Exhaust pipe resonance

Exhaust Pipe Resonance

When the exhaust port opens, a pressure pulse moves through the pipe towards the atmosphere at the tailpipe exit. At the rear cone this pulse is reflected back towards the cylinder and should be timed to arrive there shortly before exhaust port closure.
A part of this wave strikes the piston skirt covering the majority of exhaust port, this residual pulse then bounces back towards the rear cone. It too is then reflected towards the cylinder. Ideally it will arrive at the port just as it begins to open again.
The cylinder pressure and the pressure form the residual pulse combine their energy to form a super-position at the exhaust port/duct interface. The resulting combined pulse, will be far stronger than the single pulse from the previous cycle. If conditions are maintained, the combined pulse from the next cycle will be stronger still, and continues ad infinitum.
If this condition can be created then we have achieved true Pipe Resonance!

Implicit in achieving resonance is the positional timing of the piston relative to the exhaust port.
The pulse moves at exhaust port opening (EO) and must return at exhaust port closure (EC). The pulse travels at the local speed of sound and its journey will take X number of seconds.
So from EO to EC will take X seconds. The residual pulse also travels at the speed of sound, therefore must also take X seconds. It follows that the time EC to EO also takes X seconds. The time for both these events must be the same X seconds.
For this to happen the exhaust must be open for as long as it is closed, the crank angle from EO to EC and EO to EC must be 180*

So much for the theory. As always in the real world there are assumptions and caveats that confuse things, and we are repeatedly confronted by the needs of race engine demands.
The first assumption is that the returning exhaust pulse travels at the same speed as the out-going wave, they don`t. The out-going is at a sonic speed, the returning is sub-sonic. For our needs the mean of the two is assumed.

Secondly, the crank does not rotate at uniform velocity, but at peak rpm the difference is small. It is calculable but for Bantams is also ignorable!
Third assumption, the pulse starts to move the instant the exhaust port opens. Not quite, the piston velocity is so high that it has travelled a few degrees before the wave amplitude is high enough to be factored in. Port geometry can to a certain extent decide this. Does the port open gradually or over the whole width at once, does the duct roof angle sharply down wards or the port window have a radius on the top edge?

The most significant compromise is that, whilst we may have good torque at low revs at 180* timing, that it is no good for higher rpm, we need adequate blow-down, and so must be extended to 190*, or thereabouts. Lose a bit, gain a bit, but as long as torque fall is less than rev rise, the engine gains power.

Trevor

The Power Stroke?
This post dovetails nicely into the pipe-resonance article.

I guess we have all of us at some stage been warned about the power stroke!
Go too high with the exhaust port and you will lose the power-stroke, a long power stroke is essential for good torque, and so on, but is there a power-stroke at all, the raw numbers might suggest otherwise?
Stroke we know about, 58mm on a 186 engine. What about the “power, where can that part of the heading fit in? The only power available is what energy is produced from the combustion process. So it might seem that the exhaust timing has little to do with creating power due to “pressure” in the combustion chamber pushing the piston down, for longer, with “lower” timings. It is gas pressure soon tdc that creates the real power.
In a 125 Bantam engine at 10,500 with a modern retarding ignition that will occur around 20* atdc, and at around 40* after tdc combustion is over and pressure had dropped considerably.
Here is the first little problem, a 186 with its fixed timing forces a compromise between the contrasts of enough advance at low rpm and a safe level of advance at peak torque. Combustion therefore, will have to start before tdc and so it follows that it will finish earlier after tdc.
Because of the falling piston, cylinder pressure drops from a high of around 50 bar at 20* atdc to 2/3rds of the number when combustion is effectively over. Internal heat energy loss to the cooling cylinder head, piston and bore surfaces, plus the expanding cylinder volume combine to draw down remaining pressure.
Brake Mean Effective Pressure (BMEP) for a good 186 is probably 8bar, some less than this, by definition this is the constant pressure working on the piston.
The height of the exhaust port depends upon two things, for optimum pipe resonance the port needs to be open for as long as it is closed, that occurs at 180*.
But the optimum transfer port height, will leave insufficient time for the cylinder pressure to blowdown, to below that of the crankcase at transfer opening. The only alternative is to compromise true pipe-resonance, and raise the exhaust port timing to 190*
After all of the gas expansion and cooling, hence pressure fall occurring in the large surface area and stroke of the 186, the pressure at exhaust port opening will be less than a couple of bar, and the difference between 180* and 190*will make no appreciable difference to pressure exertion on the piston that creates torque. A pressure ratio of 1 means no gas can flow, as pressures are equal!

So, is there really a `Power-Stroke` at all! Anyone?

Trevor

Trevor, i would say that the pressure produced by the combustion process which acts on the piston , would be the " power stroke". But the amount of time which this pressure is allowed to have its full effect on forcing the piston back down the bore is decided upon the timing of the combustion and the opening of the exhaust port. More torque  i think would be produced if the full combustion force is allowed act for longer on the piston face as it desends back down the bore. This time it would seem can only be interupted by the exhaust port opening and stealing away some of this force. I think i can visualise this now when you see the a graph of engine torque line against the timing curve of the ignition, that this force on the piston can be manipulated by these two factors. It also cofirms that when i tried to use the info given for Robbies 175 port timing, my engine was,  (in terms of  exhaust port timing), guttless.( The other factor being that the cast barrel i had, at the time, i was unable to get the same transfer port areas as Robbies barre)l.Looking at this now i think that having a programable ignition (or exhaust valve) would have enabled me to at least get it to pull away.increasing the ignition starting  piont before tdc  at lower revs starting the combustion cycle earlier giving the force more time to act on the piston at its strongest to produce torque and effectivly  pull away before the exhaust port opened.

have i got this right,? or am i "Torquing rubbish"

I wonder how much torque is needed as a minimum to get a bantam and rider off the line at a respectable rpm and having the gearing to keep up with the screamers when their in full flow?

Nigel,
No you are not `torquing rubbish`, anyone that can conceive and manufacture your intriguing hybrid engine knows exactly what their doing, and saying. I hardly dare ask, but, are you gas tight now?... I have a feeling I may regret that phrase!

The point I have been trying to highlight in the two posts so far, is that the height of the exhaust port relative to the point, atdc, of maximum cylinder pressure is not as critical as at first may be imagined, and as historically we have been led to believe. Indeed, it is the super-position pulses at the exhaust port that create large amplitude waves running down the header pipe and into the diffuser that create a depression at the port around bdc. In terms of energy use it far exceeds any benefit a few extra degrees of power-stroke could ever do, and you can`t have both simultaneously.

Here is an alternative possibility for a given cylinder volume. By using a lower compression ratio there will be a larger cylinder volume above the exhaust port. This will allow more mixture to be stuffed back into the cylinder by the returning pulse from the rear cone. As the expansion ratio will be lower, the pressure drop after tdc will be lower, and the average pressure between tdc and exhaust port opening will be higher. This in turn means that there will be more exhaust gas energy for the pipe to work with and to work for you and produce more torque

Trevor

As I was saying earlier on here  a low compression ratio allows the revs to run on and the resonant pipe acts like a supercharger making the dynamic CR  higher than it would be with a higher static (measured) CR at the higher max revs ...  --

-- and some of us ancient  Steam Engine types refer to the stroke after combustion as the "Expansion" stroke...

The other of my so called philosophies is the shape of the torque curve. Better than (i)  a constant rising torque to max revs is (ii)  the drooping torue from max-torque-speed to max speed witzh a higher max torque than (i)...

Preferable is a `flat´ torque curve which is not possible with a Bantam.....

We called that in (ii), "Torque Back Up" for obvious reasons....

I´ll go into the reasoning of that with a disgram if necessary...

Cheeers!

About getting off the line, Nigel  --

-- it is calcuable.  Slipping the clutch, keeping revs constant as drive is taken up one can assume half the Tractive Effort at rear wheel for the period (as the  length of road) of clutch slip.

That is, for example´s sake:   if the  torque  as Tractive Effort at the rear wheel with Rolling Radius of one foot --  was a constant -- say -- 16*** pounds force  -- say,  for  100 ft of road,  you could draw a  rectangle as your  graph of  16pound on the y (vertical)  axis and the 100ft on the x (horizontal)  axis and the work-done under the graph (area of rectangle) would be 1600 ft-lbs...

... but if you were slipping the clutch for the whole 100ft it would only be the triangle drawn from from zero at x = 0lbs force to the max of 1600 ft-lbs at x = 100feet, that would be the work-done. Thus the triangle of work-done, in this example, would be  800 lbs-ft.

For optimum tractive effort (force exerted at road patch) -- and obviously optimum acceleration -- when clutching-slipping at the start --the revs should be held as close as possible to the speed of engine´s max torque
speed.
Icarus-One used to scream at 7500 rpm every time I slipped the clutch and would only rev on to 8400rpm...

I was spectating at the second  2011´s  Cadwell  meeting and the Bantam diffrence in acceleration off-the-line was huge: some Bantam riders were paddling their feet whilst screaming their engines and some were away with feet up but  one particular Bantam leapt out of the middle of the  pack and was off like a `Robber´s-Dog,´  such  that by the bottom  of the hill he had more than 25 yards lead on the second bloke.

Obviously the shorter the period of clutch slip the more force, F for acceleration...

Speaking of acceleration : that is what racing is mostly about as, "mph per second..." -- not max speed on the flat, which naturally brings us to W,- the total weight of bike & rider, F, - Tractive Effort or Force at the road patch and the formula F = ma where a is acceleration and m is mass (W/g) what we then have is.--

From, Fg/W = a and using F = 16lbs force: W = 320lbs and g = 32.2ft/sec/sec

16g/320 = 1/20 of g which is...........1.61ft/sec/sec.............

If thw W is a third more then 16g/480 is s 1/30g which is .........1.073ft/sec/sec

For a third MORE weight the acceleration is less by nearly a third.

These values of F and W are probably nothing like reality and only used here to demonstrate the fact that weighty riders are always at a disadvantage on a Bantam. Its simple stuff (which means I probably made an arithmetic error) and it is easy to see that if you double F you double the fraction of g acceleration of W....

Cheers.

*** just a figure off the top of my head to use as example -- probably more....

JayBee...

Cheers John, i suspect a good case for CVT

So Nigel, if you can factor out beer and donuts from John`s calcs you will feel a power to weight ratio benefit the equivalent of a torque increase! Be a pretty dull life though don`t you think; not sure Bantams are worth that kind of personal sacrifice?
Custard filled, eased down with a glass of cool IPA, ahh, now you`re talking!

Cheers, Trevor

Thank you both -- IPA -- aahhh! I  feel now I must tell you part of my life story -- which some of you have heard already (and is on another section here anyway) -- about the suffering of a would be Bantam racing star...

I was sucking-up to Ford and Leyland for SMU (Simms Motor Units Finchley diesel pumps & injectors ) spending expenses like a man with forty arms which had my body weight at nearly 16 stone. The Ford staff were mostly wine and exotic cocktail-stuff drinkers and most of the Leyland staff too but my boss had me  concentrate on  the Blue-Collareds, in an intelligence-gaining function and could those lads  put it away.  

Having got the Bantam message I checked with my local GP about dieting and he would not believe my weight and said try drinking gin (which I hate) when with these people,  rather than beer -- and eat what you eat in day spread over a week.  Going to Leyland I would park the car in a lay-by and run for an hour before getting stuck in on the gin & nosh. Later when doing a full week among the Lancastrians I´d go ice skating 2 or 3 evenings of the week to prevent any attempt at  eating . I cut out Brekkers all together except for black coffee and fresh fruit. I ate less than a sparrow ... After 3 months I looked like a Belsen inmate,  gaunt and ill.
  In 3 months I got down to 12stone 3lbs and was so weak I´d often get a volunteer to start the Bantam at Brands practice. That run & bump start -- which is another sad story of wretched race rules  -- used to give me nightmares. How horrible if the clutch dragged and the piston was at TDC when the bum bump came. ...
When Sir Andrew Boyle of vintage 250 RE fame leant me his 250 ABS it was joy at last with 5 gears and POWER I  hardly ever slipped the clutch. Then when I moaned about the Albion cork clutch dragging AND slipping he installed a Greeves all-metal clutch -- Wow! the racing after that was real fun -- and exciting.

Great pity I went to Canada for status-gain and more money. I say that because I´d have been having GP team bosses calling me ...

... the one regret is i only just got into real racing when it was packing-up time.  

I must add though that I enjoyed a great  many Bantam  Intermediate races which Icarus-1 WAS competitive.

It is that point I keep making -- it is so obvious that the fast Bantams are (and were)  so much faster than those at the back who don´t have the wherewithall, cash and professional-skill-facilities to get themselves qicker -- that it must have put off a lot of lads who would race Bantam  if there was a suitable class for them...


OOps! Time for dinner and a glass (or two) of Kölsch (Cologne beer that is low on calories -- so the German Brewer says...).....

Cheers!

OK -- that´s nice of you --  nobody criticised the fantastic error... 16ftlbs is without transmission loss and the torque with a Bantam at the rear wheel is more like 9 - 10ftlbs with the Tractive Effort (TE) being multiples of torque according to gear ratio.

The Tractive Effort is the torque multiplied  by the gear ratio and with a 14 : 48 sprocket set up and normal Bantam Primary gear ratio the bottom gear  ratio -- with a rear wheel Rolling Radius of 11.4" --  would be 11.787:1 making the tractive effort something more SENSIBLE  like 106.lbsfeet to 117.87lbsft....

.

So with the W at 320lbs, g at 32.2 ft/sec/sec  the acceleration would be   106.g/320  =  0.353g  =  
11.366ft/sec/sec   =   7.75mph/sec...

Probably done it again -- and retiring hurt (for the moment) because my PC wiped out a load of lovely stuff and I shall have to fall over for a while before doing it all again....


Any comments on 7.75mph/sec times 5 seconds giving 38.95mph when accelerating in 1st gear?

Should I go and hide?

Cheers!

JayBee for John-boy.

Evening PS -- I looked up Bantam Sprinters:   Brian White and Tom Miller´s times for the quarter in 2003   and Brian´s was at 16.4... and Tom´s at 16.8secs so I think the next step here is to work out how many second the "good" Bantam would be in 1st gear getting-off-the-line----

Frits Overmars………………..
When the engine is running at 13,000 rpm, the cylinder pressure in the cylinder is not capable of accelerating the piston fast enough. The conrod has to pull the piston down! So this phase of piston movement does not put energy into the crankshaft; it costs energy.

After the piston has reached its maximum velocity, the conrod has to slow it down again. Now the piston is pushing against the conrod and positive energy is delivered to the crankshaft.

After the piston has stopped again at BDC, the conrod has to push it upwards until maximum speed is reached again. Then the piston wants to continue at that speed despite the fact that the compression pressure is trying to slow it down. So now the piston is pulling the conrod, which is also delivering positive energy to the crankshaft.

The so-called “work-stroke” of the piston does not exist! Instead there are two “positive half-strokes”: from mid-position down to BDC when the piston pushes against the conrod, and from mid-position up to TDC when the piston is pulling at the conrod. In this example I am talking about a two-stroke engine, but it is not difficult to understand that the same things happen in a four-stroke.

Not my words but the author is pretty obvious, the choice of work-stroke is Frit`s preferred description but the meaning is the same as power-stroke; interesting explanation of the same phenomenon but from a different aspect.


Trevor

I can't get my head around that, Trevor. If this is an engine capable of turning at 13,000 rpm in top gear, what keeps it going, if not the expansion of the gasses? The way it is described, it sounds as though it would lose momentum, like a flywheel with insufficient power input.

We seem to be lifting ourselves off the ground by our own boot straps.

Speaking of flywheels John C... an intersesting subject --  I´d like to hear more about on here  ...


Frits Overmars  was saying ?? .... Reminds very much of hearing an engineer;   one of the audience at 1 Birdcage Walk,  London -- when the subject was "Unusual Engines" saying, "Why don´t you petrol-engine engineers get round to having combustion at BDC as well as TDC.... " He was of course thinking of the double-acting steam engine -- dozy old gitt!


Bring back the Wankel its piston just rotates ....

Cheers!

I Googled "Frits Overmars"?

What a fantanstic looking machine with neat looking pipe -- I wonder what went wrong with his getting it all together? Someone from BRC  ought to take a look...

 Seems that if the engine is running at 13,000 rpm its combustion efficiency is only sufficient to overcome its Friction Losses....

Cheers,
John-Boy.

Comments by others on that Frits Overmars site -- e.g. "Dean" and his McCulloch engine revving to 18000 rpm -- small wonder the rod couldn´t stand it...

I wonder about "engineers" and "Engineering"...??

Cheers!