Now here`s a thought!

SQUARE/CUBE LAW AND SOME OF IT`S IMPLICATIONS

It`s quite strange how a casual comment spoken or read somewhere can start a chain reaction that reverberates through to today. Just such a thing happened recently as I was browsing a near 40 year old book on racing motorcycles where a short article analysing the incredible efforts of the Spanish Ossa 250 GP racer brought up the subject of cylinder scaling. The Ossa as I`m sure you all know came within an ace of taking a world 250 championship competing against the Yamaha twins and the like. The engine was a very simple air cooled, disc valve unit with a single cylinder of 70x64.5 dimensions.
Big cylinders have inherent breathing problems that are directly attributable to the `square/cube law`.
Fundamentally, if a cylinder`s linear dimensions of bore and stroke are doubled, the surface area is increased fourfold, but the volume is increased eight times, the so called square/cube law! Relative port sizes are thus halved, making the filling and emptying of that huge volume very difficult. To reduce the effective breathing restrictions incurred, the port and duct sizes have to be made much bigger but their natural resonance frequencies will then demand much high revs. It is not easy to adequately empty and refill that large volume during each engine cycle at peak torque rpm.  The Ossa produced it`s meagre 45 or so hp at the astonishing figure of 11,000 rpm (23.65mtrs/sec), much above that and it`s innards were liable to disintegrate!
So what has all of this got to do with Bantams I hear you ask, well quite a lot in fact, particularly when comparing a big 64x58 186 engine with a square 54x54mm engine, this is particularly true when the best of both seem to produce similar track performance with neither having dominant power over the other. The figures below reveal, at times quite stark comparisons between the two types of engine!
The first and most obvious is the swept volume increase for the 186 engine of 50% over the 124cc engine, that figure alone indicates that all is not well with the bigger engine? As it is combustion that produces the pressure energy that propels the piston down and the con-rod to transfer that energy to the crank assembly it might be handy to define that process. Combustion efficiency is, on a strictly formal basis, the fraction of the potential heat energy of the fuel actually released set against the potential heat energy actually available to the engine. Heat loss to the internal surfaces, of piston, cylinder head, spark plug, cylinder walls all serve to soak heat away and reduce pressure. Also of concern is the potential to lose some fraction of power in trying to burn mixture at a reduced compression ratio with a rapidly falling piston all because of an over long flame travel. The faster combustion can made, the shorter time period the exposure all internal metal surfaces have to combustion heat. This can mean more power gets to the crankshaft and less to the cooling system, be it air, via fins, or water.


AREAS
          54mm bore has a circumference of 170mm. swept surface area of 9180sq mm.
          64mm bore………………………………….. 201mm.  ………………………………11661sq mm.
          The 64 cylinder has a 27% increase in surface area with a 50% increase in volume.  

EXHAUST PORT AREA AND DURATION

No corner radii have been included and the width for both is 70% of the bore diameter, and the port height for both is 50% of their respective strokes, of 54 and 64, and so are 27 and 29mm.

54mm bore port area is 27x 37.8 = 1020.6sq mm
64mm bore port area is 29 44.80 = 1299.2sqmm                                                                                                                                                                                                                                                                the difference in area of 278.6sq mm is 27.3% in respect of the 186cc cylinder


Durations.
For the 54mm engine I have assumed a typical 110mm rod, and for the 64mm engine a 125mm rod. These give rod/stroke ratios of 2.037 and 2.155 respectively.


54…….50% stroke at 27mm port height has a port timing duration of……………………194*
64…….50% stroke at 29mm port height has a port timing duration of……………………193.3*
Assigning a rod/stroke ratio of 2.155, meaning a rod length of 116mm, to the 54 engine then the exhaust port timing duration becomes ………………………………………………………………….193.37*
Assigning a rod/stroke ratio of 2.037, meaning a rod length of 118mm, to the 64 engine then the exhaust timing duration becomes……………………………………………………………………………194*  
All timings very comparable?

CYLINDER VOLUME AT TDC      
Assume 12:1 compression ratio for both engines.
54mm bore   11.27cc
64mm bore   16.9cc
The difference in volume is 5.63cc representing 50%

The measurable distance from the plug electrode to the cylinder bore is much longer for the larger 64mm bore diameter combustion chamber, suggesting a longer flame travel. Another way of looking at flame travel is, the minimum time duration for complete combustion!
I think all of the numbers contained here provide some food for thought, indicating there is a lot more going on than might at first be imagined?

Trevor.

Evening Trevor. so how do we speed up the flame travel or reduce the travel length? Pre combustion  combustion chambers to increase the flame size? more powerful spark, change fuel?

Lots of small dia pistons and I've often thought pre-combustion chambers as a way to go...

Lots of small dia pistons in one engine has been done -- how do we go about pre-combustion chamber?  or what about commbustion-chamber-bowl in the piston crown? Increase compression-ratio to 22-24:1 and run on alcohol
-- not my Glen Fiddick, that's for Xmas...

Have a Good One, ALL of YOU !

Cheers!

John...

Hello Nigel,
not as comprehensive reply as I would have wanted but I'm just a bit pushed for time at present and won`t be home again until next week.

               Combustion is a very large and hugely complex subject, deserving of a book all to itself, but I guess for our specific and relatively modest Bantam needs that is going a bit too far?
Essentially, combustion is a combined process, as both chemical and mechanical effects are at work simultaneously, with the whole event being initiated by an electric spark discharge.

Turbulence is absolutely critical to efficient combustion. Prior to the exhaust port closing there are several turbulence generators, first is piston motion stirring things a little, then comes the various scavenge streams together with the returning plugging pulse arriving just before port closure. It then is the task of squish action to further churn the whole mess around. The idea of turbulence is to continually offer fresh fuel to the flame front propagating through the chamber. The shorter time frame that this complete burn can be achieved in, the later we can ignite and so ensure there is no significant combustion pressure acting on the piston crown before TDC, which only serves to slow the crank and absorb power, through negative work.
The geometry of the combustion chamber can influence the quality of combustion and how quickly the burn can be achieved, for instance, a flat top piston in combination with a deep hemi chamber will suffer from having its squished mixture aiming much lower and away from the start of the flame, a toroidal chamber however with lower plug face will then have the assistance from squish action to agitate the initial burn. Flat tops have a number of other disadvantages over a conventional domed crown. A large, 64mm diameter bore has a physically longer travel from plug to cylinder wall and consequently a potentially longer burn time. Whatever the shape of the chamber it is important is to have the squish streams ejecting mixture up towards the spark plug and into the advancing flame front thereby blasting burning mixture towards all parts of the chamber simultaneously. This action will contributes enormously to achieving complete and rapid combustion.

Increasing the compression ratio accelerates flame speed by increasing pressure, but simultaneously, temperature also starts to ramp up. The safe ratio to use will ultimately be determined by the ability of the engine to cool itself. Fins have a finite rate of heat dissipation determined only by the volume of air flowing through the fin spaces. Water cooling enables the cylinder/head combination to tolerate much higher thermal loads, water being much more able to remove heat that air can.

Variations in fuel to air mixture ratios have a profound effect on flame velocity and the amount of heat in the burn. Maximum burning velocity is achieved when the mixture is a few percentage points richer than the stoichiometric value of 15-1. Lean mixtures release less heat energy which results in lower flame temperature thus less flame speed, the same conditions apply for over rich mixtures with the added prospect of incomplete combustion as all there are too few oxygen molecules chasing too many fuel molecules to react with.

As an overview, combustion cannot be instantaneous (excluding HCCI) and the chamber volume is constantly changing, the choice of ignition point with regard to crank angle can have a significant effect on just how much useful work can be accomplished during combustion. If too early, pressure release creates negative work, if too late then combustion takes place in an increasingly larger volume after TDC so the compact chamber advantage is lost. Therefore the decision as to where to ignite the combustion mixture becomes a critical factor in trying to achieve the best available torque.
All of the foregoing flies completely out of the window when running far below sensible engine revs where cylinder filling is a fraction of that at peak torque rpm!

Trevor.