Toyota MR2 Message Board - View Single Post - Getting power from a 5SFE without forced induction

mrturrari · 06-29-2008, 11:32 PM

Let me post another write-up I was working on in the background:

How to size headers for you 5sfe

If you have read and understood what I have said in my "how an engine really works" writeup (yeah I know you guys haven't seen that yet) then you understand that pipe size can be directly correlated to a torque peak at a particular RPM given engine displacement and volumetric efficiency. The balancing point where greater pressure differential starts to move fewer molecules of air instead of more happens in exhaust gases because of higher temperature at about 240-260 feet per second. This can be used to calculate the optimal size for header primaries and exhaust pipes.

One formula found here Exhaust Header Design Comments can be used for header primaries in a 4-1 or 4-2-1 header. The formula is

Area of Primary Pipe = RPM × Cylinder Size ÷ 88,200

or written another way

RPM = Area of Primary Pipe x 88,200 ÷ Cylinder Size

This formula has a few assumptions built in like volumetric efficientcy and the temperature of the exhaust gas but it is still a good way to estimate how big the primaries need to be on your header and where you are trying to make power. Using a stock 5sfe as a base and assuming a wall thickness of 0.055" on your pipes you get the following numbers:

Displacement of a stock 5sfe: 87mm(3.4278")x 91mm(3.5854") 540.95cc (33.086") per cylinder
Primaries at 1-3/8" make peak torque at 3352rpm
Primaries at 1-1/2" make peak torque at 4045rpm
Primaries at 1-5/8" make peak torque at 5224rpm
Primaries at 1-3/4" make peak torque at 5631rpm
Primaries at 1-7/8" make peak torque at 6522rpm

The primary tube diameter in my opinion is the first and most important factor in determining the right header for your engine but other factors will also influence where your header will make power. The primary and secondary length will also influence power made above and below the torque peak. A good illustration of how this works is in this article:

Exhaust & Header - Tech - Exhaust Gas Tech - Circle Track Magazine

It basically says that shorter pipes will move power from below to above the torque peak and longer pipes will do the opposite. The curve leans as you change the pipe length depending one which direction you go. This is all because of wave tuning and getting either a higher or lower pressure at the exhaust valve when it opens or before it closes. It is important to note that unlike with pipe diameter, wave tuning of this sort is very dependent on cam duration. The timing of the events is critical to determine the correct length so you will need to have some information about the cams you will be using specifically the exhaust valve closing angle.

A. Graham Bell in his book "Four-Stroke Performance Tuning" takes a slightly different approach to calculating primary length and diameter He has decided to calculate length first and then use that to also determine pipe size. In the end it is still the same basic principal at work. You choose a target RPM and then size your pipes to give you power at that RPM. He uses this formula:

Primary Length = (850 x ED / rpm) -3

ED is the number of degrees before BDC that your exhaust valve closes plus 180.

To get primary pipe diameter you then use:

ID = sqrt(Cylinder Volume in cc / ((Primary Length +3) x 25)) x 2.1

On a stock 5sfe with an ED of 210, that is just a guess on my part assuming lobe centers of 110 degrees and a duration of 200@0.050", you get the following:

According to Bell stock cams will require
Increase torque at 3500rpms length should be 48" and ID should be 1.37" which is about 1 1/2" OD.
Increase torque at 4000rpms length should be 41.6" and ID should be 1.46" which is close to 1 5/8" OD.
Increase torque at 4500rpms length should be 36.7" and ID should be 1.55" which is just over 1 5/8" OD.
Increase torque at 5000rpms length should be 32.7" and ID should be 1.63" which is 1 3/4" OD.
Increase torque at 5500rpms length should be 29.5" and ID should be 1.77" which is between 1 3/4" and 1 7/8" OD.
Increase torque at 6000rpms length should be 26.8" and ID should be 1.79" which is close to 1 7/8" OD.

You can see that the two different methods give similar results within a few hundred RPMs. When dealing with 4-2-1 headers you treat the overall length and primary diameter as if they were 4-1 headers and then, from Bell's book, use the formula IDS = sqrt(ID x ID x 2) x 0.93 to get the secondary diameter. So for a 4-2-1 header that had 1-5/8" primaries the secondary diameter would be 2" ID or about 2-1/8" OD. If you think about it that secondary is flowing 2 cylinders worth of exhaust but those pulses are happening twice as often. I'm not sure at this point if you could use that formula because of that but I don't know for sure.

The length of primary vs secondary on a 4-2-1 header is a little more of a black art. A. Graham Bell suggests that the primaries be at least 15" long and the secondaries what is left. It's a good place to start. In my opinion a 4-2-1 header will act like progressively weaker versions of 4-1 headers of the same length as the primary, primary plus secondary and secondary lengths. So if your total length is 36" and your primaries are 26" you will have peaks showing up at 4500rpms, 6000rpms and weakest secondary peak would be beyond what the motor is capable of revving. It is more complex then that though because of all the combinations of refections you can have in a 4-2-1 header. You end up with weaker but more waves and that is why they generally give you a broader power band. You can use this to your advantage by keeping your primaries and secondaries different lengths so you have more peaks. If you made them the same lengths then you would end up with fewer peaks that were multiples of each other, say 4000rpms, 8000rpms and 2000rpms. Not the best thing for having a usable power band. You want to pick peaks that are closer to each other 500-1000rpms apart for having a good usable power band. That part is more my opinion and not backed up by any data.

Lastly remember that both pipe sizing and length are robbing Peter to pay Paul. When you move the torque peak up you will also loose some torque down lower because air cannot as efficiently flow through that larger pipe at a lower rpm. And with wave tuning for every rpm that you can get a low pressure at the exhaust valve at closing there will be another rpm where it become a higher pressure and you will loose power. The trick is to get them in places where they won't negatively effect your power band.

06-29-2008, 11:32 PM	#5 (permalink)
mrturrari I <3 my 5sfe Join Date: Mar 2005 Location: Salt Lake City, Utah Posts: 511 Thanks: 2 Thanked 125 Times in 82 Posts iTrader Rating: (0/0% )	Let me post another write-up I was working on in the background: How to size headers for you 5sfe If you have read and understood what I have said in my "how an engine really works" writeup (yeah I know you guys haven't seen that yet) then you understand that pipe size can be directly correlated to a torque peak at a particular RPM given engine displacement and volumetric efficiency. The balancing point where greater pressure differential starts to move fewer molecules of air instead of more happens in exhaust gases because of higher temperature at about 240-260 feet per second. This can be used to calculate the optimal size for header primaries and exhaust pipes. One formula found here Exhaust Header Design Comments can be used for header primaries in a 4-1 or 4-2-1 header. The formula is Area of Primary Pipe = RPM × Cylinder Size ÷ 88,200 or written another way RPM = Area of Primary Pipe x 88,200 ÷ Cylinder Size This formula has a few assumptions built in like volumetric efficientcy and the temperature of the exhaust gas but it is still a good way to estimate how big the primaries need to be on your header and where you are trying to make power. Using a stock 5sfe as a base and assuming a wall thickness of 0.055" on your pipes you get the following numbers: Displacement of a stock 5sfe: 87mm(3.4278")x 91mm(3.5854") 540.95cc (33.086") per cylinder Primaries at 1-3/8" make peak torque at 3352rpm Primaries at 1-1/2" make peak torque at 4045rpm Primaries at 1-5/8" make peak torque at 5224rpm Primaries at 1-3/4" make peak torque at 5631rpm Primaries at 1-7/8" make peak torque at 6522rpm The primary tube diameter in my opinion is the first and most important factor in determining the right header for your engine but other factors will also influence where your header will make power. The primary and secondary length will also influence power made above and below the torque peak. A good illustration of how this works is in this article: Exhaust & Header - Tech - Exhaust Gas Tech - Circle Track Magazine It basically says that shorter pipes will move power from below to above the torque peak and longer pipes will do the opposite. The curve leans as you change the pipe length depending one which direction you go. This is all because of wave tuning and getting either a higher or lower pressure at the exhaust valve when it opens or before it closes. It is important to note that unlike with pipe diameter, wave tuning of this sort is very dependent on cam duration. The timing of the events is critical to determine the correct length so you will need to have some information about the cams you will be using specifically the exhaust valve closing angle. A. Graham Bell in his book "Four-Stroke Performance Tuning" takes a slightly different approach to calculating primary length and diameter He has decided to calculate length first and then use that to also determine pipe size. In the end it is still the same basic principal at work. You choose a target RPM and then size your pipes to give you power at that RPM. He uses this formula: Primary Length = (850 x ED / rpm) -3 ED is the number of degrees before BDC that your exhaust valve closes plus 180. To get primary pipe diameter you then use: ID = sqrt(Cylinder Volume in cc / ((Primary Length +3) x 25)) x 2.1 On a stock 5sfe with an ED of 210, that is just a guess on my part assuming lobe centers of 110 degrees and a duration of 200@0.050", you get the following: According to Bell stock cams will require Increase torque at 3500rpms length should be 48" and ID should be 1.37" which is about 1 1/2" OD. Increase torque at 4000rpms length should be 41.6" and ID should be 1.46" which is close to 1 5/8" OD. Increase torque at 4500rpms length should be 36.7" and ID should be 1.55" which is just over 1 5/8" OD. Increase torque at 5000rpms length should be 32.7" and ID should be 1.63" which is 1 3/4" OD. Increase torque at 5500rpms length should be 29.5" and ID should be 1.77" which is between 1 3/4" and 1 7/8" OD. Increase torque at 6000rpms length should be 26.8" and ID should be 1.79" which is close to 1 7/8" OD. You can see that the two different methods give similar results within a few hundred RPMs. When dealing with 4-2-1 headers you treat the overall length and primary diameter as if they were 4-1 headers and then, from Bell's book, use the formula IDS = sqrt(ID x ID x 2) x 0.93 to get the secondary diameter. So for a 4-2-1 header that had 1-5/8" primaries the secondary diameter would be 2" ID or about 2-1/8" OD. If you think about it that secondary is flowing 2 cylinders worth of exhaust but those pulses are happening twice as often. I'm not sure at this point if you could use that formula because of that but I don't know for sure. The length of primary vs secondary on a 4-2-1 header is a little more of a black art. A. Graham Bell suggests that the primaries be at least 15" long and the secondaries what is left. It's a good place to start. In my opinion a 4-2-1 header will act like progressively weaker versions of 4-1 headers of the same length as the primary, primary plus secondary and secondary lengths. So if your total length is 36" and your primaries are 26" you will have peaks showing up at 4500rpms, 6000rpms and weakest secondary peak would be beyond what the motor is capable of revving. It is more complex then that though because of all the combinations of refections you can have in a 4-2-1 header. You end up with weaker but more waves and that is why they generally give you a broader power band. You can use this to your advantage by keeping your primaries and secondaries different lengths so you have more peaks. If you made them the same lengths then you would end up with fewer peaks that were multiples of each other, say 4000rpms, 8000rpms and 2000rpms. Not the best thing for having a usable power band. You want to pick peaks that are closer to each other 500-1000rpms apart for having a good usable power band. That part is more my opinion and not backed up by any data. Lastly remember that both pipe sizing and length are robbing Peter to pay Paul. When you move the torque peak up you will also loose some torque down lower because air cannot as efficiently flow through that larger pipe at a lower rpm. And with wave tuning for every rpm that you can get a low pressure at the exhaust valve at closing there will be another rpm where it become a higher pressure and you will loose power. The trick is to get them in places where they won't negatively effect your power band.