Re: Conrod force/acceleration

[Luis Marques <marques@rtis.ray.com>]

Sargent Schutt <sargent@novagate.com> wrote:
> Come again? Is there not a point in time where acceleration and
> velocity are zero? I certainly think so. When there is no velocity,
> there is no acceleration. Acceleration can be zero while velocity is
> constant, but if velocity = 0, acceleration = 0; acceleration is
> nothing more than the rate of change in velocity. At TDC velocity is
> zero, and therefore acceleration is zero, too. Yet the engine is most
> definitely running.

OK, I have tried to stay out of this very hard, but since there is still
a lot of confusion out there about velocity and acceleration and all
that, I'll try to explain.  Although it may not make sense at first,
anyone who has taken a calculus course will be able tell you that
acceleration is simply the derivative of velocity, or in simpler words,
that acceleration is a measure of how fast the speed is changing.  As
such, the instantaneous velocity doesn't tell you anything about
acceleration.  It is how fast the speed is changing that tells you the
acceleration of an object.  So the fact that at an instant in time a
piston has zero velocity doesn't imply that it has zero acceleration.

For an engine at constant RPM, if one were to plot the velocity of a
piston as a function of time it will look very close to a sine wave. 
The acceleration, being the derivative of velocity, will look like a
sine wave offset by 90 degrees (cosine wave).  So the piston velocity
will be 0 at the very top and the very bottom of it's travel while the
acceleration is at maximum, and the acceleration will be zero when the
piston is at the middle of it's upwards or downward travel with maximum
speed.

> Are you suggesting a perfectly parabolic acceleration curve with no
> zero point? (1) There will be a time when acceleration is zero; (2)
> You have massive acceleration/deceleration approaching/leaving TDC, as
> a function of rapid reversal of travel. You also have zero velocity,
> and therefore zero acceleration, at one micor-instant in time (at
> TDC).

Again, zero velocity doesn't imply zero acceleration, not even at a
micro instant.  You are right about acceleration/deceleration being
highest at the top or bottom of piston travel, but the thing to
understand is that both acceleration and deceleration are the same thing
here.  From the moment the piston crosses over the middle of its upward
travel it is being pulled down and speed is decreasing, and continues to
be pulled down until it crosses over the middle of its downward travel
(when speed is highest), when it begins to be pushed up.  The instant
when the piston stops being pulled down and begins to be pushed up the
acceleration is zero (even though speed is at a maximum).

> Additional question: additional cylinders = more rapid acceleration,
> more constant crank velocity, lower piston velocity overall? Eg in a
> I-4 vs. I-5 vs. V8 vs. V12?

No. All this piston acceleration/speed, etc. depends on the connecting
rod length, crank stroke, and RPM.  Period.  An engine with the same
dimensions will have the same piston speed/acceleration, regardless of
how many cylinders it has.  The advantage of more cylinders is that they
allow a more uniform torque delivery due to piston overlap.  Hence more
"constant crank velocity" and smooth engines, and better low-end torque.

Luis Marques
'87 4kcsq