Yamaha sells the R1 engine like crossplane, due to the kinetic energy of parts into engine is due to each piston and the crankshaft.
Kinetic Energy of Piston and Crankshaft
The engine in rpm constant state, the pistons have a alternative movement, therefore have 0 and X kinetic energy, but the crankshaft, turn all time to the same rpm and therefore keep the energy. But the energy doesn't created nor destroyed, only transformed.
If we follow Newton's laws of motion, and law of conservation of energy, the energy of pistons must go to other part, therefore is energy, is gave and took other part of engine, in this case it is between crankshaft and other piston.
Engine Kinetic Energy
And relation between parts keep the energy constant. In the cross plane we see the piston when two piston is closed to maximum speed, the other 2 piston is closed to minium speed and then Exchange the energy between them, and together keep the energy constant
Video Yamaha crossplane explained
Analysis crossplane concept in R6 and R675
If we resolve the energy equation to provide crankshaft speed, we can calculate the speeds and pistons and crankshaft balance.
Equation to resolve the crankshaft speed
In the R1 with crossplane we can see this behaviour.
Yamaha R1 crossplane behaviour, with constant speed in crankshaft and with energy constant.
In last figure show with crankshaft energy without mass, and we can see that it is very balanced between pistons, and this configuration keep the energy with few variations.
If we see the other configuration we can see that they are less balanced or completly unbalanced.
Yamaha R6 flatplane behaviour, with constant speed in crankshaft and with energy constant.
Yamaha R675 behaviour, with constant speed in crankshaft and with energy constant.
Yamaha R6 flatplane reduced the energy changes crankshatf in 0.49%.
Yamaha R675 reduced the energy changes crankshatf in 0.20%.
Therefore the crossplane don't have enough impact in the behaviour in the rotational motion in the crankshaft, due to 99% of kinetic energy is the crankshaft.
Other aprox is the minimum crankshaft inertia, in ideal case, is due too for balance mass in the crankshaft, calculates in "Why should Yamaha to make a YZF R675?",
Basic Inertia crankshaft equation
YZF-R6 = ICrankshaft = 0,000388359 kg·m2 ;
YZF-R675 = ICrankshaft = 0,000714714 kg·m2 ;
Yamaha R6 increased the energy changes crankshaft until 20%.
Yamaha R675 increased the energy changes crankshaft until 4%.
But this behaviour could be to the R675 have more inertia, but if we put the same inertia in the two engines ICrankshaft = 0,000714714 kg·m2
Yamaha R6 reduced the energy changes crankshaft until 12%.
It only reduced the variations until 12%, 3 times more than R675.
If we compare the inertia on the engine, in speed for example 100km/h (36 m/s) of one motorbike with 250kg (180kg bike + 70kg pilot), we have 162 kJ and into engine to 11.000rpm the the energy is:
YZF-R6 ICrankshaft = 0,0200 kg·m2 ; Energy engine 13.3kJ 8,23% overall energy
YZF-R675 ICrankshaft =0,0175 kg·m2 ; Energy engine 11.7kJ, 7,22% overall energy
but we considered, that it needs more rpm for the same power in 4 cylinders against 3 cylinders, near of +20%, the energy in the 4cylinders reach 12% of engine,
If we analyze the construction of engine, we can see, that the Inertia an balance mass have inverse behaviour.
Balance mass to radio and the same inertia to radio
We can see that in we increase the mass balance, but we put near or turn axis for keep the balance, we have less inertia
Relationship of design parameters
Therefore if, we decrease the ratio an increase the mass balance, for example in we realize on drill in the crankshaft to r 30mm to axis, we can replace with lead to r 20mm and this weight provide 33% less of inertia.
with this we can see that a weight material in crankshaft, down the global inertia, but the ideal, is light material in the crankshaft with heavy mass to balance, something like that, aluminium crankshaft with lead mass balancer.
Conclusion, it is the crossplane, with current steel crankshaft, it don't provide a significative improvement, but Inertia in the engine is very important.
To explain the 2 stroke engines is wikipedia. (To remind is interesting read that post).
The big difference with 4 stroke is the scavenging for refill the cylinder very fast, and is more efficiency into the mechanics point of view, due to if no necessary lost energy to move one cylinder one turn without it works. The advantage for 4 strokes is the thermodynamic is easier to manage and more wide rpm band to works.
The big problem of 2 strokes is the contamination, and in the next world more green and with less emissions, the 2 stroke doesn't have gap.
In Europe, the engines needs satisfy the European emission standards, and it knows like Euro regulations. (Now it goes by Euro 6).
The problem of this engine is the mixture fuel/oil, where we want burn fuel, but the problem is burning oil too.
First problem is need use the crankcase to compress the air/fuel flow and this enter in the cylinder, and it must carry oil to lubricate the moving parts, the problem is the part of this oil enter in the cylinder and it burn with fuel.
Second problem is the noise, the exhaust pipe needs a expansion chamber, that this is used in the exhaust pipe, and this provide volumetric efficiency. (The problem is it works only in a rpm narrow band).
The first problem try to resolve with other designs, that they are used in old two stroke diesel engines to locomotives such as Uniflow engine and Stepped engines, and mitigate the second problem.
In 2015 we see Kawasaki released the H2 motorcycle
If the used this kind of supercharger plus uniflow scavenging we can use to refill the cylinder.
The advantages are:
We don't pass to crankcase, and no use fuel/oil mixture, this provide cleaner emissions.
The second part is no necessary the escape/expansion chamber, due to the pressure of air inlet, provide a fast refill.
The supercharger link to crankshaft, it increases pressure and scaveniging time is less, therefore increase the rpm band where the engine works with efficiency.
But is not all perfect, and the disavanteges are:
The injection pressure, of put injection before the supercharger, with the problems the one detonation, or direct injection in the combustion chamber, (it is expensive). In other post I show like put a injection after of supercharger, and eliminate the problems of pressure ;).
Supercharger is additional part and the have any problems of lubricants, but the industries have a lot of experience now and these problems could be assume.
Limits of speed flows, the air has one limit into the pipes, and this is the sonic speed.
In the other post puts how solutionate the injection problem, but this a problem with all supercharger engines.
