TDIMeister
Phd of TDIClub Enthusiast, Moderator at Large
A little more engine engineering for those interested. It's no big surprise that a 3.9 L 4BT develops rated power at "only" 2400 RPM (9.52 m/s mean piston speed) and the 1.9 TDI at 3750 RPM (14.875 m/s), but do you really know why? There are many factors why these two engines develop their rated powers at RPMs that they do, but many parameters scale with the very important mean piston speed (MPS, eg. in-cylinder turbulence, swirl intensity, port flow velocities, etc.). We could take the analysis further. The upper limits of MPS - high-20s m/s in F1/Cup engines, into the 30s m/s for Top Fuel drag racers, are dictated primarily by tribological considerations (maintaining an oil film in the piston ring-cylinder interface) and tensile mass forces taken up by the pistons and connecting rods.
If we set a criterion to limit kinetic energy in the reciprocating group to be roughly constant, which would translate to strain energies that the rods have to take, then the disparities of MPS between say a 4BT and an ALH TDI almost disappears.
Kinetic energy is proportional to the mass times velocity squared.
Mass is proportional to the cube of a characteristic dimension, I'll use bore diameter d here.
So, the kinetic energy is related to d^3*MPS^2.
With the criterion of constant kinetic energy, there results a relationship of bore diameter vs MPS as
MPS is proportional to d^(3/2).
Now let's plug in some numbers:
TDI bore: 79.5mm
4BT: 102mm
Taking the TDI as a baseline with MPS = 14.875 m/s,
14.875 *(79.5/102)^(3/2)=10.23 m/s, which is pretty close to the value of the 4BT's MPS at rated power. The remaining difference can be attributed to the 4BT being designed for heavier duty durability than a TDI.
The take home message here is also that it is not realistic to have a 4BT rev to the same RPM as a TDI, but one can go further to say that it is comparing apples to oranges even to match MPS. Rather, there is a physics-based rationale to relate and scale MPS between engines of different sizes using energetic or mechanical strength criteria.
If we set a criterion to limit kinetic energy in the reciprocating group to be roughly constant, which would translate to strain energies that the rods have to take, then the disparities of MPS between say a 4BT and an ALH TDI almost disappears.
Kinetic energy is proportional to the mass times velocity squared.
Mass is proportional to the cube of a characteristic dimension, I'll use bore diameter d here.
So, the kinetic energy is related to d^3*MPS^2.
With the criterion of constant kinetic energy, there results a relationship of bore diameter vs MPS as
MPS is proportional to d^(3/2).
Now let's plug in some numbers:
TDI bore: 79.5mm
4BT: 102mm
Taking the TDI as a baseline with MPS = 14.875 m/s,
14.875 *(79.5/102)^(3/2)=10.23 m/s, which is pretty close to the value of the 4BT's MPS at rated power. The remaining difference can be attributed to the 4BT being designed for heavier duty durability than a TDI.
The take home message here is also that it is not realistic to have a 4BT rev to the same RPM as a TDI, but one can go further to say that it is comparing apples to oranges even to match MPS. Rather, there is a physics-based rationale to relate and scale MPS between engines of different sizes using energetic or mechanical strength criteria.
