Re: Piston acceleration (was interferance etc)

[Arun Rao <rao@pixar.com>]

glen powell wrote:
>
> Conceptually, I find it difficult to understand how acceleration is greatest
> at TDC, as the piston stops moving up, is momentarily motionless, and
> the starts to accelerate downward. How can acceleration be greatest at the
> instant in time that upward motion has ceased, the piston is motionless
> and then downward acceleration commences? 


	OK, let me give it a shot:

	1. Piston has zero velocity both at the top and bottom of
	each stroke.

	2. It follows, therefore, that it has *maximum* velocity 	somewhere in
between.

	3. It has maximum positive velocity on the way up, and 
	maximum negative velocity on the way down.

	4. To go from maximum positive velocity to maximum
	 negative velocity, it has to decelerate (or
	negatively accelerate) continuously*.

	5. Acceleration is defined as the instantaneous 
	(i.e. at any given point in time) rate of change of velocity.

	6. It doesn't follow from the above, but because of the
	nature of the piston/crankshaft mechanism, the velocity doesn't
	have a constant rate of change between maximum positive and
	maximum negative values.

	7. It so happens that the maximum rate of change occurs at the
	point at which velocity changes direction (i.e. when it is
	zero).

	It's fairly simple math, but either requires basic calculus,
	or better ASCII art than I'm capable of!

	Hope that helps!

	-Arun

	*Continuous acceleration doesn't follow from statements
	1-3: it's a consequence of the mechanical arrangement.