The Cross-plane Crank

Crossplane_03

By Kevin Ash


Pictures: Yamaha Press




So Yamaha’s new R1 (read the test report here) has a cross-plane crankshaft: what’s that all about? A conventional four-cylinder engine has its crankpins all in the same plane – a flat-plane crank – with the two inner ones 180 degrees from the two outer ones. The inner two pistons move up and down together, and so do the two outer ones, and it’s this particular configuration which generates something called inertial torque. This is independent of the main torque output generated by the combustion and cylinder pressure and happens entirely because of the crank layout.

Crossplane_03Click on image for galleryTo understand it, first imagine a crankshaft on its own, no pistons or conrods, spinning in friction-free bearings. There’s nothing to slow it down or speed it up so it just keeps spinning at a smooth, constant speed. Now attach the conrods and pistons, and for the sake of this mind experiment, we’ll make them friction-free too, so you can spin the crank again and the pistons bob up and down, and the whole system keeps on rotating and reciprocating. At this stage there’s no combustion or valve gear or anything to confuse the issue, and crucially, there is no energy being put into our system and none being extracted or lost. This matters because it is a fundamental law of the universe that energy cannot be created or destroyed, only converted into another form – physicists know this as the first law of thermodynamics.

Within this system, the pistons are travelling at high speed when they’re half way along their cylinders, and at this point they have a lot of kinetic energy. Yet 90 degrees of crankshaft rotation later, all four pistons are stationary, two at the top, two at the bottom. Their kinetic energy hasn’t simply vanished because it can’t: instead it’s been transferred to the crankshaft, which was responsible for slowing the pistons down. As a result, the crank itself has increased its speed. Another 90 degrees on and the pistons are back up to maximum speed, accelerated by the crank which has returned some energy to them and in turn, it’s slowed down again.

Crossplane_02In a full rotation the crank will have sped up and slowed down twice, generating rapid negative and positive torque pulses completely independent of the torque produced by the combustion. This constant pulsing torque is like a background noise to the main torque output, blurring its edges and taking away a small element of rider control and precision as he tries to hold the back tyre on the very edge of its grip.

On Yamaha’s cross-plane crankshaft, these fluctuations are all but eliminated. In this layout the crankpins are distributed at 90 degrees to each other around the crankshaft (in two planes which form a cross). So as one piston is slowing down and losing energy to the crank, another is speeding up and taking the same amount back. At no point do all the pistons stop together, as they do on a flat-plane crank. Instead the energy flow is evened out and the rotation of the crank is almost completely smooth and steady.

Although I`ve talked about the torque fluctuations as background noise, in fact the scale of them is massive, dwarfing the conventional, output torque by a factor of ten. In a GSX-R1000 engine at 12,000rpm for example, the inertial torque swings from around +500 to -500lb.ft (69kg.m, 680Nm) twice in every revolution of the crank.

See a full calculation of the scale of inertial torque here

Eliminating this means you no longer have to make allowances for it in the driveline. Many clutches for example include metal springs or rubber bushes as a cush drive in the back plate to soak up the inertial torque pulsing so it doesn`t damage the gearbox. With this gone the cush drive can be deleted and the connection between crankshaft and rear wheel is more direct, improving feel for the rider.

Crossplane_05
90 degree V-twins are famous for their drive out of corners, and sure enough, they have almost zero inertial torque. As one piston is accelerating so the other is slowing down, and when one is stopped the other is at maximum speed. This is an important factor in why Ducatis have been able magically to accelerate out of corners faster than more powerful conventional fours, and it’s why the Ducati Desmosedici MotoGP bike crank is configured like a pair of V-twins.

Crossplane_04Even though Yamaha makes no claims of improved traction because of the uneven firing intervals of the 2009 R1 – the so-called Big Bang effect – there are still many who cite this as the motive behind the cross-plane crankshaft design. It’s not, it’s to eliminate the high frequency torque fluctuations, so the uneven firing intervals are only a side-effect, not the objective.

So what becomes of the Big Bang theory of improving traction by introducing uneven firing intervals? The principle behind this depends on the difference between static and dynamic friction: a big, heavy wooden box might take two people pushing to start it moving, but once it’s sliding it’s much easier to keep moving, and only one person could do it. This is because at a microscopic level the rough surfaces of the box and the ground interlock when it’s stationary, but when it’s sliding they ride over each other.

Apply that to a bike’s rear tyre being fed pulses of torque by an engine. If there are fewer pulses the tyre has time in between each to recover any lost grip, so its surface can interlock with the road’s again, but when there are more pulses (as with a four compared with a twin), once the tyre is sliding the next pulse of torque comes along more quickly, before the grip can be regained, and the tyre keeps sliding. This means more torque overall can be applied by an engine with fewer, larger power pulses, an idea that came from seeing V-twins (usually Ducatis) driving out of corners faster than the four-cylinder competition.

Crossplane_01The problem with the theory is that its main principles are for static friction, and a rear tyre is clearly not static. The behaviour of a rolling tyre is very different to a stationary box, and it is not clear if this static-dynamic situation would be the same. It’s likely to have similarities: we know from heavy braking tests that a skidding tyre results in longer stopping distances than if the wheels don’t lock up, similar to the sliding box situation. But a tyre creeping across a road, as it does under power out of a turn, is in a grey zone between sliding and grip, and we can’t be certain those principles are valid.

No proof has been offered either that the frequency of torque pulses from an engine is anything like that which might be needed to allow a tyre time to recover. Maybe they are, maybe not, but it’s vague enough to make Big Bang no more than a guess, rather than a true theory.

The evidence supporting the cross-plane crankshaft’s advantages though is clear and mathematically provable, and suggests those pursuing uneven firing intervals to achieve better grip (the Virgin Yamaha race team in the UK built an R1 with cylinder pairs firing together with a stock, flat plane crank – it wasn’t significantly better) were shooting at the wrong target.

Yamaha R1 test


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jules
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Joined: 10/12/2008

OK thanks for the very well written explanation.

However it would seem that if the torque variations due to the big bang theory or say a twin are a good thing then so are the inertial torque variations of a standard single plane crank so a cross plane crank is pointless! Furthermore it introduces all sorts of counterbalance problems doesnt it? Does the crank weigh more due to counterweights= slower accelleration due to flywheel effect??

kevash
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Joined: 05/10/2008

All good points and I can't answer them fully, but it does seem as if the whole idea of big bang torque pulses improving traction could even have been a red herring and the lumpy delivery of a twin is not what makes a difference, it's purely the lack of inertial torque which makes the difference. Or maybe both have some effect... the trouble is, there's no published empirical evidence. But the performance of Yamaha's M1s does suggest they're right to value the inertial torque factor.
Yes, the crankshaft is heavier and it will affect how fast the bike revs, although this is mainly because the crankpins are a larger diameter to maintain the crank's rigidity - the more complex shape would flex more easily otherwise, as a flat plane crank's centre two crankpins are coaxial, which is stronger. The extra weight could well be detrimental but presumably the pay-back in improved traction is worthwhile compensation. It's also more complex and expensive to make compared with a flat-plane crank.
The new R1 does still have contra-rotating balance shafts but these are also more complex... it'll be interesting to see if the engine is any more or less smooth than an 08 R1.

thomthom
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Joined: 29/01/2009

The new crankshaft arrangement allows time for the tyre to regain grip. I wonder. At 10,000rpm and 60mph say (easy figures to work with), means that the firing intervals in parts of a second would be 0.0045, 0.003, 0.0015, 0.003, which is slightly faster than the blink of an eye. However translated into distance travelled by the tyre, in inches would be 4.75, 3.17, 1.58, 3.17. These are dimensions that are more tangeable. Depending on the size of tyre fitted but say approx 60 inches circumference, the wheel has to travel another 50 odd inches before that part of the tyre feels the force of the engine to the road again. The change in firing order (and crankangles) gives a minimal change to the resting interval for a tyre, compared to the interval before it's next period of work.

However it appears to work ....but maybe for some other reason

kevash
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Joined: 05/10/2008

It might be worth having another read of this article as I think you actually agree with me... in fact what I say here is that the Big Bang theory (which is what you're describing) doesn't seem to be the reason for the effectiveness of the cross plane crank. Instead it's the way this new crank layout eliminates the sinusoidal background torque fluctuations (what Yamaha calls inertial torque), which with a conventional crank produce small torque peaks that can start off a slide. What Yamaha says about the cross plane crank suggests the Big Bang idea, that a tyre has time to regain grip between cylinders firing, has all been a red herring and isn't the case at all.

thomthom
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Joined: 29/01/2009

Kevin,
Yes, I do agree with you. I thought I was putting forward another point of view in supportive of case.

kevash
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Joined: 05/10/2008

Ah I see, I did wonder... Well I did used to reckon the Big Bang theory made some sense, especially following my own experiences with bikes off road where singles seemed to dig out far more grip than twins. But for track bikes it was only ever an idea with no real evidence and that worried me - in fact your figures are really interesting, I should have done that myself! And they do seem to weaken the case for Big Bang even more.

Morepower
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Joined: 06/08/2009

The counter balance problems can be counteracted with mass which will dampen the primary imbalance of the crank. Yes this can mean a heavier crankshaft but as the idea of this crank was for added torque it is not too much of a problem. The heavier crank will make the bike feel smoother and easier to ride. The added mass will mean the engine will pull away from the lights easier with less rpm drop as the mass of the crank will keep the engine spinning unlike a lightweight crank which will feel more likely to stall. Drag Race bikes want heavier cranks to get a good launch from the line. Race bikes want the opposite as they want the engine to spin up quicker out of corners..
The Yamaha Moto GP bikes may run the same configuration but they will alter where the mass is in relation to the crank pins and run heavy densamet counter weights on the crank to localise the mass directly opposite the crank pin to save overall weight but still damp out the primary imbalance. Hard to explain but the weight directly opposite the crank pin has the most direct effect on counter balance and the further you get away from that the effect lessens and you have to add more and more weight. Using a material like Densamet will not only reduce the overall weight of the crank but as it is localised it will still offer the same counter balance effects.

I know this is a long time after it was originally posted but it does deserve an answer...

kevash
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Joined: 05/10/2008

Some good points there, though increasing the weight of a crank doesn't increase the torque output in itself (not sure if that's what you meant, though it could be read that way), but it allows the use of lower revs with less lumpiness so lower rev torque can be designed in and still be useable.
Re Big Bang and tyre recovery, I've since spoken to tyre engineers at Pirelli and Michelin - the French in particular have done a lot research on the subject - and neither company has found any real evidence to support the theory. It seems the very nature of rubber means it simply doesn't respond fast enough for this grip recovery theory to work, instead it damps out the pulses because of its flexibility.

Morepower
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Joined: 06/08/2009

Adding mass doesn't add torque true but the spinning mass is less likely to "stall" with a heavier crank due to the added inertia. The Yamaha R7 cranks I built were light weight mostly to eliminate the flexing problems of the stock crank as the pin tops were too heavy and the riders loved this weight loss even though it was not planned to create a light weight crank. Haga, Lindholm, Hislop and Haydon all preferred the lighter crank over the OEM or the one Yamaha supplied as part of the race kits. But it took work to localise the mass to lose weight yet keep the same counter balance and keep the engine smooth.
The cross plane crank looks heavier than the older flat plane crank so the actual inertial mass will be higher than the flat plane crank but the firing order and the way it works do allow for greater throttle control. I am still not sure if this really is the right way to go but we do not need more power although we do need better delivery. We know a 120BHP 600 can lap the Nurburgring quicker than a 180BHP+ MV Agusta as it is hard to use all of the power of the MV and the Ring is such a varied track that bikes like the new Yamaha may actually get to show the real gains between the older Yamaha R1 and the new cross plane version.

kaiser soze
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Joined: 01/01/2012

To correctly appreciate the effect of the crossplane crankshaft, it is necessary to look at the inertial torque curve (over 360 degrees) and the combustion torque curve, and with how the peaks in each curve line up with the peaks in the other curve. What Yamaha asserts is that with the conventional 180-degree crank, at approximately the point where two of the pistons are 120 degrees from TDC and the other two pistons are 60 degrees TDC, combustion torque crosses to negative due to the fact that one of the pistons that is approaching TDC is nearing the end of the compression stroke. At this point, there exists a strong positive peak in inertial torque due to the fact that all four pistons are slowing down. The overall, net torque curve is dominated by the perturbation that occurs at this particular point. In fact, if Yamaha`s curves are to be believed (and why not?), net crankshaft torque at that point is actually stronger, by nearly a factor of two, than the peak in combustion torque.

Mr. Ash posits that the advantage is related to traction, but that it does not occur for exactly the reason that it is often presumed to occur. The commenter alludes to the “big-bang” effect. But it is certain that the effect of the crossplane crank is that of reducing the peak perturbations in crankshaft torque. To be sure, this is the whole point. And surely it is apparent that this is not conducive to the “big bang” theory of catch-and-release. When that effect truly does apply, it applies not so much because of the uneven spacing of the perturbations in torque, but rather because of exacerbation of the perturbations. The illustration of this is when, in parallel twins, the 180-degree crank is replaced with a 90-degree crank. The firing intervals become more uniform, and yet this effect occurs, and the reason is that when the 90-degree crank is applied to a two-cylinder four-stroke engine, the peak perturbations in torque are exacerbated, the opposite of the effect that occurs in a four-cylinder engine, when the flat crank is replaced with the crossplane crank.

The reason for using the crossplane crank is very unlikely to have anything to do with traction at all. Rather, it is so that the negative perturbations in crankshaft torque will be eliminated, which practically eliminates the need for a flywheel. The essential reason for the flywheel is to keep the negative perturbations in torque from bringing the crankshaft to a full stop. With the flat crank, the peak negative perturbations are due to the acceleration of all four pistons concurrently. Were it not for the effect of inertial torque, the strongest negative peak in net torque would occur as each piston in turn nears the end of the compression stroke. But this is offset by the positive peak in inertial torque, i.e., by the fact that all four pistons are slowing down at that point. When inertial torque is largely eliminated, the strongest negative peak that remains occurs whenever any one piston is nearing the end of the compression stroke, but this negative peak is nowhere near as strong as the negative peak in inertial torque when the flat crankshaft is used.

Thus, it all comes down to making the flywheel smaller. The benefit of doing that should be obvious to anyone who understands anything about energy. But there is no free lunch. The price paid is loss of primary balance. In a conventional four-cylinder engine that uses the flat crank, primary balance is achieved by virtue of the fact that the two inner pistons move in opposition to the two outer pistons. Rectilinear vibration at the crankshaft`s rotational frequency does not occur, although it does occur at frequency twice that frequency. Balance is compromised by the crossplane crank, and this is the reason that the crossplane crank has not been used all along. Supposedly this engine uses balancers of some sort, but the obvious question is whether that balancer could fully do away with the 1st-order imbalance without also accumulating as much kinetic energy as the flywheel does when the flat crank is used.

caracola213
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Joined: 18/03/2013

Thank you for the information! I searched all over google for this.