The real benefits of lightweight pulleys (quantified)

[Subsonic]

Hey all,

This subject has been bugging me since I joined this fine forum. Lots and lots of users on here promote the benefits of lightweight pulleys for our FA20 engine, claiming that the reduced static and rotational mass will make the car accelerate faster. I’ve seen claims that ABC pulley will make your car X seconds faster to 60, or that DEF pulley will give you Z additional horsepower (like, WTF?)

I’m an old engineer who no longer does any engineering, but on the surface, these type of claims initially looked to me like they were a bit of a stretch. I’m sure plenty of these pulleys get sold on just looks alone, and that’s OK, but just going by gut feel, I think the benefits of using these types of light weight devices would be barely detectable on a dyno, or barely noticeable on the street / track. Given the relative weights of the components, the RPM they spin at, it just looked to me like the benefit would be barely detectable. So I’ve decided to test it, and lay out my calcs for you to study if you like.

Instead of racing my car up and down the street with a datalogger, swapping out components, re running and recording the results, I thought I’d just do it the old fashioned way, and sketch it up in excel. I think there would be far too many variables that way if the benefit is small. I propose to either state up front, or use referenced material for any data, and where any assumptions are made, they are conservative on the side of proving a larger benefit to using light weight pulleys.

The Energy method:

Our recent high school graduates on here will already guess what method we are going to use to test the benefit: Energy. That’s right. The first assumption is that the energy coming out of the engine will be consumed by the two elements that we want to study: the KE of the moving vehicle, and the KE of the spinning pulley. If we consider that only the energy in these two bodies is significant, then we can vary the properties of each to compare the magnitude of the difference. Hopefully we can show how much the reduction of pulley mass (and especially it’s moment of inertia, I) contributes to the overall acceleration, and your perception of it. Note that no other spinning devices are considered. All rotational moments of inertia in flywheels, drive shafts and wheels etc are ignored. Per the conservative statement above, discounting these serves to make the benefit of the lightweight pulley more pronounced than it really is.

I’ve decided to use second gear to determine the effect. The benefit of a lightweight pulley will be greater in first gear, but often we are limited by traction in first anyway, so it’s difficult to feel any benefit. The benefit of lightweight pulleys is much, much less in all other gears. The higher you go, the less difference you might feel. Consider this test to measure the improvement in acceleration you would feel using a lightweight pulley in a second gear pull from idle to redline.

Masses and moments for pulleys I found in the Grimspeed website: http://www.grimmspeed.com/lightweigh...-frs-2015-wrx/

OEM pulley mass / moment of inertia – 2.22kg / 0.0089021kg.m^2
Grimspeed pulley mass / moment of inertia – 0.522kg / 0.0017822kg.m^2

Other Data / calcs:

FA20 redline – 7400 rpm
W (angular velocity) of spinning pulley at redline – 774.92 rad/s
FA20 HP – 205
Top speed in second gear – 59mph (26.38m/s)
Vehicle mass with driver OEM 1355kg
Vehicle mass with driver and GS pulley 1353.3kg

The Kinetic Energy of the OEM moving vehicle is the sum of its vehicle KE due to mass (1/2 M*V^2) + the KE of the OEM pulley (1/2 I W^2).
KE OEM vehicle = 471.3kj
KE OEM pulley = 2.673kj
KE OEM total = 474kj

The Kinetic Energy of the vehicle modified with a Grimspeed pulley is the sum of its vehicle ke due to mass (1/2 M*V^2) + the ke of the OEM pulley (1/2 I W ^2).
KE modified vehicle = 470.7kj
KE modified pulley = 0.535kj
KE modified total = 471.2kj

Conclusion:

From the above we can see that the lighter weight pulley offers a 0.58% improvement in acceleration in second gear throughout the rev range. Per the assumptions above, the actual improvement is less due to the other rotational elements in the car which are not considered. The portion of energy in the pulley is therefore oversated compared to the entire car at redline. Some readers may be interested to know how much horsepower this “releases”. The answer is of course none, but the mass reduction in the pulley equates to the perception of about 1.18hp in this gear.

I’ll leave it to others to conclude if this is a significant improvement or not. From my own experience however, I have found that most people cannot perceive less than 10% improvement in acceleration by butt dyno. far fewer can perceive 5%. The real dynos I have used have an accuracy of about 5% and a repeatability of a bit less than 1% between runs.

Post:

If anyone feels that any assumption here is out of whack, let me know and I’ll correct it and re-run the numbers. I still have the spreadsheet too so happy to share / modify it if needed.

Subsonic

[Trueweltall]

Well, I don't regret getting light weight pulleys regardless of the math(good job by the way!). I just like to see the RPM go up and down faster(combined with LW flywheel and driveshaft). I also bought an aftermarket intake for a deeper induction sound over the stock intake which threw off the MAF scaling until I got a tune. In short I like to waste money.

[toyubie]

Excellent write-up, an interesting read for sure. As Trueweltall said, I think the real major benefit is being able to rev much faster during aggressive driving. Definitely not worth the price tag if you're going after dyno gains but a legitimate supporting mod (in tandem with other mods and driver skill) for some nonetheless.

[86TOYO2k17]

Originally Posted by Subsonic

Hey all,


If anyone feels that any assumption here is out of whack, let me know and I’ll correct it and re-run the numbers. I still have the spreadsheet too so happy to share / modify it if needed.

Subsonic

I appreciate you taking the time to do the math, and i wont pretend i understand the exact equations/formulas used... although i understand the basic concept behind it. but

Wouldn't you need to take everything into account. Drag, speed, gearing ratios, power at each rpm, as well as the mass of all the rotational components and the diameter or circumference for the moment of inertia forces required and the heat/friction of these components and the rpms each component spins at, and probably a few other variables...

Obviously getting very complicated at this point. However i have read a few very detailed articles that did break all of this down (albeit on different platforms) but the difference losing 4 lbs on a crank pulley was basically nothing, 15 lbs reduction on a driveshaft (purely from a rotational standpoint not including overall static weight loss) was about 1/4th HP and crank pulley was about 1/8 HP. with both obviously having peak benefit in 1st gear/low speed and diminishing at higher gear/speed.

[humfrz]

Good research ….


humfrz

[churchx]

Would be nice to see "thrown into excel" also CF drifeshaft & lighter wheels. Threads about improvement from those also appear frequent.

[nikitopo]

@Subsonic: I've done such calculations in the past and at first I was a bit puzzled too. I can give you a hint that your model is not that accurate. One issue is that you're trying to calculate the moment of inertia from mass and disk radius, but you don't know how the mass is distributed on the pulley. The OEM pulley is more heavy on the outside part of the disk and the mass is not distributed evenly like your model. This means that the OEM's pulley inertia is much bigger than your number and depending the manufacturer the lightweight pulley's inertia can be much smaller than your number. Overall, it is a complicated model with too many parameters and it is the reason to insist that the only way to get a close to reality result is to make your own acceleration measurements or just stay with dyno numbers.

I placed the following dyno many times in the past and I'll place it once more. And believe me the particular manufacturer is mainly an engine builder and they would never lie with numbers (*).



(*) I asked them once about gains on an exhaust and they were sincere to say that they didn't have any measurements on the particular engine. They don't care to sell by just posting non-sense or telling lies.

[Subsonic]

Originally Posted by 86TOYO2k17

… but

Wouldn't you need to take everything into account. Drag, speed, gearing ratios, power at each rpm, as well as the mass of all the rotational components and the diameter or circumference for the moment of inertia forces required and the heat/friction of these components and the rpms each component spins at, and probably a few other variables...

I’ve tried to explain in post #1, but I’ll have another go. The things most relevant to the model, some of which you’ve listed are the mass and speed of the car, and the mass, moment of inertia and rpm of the different pulleys. Everything else is excluded from the model because it is either: Not relevant to this simple model (like heat from friction), Insignificant, or including it makes the case worse for the light pulley.

Things that make the case worse for the light pulley are the rotational inertias of all the other spinning components. Including them into the total inertia of both OEM and modified cars increases the total energy in each, making that of the pulley less significant. I would imagine that if we considered the effects of the wheels and flywheel, the performance of a lightweight pulley would be shown to be a bit worse. Question for you then, as a percentage of acceleration how much performance do you need from your lightweight pulley? What amount is so small that it’s not worth doing?

Originally Posted by 86TOYO2k17

Obviously getting very complicated at this point. However i have read a few very detailed articles that did break all of this down (albeit on different platforms) but the difference losing 4 lbs on a crank pulley was basically nothing, 15 lbs reduction on a driveshaft (purely from a rotational standpoint not including overall static weight loss) was about 1/4th HP and crank pulley was about 1/8 HP. with both obviously having peak benefit in 1st gear/low speed and diminishing at higher gear/speed.

We could add as much detail as we like, but the result is still close enough to zero. The expression “crank pulley was about 1/8 HP” is nonsense of course, but it probably helps visualise the benefit for a particular gear if you make a bunch of other loose assumptions as above. The answer: Stuff all.

Originally Posted by churchx

Would be nice to see "thrown into excel" also CF driveshaft & lighter wheels. Threads about improvement from those also appear frequent.

If you could find the masses and moments of common wheel / tyre combinations that might be fun to do, but I can’t find / haven’t looked very hard for the data.

[FRS Justin]

The cost vs performance leaves very little to be desired in these types of mods. I guess if you have to have every little part that helps then its ok but bigger gains for less money are available.

[FRS Justin]

Originally Posted by 86TOYO2k17

I appreciate you taking the time to do the math, and i wont pretend i understand the exact equations/formulas used... although i understand the basic concept behind it. but

Wouldn't you need to take everything into account. Drag, speed, gearing ratios, power at each rpm, as well as the mass of all the rotational components and the diameter or circumference for the moment of inertia forces required and the heat/friction of these components and the rpms each component spins at, and probably a few other variables...

Obviously getting very complicated at this point. However i have read a few very detailed articles that did break all of this down (albeit on different platforms) but the difference losing 4 lbs on a crank pulley was basically nothing, 15 lbs reduction on a driveshaft (purely from a rotational standpoint not including overall static weight loss) was about 1/4th HP and crank pulley was about 1/8 HP. with both obviously having peak benefit in 1st gear/low speed and diminishing at higher gear/speed.

Along with all those factors you would have to compensate for the new harmonics of the engine. Will a light weight balancer create a damaging crank harmonic at any certain rpm that causes friction on the bearings? Their are a ton of variables that come into play and the only way to answer it is actually test for it. Math will get you close but nothing is as good as real data

[mkodama]

I think power and energy have been confused in this case.

Even if that isn’t the case, adding in rotational energy of the drivetrain significantly affects your numbers, and going by your percent different of 205hp rule, the difference is less than half a horsepower. In other words, lightweight pulleys make less of a difference than the weather.

Upside is your math is right and we both estimated similar dimensions.

[Subsonic]

Originally Posted by nikitopo

@Subsonic: I've done such calculations in the past and at first I was a bit puzzled too. I can give you a hint that your model is not that accurate. One issue is that you're trying to calculate the moment of inertia from mass and disk radius, but you don't know how the mass is distributed on the pulley. The OEM pulley is more heavy on the outside part of the disk and the mass is not distributed evenly like your model. This means that the OEM's pulley inertia is much bigger than your number and depending the manufacturer the lightweight pulley's inertia can be much smaller than your number. Overall, it is a complicated model with too many parameters and it is the reason to insist that the only way to get a close to reality result is to make your own acceleration measurements or just stay with dyno numbers.

I placed the following dyno many times in the past and I'll place it once more. And believe me the particular manufacturer is mainly an engine builder and they would never lie with numbers (*).

(*) I asked them once about gains on an exhaust and they were sincere to say that they didn't have any measurements on the particular engine. They don't care to sell by just posting non-sense or telling lies.

I got the mass and polar moment of inertia from the grimspeed website linked above, not calculated. I did convert into SI units, so I get (from the link) I=30.42 lbin^2 which converts to 0.0089021 kgm^2 for the OEM pulley If you could double check my calcs for me, that would be great.

Just popped out to measure my pulley and it’s about 145mm in diameter. If it weighs about 2kg (a guess, but close enough to the grimspeed data again). The polar moment of inertial should equal 0.00526 kgm^2 if it were a disc, but as you’ve correctly stated, it has more mass on the perimeter so the moment of 0.0089021 kgm^2 calculated from the reference seems about right.

That link you posted, what is it from? It looks like a torque and power curve from an engine, showing two curves from different tests. Given the curves are showing such a large torque difference from one test to the next, it is obviously not supporting any claim that justifies a lightweight pulley at all. Benefits should be in single digit % if at all. If you’re going to use a dyno to demonstrate the benefits of a pulley, you’re either going to have to provide a lot more information (like the time base for the run), or GTFO.

Also, in all my years, I’ve never believed a claim based on faith that they are “an engine builder who would never lie”. "Extraordinary claims require extraordinary evidence", as Carl Sagan would say.

[Joesurf79]

But lightweight pulleys come in Colors! COLORS!!!


Marketing trumps science in the minds of many, plain and simple. The "revs faster in neutral" is all the snake oil confirmation that is needed to enforce the placebo effect when the 2,800+ lb car is put into gear and the "gain" is lost in the statistical noise.


Proper air pressure in the tires and has a greater effect in acceleration than a lightweight pulley, the side benefit of improving handling and braking, and also is dang near FREEEEEEE. When was the last time many of us checked our tire pressure? It's not sexy and anodized so my guess is not yet this week lol!

[why?]

Originally Posted by FRS Justin

Along with all those factors you would have to compensate for the new harmonics of the engine. Will a light weight balancer create a damaging crank harmonic at any certain rpm that causes friction on the bearings? Their are a ton of variables that come into play and the only way to answer it is actually test for it. Math will get you close but nothing is as good as real data

The harmonics and vibrations are absolutely meaningless in any near stock engine unless you want to rev it too far beyond where the engine would explode due to its well known oiling issues.

Besides I've never seen anyone say a simply pulley change is going to totally change your car, and if they did they are morons or lying.

People are taking this stuff far too seriously.