[California Saab Tuner]

Can physics and math save you money? I think it might this time.

Always wondered just how much force (torque) was wasted spinning up those heavy Saab flywheels. I took it upon myself to go and find out ...

Newton's Second Law: Rotation

Net External Torque = moment of intertia X angular acceleration

I used my C900 non-turbo as an example. It accellerates at .41 g's in 1st gear and at 6000 rpm it's at 32 mph. This gives it rotational accelleration of 27.96 radians/second/second. The turbo Saabs will accelerate a bit quicker in 1st, but not more than say 25% ...

The flywheel on the later model Saab C900s is about 10.25 KG. Moment of inertia (I) for a circular disc = 1/2 x Mass x Radius^2 ...

... I assumed a radius of about 15 cm, or .15 metres, and assumed that the mass is more or less evenly distributed through the flywheel ...

Using this, it's moment of inertia is:

.5 x (10.25) x (.15)^2 = .1153kgm^2

Putting these figures into the original equation gives:

.1153 x 27.96 = 3.22 NM or about 2.4 lb-ft of torque.

So why then are alloy flywheels considered "cheating" in some forms of professional racing? I suppose in some forms, 2.4 lb ft could be the difference between winning and losing. Given the cost it's understandable to ban them, otherwise every team would need to spend $500 just for that little "edge" ... but otherwise all it's gonna do is allow you to rev a little quicker in neutral. I can't imagine that novelty being worth $500.

Cheers,
Dubbya

 

[Vigge]

Adrian W,
Remember that you can only lighten your flywheel to a certain point. If its too light hell will brake loose, you know what I mean.

 

[California Saab Tuner]

Vigge I'm not sure what you meant by that. I'm AGAINST lightening your flywheel ... in any way. Not just against buying an alloy one.

I suppose if you shaved off a couple pounds it probably won't hurt anything. But the actual gains in horses are minimal.

Dubbya~

 

[sj]

On the road, totally pointless, but in limited formulae, any edge is worth having.

A friend of mine read the formula regulations regarding flywheels very carefully. This stated that the flywheel AND bolts together must not weigh less than XYZ Kg total, to try and prevent lightening tweaks.

He then had his heavy steel flywheel machined down to minimal thickness especially around the outer edge, and had some special bolts made. These were M30 (I think) with apropriately large heads, which had the shank and thread machined down to M10 to fit the flywheel.

Flywheel AND bolts toegther weighed exactly regulation minimum, but moment of inertia was substantially reduced. Net effect minimal, but all the little bits add up and he did win the championship.

 

[ylee coyote]

as I understand it true horsepower is unnafected
but it is the reduction in horspower to acheive a certain rpm is

The fly wheel is a energy storage device
designed to keep the engine running on idle ie have enough stored energy to take it through the compression cycle.
It is normal to vastly over-engineer this part of it so there is a chance to reduce the mass and hence reduce the total amount of energy that is saved in the device
to work out what the difference is you would have to know where the weight was removed /differed from standard...
only from this could you calculate the difference in angular inertia and make an estimation vis a vis the difference in power needed to accelerate the flywheel
I have seen estimates that differ by factors from your calculation...

anyway my flywheel is being lightened (for £50)

 

[California Saab Tuner]

My calculation is based on ALL of the weight being removed. Obviously any part of that would be less than the whole.

If you can find any hole in the problem that I might have missed feel free to point it out. I tried it several times trying to make sure that was accurate. Especially given the number of flywheels sold out there.

I think the real benefit is with formula cars where when shifting the lower mass will impose less strain on the gearbox when the RPM drops suddenly. Or when revving quickly up on the downshift.

1st gear will see the highest losses, and I calculated that in 1st gear. Unless I did something wrong there's no way you could get more than maybe 2 lb ft of torque. It will rev a bit free-er. My point was just that it's not worth the $500 charged to get an Alloy one ... not if you're looking for horses anyway.

Dubbya~

edit: I can't understand why numbers would vary by any whole magnitude. It's a pretty straightforward calculation. Not sure where they would get large differences ... and of course I could work out how much hp you'd save if I had exact specs for where weight was removed. Though it might require calculus, or just estimation depending on the shape of the removed weight. I just removed the whole thing and only saw 2.4 lb ft ... couldn't be much more just taking off part.

 

[Eric van Spelde]

With this kind of mods, we're generally not looking for horses - we're looking for driveability. Nothing worse than an engine that feels like it has a millstone for a flywheel when you're trying to shift quickly and smoothly.

That, and the lessening of load on the gearbox main shaft/bearings should be an important consideration, at least on a c900...

 

[California Saab Tuner]

Here's an interesting example:

Say you're shifting between 3rd and 4th gear and you go from 6k - 4k rpm during the shift. Let's also say that your shift takes .25 seconds. Pretty normal shift ... angular acc = 133 rad/sec/sec ... same moment of inertia as before ... gives you 15.37 NM. Given that your gearbox survives 300+ NM I can't see 15 NM wearing it down too horribly quickly.

Now if you had a car with clutchless shifting, you might really notice an Alloy flywheel. They shift much more quickly and the RPM drop is nearly instantaneous. I think that's probably what alloy flywheels were created for in the first place.

Dubbya~

 

[jos]

Less weight on the flywheel gives you more spontanious revving, "the engine hangs under your foot". Downside is that when idling it can not give any comfort, because the flywheel doesn't keep the engine at a smooth pace.
So: good for on the track but very uncomfortable for everyday road-use.
grtz, JosG

 

[Eric van Spelde]

http://www.pumaracing.co.uk/flywheel.htm

 

[mark e]

Excellent article, Eric. Following the logic, it would therefore seem that any effect from removing the balance shafts from Bxx4 engines is going to be minimal due to the small radius.

 

[California Saab Tuner]

In the interest of honesty I just went through my calculations and found that the previously mentioned numbers should be multiplied by 2pi! (2 lb ft did seem a bit suspicious, no?) That would give 20.1 NM or about 15 lb-ft. This is of course removing the entire mass of the flywheel. Removing about half, as is done with the alloy ones, will give about 10.1 NM 7.5 lb ft. On high revving engines this will show up as much more hp than it does on our Saabs.

That site has an interesting way to look at it EVS, but unfortunately if our Saabs had any more power in 1st gear they'd just spin the tires, whereas if you can get weight off the rear end you'll actually go quite a bit faster!

Oh and with the ballance shafts I think it's more a frictional thing. They cause like 5-6 hp worth of friction is what I heard ... not sure about that though. Friction can only be estimated rather than calculated ...

Dubbya~

p.s. Apologies for forgetting to multiply by 2 pi ... dunno where my brain went on that one. Still not worth $500, or even close! But if you're going to get some machine work done anyway. Nothing wrong with taking a little off the top. So to speak ...

I'm going to try to get some estimates on power increase by lightening con rods/pistons. It'll take quite a while as the motion is far more complex (see engine forces post) ... but eventually I hope to have some good figures on that. I'll try to check my work more carefully!

 

[billj]

Originally posted by Mark E:
[qb]Following the logic, it would therefore seem that any effect from removing the balance shafts from Bxx4 engines is going to be minimal due to the small radius. [/qb][/b]

I understood that the primary benefit from removing the balance shafts was due to a reduction in frictional losses rather than any reduction in rotational inertia. Unlike lightening the flywheel, disconnecting the balance shafts removes some bearings from the system, along their associated frictional losses. Remember that these bearings operate at twice the crankshaft speed. I can't remember the relationship right now, but I know this will increase their frictional loss beyond what it would be if they were rotating at crankshaft speed. At least twice as much, I would guess, since they're effectively geared up by a factor of two, and I get the feeling that the friction might increase even more at higher speeds.

 

[billj]

Oops. Adrian beat me to it

 

[California Saab Tuner]

Beat ya to it Bill.

edit: And YOU beat me to noticing!

 

[philip hs]

This is really a topic we didn´t discuss yet (I think), and I find it really interesting! Thanks for starting it, Andrian!

Yours,

Philip

... who, after more than six weeks, is still waiting for getting his Viggen back from Heuschmid

 

[ylee coyote]

lightening crankshafts and conrods and pistons
there is still a rotational inertia (crankshaft) and there is a simple mass acceleration (piston)but the con rod in between is both!!
however lightening piston /con rod assemblies reduces forces on the crank shaft ie when the crank is pushing the piston and accelerating it ...
however the main benefit is to allow a higher rev limit assuming the same allowable max force on the crank it will arrive at a higher rpm because the assembly is lighter...

Now can some-one work the Math.....!!!!
(I certainly cannot !!)

And if your engine fettler is good and match weights all the pistons/con rods ..the engine will be as smooth as butter .....

So we will see .... this is exactly what I have asked my engine builder to do
rev limit will be 6,700 ..hydraulic cam followers are getting iffy after this

 

[California Saab Tuner]

Now can some-one work the Math.....!!!!
(I certainly cannot !!) -ylee

I'm workin' on it! I've got the formula for motion of the piston down (a= conrod length center to center, b= half the stroke of the engine, x= distance from center of crankshaft to center of wrist pin, invsin= inverse sin function or sin^-1):

F(x) = bcos(x) + acos[invsin(b/asin(x))]

F' and F are hideously complex! F represents the acceleration formula for the piston. But this does not quite even give the loss in torque due to movement as it must be converted using crank angle relative to the piston.

This could take a while ...

Dubbya~

edit: I could really use some exact weights for pistons and con rods on various Saab applications! Especially the B235R which is what I'm working on at the moment! Also exact measurements of conrod length center to center etc ...

 

[California Saab Tuner]

Oh and ylee ... if you get lighter valves you can safely increase the max RPM with stock lifters. You can almost cut the weight of the valves in half using titanium. That would make for a valvetrain capable of about 8K rpm.

Dubbya~

 

[Eric van Spelde]

Yours,

Philip

... who, after more than six weeks, is still waiting for getting his Viggen back from Heuschmid      [/b]

What's the story? Unanticipated setbacks (i.e. more work needed than assumed or waiting for parts) or just too much work taken in commission?


Oh well, I'm still waiting for the d*mn air/liquid intercooler core from Sweedspeed to materialize. Last Sunday on the Race & Rally fair, he said it was ready and he only needed to pressure test it...
And I have an appointment lined up for fault on the rolling road next Tuesday - aargh!