Hi Paul,

The motion of the piston is a sine wave and you can get a the
exact value for the instantaneous acceleration by taking the
derivative of the motion.  (My wife is waiting to go to dinner,
so I can't think about it right now, but it's pretty
straightforward.)

Bob White

--
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When you get a chance please explain in layman's terms and we will
rewrite it.

Paul Lamar

While Bob is enjoying his dinner, I will give it a try.

Besides a distorted sine wave due to the connecting rod (it gets
shorter along the piston travel direction at the 3 and 9 o'clock
positions), one can simply use the acceleration of a rotating body
and add a + or - value for the ratio of crank radius ?r? to
connecting rod length ?l? for TDC and BDC positions.

Angular velocity: w  = Pi * n / 30,  here: w = 3.14 * 2500 /30 = 262
Rad/s.

Acceleration: acc = w^2 * r, here, acc = 262 * 262 * 5?/12 = 28,600
ft per sec per sec.

(Also: acc = velocity ^2 / r. Velocity = r * Pi * n / 360 = 5? *
3.14 * 2500 / 360= 109.1 ft/sec
Acc = v^2/r = 109 * 109 / 5 * 12 = 28,600 Rad/sec^2. )

The maximum acceleration is at TDC where velocity is zero, a peak is
also at BDC, while the acceleration is zero at maximum velocity near
3 and 9 o'clock positions. When the crankshaft rotates 90 degrees
from TDC the piston has move down more than half its travel.

Here the ratio of r/l comes into play, which is between .25 to .30
or more, normally about .28 in automotive engines.

This value has to be added at TDC and subtracted at BDC. TDC =
1+.28, BDC = 1-.28= .72.

So, maximum acceleration at
TDC is 28,600 * 1.28 = 36,600 ft / sec^2, and at
BDC = 28,600 * 0.72 = 20,600 ft/sec^2.
Accelerations at all other crank positions are in between these two
values.

For positions at a certain crank angle sin- and cos- functions of
the rotation angle and the value r/l apply.  Likely Bob will explain
this, (after dessert).

Regards
Rolf

Thanks Rolf.

Paul Lamar

Hi Rolf,

I'm not sure I understand why r/l would be added and subtracted at TDC
and BDC.  Since the connecting rod is inline at these points, the
variaton from the sine wave is minimal, increasing to maximum variation
at the mid-rotation point on the crank.  The largest position difference
is at mid-rotation, and I would think the largest difference in velocity
and acceleration would be there also.

We differ by about a factor of 2 in our answers.  I'm not sure why yet.

Bob White

--
http://www.bob-white.com
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