The Cross-plane Crank
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.
Click 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.
In 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.
This improves the ability of a cross-plane-crank, in-line-four bike to accelerate out of corners. To see why, imagine a bike at the apex of a turn, where it’s fully leaned over and the rider is about to apply the throttle to accelerate. The rear tyre is already close to its limit from the cornering forces so it can’t take much torque without sliding. Let’s suppose it’ll just take 20lb.ft of engine torque before losing grip. On a cross-plane four with no inertial torque the rider can carefully turn the throttle until he feels the tyre just sliding – at that point he’s getting the engine to deliver 20lb.ft and he gets the maximum acceleration possible, with no interference.
With a flat-plane four the inertial torque effect means there’s a background torque pulsing of, say, 2lb.ft: 1lb.ft is added to the total output as the pistons are slowing down and the crank is accelerating, while 1lb.ft is taken away when the pistons are speeding up and slowing the crank again. If the tyre is going to slide at 20lb.ft, then the rider can only turn the throttle enough to deliver 19lb.ft, because twice every crank revolution the inertial torque is going to add another 1lb.ft and take it up to that 20lb.ft limit. Twice more per engine rev, the torque will drop to 18lb.ft, so the average delivered is still 19lb.ft. But that’s 1lb.ft less than the cross-plane-crank engine before the tyre begins to slide, and if that doesn’t sound like a lot, it’s five per cent, which is a big difference in racing, equivalent to a peak power disadvantage of 12bhp on a MotoGP bike. So the engine with no inertial torque can accelerate harder out of corners, and it also gives the rider finer control as there’s no fuzziness to the output.
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.
Even 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.
The 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
Other Technical
Wed, 10/12/2008 - 22:50
#2
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.
Thu, 29/01/2009 - 16:44
#3
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
Thu, 29/01/2009 - 20:04
#4
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.
Thu, 29/01/2009 - 23:51
#5
Kevin,
Yes, I do agree with you. I thought I was putting forward another point of view in supportive of case.
Fri, 30/01/2009 - 00:06
#6
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.
Thu, 06/08/2009 - 10:02
#7
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...
Thu, 06/08/2009 - 21:26
#8
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.
Mon, 21/09/2009 - 21:57
#9
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.
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??