I wanted to continue the discussion on wheels and HP.
This thread is not meant to insult anyone, it is a discussion about how wheels can effect HP, do not comment on other topics please. Jokes are welcome (on the topic of wheels) I have a great sense of humor. if you are insulted I apoligize.
Back to the point:
We were bickering about wheels causing HP loss.
Anyway I spoke to one of the physicists at the NASA club.
YES it is true he is supposed to send me the formula that helps you determine the size of a rotating object Large/Small/Weight and how it causes stress on the axis it spins on. Then he said to me, "you changed the drive pulley to a smaller one right? Didn't that cause less stress on the engine allowing it to free HP as well" so I asked if it is the same principle he said yes. "The pulley is a smaller lighter wheel, the belt would represent the road surface just as the ground rolls under the car the belt rolls around the wheel" it makes sense this is coming from a NASA Physicist (JWST program). I even asked if he would mind being in a video of my car on the dyno with 20" wheels then 19" wheels explaining how it effects the HP loss. As soon as he sends me the email -on his busy schedule I will post it here.

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Cayman GT
369BHP 325LBSTQ
313WHP 276WTRQ
some people like the regular stock factory look, cool people modify the car.

p4ed - there was a reasonably good thread that started getting into the mathematics - probably 4-6 months ago. Some interesting observations were made there in relation to upsizing and the fact that the outside diameter of the tire itself doesn't change much - so that part of the equation remains fairly static. What is effectively happening though in an upsize case is that the slightly heavier wheel is partially offset by a lighter tire and we see a shift in the distribution of weight relative to the distance from the axis of rotation. The trick though is to determining the MOI, or moment of inertia for each of the two components and seeing what the trade off is there to determine the final effect on WHP. One of the sports car magazines had a really good write up a few years ago on this whole topic - I'm going to see if I can find it over the next day or so.

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If the diameter (gearing) and weight (unsprung) are the same, and contact patch (drag) is the same. Why does rim size matter?

If the mass of weight is moved further out from center it will change the amount of energy needed to start and maintain motion. Something I learned when balancing helicopter blades.

So if we push the rim size from say 17" up to 20" and drop the profile of tire to keep the diameter exactly the same. We have increased the weight near the outside.


Take a bicycle flip it over, spin the front wheel, then slam on the brakes.
Then cut out 90% of the spokes and glue them to tread on the tire.
Do the same thing, and see if the braking seems any harder.
Caution watch for flying spokes...

The pulley you talked about increases hp output because of gearing not moving mass. It reduced the gear ratio by small amount, which reduced the driven load by a small amount, yet large enough to be noticed on the dyno.

Now a light weight flywheel is more along the lines of what you have discribed as less weight, which most likely would change the curve of the dyno reading but not max output.....?? I would assume thats why the call it an under drive pulley and not a light weight pulley.

Agreed. The advantage to the pulley is that it drives the other accessories slower, because it is smaller, which saves more horsepower for the engine. It isn't much different than removing powersteering and AC from an older car to free up horsepower.

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"The Cayman doesn't need any more toys." -- My wife

You all are referring to mass moment of inertia, or the resistance of an object to changes in rotational speed. The less mass, and the less distance from the axis of rotation the mass is, the easier it is to rotate the object. So large wheels, or even the same mass wheel with more of its mass near the outside edge, rob you of more power on acceleration and require more effort to brake. It's why figure skaters spin faster when they draw their arms to their sides. Calculating mass moment of inertia for a real wheel shape is beyond a simple formula- you have to have a CAD program. But if you simplify it as a hollow cylinder, the mass moment of inertia about the axis = mass x (outside radius^2+inside radius^2)/2, or alternatively pi x density x width of rim x (outside radius^4-inside radius^4)/2.

An engine with a smaller pulley will run accessories slower (and avoid some of the inertial load imposed by them) and will also benefit from less inertia in and of itself.

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Yeah....hmm what he said!

I guess this debate started when you and I were arguing about your wheels adding power to your car. Of course I dispute that claim. No matter what wheels I put on my Cayman, my horsepower will remain unchanged.


Your NASA friend:

When you mentioned your friend, the NASA expert, you had me impressed and wanting to hear more. Then you told me what he said about the pulley and I realized that this guy is not much of an expert. The reason an UDP (Under Drive Pulley) adds power is because it changes the gearing and rotational speed of the parasitic accessories.


How an Under Drive Pulley adds horsepower:

It's a pretty simple concept. For those who don't fully understand, imagine riding a bicycle up a slight hill in say 5th gear. You will feel some real resistance. Then imagine shifting it down to 2nd gear. What happens to that resistance? It's reduced big time. The down side, the bicycle moves more slowly. This is exactly what's happening when you change your pulley to an UDP. The resistance presented by the Power Steering Pump, A/C Compressor, Alternator and Water Pump is reduced so they consume less horsepower and now spin more slowly.


Back to discussing Wheels:

I don't dispute the fact that larger heavier wheels (or pulleys) do add more rotational mass and that mass has inertia which will slow acceleration or deceleration. What I do not agree with is whether or not that change is significant. For example, I say that the difference between spinning a 19" wheel versus spinning an 18" wheel is insignificant when compared to the total weight of the vehicle that we are trying to accelerate.

Anyone who's every driven on ice, or should I say ever 'played' on ice with a car, will know that once traction is gone, the rear wheels will accelerate very quickly. Anyone here ever done this? Have you done donuts on ice? What happens when you plant your right foot? I'll tell you. The engine spins the wheels so freely that it's not much different than if the car were in neutral. The time required to go from idle to red line is nearly non existent. Could your car ever move through the revs this quickly if you were on dry pavement? No, of course not, because it needs to move a lot of mass. So where is all of that wheel inertia that's supposed to be holding the engine back and consuming all of that power? It's there. It's just insignificant.

I'm sure we can find a formula that would help us understand the exact effect, but this debate is pretty unimportant to me so I will leave it to someone else to do the digging.


Dyno Testing and Wheels:

You mentioned that a dyno test that you ran showed more power with your new wheels. Let me try to help you understand why this happened.

People in this club like to compare RWHP (rear wheel horse power). As we all know, RWHP is always less than BHP (bulk horse power). But what is RWHP? It's what a dynamometer 'thinks' it is seeing. In order to understand this better, we first need to better understand how a dynamometer works.

Horsepower is work over time. It is therefore pretty hard to measure with any type of test equipment. Dynamometers don't measure horsepower, they 'calculate' horsepower. Here's how. They have a roller that has a known weight. By knowing the weight of the rollers, they can basically calculate horsepower by measuring how quickly a car can cause that known weight to accelerate. In theory, this can work, but there are many unknown variables that the calculation can NOT take into consideration (because they are unknown). The most significant of those variables is the rotational mass of all of the drive train components. These items including the flywheel, clutch, pressure plate, transmission shafts, gears, differential, CV joints, axles, brake rotors, hubs, lug bolts, and the wheels. All add rotational mass to the equation, mass that was not included when the dynamometer was calculating horsepower. This is where we get what everyone likes to call 'drive train loss'. It's not really loss. It's error. It's a variable that the dynamometer did not count on. Everyone likes to think that we can quantify and define it at 12%. But we can't because every car is so different. (Different transmissions, wheels, brakes, TPMS, Tires, etc...)

So, in theory, if you dyno'd your car and got a RWHP of say 260, and then changed your wheels and got another reading of 270, did you gain 10 hp? No. You did not. You simply changed the amount of error that the dynamometer experienced. This is why we can't compare dyno runs from one car to another. It's also why we should all be looking at corrected BHP numbers, not the RWHP number that so many people here like to compare.


Summary:

So, to recap, as you can see I do believe that additional rotational mass can make a difference, but I do not believe that the small difference between a 19" and 18" wheel will make any noticeable or measurable difference. If a small weight difference in wheels does make a difference in acceleration, wouldn't your wheels be worse than the factory 18"s?

You mentioned in your article that with your tires your BBS wheels weigh 48 lbs in the front and 53 lbs in the rear. Ken weighed the factory 18" wheels back in 2006 and discovered that with Michelin PS2s they weighed 45 lbs in the front, 49 lbs in the rear. Your 19" BBS wheels weigh 6-8% MORE than the factory 18" Cayman S wheels. So, if your theory was correct, you should have lost horsepower by putting the 19" BBS on your car (when compared to a car with 18" Cayman S wheels). No?

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Gator,
Nice write up, but BHP is Brake horsepower not Bulk, I *think* the term coming from placing an engine on an engine dyno and then applying a brake to it for gauging the power of the engine.

I should also point out that if you use a dyno like a dyno pack you cannot use the same drivetrain loss % as you would with say a Mustang or DynoJet dyno. While the Mustang or Dynojet might be 12% or around that mark, on a dyno pack dyno it is maybe 3-5% so you can't take rear wheel hp numbers and compare between dynos, but you already knew that, just pointing out that the dyno type makes a difference too.

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