Talk:Piston motion equations

What cleanup changes would be required (I am still failrly new to Wiki)...? joecar joecar I agree. Very clean, precise, succinct and well written article. David UtidjianPortknocker 04:22, 1 September 2006 (UTC) I agree with you. Great article. Maybe they are talking about de writing of the formulas. --Cduv 10:34, 20 October 2006 (UTC) Thanks. I want to make the equations look more math style, but I'm having some trouble understanding how to do it. joecar 23:26, 20 October 2006 (UTC)

The statement regarding maximum velocity occurring when L and R are at 90° to each other is False: e.g. For L=6 and R=2, you can calculate A=73.17615°, and then calculate angle between L and R as 88.21779°, which is clearly not 90°.

joecar (talk) 18:10, 8 October 2008 (UTC) Help: I want to update the graph at the bottom of the article with this new/improved one: http://commons.wikimedia.org/wiki/Image:Graph_of_Piston_Motion.png How do I go about replacing the old image with this new one...? Ah... I have figured it out. —Preceding unsigned comment added by Joecar (talk • contribs) 18:18, 8 October 2008 (UTC)

Someone please take note of this: The statement regarding maximum velocity occurring when L and R are at 90° to each other is False; e.g. For L=6 and R=2, you can calculate A=73.17615°, and then calculate angle between L and R as 88.21738°, which is clearly not 90°.

i.e unless the 90° statement can be mathematically arrived at or otherwise proved, then it should be excluded.

joecar (talk)

Efficiency
How efficiently does a crankshaft convert reciprocating motion to circular motion? It would be 100% if the force on the crank pin always acted tangentially to the circumference of rotation. But this occurs only at one point within 180°. All other points depend on the angle between the connecting rod and the circumference of rotation. A scotch yoke gives a sine wave. What does a crankshaft give?

AdrianAbel (talk) 16:58, 23 April 2009 (UTC)

You are correct about the non-tangential-ness of the crank mechamism.

However the Scotch Yoke does not provide tangetial force application either, I missed the point you're making; also, the disadvantages of the Scotch Yoke make it unsuitable for common automotive use.

Crankshaft gives a non-sinuoidal waveform (see the article).

joecar (talk) 19:23, 8 September 2009 (UTC)

Example
For a stroke of 4 a rod length of 6 in the example seems rather short to me. Can anyone reference a motor with such a small rod to stroke ratio? More commonly the rod length is twice the stroke often more. With a crank radius of 2 a rod length of 8 would be more appropriate.

AdrianAbel (talk) 15:06, 15 May 2009 (UTC)

The GM Gen III/IV engines use a 6.098" rod with stroke ranging from 3.622" to 4.125". The GM Gen I (SBC) engines came with a shorter 5.7" rod length with similar stroke range. There are very few (if any) passenger car engines with a 8" rod length, the engine simply won't fit under the hood. See this link: http://users.erols.com/srweiss/tablersn.htm

joecar (talk) 19:12, 8 September 2009 (UTC)


 * Many thanks for the link. It fully justifies the example in the main article as far as automobile engines are concerned..
 * My information is derived from the design of motorcycle engines which are probably not as restricted in overall height as in automobiles. My reference is "Motorcycle Engineering" by P.E. Irving, Temple Press Limited, London. On Page 276 Phil writes: "The piston would then possess what is known as simple harmonic motion, or S.H.M., but this condition never exists because, for reasons some of which are obvious and some are not, the con-rod has to be shorter than infinity and is usually somewhere around four times the crank radius or twice the length of the stroke."
 * Phil assumes this ratio in other explanations in his book.

AdrianAbel (talk) 09:02, 28 September 2009 (UTC)

In the equations of piston motion, if rod length (L) is made appreciably large compared to crank radius (R), say by 100x or 1000x, then you will see that the waveforms (position, velocity, acceleration) approach sinusoidal... with real world dimensions (e.g. L=6", R=2"), the motion equations contain several components: Simple Harmonic Motion (SHM) plus non-fundamental harmonic motions (would this be called Complex Harmonic Motion); the squareroot terms actually graph out to sinusoids.

joecar (talk) 23:41, 30 September 2009 (UTC)

4D Animation
To whomever add this animation: This animation doesn't make sense... the crank/rod/piston mechanism in an internal combustion engine (as stated at the beginning of this article) has a fixed length rod and a fixed radius crank... your 4D animation shows a variable length rod and variable radius crank... that doesn't fit in this article, it should have its own article regarding "variable geometry" mechanism. —Preceding unsigned comment added by Joecar (talk • contribs) 08:36, 26 February 2010 (UTC)
 * You're right, I created another animation containing three pistons with the parameters of your example graph of piston motion : same values and same colors.Patrhoue 16:10, 8 August 2011 (UTC)

Thanks (sorry, late) for correcting the animation to match the graph :) joecar (talk) 07:36, 8 January 2022 (UTC)

This article does not cite any references or sources.
What if the article is a derivation from first principles...? —Preceding unsigned comment added by 72.129.20.215 (talk) 06:04, 15 May 2010 (UTC)

In the animation, can the 3 colored pistons be made transparent to emphasize the position of the piston pin...? 98.154.202.50 (talk) —Preceding undated comment added 14:57, 20 September 2012 (UTC)
 * Thank, I have uploaded a new animation.Patrhoue 21:31, 20 September 2012 (UTC) — Preceding unsigned comment added by Patrhoue (talk • contribs)

Thanks for updating the animation. joecar (talk) 07:37, 8 January 2022 (UTC)

Skarmenadius
I don't understand one of your edits... how would this phrase contradict the article (regarding velocity maxima/minima which is how they are defined): "and correspond to the crank angles where the acceleration is zero (crossing the horizontal axis)."

Additional Links
I tried to add this desmos link to the page showing position velocity acceleration ect of a piston with various rod ratios but it was taken down so If someone wants to add it to the links so that the next person can visualize accelerations of pistons https://www.desmos.com/calculator/xalfht9bqc — Preceding unsigned comment added by 107.167.221.147 (talk) 19:42, 29 August 2020 (UTC)

Position
Someone changed the position in angle domain to the incorrect equation. I have since fixed this. If you believe that it is currently wrong please discuss here before making changes. — Preceding unsigned comment added by ConanTheGardener (talk • contribs) 06:49, 4 October 2020 (UTC)

I don't believe it is currently wrong. I believe the steps can be simpler as follows:

l^2 = r^2 + x^2 - 2.r.x.cos(A) l^2 - r^2 = (x - r.cos(A))^2 - r^2.cos^2(A) l^2 - r^2 + r^2.cos^2(A) = (x - r.cos(A))^2 l^2 - r^2.(1 - cos(A)^2) = (x - r.cos(A))^2 l^2 - r^2.sin^2(A) = (x - r.cos(A))^2 x - r.cos(A) = sqrt(l^2 - r^2.sin^2(A)) x = r.cos(A) + sqrt(l^2 - r^2.sin^2(A))

joecar (talk) 01:11, 8 November 2020 (UTC)

it ran together arrghhh joecar (talk) 01:12, 8 November 2020 (UTC)

let me paste again, hopefully it doesn't all get all run together:

l^2 = r^2 + x^2 - 2.r.x.cos(A)

l^2 - r^2 = (x - r.cos(A))^2 - r^2.cos^2(A)

l^2 - r^2 + r^2.cos^2(A) = (x - r.cos(A))^2

l^2 - r^2.(1 - cos^2(A)) = (x - r.cos(A))^2

l^2 - r^2.sin^2(A) = (x - r.cos(A))^2

x - r.cos(A) = sqrt(l^2 - r^2.sin^2(A))

x = r.cos(A) + sqrt(l^2 - r^2.sin^2(A))

joecar (talk) 02:34, 8 November 2020 (UTC)

note that the intetmediate steps are simpler (completing the square, sin^2 + cos^2 identity). joecar (talk) 02:38, 8 November 2020 (UTC)

Avoid over-reducing derivative expressions
I strongly suggest to avoid over-reducing the derivative expressions since doing so leaves the final expressions more complicated compared to keeping the separate terms.

And, for example, the final expression of x' (velocity wrt angle) does not allow logical follow on to x" (acceleration wrt angle).

Keeping the separate terms gives insight into the contributing components of what would be call complex harmonic motion.

And it appears that over-reducing has introduced errors in the final expressions. joecar (talk) 00:44, 6 November 2020 (UTC)

Discussion of velocity in angle domain
The discussion of velocity following the velocity-wrt-angle expression should really be in a separate section, possibly its own section.

Also the discussion should be rephrased in terms of range -180° to 0° and range 0° to 180°. The discussion does not seem correct, it compares to r.sin(A) instead 1 which is the first term inside the parens of the velocity expression).

And the discussion should include acceleration, or accel could have its own section. joecar (talk) 00:24, 8 November 2020 (UTC)

i.e. the discussion should be separate from the derivation. joecar (talk) 06:42, 8 November 2020 (UTC)

Simplification and style
11:17, 8 November 2020 by joecar

Simplified rearranging of position equation. Removed factoring of velocity and acceleration equations. Corrected multiplicative dots. Added missing multiplicative dots. joecar (talk) 11:33, 8 November 2020 (UTC)

12:16, 8 November 2020 by joecar

Added explanation of position equation manipulations, added missing dot. joecar (talk) 12:19, 8 November 2020 (UTC)

21:43, 8 November 2020 by joecar

Removed line break as it was unneccessary. joecar (talk) 21:45, 8 November 2020 (UTC)

21:55, 8 November 2020 by joecar

Added mention of example graph to 90° counter example discussion. joecar (talk) 22:00, 8 November 2020 (UTC)

Keep final equations in simplified form
Please keep the final angle domain equations in simplified form. If you want to further manipulate the equations then please add a subsection for this (including a sentence indicating the intent of the maniipulation). Thank You.
 * ) joecar (talk) 02:11, 20 December 2020 (UTC)

Désaxé engines' Piston motion equation
Should this be added as a section here? — Preceding unsigned comment added by 2604:2D80:9C8E:D100:8C6E:CD37:DDFE:547A (talk) 01:52, 17 February 2021 (UTC)

https://en.m.wikipedia.org/wiki/Desaxe

aka: offset piston pin

The motion equations for offset piston are slightly different. For the offsets typically used in automotive applications (less than 0.1"), the example graphs are negligently different from the non-offsrt case.

Since the offset case now involves extra acceraleration "flicks" that affect NVH, I think a separate wiki article will do better justice to the offset case. joecar (talk) 07:57, 8 January 2022 (UTC)