Technical advice requested - pulley size versus boost

[pokeybritches]

I'm trying to wrap my head around pulley size versus boost. Is the relationship between impeller speed and boost generated linear or exponential?

I'm figuring out my ultimate goals with the non-M 3.0i, as AA's M54 kits run 10.5 psi without meth. I'm interested in figuring out how small of a pulley I can put on without getting belt slip based on others' experiences, and how much boost that will generate. Obviously I don't want to exceed the capacity of the injectors or fuel (detonation due to heat), so I need a ballpark idea of what pulley size will give me what boost. I'm thinking of doing it in two stages: 7-8 psi + cams + WMI + tune, and then ultimately 10-11 psi + injectors + intercooler.

My VF kit is rated at 6 psi. The kit has a 3.6" Vortech pulley.

A pulley that's half of the size of the original pulley should spin the blower twice fast (this is just an example... I don't plan to actually do this because it would overspeed the blower and the belt would slip). If the relationship between supercharger rpm and boost is linear, then I would need a 1.8" pulley to generate 12 psi. The dyno seems to support that with a Vortech, boost is generated linearly.

However, the rule of thumb I keep hearing is that if you go down one pulley size, you generate an extra 1/2 psi (some say 1 pulley size = 1 psi). I hate rule of thumbs when talking about automotive applications, because a 4 cyl Honda and Dodge Viper are so different that I can't see the same swag applying to both. Regardless, based on this "rule", a 2.87" pulley would get me 12 psi (or 9 psi depending on which rule you use).

Saying that a 3.6" pulley actually generates 20.7 psi of pressure (atmospheric pressure of 14.7 psi + 6 more psi from the pulley) seems to support a different relationship between boost and impeller speed, and the rule of thumb that 1 pulley size = 1 psi. To get 12 psi:

3.6" * (20.7 psi) / (26.7 psi) = 2.79"

I realize it all depends, due to the efficiency range of the blower, and boost will eventually cap out as the blower reaches its max speed. I've looked at the compressor map of the V3 SCi. The x axis is cfm, which I haven't measured nor do I know how to do so very easily. Pressure ratio versus impeller speed would be more useful.

Anyone have thoughts or experiences?

[Steeler]

This is all German to me Josh

But thanks for the equation towards the end, it reinforces my thought process on the amount of boost I want to reach. Having 3 different smaller pulleys to try I will start with the 3.33 one and see how it runs.

This post may be better posted on an FI forum on the other 2 sites.

[pokeybritches]

Originally Posted by dbarton62

This is all German to me Josh

But thanks for the equation towards the end, it reinforces my thought process on the amount of boost I want to reach. Having 3 different smaller pulleys to try I will start with the 3.33 one and see how it runs.

This post may be better posted on an FI forum on the other 2 sites.

Dave, I think I figured it out. I sent you an email on it. It's somewhere in the middle.

I found a dyno of an S2000 that generates 3.5 psi of boost at 4000 rpm, and 14 psi at 8000 rpm. This sounds exponential (2 times the rpm = 4 times the boost), but the boost doesn't ramp up sharply enough to be a simple equation like boost=(c*rpm)^2. The line looks almost linear, but it still has a curve to it.

Basically, once you start to get into the efficiency range of the blower it ramps up, and there's nothing down low. When it ramps up, it will eventually stop increasing quite so quickly and then level off.... I'm thinking like a stretched s shape. There will be a time when a small change in pulley size makes a huge 1 psi difference in boost, but it will only do so if the blower is properly sized for the application, because you are making these changes when it's within its efficiency range. That's where the rule of thumb comes from. The rule of thumb only applies to making pulley changes on a blower sized appropriately to the project... so the rule would not apply to an oversized Vortech T-trim or Si trim on a non-M car.

I messed around graphing a few equations until I got one that I feel accurately shows boost vs rpm. Don't get caught up in the equation itself or the numbers on the graph. It's just meant to show the shape.

[pokeybritches]

Attached.

[pokeybritches]

If you're making pulley changes before the blower has reached its stride (below 0.4 on the x-axis of my made up graph), it looks like boost is exponential. Once it's spun up to the heart of its efficiency range (0.4 - 0.7), boost vs rpm is a straight line (linear). As it approaches max speed (0.8), it peaks out and starts to choke.

[ZStig]

I can chime in.

Use this to calculate the impeller speed so you don't max out the blower:
http://www.vortechsuperchargers.com/page.php?id=33511

use this to check available sizes:
http://www.vortechsuperchargers.com/page.php?id=30042

3.125" and below will slip. I've tested 2.87 and it slips badly (ess vt2-500), and Ess themselves moved away from 3.125 as that slips too.

3.25 is the smallest I'd go. Assuming you have the correct pulley offset before you install it.

Other than that, its hard to predict your boost. I couldn't even find the correlation on the S54 myself. The e46m3 seems to require less boost to make same power. No experience with M54.

The legit option is a bigger crankshaft pulley. 2mm increase is 1-2 psi. You will start to overdrive your waterpump and other accessories though.

[pokeybritches]

Thanks for the info. Any idea on where to get a smaller (edit: bigger) crank pulley? The thought had crossed my mind to buy some underdrive pulleys for the accessories and then get a larger crank pulley, but I haven't seen much info out there. I'll probably do the harmonic damper at the same time if I go that route.

Good to know that the 3.125 will slip with the ESS kit. I'm going to compare belt wrap between the two kits. I'm hoping there's a little more wrap on the VF kit. I have no idea why Vortech doesn't use a different internal step in order to run larger pulleys with less slip. The ASA blower probably has twice the belt wrap. The coatings some aftermarket companies offer can eat through belts. It would be much easier to have a larger pulley.

I have a pretty interesting project I'm working up, similar to the AA Prima Plus kits for the E46 M3. The car will normally run 6-7 psi, but when you press the sport button, WMI will be activated and boost will increase to 9-10 psi. The car will have a bypass that opens to limit boost for daily driving, or when WMI isn't used. It's not the most efficient way to do things, but then again I won't be running to high rpm (where the bypass would activate) without turning on WMI anyway. This would give me more power down low than I have now without having to do extensive modification for an aftercooler. The bypass would also open if there was any problem with the WMI or detonation. I have an AEM wideband failsafe that I may hook up with an additional electronic bypass as a second safety net should AFR's go out of range. I'm thinking with cams and 9-10 psi I should see 360-370 whp.

[ZStig]

Yeah you need a bigger, not smaller crankshaft pulley. I think RMS does them for about $600

My 2.87 was carbide custom coated, but that wore out after a month

[pokeybritches]

Good catch. Edited for accuracy.

I'll check out RMS.

[Steeler]

Originally Posted by pokeybritches

I have a pretty interesting project I'm working up, similar to the AA Prima Plus kits for the E46 M3. The car will normally run 6-7 psi, but when you press the sport button, WMI will be activated and boost will increase to 9-10 psi. The car will have a bypass that opens to limit boost for daily driving, or when WMI isn't used. It's not the most efficient way to do things, but then again I won't be running to high rpm (where the bypass would activate) without turning on WMI anyway. This would give me more power down low than I have now without having to do extensive modification for an aftercooler. The bypass would also open if there was any problem with the WMI or detonation. I have an AEM wideband failsafe that I may hook up with an additional electronic bypass as a second safety net should AFR's go out of range. I'm thinking with cams and 9-10 psi I should see 360-370 whp.

Interesting.
In for updates.

And Josh thanks for leading the way for us no M types