Friday, 3 August 2012

Engine Architecture and Mathematical Design cont....

Mean Piston Speed

Well since I've mentioned mean piston speed some of you may be wondering what I'm taking about, so I will go over it briefly now and discuss piston speeds with regards stroke and piston areas with regards pressures and compression ratio in depth later. It will tie in quite nicely now so you can use the formula to decide on your own engine architecture. 

So mean piston speed is the average speed the piston travels at in the cylinder at a given RPM. I will assume you all have some knowledge of internal combustion engines and in this instance 4 stroke engines. n.b. if not please carry out a search on Google as there is a plethora of information on the four stroke cycle.

So in one revolution of the crankshaft the piston moves down the cylinder and back up (2 strokes) in this time it accelerates from a stop, peak piston speed is produced half way during the stroke (dependant on con rod/crankshaft offsets etc. again this will be detailed later in the blog) and then it slows to a stop at the bottom of the stroke before changing direction and accelerating back up the cylinder before stopping once again at the top. So we have slow speeds and extremely high speeds, the average across the stroke is the mean!

The formula for mean piston speed (Cp) is as follows;

Cp  =2 x  S/10^3   x  N_RPM/60

We can simplify this as
Cp= ((S x 2) N_RPM)/60000

This equation shows the Stroke(S) times 2 (as we have 2 strokes in 1 revolution), multiplied by the RPM of the engine divided by a constant (60000). This constant is because we are use mm for the stroke and minutes for the engine speed. Mean piston speed is calculated as metres per second. 1000mm in a metre and 60 seconds in a minute. Times one by the other and voila 60000!

So an example once again, let us use the example from the Formula 1 engine that was a guesstimate in the first article;

We had a 45mm stroke so if we calculate mean piston speed at the engine speed ceiling imposed by the FIA (18000RPM) we can calculate the 

Cp= (45 x 2)x18000/60000

Cp= 1620000/60000

= 27m/s

Now this is where we have to compromise, the engine has to last so many events which transposes into a certain amount of kilometres. A race engine with exotic materials can last possibly through one qualifying event at mean piston speeds of 27.4m.s. 24 - 27 m/s is the norm and 25.2 - 26 would be deemed as safe, as most exotic materials are now banned in F1 with regards friction/piston and cylinder wall materials and coatings. It can be seen we are high on the mean piston speed but we guessed a stroke of 45mm. Our bore was well under the limit so if we up the bore size to maximum and shorten our stroke we can reduce the mean piston speed to a safer speed. 

If you have read this far and a re still interested where this blog will go then please feel free to transpose the capacity formulae to make the stroke the subject and so you can enter a bore or transpose the above Cp formula and make the stroke the subject and enter a safe mean piston speed. I will add a table in a few days with various bore, stroke and piston speed examples for you to compare. You will then have taken the very fisrt step into designing your own parametrised engine.





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