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 [GP125] All that you wanted to know on Aprilia RSA 125, and more, by Mr Jan Thiel and Mr Frits Overmars (PART 2) (Locked)

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AuteurMessage
Vagelis




Nombre de messages : 30
Localisation : Greece
Date d'inscription : 09/07/2011

2013 - [GP125] All that you wanted to know on Aprilia RSA 125, and more, by Mr Jan Thiel and Mr Frits Overmars (PART 2) (Locked) - Page 22 Empty
MessageSujet: Re: [GP125] All that you wanted to know on Aprilia RSA 125, and more, by Mr Jan Thiel and Mr Frits Overmars (PART 2) (Locked)   2013 - [GP125] All that you wanted to know on Aprilia RSA 125, and more, by Mr Jan Thiel and Mr Frits Overmars (PART 2) (Locked) - Page 22 Icon_minitimeSam 17 Nov 2012 - 7:46

I found a few!

[Vous devez être inscrit et connecté pour voir cette image]

:)
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https://s736.photobucket.com/albums/xx5/Vag1-2/
Jan Thiel




Nombre de messages : 517
Age : 84
Localisation : Bangkok
Date d'inscription : 12/10/2010

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MessageSujet: Re: [GP125] All that you wanted to know on Aprilia RSA 125, and more, by Mr Jan Thiel and Mr Frits Overmars (PART 2) (Locked)   2013 - [GP125] All that you wanted to know on Aprilia RSA 125, and more, by Mr Jan Thiel and Mr Frits Overmars (PART 2) (Locked) - Page 22 Icon_minitimeSam 17 Nov 2012 - 7:52

More MBA cylinders than I ever saw!
Old fashioned now.
You can see very well how the cylinders were fixed to the crankcase.
This is the best system by far!
Designed by Jorg Moller.
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michaelten




Nombre de messages : 39
Localisation : Australia
Date d'inscription : 31/10/2012

2013 - [GP125] All that you wanted to know on Aprilia RSA 125, and more, by Mr Jan Thiel and Mr Frits Overmars (PART 2) (Locked) - Page 22 Empty
MessageSujet: Re: [GP125] All that you wanted to know on Aprilia RSA 125, and more, by Mr Jan Thiel and Mr Frits Overmars (PART 2) (Locked)   2013 - [GP125] All that you wanted to know on Aprilia RSA 125, and more, by Mr Jan Thiel and Mr Frits Overmars (PART 2) (Locked) - Page 22 Icon_minitimeSam 17 Nov 2012 - 10:21

Vagelis a écrit:
Romeuh, the target power does not refer to wheel or trans.shaft power, but 'crank' power or better target BMEP power. Wink
Here's a shortcut to the math in case somebody runs out of ink: [Vous devez être inscrit et connecté pour voir ce lien]

A question on the inputs required for this pipe software.

How do you determine the wave speed?


Thanks

Michael
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Vagelis




Nombre de messages : 30
Localisation : Greece
Date d'inscription : 09/07/2011

2013 - [GP125] All that you wanted to know on Aprilia RSA 125, and more, by Mr Jan Thiel and Mr Frits Overmars (PART 2) (Locked) - Page 22 Empty
MessageSujet: Re: [GP125] All that you wanted to know on Aprilia RSA 125, and more, by Mr Jan Thiel and Mr Frits Overmars (PART 2) (Locked)   2013 - [GP125] All that you wanted to know on Aprilia RSA 125, and more, by Mr Jan Thiel and Mr Frits Overmars (PART 2) (Locked) - Page 22 Icon_minitimeSam 17 Nov 2012 - 11:07

Wave speed changes along with the exhaust gas temperatures. How exactly one can calculate the expected temp -and thus wave speed- from the engine's characteristics/timing/afr/fuel/etc, I do not know. Embarassed
And I suspect the formula's proprietor, Frits, doesn't have the time to explain the whole physics (AND math) behind it, so that we can calculate it on our own.

If you think backwards though, you can feed all inputs from e.g. RSA or (honda) RS and play with wave speed until you get the tuned length of their pipes. Or of course any other engine you know of the timing, max HP revs and tuned length (you'll find only these 3 matter for this formula). And make your own rule-of-thumb for 'racing', 'mass-production' and 'home-tuned' engines wave speed ranges.
Also, Frits have said that 550m/s would be a number to get you started.

To save you the trouble, the 550m/s would correspond to ~550°C and "RSA's" 580m/s to ~680°C. Beyond these plain numbers though, I can provide you with little help.
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https://s736.photobucket.com/albums/xx5/Vag1-2/
Frits Overmars

Frits Overmars


Nombre de messages : 2639
Age : 76
Localisation : Raalte, Holland
Date d'inscription : 12/10/2010

2013 - [GP125] All that you wanted to know on Aprilia RSA 125, and more, by Mr Jan Thiel and Mr Frits Overmars (PART 2) (Locked) - Page 22 Empty
MessageSujet: Re: [GP125] All that you wanted to know on Aprilia RSA 125, and more, by Mr Jan Thiel and Mr Frits Overmars (PART 2) (Locked)   2013 - [GP125] All that you wanted to know on Aprilia RSA 125, and more, by Mr Jan Thiel and Mr Frits Overmars (PART 2) (Locked) - Page 22 Icon_minitimeSam 17 Nov 2012 - 12:36

Thank you, Vagelis.
I wish to emphasize once more that this FOS exhaust concept is only meant to help beginning tuners on their way and a lot of important facors, like compression ratio, ignition timing, type of fuel, carburetter diameter, crankcase volume, and port angle*areas, are not taken into account. Instead of all those factors that I left out, I included one variable, the speed of sound. Starting with 550 m/s will get you in the right ballpark, after which you can vary this value according to your findings.
Final remark: the calculation of the tailpipe restrictor diameter is critical: you can only apply it to engines that are thermally sound. Air-cooled engines are not...
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Daniel A.




Nombre de messages : 55
Localisation : Germany
Date d'inscription : 20/02/2012

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MessageSujet: Re: [GP125] All that you wanted to know on Aprilia RSA 125, and more, by Mr Jan Thiel and Mr Frits Overmars (PART 2) (Locked)   2013 - [GP125] All that you wanted to know on Aprilia RSA 125, and more, by Mr Jan Thiel and Mr Frits Overmars (PART 2) (Locked) - Page 22 Icon_minitimeSam 17 Nov 2012 - 14:22

Frits Overmars a écrit:
Final remark: the calculation of the tailpipe restrictor diameter is critical: you can only apply it to engines that are thermally sound. Air-cooled engines are not...

I found out factor 3,30 working good on an air-cooled engine instead of 3,06 :)

With 3,06 it didn't rev.
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Howard Gifford




Nombre de messages : 140
Age : 68
Localisation : Ottawa Canada
Date d'inscription : 01/05/2012

2013 - [GP125] All that you wanted to know on Aprilia RSA 125, and more, by Mr Jan Thiel and Mr Frits Overmars (PART 2) (Locked) - Page 22 Empty
MessageSujet: Re: [GP125] All that you wanted to know on Aprilia RSA 125, and more, by Mr Jan Thiel and Mr Frits Overmars (PART 2) (Locked)   2013 - [GP125] All that you wanted to know on Aprilia RSA 125, and more, by Mr Jan Thiel and Mr Frits Overmars (PART 2) (Locked) - Page 22 Icon_minitimeSam 17 Nov 2012 - 18:54

Jan Thiel a écrit:
Howard Gifford a écrit:
Manuel we tested 160 opening timing. It did not help or hurt power at the usable powerband but made slightly less power at low rpm and made starting more difficult. 150 seems to be the magic number. 145 made less power all through the powerband.
Our engine has a design drawback in that one inlet port opens from the bottom and one opens from the top. The one that opens from the top has less airflow and I suspect less power than the one that opens from the bottom.

I thought about this when we designed the RSA.
And made te inlet open from the bottom!

Firing 90 degrees is not possible. It would put the inlet ports above the top of the case. 120 degrees would be perfect because we could fire the plug 3 times per revolution at 120 degree intervals. Our rules state we must use a snowmobile ignition and a 3 cylinder Rotax snowmobile ignition would fit nicely into our twin cylinder case. If 90 degrees works well and 180 works well I suspect 120 would work just as well since it is 1/2 way between. With the port now unobstructed perhaps it would make more power.
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michaelten




Nombre de messages : 39
Localisation : Australia
Date d'inscription : 31/10/2012

2013 - [GP125] All that you wanted to know on Aprilia RSA 125, and more, by Mr Jan Thiel and Mr Frits Overmars (PART 2) (Locked) - Page 22 Empty
MessageSujet: Re: [GP125] All that you wanted to know on Aprilia RSA 125, and more, by Mr Jan Thiel and Mr Frits Overmars (PART 2) (Locked)   2013 - [GP125] All that you wanted to know on Aprilia RSA 125, and more, by Mr Jan Thiel and Mr Frits Overmars (PART 2) (Locked) - Page 22 Icon_minitimeSam 17 Nov 2012 - 20:42

Thank you Vagelis and Frits.

I will give 550m/s a try and work from that.

I am going to make a set of pipes for a TZ250 5KE, I will let you know how they go.
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Forgi




Nombre de messages : 29
Age : 42
Localisation : Budapest
Date d'inscription : 19/09/2012

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MessageSujet: Re: [GP125] All that you wanted to know on Aprilia RSA 125, and more, by Mr Jan Thiel and Mr Frits Overmars (PART 2) (Locked)   2013 - [GP125] All that you wanted to know on Aprilia RSA 125, and more, by Mr Jan Thiel and Mr Frits Overmars (PART 2) (Locked) - Page 22 Icon_minitimeSam 17 Nov 2012 - 21:14

Jan Thiel a écrit:


Forgi,

What really counts is blowdown.
But discharging of the burned gases may not be complete until BDC.
In this case you get 'short circuiting' of the fresh charge from the transfer ports into the exhaust.
By using auxiliar exhaust ports you can improve blowdown quite a lot.
So that you might be able to raise the exhaust's 'floor'.
This helps improve blowdown flow, as seen on a flowbench.
In 2007 we started to raise the underside of the exhaust port.
The first results were very promising!
But at the end of 2007 I retired, so I could not finish what I started.
The idea was to raise the exhaust underside as much as possible until power dropped.
And then, with a smaller exhaust port underside it might have been possible to widen the A-ports more
without losing the fresh charge into the exhaust.
The ideal situation would, of course, be that all the burned gases are discharged from the cylinder before
the transfer ports start opening.
So it is difficult to have too much blowdown.
But in trying to achieve enough blowdown you can arrive at a too high exhaust port.
Which first causes power loss at low revs, and if exaggerated still more also a loss of max. power.
Because of shortening the power stroke.

Dear Jan,
I would have a rare question.

Well I have got two very similar 70cc cylinder, only their exhaust ports are different.
One of them has an angle of 184 degrees with an auxiliary port, the other has an angle of 193 degrees without an auxiliary port.
Their blowdown and their time area are about the same. Both of them have the best power at 10K rpm, and of course the length of their exhaust pipe is different for the same rpm.
What is strange that the cylinder with 193 degrees is better, but I don't know the reason.
Is it possible that the power stroke has a minimum and a maximum value? In other words it is impossible to decrease the exhaust's angle neither if the blowdown is ok.

It reminds me of Graham Bell's book, where you can find suggestions for the angles.

There are also extreme cases for example 100cc kart engines where the exhaust port's opening angle is very small but of course it is necessary to get a wide capacity zone.
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Forgi




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michaelten a écrit:
Thank you Vagelis and Frits.

I will give 550m/s a try and work from that.

I am going to make a set of pipes for a TZ250 5KE, I will let you know how they go.

Hello Michaelten!

We can calculate the wave speed of the exhaust gas as follows:

sqrt ( 392 x ( temp+273 ) )

for example:

temp=500 C

sqrt ( 392 x ( 500 + 273 ))

sqrt ( 392 x 773 )

sqrt 303016

wave speed: 550 m/s

It is also another question where do you measure the temperature in the duct or you take an average.
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Forgi a écrit:
...I have got two very similar 70cc cylinder, only their exhaust ports are different. One of them has an angle of 184 degrees with an auxiliary port, the other has an angle of 193 degrees without an auxiliary port. Their blowdown and their time area are about the same. Both of them have the best power at 10K rpm, and of course the length of their exhaust pipe is different for the same rpm. What is strange that the cylinder with 193 degrees is better, but I don't know the reason. Is it possible that the power stroke has a minimum and a maximum value? In other words it is impossible to decrease the exhaust's angle neither if the blowdown is ok.
It reminds me of Graham Bell's book, where you can find suggestions for the angles.
Forgi, I hope you don't mind me answering instead of Jan.
Graham Bell's suggestion that there is a relationship between rpm and port timings, is not correct; the optimum timings for any two-stroke engine are about 190°/130°, irrespective of rpm. The necessary angle areas must be realised via the port widths.
If you follow Bell's guidelines and relentlessly raise the port timings, especially the transfer timing, in order to achieve a high rpm, you risk destroying your cylinder.

Now your question about two exhaust ports with different timings and identical angle areas. The 184° port has two disadvantages: the longer power stroke extracts more energy from the exhaust gas before it enters the pipe, and the timing is too short for true resonance.
This probably needs some explaining.
When the exhaust port opens, a pressure pulse starts moving through the exhaust pipe. It is reflected at the end cone and it should be back at the cylinder just before the exhaust port closes.
Next a part of this reflected pulse bounces off the partly-closed exhaust port and a residual pulse starts moving down the exhaust pipe. This residual pulse too is reflected by the end cone and starts moving back to the cylinder. Ideally it will arrive at the exhaust port just when the port opens again. Then the cylinder pressure and the pressure of the residual pulse combine their energy and the resulting pulse will be stronger than the pulse from the previous cycle. And the combined pulse from the next cycle will be stronger still, and so on; we have achieved true resonance.

Some may argue that we want a low pressure in the exhaust pipe when the port opens because then the spent gases will experience less resistance while leaving the cylinder. But that is not true. Gas flow depends on a pressure difference ratio. But once that ratio reaches 2, the flow velocity will reach Mach 1, the speed of sound. Raising the pressure difference any further will not raise the flow velocity any further.
The cylinder pressure at exhaust opening can be as high as 7 bar and the pressure of the reflected pulse will be about 2 bar. Thus the pressure ratio is well above 2, so lowering the pressure in the exhaust duct outside the cylinder will not do any good to the flow.

What has the exhaust timing got to do with the 'true resonance' I mentioned above?
The initial pulse starts moving at Exhaust Opening and it has to be back at Exhaust Closing, or a little earlier. This pulse travels with the speed of sound and its journey up and down the exhaust pipe will take t seconds.
The residual pulse starts moving at Exhaust Closing and it has to be back at the next Exhaust Opening. This pulse also travels with the speed of sound and its journey up and down the exhaust pipe will also take t seconds.
So from EO to EC takes t seconds and from EC to EO also takes t seconds. In English: the exhaust port should be open just as long as it should be closed.
Assuming that the crankshaft rotates with a uniform speed, this means that the crank angle during which the exhaust is open must be equal to the crank angle during which the port is closed. So both angles must be 180°.

I developed this line of thought some 40 years ago, but when I first published it in 1978 (in the motorcycle magazine Moto73 of which I was the technical editor) everybody called me crazy (some people still do, but I got used to it Wink ).

Above I made a couple of assumptions. The crankshaft does not rotate with a uniform speed, but at high revs the deviation is negligible. In case you really want to know, I did the math for the Aprilia RSA125. At a nominal rpm of 13,000 the minimum rotation speed is 12970 rpm @ 107° after TDC and the maximum value is 13031 rpm @ 356° aTDC. What's more significant: the deviation in crankshaft position from truly uniform rotation is always less than 1°. So that really is negligible.

Second assumption: both the initial pulse and the residual pulse move with the speed of sound. Not true: the pulse pressures in exhaust waves are so high that acoustics rules do not apply any more. We are dealing with gas dynamics here and the stronger a pulse, the faster it moves. Since the residual pulse is weaker than the initial pulse, they move at different speeds. But we will leave this aside for now.

Third assumption: the initial pulse starts moving as soon as the exhaust port starts opening. More or less true, but we are not interested in the first weak appearance of the pulse; we want to know when the pulse reaches its maximum amplitude. And that requires a certain amount of open exhaust port area. It turns out that for our desired theoretical exhaust timing of 180° we will need a geometrical exhaust timing of about 190°, depending on the shape of the port: does it open gradually or does it open over its full width all at once.

The obvious question will be: why has the Aprilia RSA125 a geometrical exhaust timing of about 200°? True, at 190° the maximum torque value would be higher, but the engine would not want to rev because the blowdown time.area would be too small.
The 200° are a compromise: a bit less torque and a bit more revs; as long as the torque decline is smaller than the rpm rise, we gain horsepower.
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thanks Howard and Jan

thanks also tho Frits vor his detailed explanation.
I'd like to request you to write a book about all these things. It would be a shame if all this knowledge will be lost. I think all hir in this forum and still 1000s more would pay good money for such a book. Jan has given you all the things about the RSA, so only you can do something with it.

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a question:

we have a saying:
you can do 2 things to get more hp, 1 thing ist, rise the ccm. if you can't raise the ccm you should raise the RPM.

ist the best number of revolutions vor a 2 stroke engine about 13000 or can you get more hp wen you let an engine rev 16000 or more?
did you tried on the RSA other somewhere else?

Manuel
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Daniel A.




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If you have your maximum power at 16000 you will loose a lot of torque, because you are in lack of time area. The torque decline will be bigger than the rpm rise brings, so you will loose power.

But Frits knows how to solve this problem Wink
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This is the most interesting thread that I have read in my life about 2 strokes technology. Thanks to all the people that share your knowledge in this thread, especially Jan and Frits. Your generosity are extraordinary 2013 - [GP125] All that you wanted to know on Aprilia RSA 125, and more, by Mr Jan Thiel and Mr Frits Overmars (PART 2) (Locked) - Page 22 241515

We want a book written by Jan and Frits!!!! That book would be priceless
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Forgi




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Frits Overmars a écrit:
Forgi a écrit:
...I have got two very similar 70cc cylinder, only their exhaust ports are different. One of them has an angle of 184 degrees with an auxiliary port, the other has an angle of 193 degrees without an auxiliary port. Their blowdown and their time area are about the same. Both of them have the best power at 10K rpm, and of course the length of their exhaust pipe is different for the same rpm. What is strange that the cylinder with 193 degrees is better, but I don't know the reason. Is it possible that the power stroke has a minimum and a maximum value? In other words it is impossible to decrease the exhaust's angle neither if the blowdown is ok.
It reminds me of Graham Bell's book, where you can find suggestions for the angles.
Forgi, I hope you don't mind me answering instead of Jan.
Graham Bell's suggestion that there is a relationship between rpm and port timings, is not correct; the optimum timings for any two-stroke engine are about 190°/130°, irrespective of rpm. The necessary angle areas must be realised via the port widths.
If you follow Bell's guidelines and relentlessly raise the port timings, especially the transfer timing, in order to achieve a high rpm, you risk destroying your cylinder...............................


Hi Frits! I'm glad that you have answered, your comments are just as interesting to me as Jan's explanations.

What's more you have written something that came to my mind before, and you have verified me that my thoughts were right.

So you are telling me that an engine at 6000 rmp have to has an exhaust port with an opening angle of 190 degrees, and it is the ideal. I think that in this case the exhaust port has to be very small to avoid to get a too huge angle area, am I rigth? Well it is obviously a marginal example but according to the theory it is right, isn't it?

By the way what is your suggestion for a given rpm which is the best angle area?

So if we take an average exhaust port, after its opening at 10 degrees will be the maximum of the amplitud, that's why you said 190 degrees, didn't you?
The simulators count with 15 degrees as a maximum of the amplitud after the opening of the port. But I think it is not the same in case of a port with or without auxiliary port. In your opinion the difference is it significant?

Regarding to the transfer port why 130 degrees are the best? Have you any explanation?
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romeuh80




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Daniel A. a écrit:
Frits Overmars a écrit:
Final remark: the calculation of the tailpipe restrictor diameter is critical: you can only apply it to engines that are thermally sound. Air-cooled engines are not...

I found out factor 3,30 working good on an air-cooled engine instead of 3,06 :)

With 3,06 it didn't rev.

That factor is from FOS exhaust comcept or for cross area factor?

Is too low right?

If you compare this with the Honda Exhaust, a cross area factor of 3.3 area in 36.7mm exhaust duct effective diameter would give a small 20,2mm stinguer. While Honda used 22mm for years, and now seems to be 23mm.
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I have just finished to read the numerous posts of this topic. My brain is in high revs but what a pleasure to learn from all of you!

Thank you for sharing your know-how!
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Jan.
Would you have run more compression if the rules allowed a leaded fuel?
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Frits Overmars

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Forgi a écrit:
....So you are telling me that an engine at 6000 rmp have to has an exhaust port with an opening angle of 190 degrees, and it is the ideal. I think that in this case the exhaust port has to be very small to avoid to get a too huge angle area, am I rigth? Well it is obviously a marginal example but according to the theory it is right, isn't it?
Yes, that is what I meant. But when I wrote 'any two-stroke', I meant any racing two-stroke, where the influence of the exhaust pipe must be used to the maximum to be competitive. If power is not important and all you want is an easy to ride bike without temperament, you can use lower timings.
Citation :
By the way what is your suggestion for a given rpm which is the best angle area?
This picture of the Aprilia values may give you an impression:
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Citation :
So if we take an average exhaust port, after its opening at 10 degrees will be the maximum of the amplitud, that's why you said 190 degrees, didn't you? The simulators count with 15 degrees as a maximum of the amplitud after the opening of the port. But I think it is not the same in case of a port with or without auxiliary port. In your opinion the difference is it significant?
A single port cannot open the same amount of area per crankshaft degree as a double or triple port because its shape is limited by piston ring life. So yes, the difference can be significant.
Citation :
Regarding to the transfer port why 130 degrees are the best? Have you any explanation?
That is rather empirical; lower transfers limit the rpm at which the cylinder can still be adequately scavenged; higher transfers limit the exhaust blowdown angle.area. In my FOS scavenging concept (picture below) there is so much blowdown angle.area available that the transfers could have been higher than 130°, but I stuck with these 130° because higher transfers will narrow the powerband; exhaust pulses returning too early would have more opportunity to push the fresh charge back from the cylinder into the crankcase.
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@romeuh80:

I meant Frits' concept.
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p12palof a écrit:
This is the most interesting thread that I have read in my life about 2 strokes technology. Thanks to all the people that share your knowledge in this thread, especially Jan and Frits. Your generosity are extraordinary 2013 - [GP125] All that you wanted to know on Aprilia RSA 125, and more, by Mr Jan Thiel and Mr Frits Overmars (PART 2) (Locked) - Page 22 241515

We want a book written by Jan and Frits!!!! That book would be priceless

A book would be great 2013 - [GP125] All that you wanted to know on Aprilia RSA 125, and more, by Mr Jan Thiel and Mr Frits Overmars (PART 2) (Locked) - Page 22 771973
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A book would be great..... but you cannot ask questions to a book!

In fact, yes, you can.
But the book will not answer you...

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Frits or Jan , .... 200 Deg. ex duration and 130 deg. transfer duration means exhaust open at 80 deg. atdc and transfer open at 115 deg atdc which gives a blowdown interval of 35 deg. This is at least 3 deg. more blowdown interval than we have been using... Our Rotax snowmobile race engines come stock with more generous timings by a couple of degrees ... The auxilliary exhaust on these cylinders in stock form is only approx 85% chordal .. Most of our race prepped cylinders with auxilliaries widened have eo of 79 deg. with 32deg. blowdown ... If we widen the auxilliaries to closer to 100 % chordal , which will greatly increase blowdown and widen the transfers so that the septums are like the RSA should we be reducing the timing angle of all the ports to less than stock timings and also increase the blowdown interval to 35 deg..? 2013 - [GP125] All that you wanted to know on Aprilia RSA 125, and more, by Mr Jan Thiel and Mr Frits Overmars (PART 2) (Locked) - Page 22 980796
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Hard to say, Mike. So your transfers have a timing of 138°? By today's standards that is huge; it will not do your powerband any good, but then you have a CVT to take care of that problem, haven't you?
The right way to go about this is to establish the angle.areas for blowdown and transfer, divide them by cubic capacity and by rpm of max.torque, which will give you the specific time.area values, and compare those to the Aprilia values.
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I think that blowdown should not be primarily referred to as a degree quantity, but as an area quantity (which can't be irrelevant to engine speed, so it becomes time-area).
If -in an imaginary engine and left aside all other exhaust/transfer timing effects- we could have all the required blowdown t-a, within 1 degree of revolution, for every rpm, cylinder would be evaquated, pressure would fall, pwer would be produced etc etc.
Obviously there can't be such an extreme, since neither blowdown is irrelevant to both exhaust and transfer timings nor can be infinite rising area, but hypothetically speaking, it wouldn't matter if blowdown is 1 or 40 degrees, as long as you have the required area to do its job in time.
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