Another Math Problem

[steamer]

Beat me to it Tom...Nicely done

The non symetric accel is due to angularity affects of the connecting rod I suspect. If you make the rod "infinitely long....say 10 times the stoke, what do you get?

Dave

 

[kcmillin]

Very interesting result Tom. Ans thanks for adding a few tenths of a MPH to my 'Brag Bag' :big:

Kel

 

[DavesWimshurst]

Tom,
I could be wrong but I get a 2 in front of the sin^2 term in the numerator of the middle term of the
v' equation something like:

c^2*w^2*[2*sin^2(wt) - 1]

I agree with all the other terms.
Dave

 

[Ken I]

As an estimate of max. piston velocity take the average and multiply it by the square root of 2 (1.414..).
That would be correct for simple harmonic motion (which a motor isn't) - but its not far out.

Ken

 

[mu38&Bg#]

Mean piston speed is the term used in engine design. The equation is simple; mean piston speed = 2 x Stroke x RPM. Using feet for stroke will yield ft/min. In SI units revolutions per second and meters is used to yield m/s.

So, 9000*.5/12= 375ft/min. This is at the low end of the scale. In the more common metric units it's 1.9m/s. Wikipedia has a decent reference for basic engine types mean piston speed.

http://en.wikipedia.org/wiki/Mean_piston_speed

Little engines can have high piston speeds. A two stroke engine for an RC car of 3.5CC displacement can run 35,000 RPM and has an MPS of 9.3m/s. A 6.5CC model airplane racing engine running 32,000 RPM and has an MPS of ~10 m/s.

 

[mklotz]

Beat me to it Tom...Nicely done

The non symetric accel is due to angularity affects of the connecting rod I suspect. If you make the rod "infinitely long....say 10 times the stoke, what do you get?

You're correct, Dave...

As 'l' approaches infinity, the last two terms in the v' equation go to zero and only the cosine term remains so the acceleration becomes a pure sine wave.

 

[ttrikalin]

Tom,
I could be wrong but I get a 2 in front of the sin^2 term in the numerator of the middle term of the
v' equation something like:

c^2*w^2*[2*sin^2(wt) - 1]

I agree with all the other terms.
Dave

you are right - I stand corrected

FWIW my acceleration plot is correct (using the 2 I omitted in the posted equation) -- I'll go back and correct the equation when I get home...

take care,

tom in MA

 

[bezalel2000]

mean piston speed = 2 x Stroke x RPM.

So, 9000*.5/12= 375ft/min.

I don't know what's the cause of it,

I think perhaps there is a "2" thief in the server ??? ??? ???


Bez

 

[ttrikalin]

[EDITED TO CORRECT FORMULA -- THE RED 2 WAS MISTAKENLY OMITTED -- THANKS DAVE!]

For completeness, formula for acceleration corrected.

take care,
tom in MA