I'm going to attempt to clear up some misconceptions by explaining
what exactly is happening under the floor.
Which is faster, the R68 or the R40? The answer is: it depends.
I can say for sure that between 0 and 15 MPH, these cars will be
dead even. Why? Because the TA calibrates them to accelerate at
2.5 MPHPS. There are 3 portions of the acceleration curve. In
the low-speed portion, the grid resistance is being notched out
to maintain a nearly constant current, and hence acceleration rate.
That period ends when all of the resistance is out of the circuit.
There is also a series-parallel transition which isn't important
to this discussion. At the conclusion of the low-speed portion,
each motor PAIR has 600 volts across it (each PAIR of motors is
permanently wired in series because all cars use 300 volt motors).
That all cars accelerate at this 2.5 rate during the low-speed portion
should not be under dispute. We'll assume that the cars were
calibrated and that continues to be routinely checked. We'll also
assume that the load weight compensation works as designed.
75 foot cars have a lower gear ratio than 60 or 51 footers. I
don't have the ratios handy, but I believe it is something like
5.5:1 for the 75' cars and 7:1 for all others. I'm sure Train
Dude has this info.
I said there are 3 parts to the speed curve. After the resistive
acceleration, there is a mid-range portion and then the last
part, balancing speed, where the motors reach their equilibrium point.
The gear ratios now come into play. Remember, all of the motors
in use by all of the cars (other than the AC traction cars) are
electrically identical motors rated at 115 HP.
One immediate implication is that the 75' cars should have a higher
top end speed. This is because for a given car speed, their motors
are not rotating as quickly. This only holds for level tangent
track where the weight of the car doesn't make much contribution
to the balancing speed.
The performance of the motor after resistive notching is over
(i.e. with the full voltage across it) is characterized by
a complicated graph known as the motor curve. Basically, tractive
effort is related to rpm by what looks something like a 1/x curve.
Under low tractive load, such as balancing on level tangent track,
the diminished TE/torque ratio of the reduced gearing doesn't make
much difference because the torque-speed curve is pretty flat, but
the lower gear ratio scales directly out to higher speed. That is
why I say under those circumstances the 75' cars will be faster
on the top-end.
Under high tractive load, such as ascending a long, steep grade,
the balancing speeds will be about even between the two car classes,
and perhaps the 75' cars will come up slightly slower.
It is in the middle of the acceleration range that things get tricky.
Thankfully, the TA removed the field shunting notches which were
a messy calculation. So, after resistive notching is over,
accel rate will NOT be 2.5 MPHps. It will gradually fall off as
it is no longer under control of the notching relay. All other things
being equal, the curves of the two car classes should cross twice.
My theoretical prediction of an imaginary race between a 75' car
and a 60' car: Both cars start at the same time and are dead
even until they reach a speed of about 15 MPH. The 75' car starts
to pull away slightly (because it reaches the end of its 2.5 MPHPS
portion at a higher ground speed). The 60' car then starts to
catch up, then it reaches balancing speed, and the 75' car ultimately
reaches a speed a few MPH faster, winning the race in the long-haul.
Someone mentioned motor load. The motors are not being unduly
stressed in the 75' cars, despite the fact that they must produce
more tractive effort because of the weight of the cars, and that
effect is magnified by the reduced gearing. When a traction motor
is rated for 115 HP, it means it can output that amount of mechanical
power at a certain target speed and torque, for a period of one
hour, with a temperature rise not to exceed 75C above ambient.
This is clearly not how motors are used in subway service. It is
routine during the brief acceleration phase to load the motors 150-200
% above nominal rating. No harm will be done to them from this.
In fact, the 115 HP motors in the 75' cars are being loaded normally,
and the 115 HP motors in the lighter cars are actually being
under-loaded.