Hello Tommy Cookers.
Here is the comparison of the unbalanced inertia moments of the in-line even-firing 3-cylinder with the crossplane uneven-firing Fath-Kuhn 4-cylinder (same pistons, same piston stroke, same distance between neighbor cylinder axes, same revs).
At 0:15 of the following “Introducing the Triumph Moto2 765cc triple engine” video, it is shown the first order balance shaft (great sound):
- The engine
Based on the new 2017 Street Triple engine, the Triumph Moto2TM 765cc triple engine was developed and tuned for a major step up in power and torque.
In ‘road’ setup the new 765cc engine delivers the highest-ever level of performance for a Street Triple, delivering 121 horsepower at 11,700 rpm and 57 foot-pounds of torque at 10,800 rpm.
Without the balance shaft, power, cost and weight is saved, yet they use a balance shaft.
Quote from page 222 for a twin even-firing two-stroke:
- I built a balance shaft and bolted it up externally to the engine as a test - with counter rotating bob weights flying around in mid-air. The difference was like night and day! I could not believe how smooth this new addition made the engine feel.
As the crossplane 4-cyl, similarly the plane-crank 4-cyl “gives nil unbalanced primary inertia forces .”
the ~15,000N unbalance 2nd order inertia force of the plane-crank 4-cyl with the ~4,000mN (mainly 1st order) unbalance inertia moment of the corssplane 4-cyl Fath-Kuhn (same pistons, same stroke, same cylinder-to-cylinder offset same r.p.m).
Let’s suppose that there are only two mounts, both at the bottom of the engine at a, say, 0.33m distance from each other, the one at the left side of the motorcycle frame, the other at the right side of the motorcycle frame.
Each of the mounts of the flat-crank engine receives a force of 15,000/2=7,500N of 2nd order (parallel forces at the same direction).
Each of the mounts of the cross-plane engine receives a force of 4,000mN/0.33m=12,000N of 1st order (parallel forces at opposite direction).
I.e. as compared to the cross-plane mounts, the mounts of the Flat-crank deal with weaker forces having double frequency.
With the engines revving at the same rpm, the time the second order force of the flat-crank acts on its mount at a direction (say upwards), is half than the time the first order force of the crossplane acts on its mount before changing direction, which means the deformation of the frame at the mounts is substantially larger in the case of the crossplane because the forces are heavier and because they act at a direction for longer (suppose there are no elastic mounts).
Having said these, maybe Fath who
- “had tried eg the Camathias Gilera - and found vibration from its unbalanced secondary inertia forces (he had no problem with his crossplane at 14-15000 rpm) ...”
was meaning (by vibrations) not the unbalanced inertia forces of the plane-crank 4-cyl engine but the heavy second order inertia-torque passing through the transmission line to the rear wheel spoiling the feeling of the rear tire hooking with the road.
“So for example if the inline 4 engine is boosted it would produce a high 2nd order firing excitation at a low engine speed. The PatVRA would only produce a weak "cancelling" torque with a phase angle which would be different than the ideal 180 degrees. By contrast a CPA tuned to the 2nd order has free rollers which will respond with the correct phase angle to whatever the perturbation is because they are not kinematically constrained.”
The PatVRA cancels out the second order inertia torque of the flat-crank even-firing four-in-line and passes to the transmission line only the combustion torque.
I.e. it does what the V-8 engines do internally (there are two sets of four pistons, with each set of four pistons having a significant variation of its kinetic energy during a crank rotation, and with the total kinetic energy of the two sets of pistons being constant during a cycle), and what the Wankel Rotary engines do: it allows only combustion torque to pass to the transmission.
The PatVRA does what the cross-plane 4-cylinder R1-Yamaha engine, but better: because the power pulses have equal distance from each other and are all equal in size.
If a V-8 or a Wankel Rotary is boosted, the power pulses arriving to the gearbox increase in size.
I can't see the problem.
If an inline-4 crossplane YAMAHA R1 or FATH-KHUN is boosted, the power pulses arriving to the transmission would increase just like the power pulses in the case of the PatVRA with the flat-crank.
Again I can't see the problem.
The PatVRA cancels out the inertia torque and passes to the gearbox, just like the V-8, the Wankel Rotary and the crossplane 4-cyl, pure combustion torque pulses.
At the middle of page 244, the post with the speed of the air hitting the pilot (a more interesting topic than the vibrations of the reciprocating piston engines) is still unanswered.
May I suppose that there are no objections?