freddie]

I don't have the book in front of me right now, but do you use the theoretical formulas or his empirical formulas? "Design and Simulation of Four-Stroke Engines" has two chapters about empirical design (one for intake and one for exhaust), the formulas presented there seems to give "better" values than the ones based purely on theory. But they do require some work. In the chapter about exhaust system design, he talks about having to adjust the exhaust temperature from a real(istic) value towards something that actually works (when looking at dyno data). If I remember it correctly, Blair ends up at an exhaust temperature somewhere around 500 degrees Celsius, which seems to check out when looking at the stock exhaust for our CBR engine and guesstimating where Honda would put torque peaks. I just checked in our design report, and I tweaked it to 550 degrees after consulting with an expert.

Since this is done for the car that will hit Silverstone this year, I only have the theoretical analysis to give you, but we did a flow analysis in Ansys on each individual pipe (for steady-state if I remember correctly, CFD is not my field of expertise). Our silencer was designed according to Coates and Blair, but we still have to tune it on our dyno so the calculations are only approximations with some safety margin. Hopefully we will be able to test some different heat loss prevention during spring.

This may be borderline off-topic, but how do your intake and exhaust system work with each other? It's not the easiest, but trying to design both systems simultaneously, or with the other system as a known design, will probably help you get better results. Where are your intake torque peaks located? Do you want to hit those with your exhaust as well (maximizing brake horse power) or make your exhaust resonate between your intake peaks (sacrificing power for a broader power band)? And no, it won't get any easier ...