tiptronicS final drive into 5 speed manual

[Topless]

Originally Posted by Focusyn

I didn't do the math on your numbers, but I know my 2000 base 5spd gets to the limiter just above 70mph in 2nd gear, and that is because of my 19" rims. According to my owner's manual, the 2000 base and S-models have the same top gear size and final if i'm not mistaken. The S model has about 10mph more top speed at the same RPM, due to the 1" increase from 16" stock rims on the Base to 17" stock rims on the S. Gearing being equal, the larger the wheel diameter, the higher the top end speed but the lower the low-end torque because you have to overcome more inertia.

Not exactly true here. Each of these wheel sizes carries a different tire sidewall so the final diameter is essentially the same (25") whether you are on 16,17,18, or 19" wheels.

There are a few competition tires that have a smaller sidewall in 16" but they won't fit over his "S" brakes in front.

[Focusyn]

Originally Posted by Topless

Not exactly true here. Each of these wheel sizes carries a different tire sidewall so the final diameter is essentially the same (25") whether you are on 16,17,18, or 19" wheels.

There are a few competition tires that have a smaller sidewall in 16" but they won't fit over his "S" brakes in front.

I dont totally disagree; I didnt mean what I said about a 1" increase quite so literally - more trying to make ananology about your wheels/tires being another gear in the equation without actually doing the math. It's 100% fact that it's the outer diameter that factors in to the equation and not really the rim size, but with the Porsche approved tire sizes, the 17 has a bigger outer diameter than the 16, the 18 larger than the 17, and the 19 larger than the 18. While they are all similar in that they are all close to to 25", none is exactly 25, and the OD has a non-deviating increase trend as you increase rim size with the recommended/approved tires. It is also true that the deviation from one size to the next is never more than a small fraction of an inch, but when you consider the big picture, those fractions of an inch are per revolution of the tire. When you then factor in that your tires need to rotate in the neighborhood of 2500 times to travel 1 mile (again plus or minus, depending on OD), the deviation between rim sizes over 2500 revs becomes fractions of a mile, not fractions of an inch. When you're talking about speeding up and slowing down and climbing back up the torque curve repeatedly in autocross racing, those numbers become very significant.

Also I double-checked my owner's manual and the S-model final was a different size. I have a minor dyslexic affliction and I flip-flopped the S model numbers when I read them. The reverse gear in the S is equal to the final in the base. Those two numbers are crunched together spaced far from the rest for each model and I got em "Reversed."

I did do the math all the way through on the outer diameters for all four sizes 16-19 though after I saw your claim that they are all 25", just to make sure I wasn't smoking something (even though at least for my model they didnt officially recommend or approve 19's at all - I used the size I've got which is the same as just about every other Boxster I've heard of with 19's and is I believe the approved size for the 19" on the 996).

I'm posting from my cell right now, but when I get home and hit the laptop I will post the numbers, showing my work in case I made any mistakes. This is not to create or provoke an e-whizzing contest with you Topless - I am convinced you do know your stuff. I just think it would be a neat piece of info to have available, because your are right; in terms of outer diameter of one tire standing still on a bench, all four are near 25", but when you see the trending over real world driving versus just the individual tire measurement standing still, you will see that those fractions of an inch equal a significant difference in the amount of energy needed to spin 19" rims (275/30/19) two and a half thousand times versus spinning 16's (225/55/16) the same number of revolutions.

[Focusyn]

Sorry for the quasi-hijack BigSmoothLee - but it's related, and not necessarily a hijack - the numbers imply that going to 17's, which I think should fit around your S model brakes depending on year of your car/brakes, will still result in a potentially high gain in acceleration torque in the speed ranges you're doing in autocross assuming spec tire sizes...

Thanks be to you and Topless for giving me a keen idea for a new component to build in to my home-brew Porsche software

Previous post about the numbers was off the top of my head and I totally mis-stated the revolutions per mile - I did the math in my head without the numbers in front of me, and I mistakenly based distance per rotation on the diameter and not the circumference. Oops again. Also put the front wheel aspect ratio of the 16 in that post (55) instead of the rear, which is 50, and is accurate in the numbers below.

It turns out that per mile, the 16" rim/tire combo needs to spin just under 20 additional full revolutions over the 19", i.e. more low-end torque and faster low-end acceleration but lower speed at rpm limit for any given gear.

Here's the math:

Constants used for calculation:
pi = 3.1415926535897932384626433832795
1 mile, in inches = 63,360
rotations or revolutions refer to (1) full rotation of
the tire, NOT engine rpms

Recommended / Approved tire sizes based on rear wheel summer tires from 2000
model year owner's manual for 986/986S for 16-18" sizes. No 19" sizes
are approved or recommended for 2000 model year, so I used the actual rear wheel tire size on my particular car. I picked 2000 because that's the only manual I have handy, but I believe the general trends will apply to most if not all other model years due to the Deutsche formulas Porsche uses to calculate their recommendations.

With transaxle RWD, REAR wheel tire rotations are directly proportional to engine rpms, regardless of actual gear/final sizes - that's why I stuck with tire rotations and not engine rpms, as those will vary with your partiular gearing. As the engine
spins several times per rotation, differences would appear much more significant
if calculated as engine rpms using actual gear/final constants. I am an engineer but not a mechanical one, so frankly I just don't know all the math that goes in to calculating it that way off the top of my head.

Sorry for the huge numbers of decimals making it a bit of a bear to follow, but to calculate deviations or trending accurately requires a high level of precision in variables. If you do enough rounding, you will end up with equal numbers (for example if I rounded all the OD's to 25" instead of leaving the high precision numbers in there ).

I got lazy and used Google to make the conversions from
mm to inches for section, so actual deviations may vary very slightly depending
on the precision of their conversion algorithm variables.

--------------------------------------------------------------------------
225/50/16
225/50 = 4.429135" section height
* 2.000000 (account for section height on top and bottom in total diameter)
-----------
8.85827" (total diameter added by sidewall/tread)
+16.00000" (rim diameter)
----------
24.85827" total OUTER DIAMETER

Circumference = 2π(24.85827/2) = (6.283185307179586476925286766559)(12.429135")
OR Circumferece = 78.094558412951549565878774135275" distance travelled per revolution
OR, this rim/tire combo needs to spin 811.32413432652300214910170718101
times to travel 1 mile
OR, this combo travels 1.2325530052549171332998543897612 miles per 1,000 rotations


--------------------------------------------------------------------------
255/40/17 =
225/40 = 4.01575" section height
*2.0
---------
8.03150"
+17.00000"
---------
25.03150" OD
Circ = 2π(25.03150/2) = (6.283185307179586476925286766559)(12.51575")
or 78.638776508332909448577657848561" per revolution
or 805.70938172322781090357950960051 wheel revolutions per mile
OR, this combo travels 1.2411423060027290001353797008927 miles per 1,000 rotations


--------------------------------------------------------------------------
265/35/18 =
265/35 = 3.6515748" section height
*2.0000000
----------
7.3031496"
+18.0000000"
----------
25.3031496" OD

Circ = 2π(25.3031496/2) = (6.283185307179586476925286766559)(12.6515748")
or 79.492188896043515345888739538571" per revolution
or 797.0594454614842473457513958881 wheel revolutions per mile
OR, this combo travels 1.2546115671724039669490015710002 miles per 1,000 revs

--------------------------------------------------------------------------
275/30/19 =
275/30 = 3.248031" section height
*2.000000
----------
6.496062"
+19.000000"
----------
25.496062" OD
Circ= 2π(25.496062/2) = (6.283185307179586476925286766559)(12.748031")
or 80.098241074669890975024340383984" per revolution
or 791.02860624534788739660856231704 wheel revolutions per mile
OR, this combo travels 1.2641767846380980267522780994946 miles per 1,000 revolutions