116 replies to this topic

[hydra]

Now I'm sure we've all heard over and over again that one shouldn't go much above a mean piston speed of 4000-4500 feet/min for a roadgoing engine. What I'd like to know exactly, is if this is due to frictional/wear considerations (skirt/rings rubbing against the bore), or due to accelerational loadings, which increase with the square of piston speed. ( mrw2 (1 + r/L) )

For example, lets take 2 similar engines, varying only stroke and peak rpms (while keeping r/L ratio constant), and lets assume that the rotating parts in question can handle the required loads.

with a 3 inch stroke, 4000fpm = 8000rpm, whereas with a 3.5" stroke it is equal to 6860rpms. If we were to impart identical tensile loadings we would have to rev the second engine up to 7410rpm, bringing its mean piston speed up to 4320ft/min, which brings us back to my original question... Just how relevant is mean piston speed when taken on its own? Just what prevents me from going to extremes and revving an engine with a 6" stroke up to 5660 rpm, loading it just as much as our first engine while giving a (very high) mean piston speed of 5660 feet per minute?




P.S. I do realize that there are a few production engines like the M3 and the S2000, or any other high-revving honda lump for that matter that go well above 4500fpm in STOCK form. However, most high-end supercars (Enzo, Carrera GT et al) barely touch 4000fpm. What gives?

[McGuire]

It's not so much about mean piston speed as acceleration, which is a function of crank speed, stroke, rod length, and crank angle. (Trig anyone?) But since they tend to fall within a given range relative to rpm for typical engines (and people tend to hate trig) mean piston speed is thrown about as a useful rough indicator.. with the issue being not friction but inertia loadings.

In the old days the informal rule-of-thumb limit was 3500 fpm, then 4000-4500, then 5000 fpm or thereabouts...I don't know where the line would be today, or if there even is one due to all the different types of usage and other variables. IMO much of the emphasis on piston speed in the collective knowledge base is a legacy of iron pistons and long strokes.

[red300zx99]

From what I remember from working at an engine shop was the use of piston speed as some sort of indication of dwell or something like that, slips my mind, but maybe someone else knows what I'm talking about.

[McGuire]

Originally posted by red300zx99
From what I remember from working at an engine shop was the use of piston speed as some sort of indication of dwell or something like that, slips my mind, but maybe someone else knows what I'm talking about.

Piston dwell refers to the duration per crankshaft rotation (in percentage or degrees) the piston stays at/near top dead center, which is a function of the ratio of crank throw radius (i.e., half the stroke) to connecting rod center-to-center length. The longer the rod relative to crank throw radius, the greater the dwell. Piston dwell influences intake/exhaust port flow, combustion, and compression, roughly in that order.

However, this influence is subject to a host of factors, including piston and chamber design, port volume, and valve timing. Unless these variables are somehow constrained by some other consideration (say, in production-based engines where port volume and valvetrain dynamics are limited, or the combustion chamber is compromised) there is seldom very much to be gained by fiddling with rod length...except that in general, a longer rod decreases both angularity and peak inertia and thus is a good thing all around.

But back in the day, the small block Chevy always seemed to like a longer rod, often showing a measurable power gain on the dyno in certain combinations...especially with the old Crane 550 roller cam. It was generally presumed that the engine's limited port intake port volume (due to the "book-fold" siamese head layout) worked better with slower cylinder-filling. Meanwhile the SB Cleveland Ford never responded to the longer rod quite as well, probably due to its giant, overkill ports. The current racing versions of these engines are pretty well optimized and very similar to each other as well, so there isn't much difference anymore. Those who run large volumes of nitrous oxide claim their combination actually responds to a shorter rod, but I don't know about that.

[J. Edlund]

Usually it's hard to find engines that have a piston mean velocity much over 25 m/s (would give around 5000 ft/min or so), this independant on the piston acceleration.
Comparing different strokes a short stroke engine will have a higher piston acceleration for any given piston mean velocity, lets take three examples:

NASCAR engine, 83 mm stroke and 9000 rpm
24.9 m/s
4,000 g

F1 engine, 40 mm stroke and 19,000 rpm
25.3 m/s
9,800 g

3.5cc R/C racing engine, 16 mm stroke and 48,000 rpm (typical 30k-50k rpm dependning on application)
25.6 m/s
26,000 g

So it seems like, that for a racing engine the piston velocity is the limit, not the piston acceleration.

One can say that the friction loss is in relation to the mean piston velocity, so using high velocity will increase the friction loss. But I assume that there are also tribological reasons for this, which probably are the limiting ones when it comes to velocity. This is what for example limit the engine speed of a rotary engine and is also why Nikasil was developed which origianally was developed for rotarys to solve the sealing during high sliding speeds.

Finally, by this I don't mean the piston acceleration isn't a limit, the piston acceleration together with the mass of the reciprocating parts loads the con-rods and crankshaft but this can usually be solved to some degree by using stronger and lighter parts, the much lighter parts of the 3.5cc engine compared with for example the F1 engine is also the reason that such high piston acceleration can be used. So I think the sum of this is that the acceleration*reciprocating mass together with the sliding speed of the piston sets the limit of what revs/mean velocities that can be used. If it only was the acceleration*mass that set the limit we would have seen long stroke engines with higher piston velocities.

[jgm]

It is perhaps worth reflecting that 4500 fpm is about 51 mph - not exactly hypersonic and, by itself, hardly likely to be destructive of a rice pudding let alone a piston.

[hydra]

Originally posted by jgm
It is perhaps worth reflecting that 4500 fpm is about 51 mph - not exactly hypersonic and, by itself, hardly likely to be destructive of a rice pudding let alone a piston.

Yes but apparently anything much above 5000fpm, which is about 57 mph - still not exactly hypersonic, is pretty likely to destroy a piston and/or rotating assembly.
Not a rice pudding though, I hear those are indestructible :-P


As an aside J.Edlund, does rod ratio, and thus maximum side load on the piston, affect the maximum piston speed we can run? Suppose we had an engine with a really long rod ratio, or better yet a scotch yoke/epicyclic/cam-follower mechanism with an infinite rod ratio and very small side loads. Could we "compensate" by pushing piston speeds to the point where side loads would be equivalent to where they were previously (say with a 1.6 rod ratio running X rpms), or would we encounter problems with the oil film breaking up - or whatever- well before that?

[Greg Locock]

It is perhaps worth reflecting that 4500 fpm is about 51 mph - not exactly hypersonic and, by itself, hardly likely to be destructive of a rice pudding let alone a piston.

Ah, but you are trying to slide two metal surfaces against each other, non destructively, while running quite high load sthrough the interface. Try rubbing your hand against the road at 50 mph and tell me about rice pudding.

[McGuire]

Originally posted by jgm
It is perhaps worth reflecting that 4500 fpm is about 51 mph - not exactly hypersonic and, by itself, hardly likely to be destructive of a rice pudding let alone a piston.

I'll say again: it's not really about mean piston speed, though there are some interesting symmetries among various engines (depending which engines you select and how you compile the numbers of course). It's just a very rough rule of thumb.

It's really about piston acceleration. For example, there is absolutely no way to calculate inertial loadings on the reciprocating assembly from mean piston speed. If the cranktrain were in constant uniform motion as this figure implies, there would be none eh. The average speed of the piston in one crank rotation may only be 51 mph, but the peak acceleration may be on the order of 9,000 g, generating inertia loads on the order of eight metric tons. So what does mean piston speed tell us, really? If you are designing an engine, it's rather like trying to ford a creek with an average depth of three feet.

[J. Edlund]

Originally posted by hydra


Yes but apparently anything much above 5000fpm, which is about 57 mph - still not exactly hypersonic, is pretty likely to destroy a piston and/or rotating assembly.
Not a rice pudding though, I hear those are indestructible :-P


As an aside J.Edlund, does rod ratio, and thus maximum side load on the piston, affect the maximum piston speed we can run? Suppose we had an engine with a really long rod ratio, or better yet a scotch yoke/epicyclic/cam-follower mechanism with an infinite rod ratio and very small side loads. Could we "compensate" by pushing piston speeds to the point where side loads would be equivalent to where they were previously (say with a 1.6 rod ratio running X rpms), or would we encounter problems with the oil film breaking up - or whatever- well before that?

A guess is that it affects how large skirt that might be needed.

Pistons without side loads are otherwise used in large engines like ship engines, where I can guess that the increased weight doesn't matter much.

[hydra]

Aah... Good point, this brings up another question... Just how much piston side force can be tolerated in a modern hi-performance engine with say coated aluminum bores? Any data, empirical or otherwise, would be appreciated.

[Bill Sherwood]

Originally posted by hydra


Yes but apparently anything much above 5000fpm, which is about 57 mph - still not exactly hypersonic, is pretty likely to destroy a piston and/or rotating assembly.
Not a rice pudding though, I hear those are indestructible :-P

FWIW the Honda S2000 engine at redline has a piston speed of around 5300 ft/sec.
That's just a road engine, not a full-race engine. For sure with better materials even more piston speed could be had, but I have to ask why would you want to?
(I'm a short-stroke fan myself)

[hydra]

Originally posted by hydra

P.S. I do realize that there are a few production engines like the M3 and the S2000, or any other high-revving honda lump for that matter that go well above 4500fpm in STOCK form. However, most high-end supercars (Enzo, Carrera GT et al) barely touch 4000fpm. What gives?

Why would you want to that? Oh I dunno... maximize power density without compromising chamber shape, amongst other reasons... Its not the best way to do things, but it definitely has its advantages. The way I see it, for a well-rounded road-going engine, there's little to no point going above 8000-8200 rpms, so you'd build a motor with the highest piston speed you can get away with for a given bore, thereby maximizing displacement and thus mid-range torque. Remember; rpm = ruins people's motors

[McGuire]

Originally posted by Bill Sherwood


FWIW the Honda S2000 engine at redline has a piston speed of around 5300 ft/sec.
That's just a road engine, not a full-race engine. For sure with better materials even more piston speed could be had, but I have to ask why would you want to?
(I'm a short-stroke fan myself)

The Honda S2000 engine in pre-2004, 2.0 liter form has a 87mm bore x 84mm stroke (3.307") and makes 240 bhp at 8300 rpm.

So here, mean piston speed is 4575 feet per minute. (23.24 m/s.) That is indeed rather high for a 2.0 liter four cylinder production engine, due of course to its higher rpm range. How do they get away with it?

In large part Honda managed this by using a very long connecting rod: 153mm (6.0236"), a good half-inch or more longer than typical practice for production engines of this type. The longer connecting rod reduces piston acceleration. Classic crank arm reciprocating motion, as found in any number of textbooks: The longer the rod relative to crank throw radius and crank angle, the closer to uniform motion is the piston's travel.

Once again, the issue is not really "mean piston speed." It's piston acceleration, and the inertia loads which result. Twice per crankshaft rotation, at TDC and BDC, the piston must come to a full stop in order to change direction. The piston is then accelerated to its maximum speed around mid-stroke, also twice per crank rotation. NOTE: When the piston is traveling its slowest, its acceleration is greatest, and vice versa. And this happens twice every time the crankshaft rotates once.

So obviously, the average or "mean" speed of the piston (here, 4575 ft/min, or 51 mph) is not going to tell us much if anything about what is happening inside our engine. For example, it tells us nothing about the reciprocating inertia loads, which are a function of the piston's vertical acceleration, not its speed.

[McGuire]

Originally posted by J. Edlund


A guess is that it affects how large skirt that might be needed.

As a practical matter, how little piston skirt you can get away with depends mainly on how much wear and oil consumption the design mission can tolerate, as well as how well they can be managed. It's really about the care and nurturing of the piston rings, as they are the vulnerable point in the ring/piston/bore interface. There is fairly direct connection between skirt length and ringset life. The shorter the skirt the less stability for the ringset in the bore and as the rings deteriorate, leakdown (blowby) increases and output drops. Naturally, ring flutter etc. are worst at max piston acceleration, which occurs when the piston is traveling its slowest, eh -- at near TDC/BDC.

[McGuire]

Originally posted by hydra


Why would you want to that? Oh I dunno... maximize power density without compromising chamber shape, amongst other reasons... Its not the best way to do things, but it definitely has its advantages. The way I see it, for a well-rounded road-going engine, there's little to no point going above 8000-8200 rpms, so you'd build a motor with the highest piston speed you can get away with for a given bore, thereby maximizing displacement and thus mid-range torque. Remember; rpm = ruins people's motors

Quite so. There is no better example than Honda's changes to the S2000 for 2004. The earlier version displaced 2.0 liters (87mm bore x 84mm stroke) and produced

240 bhp at 8300 rpm
153 lb ft of torque at 7500 rpm

Conversely, since we know HP = torque x rpm/ 5252, we also know this engine develops

151 lb ft of torque at 8300 rpm
218 bhp at 7500 rpm

For the 2004 version, Honda lengthened the stroke to 90.7 mm (behold, an undersquare sports car engine!) to increase the displacement to 2.2 liters. It now develops:

240 bhp at 7800 rpm
162 lb ft of torque at 6500 rpm

And so:

161 lb ft of torque at 7800 rpm
200 bhp at 6500 rpm

The engine now makes exactly the same max hp as before (240) but at 7800 rpm instead of 8300 rpm. And the engine's horsepower trend appears peakier. However, the engine now makes more torque over a broader range, which provides more acceleration with fewer gear changes, which makes the engine seem more powerful to the driver, and on a closed course will result in lower lap times. Since max hp has not changed at all, top speed remains identical.

Of course, the increase in stroke resulted in a slight increase in piston speed, despite the reduced rpm (4641 ft/min vs 4575 ft/min) And due to the limitations of the engine's architecture, the connecting rod had to be shortened from 153mm to to 149.65mm in order to accomodate the longer stroke, which increases the inertial loads slightly as well. Needless to say, Honda must believe it's not anything they can't handle.

This comparison also obviously points to a brisk discusssion earlier, on the relative merits of horsepower vs. torque. At the risk of reopening that energetic can of worms:

In any gear, top speed occurs at the rpm of peak hp.
In any gear, maximum acceleration occurs at the rpm of peak torque.

[hydra]

Originally posted by McGuire


As a practical matter, how little piston skirt you can get away with depends mainly on how much wear and oil consumption the design mission can tolerate, as well as how well they can be managed. It's really about the care and nurturing of the piston rings, as they are the vulnerable point in the ring/piston/bore interface. There is fairly direct connection between skirt length and ringset life. The shorter the skirt the less stability for the ringset in the bore and as the rings deteriorate, leakdown (blowby) increases and output drops. Naturally, ring flutter etc. are worst at max piston acceleration, which occurs when the piston is traveling its slowest, eh -- at near TDC/BDC.

Excellent post McGuire, I'm glad you brought piston skirt length up... Let's assume for the moment that we're talking about a hardcore STREET engine expected to last oh I dunno... 60-100k miles between rebuilds? (Is that reasonable?) How would you go about managing wear and oil consumption? Small clearances to minimize piston rock? Teflon coated skirts? Vacuum in the crankcase to minimize blow-by/oil consumption? What else is there? Another thing, is there any empirical relation or rule of thumb for piston skirt length and the other related variables?

[J. Edlund]

In any given gear acceleration will be greatest at maximum torque, and I think this confuses some people since the most powerful car will accelerate fastest, not the car with the most torque. This is quite simple, F=ma where F is the torque on the driven axles acting on the radius of the wheels. Of this reason, for any given mass, the acceleration will be highest when torque is highest. What is important to know is that the maximum torque on the driven axle will be reached with the most powerful engine, independant on engine speed. Since the gearbox acts as a torque multiplier the maximum torque at the rear wheels, and therefore acceleration will be greatest at maximum torque. This does however not indicate that maximum performance will be reached at peak torque, but by uing a lower gear and keep the engine speed more close to maximum power.

Furthermore it should be noted that widening the powerband isn't equal to lowering it. In the case with the Honda engine the numbers actually indicate that the shortstroke version should be the fastest of the two even given equal numbers of gears (with different ratios for the two engines).



So the reason for the increased stroke is likely to be of other reasons like increased driveability. Since low engine speeds aren't used in racing (the exception is some low speed turns) it will have little impact on performance, the increased performance at high engine speeds are much more important, which also have been stated by for example Ilmor.

Regarding the piston velocity, piston acceleration alone cannot explain it all, this since two engines with equal bore but different strokes can use about the same mean velocity but the shortstroke engine will have higher accelerations. Perhaps some can be explained by con rod length, an engine at lower speeds tend to perfom better with a short er rod which increase the acceleration, also with a given deck height a longer rod will not fit. But with a piston travelling at a mean velocity of over 40 m/s (almost twice the mean velocity), and the piston is pushed against the cylinderwalls as well as the piston rings, and they aren't fully separated by an oil film.

[Greg Locock]

A great deal of rubbish is posted about piston accelerations. To a first order approximation, they obey simple harmonic motion. This treats them as Scotch Yokes, or assumes that the conrod length L is infinite.

So, for N rpm the angular velocity w is N/60*2*pi radians per second, and with a stroke 2*r with r in metres

we have

max velocity = w*r m/s

max acceleration= w^2*r m/s/s

That's it.

We can then multiply this by a 2nd order correction for the L/r ratio, sadly it gets rather complicated, but it would seem to be

max acceleration= w^2*r*(1+r/L+1/4*(r/L)^3+15/128*(r/L)^5...)

I did not add the ellipsis, the Bosch blue book did. I'm surprised by the r/L term, that is a big one for realistic r/L s

[J. Edlund]

"The maximum speed of rotation of an engine depends on several factors, but the principal one, as demonstated by any statistical analysis of known engine behavior, is the mean piston speed. This is not surprising as a major limiting factor in the operation of any engine is the lubrication of the main cylinder components, the connecting rod, the piston, and the piston rings. In any given design, the oil film between those components and the cylinder liner will deteriorate at some particular rubbing velocity, and failure by piston seizure will result."

Gordon P. Blair, Design and Simulation of Four-Stroke Engines.

[McGuire]

Originally posted by J. Edlund
"The maximum speed of rotation of an engine depends on several factors, but the principal one, as demonstated by any statistical analysis of known engine behavior, is the mean piston speed. This is not surprising as a major limiting factor in the operation of any engine is the lubrication of the main cylinder components, the connecting rod, the piston, and the piston rings. In any given design, the oil film between those components and the cylinder liner will deteriorate at some particular rubbing velocity, and failure by piston seizure will result."

Gordon P. Blair, Design and Simulation of Four-Stroke Engines.

A wonderfully global generalization, typical (and neccesary) in textbooks and technical support literature. I'm sure Dr. Blair didn't mean to have his meaning taken with such literal specificity. When we examine the value of the statistic "mean piston speed," we need to ask: at what point in its remarkable journey is the piston actually traveling at "mean piston speed"?

For example: The piston makes a full stop twice per crank rotation. In the Honda S2000 2.0 liter engine previously mentioned, at 8300 rpm the piston makes 276 stops per second. The piston is then accelerated at several thousand g, also twice per crank rotation. In the Honda, from -4125 g off TDC, to +2416 g at 155.5 degrees ATDC. But if we assume as with mean piston speed that the piston is traveling in uniform motion at constant velocity, how can we possibly calculate the reciprocating inertial loads on the piston, pin, connecting rod, and crankshaft? If the piston is moving at a constant rate it has no reciprocating inertia at all. We know that isn't true, but mean piston speed does not tell us any different. And don't oil molecules have inertia too?

In the Honda engine above, mean piston speed at max rpm is 4575 ft/min. (52 mph, 23.24 m/s) Minimum piston speed is zero while max piston speed is 7456 ft/min (85 mph, 37.87 m/s) at 75.8 degrees ATDC. So: do we design the lubrication system to deliver sufficient oil volume for minimum piston speed? Or for mean piston speed? Or for the piston's maximum speed, when the piston and rings are covering 65% more real estate than was predicted by mean piston speed?

How piston/ring/wall lubrication really works: at mid-stroke, piston velocity is sufficient to obtain hydrodynamic lubrication. Off midstoke, lubrication is by thin film while at/near TDC when the piston is near a standstill, the film breaks up and the rings operate largely in boundary lubrication. (And not surprisingly, that's where the cylinder wear is found.) If we just conveniently assume the piston moves at a constant rate, all that is beyond our view.

When you get right down to it, there really isn't a specific aspect of engine design or operation which can be quantified with meaningful precision via mean piston speed. We can't calculate the vertical inertial loads, the angular or side loadings, the actual lubrication requirements, or anything else. It's just a general rule of thumb -- only useful if you understand the limitations of its meaning. That is the trouble with average or mean representations of anything. In a dynamic system, these statistics don't speak to what is happening in real time. If Michael Schumacher's average lap speed is 98 mph, how much does that tell us about the vehicle's dynamics at the end of the main straight?

[McGuire]

Originally posted by hydra


Excellent post McGuire, I'm glad you brought piston skirt length up... Let's assume for the moment that we're talking about a hardcore STREET engine expected to last oh I dunno... 60-100k miles between rebuilds? (Is that reasonable?) How would you go about managing wear and oil consumption? Small clearances to minimize piston rock? Teflon coated skirts? Vacuum in the crankcase to minimize blow-by/oil consumption? What else is there? Another thing, is there any empirical relation or rule of thumb for piston skirt length and the other related variables?

In reference to your last question, then I'd have to kill you. I don't own that info and people still know where to find me. I can be more generous with street engine info gathered on my own time. Having built dozens of high performance street/club racing engines (mostly Chevrolet) with sometimes varying results, I have become a major fan of the Keith Black 18% hypereutectic permanent-cast piston. If it is installed properly (it has some special needs) in a suitable combination it is ideal for a high-performance street engine. Are you interested in the specifics?

[hydra]

Sure! Bring it on!!

[WPT]

McGuire said , "In any gear, maximum acceleration occurs at the rpm of peak torque. "

True, but at any speed maximum acceleration occurs in the gear that delivers the most hp.
WPT

[Greg Locock]

McGuire said , "In any gear, maximum acceleration occurs at the rpm of peak torque. "

Not to be too picky but that is not quite true. It depends a bit on the gradient of the resistance curve and the gradient of the torque curve. Consider for example the case of an engine with a very gently rising torque curve. Acceleration could be greater at lower speeds, where the vehicle resistance is less, than at the redline where the peak torque is.

[WPT]

Every text book I have seen (not that many) that derives the piston velocity and acceleration equations simplifies the the calculation by using the fact that for small angles the cos very nearly equals 1. This is justified because the resulted equations give exact answers at TDC and BDC, only small errors at inbetween crank angles, and eases the mathematics somewhat. It is interesting to note that exact solutions can be drived if one is willing to wade through the math. If requested I can post the exact equations.
Having the exact equations I wondered how the Fourier componets would match with the simplified equations. The results for a r/l=0.248 (because I own a Ducati with this ratio) with the wr^2 term factored out: For the simplied equation of course; w(1) = 1.00000, w(2)= 0.248
and for the eact equation; w(1)=0.99955, w(2)=0.25193, w(4)=-0.00400, and w(6)=0.00007.
All the componets are for the cos terms. All the sin terms and the rest of the cos terms to w(18) were effectly zero. More justification for using the simplied derivation.
In Wright's recent Ferrari book one can use the cross-sectional engine veiw and/or the reported data for max piston acceleration to determine the rod length. The rod length calculates out to 111.7 mm center to center. Thus, for the Ferrari r/l=0.185, or l/s=2.70. WPT

[McGuire]

Originally posted by hydra
Sure! Bring it on!!

Since the KB hypereutectic piston is a permanent-mold casting with very nice thermal expansion properties, you can run much tighter clearances: .001skirt-to-wall, as opposed to .0035 to .0075 with a forging (why forged pistons kinda suck for real street engines.) I run .0012-0015. With very little piston rock the deck clearance can be held very tight, which will show up on the dyno up and down the range thanks to superior quench.

"Hypereutectic" of course means that the aluminum alloy is saturated with silicon via a special melting process; with the KB piston 18%. With little silicon nodes sticking out of the piston, dry sliding friction is very low. Even with the ridiculously tight clearances I run, I have never seen any scuffing or galling. The 390 alloy is heat-treated to T-6, more than strong enough for high-performance street use, either normally aspirated or supercharged at real street boost levels. For nitrous or turbo use you are probably better off with a forged piston, mainly for some of the nasty thermal issues you can get into with these applications.

The KB piston is extremely thermally efficient, so much so that you can get into trouble if you don't know what you are doing. With the top ring groove cut relatively close to the crown, you have to gap the top ring as if it were a step seal or gas port ring: .0065" per inch of bore, or .026 for engines in the 4"/100mm bore range. If you run standard ring gap, say .017", the ring will butt and pull the top land right out of the piston. (At which point the usual idiot says, "cheapass cast pistons....") But if you assemble it properly, this combination in a normally aspirated SB Chevrolet will easily go 100,000+ miles without significant degradation in leakdown. And it runs so cool you can fill the water jackets with block cement up to the front core plug and run the small water pump and stock radiator, pulling 450+ bhp with excellent BSFC.

One side benefit of the KB piston is cost: roughly half the price of any QUALITY forged piston (the only kind you want to run). Hot rod lore says "forged pistons are better." Well, not if they are junk, which many are. A cast piston is more or less homogeneous, while a forged piston has a directional grain structure so it will be stronger... in theory. But if a number of part numbers share forging blanks as with many "bargain" forged pistons, the material thickness will not be where it is supposed to be for optimum strength, lightness, or thermal expansion. (Why some need .0075 skirt clearance. Ugh. I hate piston slap in street engines.) The same company which produces the KB piston also markets a cheaper piston with lower silicon content under the Silvolite brand. It's a nice piston for OEM replacement use, but it's not intended for performance applications.

Federal Mogul / Speed Pro makes a piston with slightly lower silicon content than the KB, 14% or so but with a moly-graphite insert in the thrust faces. I find no measurable benefit. In general I distrust coatings (both anti-friction or thermal barriers) unless they are applied and vouched for by the piston mfg'er or there is some special need involved. If you look at the various claims there are indeed incremental but measurable gains. But they have considerable nuisance value vs. my totally anal approach to dimensional control in assembly, and THEN when I find flecks of the magic moonglow winking back at me in the oil screen after the first dyno pull...no thanks. From there it comes down to careful assembly and the zero-tolerance approach to tolerances. Tolerance ranges mainly exist to leave room for error, so the trick is not to make any. There are no secrets there at all. Many engine builders are just to lazy to actually do it.

[McGuire]

Originally posted by Greg Locock


Not to be too picky but that is not quite true. It depends a bit on the gradient of the resistance curve and the gradient of the torque curve. Consider for example the case of an engine with a very gently rising torque curve. Acceleration could be greater at lower speeds, where the vehicle resistance is less, than at the redline where the peak torque is.

First, I assume that you don't mean to imply that peak torque occurs at engine redline...Anyway, sure. But if the load is lesser that's not really maximum acceleration, is it? But this is an interesting point: in effect you are describing the classic case of the overgeared vehicle. For the extreme case, imagine a farm tractor at WOT with its harrows dug in when the pin comes out of the drawbar.

In the interest of strict technical accuracy at the risk of obfuscation, we could my amend my statement to read: "In any gear, maximum accleleration *relative to load* occurs at the rpm of peak torque." But then we are simply stating a redundancy, as the load is what we are accelerating here, eh.

[McGuire]

Originally posted by WPT
McGuire said , "In any gear, maximum acceleration occurs at the rpm of peak torque. "

True, but at any speed maximum acceleration occurs in the gear that delivers the most hp.
WPT

Sorry, I don't know quite what you mean. Gearing cannot multiply horsepower. Gearing can only multiply torque. If you are stating that the top of each gear must be selected to match max hp rpm in order to achieve top speed for each gear, that is quite correct. But that also means that +/-100% of the acceleration in each gear occurs BELOW the rpm of peak hp.

Meanwhile, max acceleration in each gear occurs at the rpm of peak torque (subject to the apparent exception previously discussed). That is when the maximum force per rotation of the crankshaft is being exerted. Yes, we can make more power by turning the crankshaft faster than peak torque rpm (to get more more revs per unit of time) but maximum force per crankshaft rotation is exerted at the rpm of peak torque, by definition. And again, gearing cannot multiply horsepower, only torque.

[McGuire]

Originally posted by WPT
Every text book I have seen (not that many) that derives the piston velocity and acceleration equations simplifies the the calculation by using the fact that for small angles the cos very nearly equals 1. This is justified because the resulted equations give exact answers at TDC and BDC, only small errors at inbetween crank angles, and eases the mathematics somewhat. It is interesting to note that exact solutions can be drived if one is willing to wade through the math. If requested I can post the exact equations.
Having the exact equations I wondered how the Fourier componets would match with the simplified equations. The results for a r/l=0.248 (because I own a Ducati with this ratio) with the wr^2 term factored out: For the simplied equation of course; w(1) = 1.00000, w(2)= 0.248
and for the eact equation; w(1)=0.99955, w(2)=0.25193, w(4)=-0.00400, and w(6)=0.00007.
All the componets are for the cos terms. All the sin terms and the rest of the cos terms to w(18) were effectly zero. More justification for using the simplied derivation.
In Wright's recent Ferrari book one can use the cross-sectional engine veiw and/or the reported data for max piston acceleration to determine the rod length. The rod length calculates out to 111.7 mm center to center. Thus, for the Ferrari r/l=0.185, or l/s=2.70. WPT

The big end of the connecting rod travels on a circular path described by the crankshaft's offset radius (half the stroke) through all 360 degrees of crankshaft rotation. That is, the crankpin is describing a circle through space, orbiting above the crankshaft CL at 2r*pi per rotation. For example: assuming say, a stroke of 4" and 7000 rpm, the crankpin is traveling at a constant 7350 ft/min, and therefore, so are the rod the piston.

However, the piston is fixed at the other end of the rod, restricted to reciprocal motion by the cylinder bore. Referring to TDC as 0 degrees in 360 degrees of crank rotation, we will find that from this point piston acceleration is at maximum. Meanwhile the cosine of 0 or 360 degrees is one. Thus if you take the various common formulas (note 1) for piston acceleration relative to crank angle, throw out the trig functions and substitute unity, you will get a fairly decent approximation of what is typically called "maximum piston acceleration," though it is really merely peak NEGATIVE acceleration.

So just as with mean piston speed, this figure too is of limited utility. We know the piston/rod assembly is subjected to both positive and negative (and angular) accelerations, and so there are tensile, compressive and side loadings to deal with. (If you find a connecting rod with an "L" bent into it, it probably didn't happen at TDC.) For example, in the Honda engine above, peak positive piston acceleration occurs at 155 degrees ATDC. Meanwhile peak velocity is at 75.8 degrees ATDC.

(Note 1) these formulas typically employ language something like (cos a + r/l cos 2 a). The first cosine is the effect of instant crank angle. The second reflects rod angularity, where l is the length of the rod and r is the crank throw radius (not the stroke but half the stroke). Thus the Ferrari 049 has a r/l ratio of 20.7 to 111.7mm, or around 5.4:1 in the vernacular. Assuming a rod length of 111.7 mm, of course...when you saw that drawing in Wright's book, you got exactly the same idea I did. What a great book, full of wonderful diversions and adventures such as these.

[Engineguy]

Piston acceleration curves for:

Honda S2000 at 8300 RPM = 4000 G max
NASCAR V8 at 9500 RPM = 6000 G max
Ferrari F1 at 18500 RPM = 10000 G max

TDC at far left, BDC at center of graph, and back to TDC at far right side... 1000 G per grid line.

[WPT]

McGuire said:


"Sorry, I don't know quite what you mean. Gearing cannot multiply horsepower. Gearing can only multiply torque. If you are...."

I mean that at any given road speed the max acceleration is given by selecting the gear that delivers the most hp to the drive wheels at that given speed. WPT

[WPT]

McGuire said:

" (Note 1) these formulas typically employ language something like (cos a + r/l cos a). The first cosine is the effect of instant crank angle. The second reflects rod angularity, where l is the length of the rod and r is the crank throw radius (not the stroke but half the stroke). Thus the Ferrari 049 has a r/l ratio of 20.7 to 111.7mm, or around 5.4:1 in the vernacular. Assuming a rod length of 111.7 mm, of course...when you saw that drawing in Wright's book, you got exactly the same idea I did. What a great book, full of wonderful diversions and adventures such as these. "

As I said, (cos a + r/l cos 2a) is derived from a simplified calculation. To get the actual frequency spectra use the exact eguation for a given r/l, and then determine the Fourier componets. That is what I did for r/l=0.248.
If r=20.7 and l=111.7, how is r/l=5.4? Think you have inverted the numbers in your calculation. Of course, 's' is the stroke, so l/s=2.70 for the Ferrari. WPT

[Greg Locock]

The resistance equation for the vehicle is F=m*a+1/2*rho*CdA*V^2+ Crr*m*g

F=T/r*Gearing

The net acceleration is therefore T/r*Gearing/m-(1/2*rho*CdA*V^2/m Crr*g) - if we ignore rotational inertia, which is unwise in first gear but generally OK after that.

The bit in brackets is the steady state resistance

So, to reiterate, the acceleration is proportional to the difference between the (scaled) torque and the steady state vehicle resistance force. If that difference is smaller, the vehicle will accelerate at a lesser rate, even if the available torque at the flywheel is greater.

Incidentally why can't an engine have max torque at the redline? It is not usually a sensible thing to do, but in principle you could do it.

[WPT]

I know that Yamaha's RD-400 (1978?) had its torque peak at engine redline (from actual dyno test in "Cycle" magazine). WPT

[Engineguy]

Redline is of course an arbitrary number chosen from a variety of considerations... everthing from actual physics of the engine (i.e. things like max piston accel/speed/wear) to expected engine life to manufacturing cost and potential warranty cost tradeoffs.

I don't think I've seen a torque curve that falls off fast enough that max power didn't occur at a substantially higher RPM than max torque. The HP equation almost fobids it.

A case where redline is set unusually low (at max torque) might be because of breathing capabilities that far exceed, say, the quality of the connecting rods. Pretty good high performance connecting rods can be manufactured for $12 each, but rods that will safely tolerate 10% higher RPM may cost $60 each to manufacture. An extra $192 (four rods) manufacturing cost in a very competitive market segment is brutal. The serious racer can drop in aftermarket rods, run higher redline, and make use of the added power that was always there beyond the redline.

[McGuire]

Originally posted by WPT
I mean that at any given road speed the max acceleration is given by selecting the gear that delivers the most hp to the drive wheels at that given speed. WPT

No. That is a common misconception, but one that still never fails to surprise me when I hear it stated by knowledgeable auto enthusiasts. Anyone who can drive a stick-shift car knows this is not really true intuitively (if not conciously). Acceleleration is greater at the bottom of each gear, while speed is greater at the top of the gear. When max engine rpm and vehicle speed in a given gear are reached, we know in the seat of our pants it is time to upshift to the next gear. The statement also includes a logical paradox. We know that every gear has a top speed, and that top speed in any gear occurs at the rpm of max horsepower. If the vehicle is already at top speed for that gear, how can it also be increasing in speed at the same time?

In truth, the only way to accelerate the vehicle from that point is to upshift to a higher gear, at which point engine speed can only drop below the rpm of max hp. We have increased the number of wheel rotations per crankshaft rotation in order to increase the vehicle's ground speed relative to engine rpm. How great the rpm drop is a function of engine torque, the number of gears in the box, and the spread between them etc. But this we know: if the engine is truly at max hp the vehicle is not accelerating in that gear. It's done accelerating.

Top speed occurs at the rpm of max hp, while maximum acceleration occurs at the rpm of peak torque. By definition, peak torque rpm is where maximum force at the crankshaft per unit of crank rotation is obtained. This force is multiplied through gear reduction and the tire's loaded radius to produce a quantity of wheel thrust, which accelerates the vehicle in real time. Where does hp fit into this? Horsepower doesn't exist in instantaneous time -- it's mathematical artifact, representing the amount of torque the engine can produce in one minute. Dynos can't measure it either. They can only measure torque.

Top speed -- maximum distance covered per unit of time -- occurs at the rpm of maximum horsepower, because that is the crank speed where the engine produces its maximum torque per unit of time. And so we gear the car for max hp rpm, not max torque rpm (and then put a bunch of change speed gears in the box to provide torque multiplication so we can accelerate the vehicle too.) If we gear the engine 2:1 (2 crank rotations to 1 axle rotation) we will double the torque, but not the horsepower because we have also reduced by half the number of axle revolutions per unit of time. Horsepower remains the same. Torque * rpm/ 5252 = HP. Double the torque, cut the rpm in half and see what happens: Gearing can only multiply torque, not horsepower. Horsepower is simply torque over time. (5252 is 33,000/2pi. One hp = 33,000 ft-lb/min. of work.)

[McGuire]

Originally posted by Greg Locock
Incidentally why can't an engine have max torque at the redline? It is not usually a sensible thing to do, but in principle you could do it.

Perhaps, but only by lowering the rpm of peak hp, not by raising the rpm of peak torque to match peak hp (a violation of the laws of thermodynamics). There are any number of things one can do to an engine which are not sensible, and I am not sure it's relevant to explore them all here.

[McGuire]

Originally posted by WPT
As I said, (cos a + r/l cos 2a) is derived from a simplified calculation. To get the actual frequency spectra use the exact eguation for a given r/l, and then determine the Fourier componets. That is what I did for r/l=0.248.
If r=20.7 and l=111.7, how is r/l=5.4? Think you have inverted the numbers in your calculation. Of course, 's' is the stroke, so l/s=2.70 for the Ferrari. WPT

LOL as I said, 5.4:1 *in the vernacular*, as the ratio is typically described con rod first in this fashion, in texts etc. It's often helpful to know the common terminology. However, in the typical formulas for approximating piston accleration it's r over l. I'm not sure about Fourier components. Are you getting similar figures for TDC and BDC?

[McGuire]

Originally posted by WPT
I know that Yamaha's RD-400 (1978?) had its torque peak at engine redline (from actual dyno test in "Cycle" magazine). WPT

Sure, it's an unscavenged two-stroke. Yamaha's figures for the 1978-9 Yamaha RD 400E are

40 hp @ 7000 rpm
4.2 kgm @6500 rpm

while the Cycle magazine dyno test (November 1977) of the 1978 RD400E found

34.18 bhp @7500
25.55 lb ft @7000

So peak torque does not come exactly at redline (calling peak hp rpm redline, which may or may not be applicable here as the things would zing to 9000+, but here we will call it the useful limit) as the hp peak is 500 rpm beyond peak torque. That said, here the hp and torque peaks are very close, and there are engines in which they fall even closer, to right on top of each other. This is a well-known trait of unscavenged two-strokes: Once peak BMEP and Ve are attained (at/near the point of peak torque) they fall off so rapidly that often, little if any more hp can be obtained above that speed. This is due of course to the obscene pumping losses these engines suffer.

One might think that having the hp and torque peaks at roughly the same rpm would be good thing for driveability and the acceleration curves, but not so. This and the lack rotating/recip mass and engine braking with these engines often make the throttle feel like an on/off switch.

Less often, you will also sometimes find similar in four-strokes, namely small-displacement, multi-cylinder engines at high specific output, due in part to their relatively high fhp as well as their pumping losses. (Some 750cc-and-under fours used in older motorcycles for example.) In their dyno charts, this is often accompanied by the presence of double humps in the hp and torque curves...a sure sign that the engine's state of tune or development is in some way screwed up. These are bad things in engine development and to be avoided.

[McGuire]

more about mean piston speed...

There is more than one way to calculate piston speed. One interesting method is known as the "square root mean" or Lanchester method (he of Lanchester balancer fame). Mean piston speed is calculated in the familiar mode (stroke x rpm / 6) but this figure is then divided by the square root of the stroke/bore ratio to arrive at a "corrected" result. This figure apparently more accurately reflects whatever Lanchester thought mean piston speed ought to. (If I ever knew exactly what he was driving at with this, I'm sure I've forgotten.) But it is interesting to ponder the various relationships while trying it on various engines. Bore may speak to piston mass, just to toss out one tenuous possibility.

Bet you won't find that one in the Bosch Handbook.

Earlier, some note was made of the interesting similarities in mean piston speed among various engines of wildly differing type. You can find some texts which suggest this may be somehow related to a connection between piston speed and airflow mach index. I don't know about that one either but it is one more thing to think about.

[VAR1016]

Originally posted by McGuire
more about mean piston speed...

There is more than one way to calculate piston speed. One interesting method is known as the "square root mean" or Lanchester method (he of Lanchester balancer fame). Mean piston speed is calculated in the familiar mode (stroke x rpm / 6) but this figure is then divided by the square root of the stroke/bore ratio to arrive at a "corrected" result. This figure apparently more accurately reflects whatever Lanchester thought mean piston speed ought to. (If I ever knew exactly what he was driving at with this, I'm sure I've forgotten.) But it is interesting to ponder the various relationships while trying it on various engines. Bore may speak to piston mass, just to toss out one tenuous possibility.

Bet you won't find that one in the Bosch Handbook.

Earlier, some note was made of the interesting similarities in mean piston speed among various engines of wildly differing type. You can find some texts which suggest this may be somehow related to a connection between piston speed and airflow mach index. I don't know about that one either but it is one more thing to think about.

Yes, I had thought to post about this, but in this company I tend to read rather than write...

I first came across the concept in Karl Ludwigsen's book "Classic Racing Engines" and it seems that the longer stroke engines have a lower corrected piston speed for a given RPM .

PdeRL

[WPT]

McGuire said: "Are you getting similar figures for TDC and BDC?"

As I said before, for r/l=0.248 the simplified derivation gives (with the rw^2 factored out) cos(A)+0.248cos(2A). Using the four terms from the Fourier series analysis gives 0.99955cos(A)+0.25193cos(2A)-0.00400cos(4A)+0.00007cos(6A). One could use more terms in the Fourier expression to obtain more accuracy. In any case, with the four terms used here it is more accurate than the simplified version at crank angles between TDC and BDC. Note how the actual magnitude of the secondary is 0.25193 and not 0.248. WPT

[WPT]

McGuire said: "No. That is a common misconception, but one that still never fails to surprise me when I hear it stated by knowledgeable auto enthusiasts. Anyone who can drive a stick-shift car knows this is not really true intuitively (if not conciously). Acceleleration is greater at the bottom of each gear, while speed is greater at the top of the gear. When max engine rpm and vehicle speed in a given gear are reached, we know in the seat of our pants it is time to upshift to the next gear. The statement also includes a logical paradox. We know that every gear has a top speed, and that top speed in any gear occurs at the rpm of max horsepower. If the vehicle is already at top speed for that gear, how can it also be increasing in speed at the same time?"

I am not sure you understand what I'm trying to say. At any given road speed one usually has two or more options in gear selection. Say at 'X' mph I might have available to me 2nd, 3rd,4th,or 5th gear. For max acceration at 'X' mph select the gear that delivers the most hp to the drive wheels. WPT

[WPT]

I stand corrected concerning the RD-400 dyno tests in "Cycle" magazine. I was wrong, sorry.
WPT

[flannel]

From what has been said about hp/torque, to get the best acceleration from a standing start through the gears you would:

accelerate in 1st until just past the max torque RPM and then change up.
then repeat this for each gear until the last one where you redline it.
(Doing this would use the highest part of the torque curve)

I always thought the best way to accelerate was to redline each gear before changing up.

Am I wrong?

Also, I think that in F1 they tune the engine so that max torque occurs just before Max RPM and thus both of the above methods are the same.

[McGuire]

Originally posted by flannel
From what has been said about hp/torque, to get the best acceleration from a standing start through the gears you would:

accelerate in 1st until just past the max torque RPM and then change up.
then repeat this for each gear until the last one where you redline it.
(Doing this would use the highest part of the torque curve)

I always thought the best way to accelerate was to redline each gear before changing up.

Am I wrong?

Also, I think that in F1 they tune the engine so that max torque occurs just before Max RPM and thus both of the above methods are the same.

No, you are right. You want to accelerate the engine to the rpm of peak hp in order to obtain maximum speed in that gear, then upshift. (However, peak acceleration will occur at the rpm of max torque.) As a practical matter, on a road course gearing will be selected so that the shift points are slightly above peak hp rpm... if the engine can stand it. So really we gear the car for speed, not for torque. Meanwhile gearing can only multiply torque, not hp. It's not so surprising people get confused.

In some ways it would be nice if peak hp and torque appeared at the same crank speed, but that would require throwing away hp. By definition, peak volumetric efficiency and cylinder pressure occur at the rpm of peak torque. Above that rpm the engine can potentially produce more work per unit of time, but is exerting less force per unit of crank rotation. In modern F1 engines peak hp will appear around 18-19K rpm, with peak torque about 3K rpm below that.

[WPT]

To obtain best shift points for best acceleration graph on a single sheet of graph paper the hp vs. road speed for each gear in the transmission. You will need to know the overall gear ratios, the drive tires rolling radius, and of course the results of a dyno test (hp vs. rpm) of the engine. Where one hp curve intersects the next hp curve is your ideal shift point for best acceleration. If there is no intersection, then shift at redline. WPT

[WPT]

McGuire said:

"We know that every gear has a top speed, and that top speed in any gear occurs at the rpm of max horsepower. If the vehicle is already at top speed for that gear, how can it also be increasing in speed at the same time? "

"But this we know: if the engine is truly at max hp the vehicle is not accelerating in that gear. It's done accelerating."


In top gear where the ratio has been chosen for top speed this is true. But, for any lower gear this is false. In lowere gears the thrust force is greater than the drag force and we have acceleration past the power peak rpm if one so wishes. WPT

[WPT]

McGuire said:

" Horsepower doesn't exist in instantaneous time -- it's mathematical artifact, representing the amount of torque the engine can produce in one minute. Dynos can't measure it either. They can only measure torque."


For a brake type dyno this true. However, inertial drum dynos are very popular now. Here a drum is accelerated by the drive wheels of the test vehicle and the speed sensor for the drum inputs to a computer. There are two ways the the computer can do its calculations. The first is to use the equation; T=aI where T is the torque, a is the angular acceleration of the drum, and I is the mass moment of inertia of the drum. This will yeild a torque vs rpm graph from which the horsepower can be calculated.
Or, the computer can use the speed input to calculate the change in kinetic energy of the drum (KE=1/2*I*w^2, where w is the angular velocity of the drum in radians/sec) in a given interval of time (dt). The change in KE is equal to the work done during dt. This is power, work per unit time. This output is power vs rpm from which the torque curve can be calculated. I do not know which calculation is actually used. WPT