View Full Version : Engine Equations

Cannon Fodder MOO
05-05-2003, 03:15 AM
I've been reading engine equations on mac dizzy's site and had a few questions.

1. Can you calculate the predicted potential power a motor could make from theory? ie purely from size and compression ratio?

2. What is the stroke in the RS/RGV250 motor?

3. What specifically is the Piston Acceleration formula used for? I understand that if rods are too short/long then there will be inherent problems but haven't found any guides based on the formula.

4. Are there critical numbers for crankcase volume/primary compression ration?

5. Why would it be necessary to calculate piston height at any time?

The equations are comprehensive but I was wanting to extract more meaning out of them.

05-05-2003, 04:57 AM
1. The potential power (in the broadest sence) can be estimated using thermodynamics - this should really be viewed as theoretical power as most engines are in th 30-40% efficency region - IE they only achieve a fraction of the theoretical power... For a given engine configuration you can probably get a lot closer, but what you end up doin is simulating the engine by hand. (For example there are 'flow' tables that give air flow into a cylinder by valve configuration, balance tables to give the type of balancing shaft required for a given cylinder configuration). See wright.nasa.gov/airplane/ottoa.html (http://wright.nasa.gov/airplane/ottoa.html) for a description of thermodynamic efficency. But in the broadest sence we can say that more power is available then the intake air is colder, heat wasted in the exhaust is less, heat transferred into the cylinder is less (ie lower engine running temperature), and the less sound an engine makes...

2. I think its 56x50.6 mm (50.6 would be the stroke)

3. Piston accelleration is used to calculate the stress on the con-rod... Basically max RPM is limited by the con-rod strength.

4. Hmm, This is worth a topic in itself (infact I was going to start one after the ignition timing thread has run out of steam... as this is the next design area I wanted to explore). - The shortest explanation is to say its the same as the exhaust and the same as the inlet system! This is where power can be made and lost, there is no one way to do it - it all depends on the kind of engine response you want. Assuming all you care about is peak power then start from the primary exhaust resonance, and tune the resonator formed by the crank volume and tranfer ports to the same frequency. Finally the airbox and carb bore rubbers form another resonant assembly, and this should be tuned to the same frequency as well... This is simplistic.

5. Piston height is used to convert an engine model to a scheme for porting. For example lets say your calculations on exhaust resonance suggest that at 12000 rpm you need to site the exhaust opening at 90 degrees ATDC, you can convert this to a height in mm from TDC and use this to mark the cylinder bore for cutting.

The equations present a compact form for calculation, really it is the physics of engines that provide understanding. Most engine workings are covered by thermodynamics. This however leaves most of the useful stuff for two strokes out - here acoustics and thermoacoustics are probably more relavent.

Cannon Fodder MOO
05-05-2003, 08:00 AM
Thanks for the comprehensive reply. :D

1. the thermo dynamics stuff looks good so hopefully I'll have a better read soon, and perhaps find what other bike motors are running.

2. then by my calculations of mean piston speed (RS250) at 12 000 RPM is 20.24 m/s, at 12 500 is 21.08 m/s and at 13 000 RPM is 21.93 m/s. The 95 CBR 600 at 13 500 had a mean piston speed of 20.01 m/s which is just under 4000 ft/min. [4000 ft/min is about 20.32m/s] I think even back then honda used to run motors at redline for 24 hours in the test phase. Also 4000 ft/min seems to be a barrier not often pushed by engine manufacturers and it is claimed that speeds above this lead to very short engine life. The E34 BMW M5 just pushed this barrier (4076 ft/min). Thus constant revs over 12 000 in the RS motor will lead to higher maintenance (probably common knowledge :p )

I haven't even bought my RS yet (falco's still in the shop) but it seems pipes that increase my rev range may not be the way to go, unless I get a good sponsor for bracket racing (not likely :rolleyes: most of the chicks get their entry paid but I doubt I'll even get that)

SIDENOTE: If ya got any ideas about how I sould go about rasing sponsorship let me know. Bracket racing's not real racing but then it doesn't cost sponsors as much.

The alternative is to obtain a fatter horsepower curve/torque curve but in the end it will puound the bottom end, so I gotta ask (excuse my impertinance) what s the bottom end like and whats it cost to rebuild (I haven't met anyone who has done this).

3. It would be a good exercise to find some tables on this, maybe later.....

4. Please start your new thread when you're ready 8o I'm just trying to understand out of order, ie combustion then crankcase and finally exhaust. If the exaust scavenging is optimal, and the reverse pulse prevents much fresh air/fuel mix from escaping then correct crankcase size will deliver an optimal delivery of air/fuel mix. If for a basic model one assumes perfect reverse pulse (ie model without exhaust port) then one should be able to find an optimal range of sizes for the crankcase. Too small and there will be a great injection effect, unfortunately without enough air/fuel mix. Too large and there is plenty of air/fuel mix but no real compression of the mix to supercharge the compustion chamber. i suppose the factory would have this near the mark.

5. Excellent when I get my hands on an old 2-stroke bore I'll go through the exercise of port/cylinder mapping. That should help with my understanding!

on the physics bit I was poor at physics but good at maths, one day I realised physics was mainly maths with interpretation. Thermodynamics isn't a problem, just equations like the 3D advection/diffusion/convection equation (hope thats it:rollin: ) I have never seen thermo acoustics equations but figure that mathematical modelling is mathematical modelling. I'll also point out that my modelling is average and during honours I only modelled 2D fluid mechanics using finite difference methods as opposed to finite element techniques (I was an applied maths student not an engineer). It's a bitch doing that stuff from scratch but once you've got a nice model coded and calibrated you can have some fun :eek: .

Anyways It'll be good to read these threads and learn some more about great little motors. My g/f gets back tommorow so I don't know how much reading I'll get done but I must say this is fascinating. If someone modelled the RS250 motor a lot of things could be held constant to examine the crankcase side of things. Damn you know I want to pull down a motor just for a look 0] .

thanks for a great response. :)

05-06-2003, 03:07 AM
I have just checked the bore and stroke, it appears I made a mistake, and the bore is 56 the stroke is 50.6 - (if you work backwards and caclulate the engine cc 50.6x56 ~= 225cc and 56x50.6 ~= 249cc) so that should improve things for piston accelleration. I get 4392 ft/s with a stroke of 56mm (wrong) but a much more respectable 3968 ft/s with the correct stroke of 50.6mm.

working backwards if the limit is 4000ft/s then the max RPM would be 12097 RPM...

reducing stroke by 10% would give a limit of 13440, and the new dimensions would be 59x45.5 - this would require over-boring by 1.5mm (I think this is quite possible as if you leave the stroke alone you would get a volume of 277cc and over-bores of 316 are possible - if unreliable). If you're going to do that it may be better to use the full stoke (and easier, no offset pins in the crank) and get the power from the CCs not the RPM.

Based on this it seems sensible to concentrate on the power curve under 12,000 RPM. I the engine can be made to over-rev to 12,000 at more or less peak power (maybe a little under)... We have seen from the RS50 that it is possible by altering timing (or cylinder mapping) to get a good 2000 RPM over-rev -so that would suggest the ideal exhaust tuning would be about 10000 RPM for the RS250, which would give good power (but tailing off towards the top) to 12,000 RPM. This may mean exhausts with close to stock tuning are better! (once the timing has been adjusted - or the porting modified)

As for the bottom end - I have striped an re-built the gearbox, (nasty smelly oil) and replaced the crank. The hardest thing is getting the engine back in the frame... splitting the crank is easy, just take out ALL the bolts (mostly allen keys) and tap for ages with a rubber mallet until it starts to split. Inside is the crank - its that simple... (so many less parts than a 4 stroke!) - I would recommend sending (or taking) the completed crank/conrod/piston assembly to be balanced (it is better if it is ballanced with the pistons on - if you cant get it balanced with the pistons on, use a very sensitive balance to balance the pistons yourself before putting them on the balanced crank).

I also think some parts of the bottom end are better than others - basically I think the crank can take a bit more HP - but the gearbox is dodgy on low gears especially 1st/2nd changeover. I the gearbox starts having trouble staying in second (pops out) - stop driving and replace the cogs for both second ant top - otherwise the damage could be much worse (like new engine time due to holed crankcases)