Guesses about Gear Ratios and Wheel Torque

[Want.FR-S]

Originally Posted by serialk11r

So the question is, why does some official tire spec regulatory body in Europe say a 215/45/17 tire is 23.9" when the way tires are measured implies it's 24.6"? Why is the car not hitting 60mph in 2nd gear if the tire is indeed 24.6"?

For the first part, do you have any link or page where it said it is 23.9"? There might be a different standard used in Europe, or the P type wheel (P215/45/R17). I am guessing this might be the case.

Second part, Based on the spreadsheet, in order to hit 60 MPH mark on 2nd gear, some conditions need to be met:

1. the tire circumference is indeed based on the ideal value of 24.62" diameter.
2. the tester actually revved it all the way pass 7300 rpm or be hugging 7450 before up-shift. I think this is not the case where insideline test their sample of BRZ.
3. the other tester who can clock faster 0-60 time may also be using the automatic, as seen in the spreadsheet that it can reach 60 MPH sooner at 7000 RPM.

[Dimman]

Too much reliance on math... Section/aspect ratio is an approximation given different companies manufacturing. They have specific measured dia/circ numbers for specific tires and they don't all match the formula numbers.

[DSPographer]

[QUOTE=Want.FR-S;171844]For the first part, do you have any link or page where it said it is 23.9"? There might be a different standard used in Europe, or the P type wheel (P215/45/R17). I am guessing this might be the case.

The reduced diameter is not from squish. It is from the difference between official tire specifications and the rough number calculated from the wheel diameter plus the nominal aspect ratio times width. The 1906mm rolling circumference is from official ETRTO tire specs. (I don't expect that tire size standards vary between Europe and Japan and the US. From the wikipedia ETRTO entry it just looks like Europe standardized tire sizes first.) Here is a source for ETRTO standard tire circumference:
http://www.club80-90syncro.co.uk/Syn...calculator.htm
Here is a calculator for circumference including increase in circumference with speed:
http://bndtechsource.ucoz.com/index/...alculator/0-20
Here is a Yokohama tire size chart where you see a circumference of 1906mm for the 215/45R17 tires:
http://www2.yokohama-online.com/gb/t...php?page=23084
So, until someone posts a better link to tire circumference info, I think the 215/45R17 tire has a 23.9" effective diameter.

[Edit] OK, reading Tirerack's explanation maybe the difference is due to "squish":
http://www.tirerack.com/tires/tirete...jsp?techid=203
Looking up the Primacy HP, Tirerack doesn't list a revs per mile number. But, they do have one for the Michelin Pilot Sport 3 in a 215/45 R17 size, and the value is 844. This is a 23.9" equivalent rolling diameter so I still think we should use 23.9" for calculating wheel RPM vs speed.

[Want.FR-S]

Originally Posted by Dimman

Too much reliance on math... Section/aspect ratio is an approximation given different companies manufacturing. They have specific measured dia/circ numbers for specific tires and they don't all match the formula numbers.

Originally Posted by DSPographer

The reduced diameter is not from squish. It is from the difference between official tire specifications and the rough number calculated from the wheel diameter plus the nominal aspect ratio times width. The 1906mm rolling circumference is from official ETRTO tire specs. (I don't expect that tire size standards vary between Europe and Japan and the US. From the wikipedia ETRTO entry it just looks like Europe standardized tire sizes first.) Here is a source for ETRTO standard tire circumference:
http://www.club80-90syncro.co.uk/Syn...calculator.htm
Here is a calculator for circumference including increase in circumference with speed:
http://bndtechsource.ucoz.com/index/...alculator/0-20
Here is a Yokohama tire size chart where you see a circumference of 1906mm for the 215/45R17 tires:
http://www2.yokohama-online.com/gb/t...php?page=23084
So, until someone posts a better link to tire circumference info, I think the 215/45R17 tire has a 23.9" effective diameter.

Cool, thanks for the links. With this said it is more accurate to calculate the numbers based on the actual circumference rather than wheel width/ratio/diameter. With that revised number, one *cannot* hit 60mph (59.04) with Toyo's 215/45/R17 tire.

Just check Michelin's website, the Primacy HP 215/45/R17 has 844 rev per mile. with 24.7" as the overall diameter. Convert that using one mile - 1609.344 m, it comes to 1.9068 m per rev. So we should stick the circumference number for calculation purpose.

I would think there is no need to reverse calculate the *effective diameter* as this may confuse people and trying to reason it with deformation or other effect. In fact, if you know the rev number per mile/km, it is easier to calculate the circumference more precisely. Otherwise, how one could explain the difference between 24.7" and 23.9"?

[Brzer]

Revs per mile by Michelinman.com for Primacy HP 215/45/17 is 844.

[DSPographer]

Originally Posted by Want.FR-S

Cool, thanks for the links. With this said it is more accurate to calculate the numbers based on the actual circumference rather than wheel width/ratio/diameter. With that revised number, one *cannot* hit 60mph (59.04) with Toyo's 215/45/R17 tire.

Just check Michelin's website, the Primacy HP 215/45/R17 has 844 rev per mile. with 24.7" as the overall diameter. Convert that using one mile - 1609.344 m, it comes to 1.9068 m per rev. So we should stick the circumference number for calculation purpose.

I would think there is no need to reverse calculate the *effective diameter* as this may confuse people and trying to reason it with deformation or other effect. In fact, if you know the rev number per mile/km, it is easier to calculate the circumference more precisely. Otherwise, how one could explain the difference between 24.7" and 23.9"?

Yes, I agree we should just use the revs per mile or circumference value. I am not sure what the 24.7" number really means: Maybe the tire bows upward in the middle when unloaded.

[Ryephile]

Originally Posted by serialk11r

Tire deformation is going to be very small if you think about it. The rolling circumference of the tire is the length of the tread. The tread itself is reinforced with steel underneath, so only the surface can experience minor stretching. The rubber part of the tire is well under an inch thick.

So the question is, why does some official tire spec regulatory body in Europe say a 215/45/17 tire is 23.9" when the way tires are measured implies it's 24.6"? Why is the car not hitting 60mph in 2nd gear if the tire is indeed 24.6"?

Originally Posted by DSPographer

[Edit] OK, reading Tirerack's explanation maybe the difference is due to "squish":
http://www.tirerack.com/tires/tirete...jsp?techid=203
Looking up the Primacy HP, Tirerack doesn't list a revs per mile number. But, they do have one for the Michelin Pilot Sport 3 in a 215/45 R17 size, and the value is 844. This is a 23.9" equivalent rolling diameter so I still think we should use 23.9" for calculating wheel RPM vs speed.

You guys are forgetting the obvious; we're working with pneumatic tires. The rolling radius is entirely dependent on inflation pressure and loading weight. The circumference is always the same, but since the vehicles weight is resting on the tire, the tire itself forms a "D" shape when viewed from the side. Tire Rack's listing of "Revs per mile" is the only useful statistic if you're trying to calculate speed from a known axle RPM. Of course, that measurement is entirely assuming a typical inflation pressure and loading weight. The "overall diameter" has nothing to do with the tire mounted on your car and sitting on the ground.

Deslock's chart's using an approximate 24" rolling diameter are appropriate for the stock 215/45-17.

[DSPographer]

Since I just calculated the exact 6MT gear ratios I can post the exact speed vs RPM for the standard 215/45R17 Tires using the known ETRTO spec of revs per mile for the tires which is 844.4:

RPM- : 1st- | 2nd- | 3rd- | 4th- | 5th- | 6th-
-------------------------------------------------------
1000 : +4.8 | +7.9 | 11.2 | 14.3 | 17.3 | 22.6
1250 : +6.0 | +9.9 | 14.1 | 17.9 | 21.7 | 28.2
1500 : +7.2 | 11.9 | 16.9 | 21.4 | 26.0 | 33.9
1750 : +8.4 | 13.9 | 19.7 | 25.0 | 30.3 | 39.5
2000 : +9.6 | 15.8 | 22.5 | 28.6 | 34.7 | 45.2
2250 : 10.8 | 17.8 | 25.3 | 32.1 | 39.0 | 50.8
2500 : 11.9 | 19.8 | 28.1 | 35.7 | 43.3 | 56.5
2750 : 13.1 | 21.8 | 30.9 | 39.3 | 47.7 | 62.1
3000 : 14.3 | 23.8 | 33.7 | 42.9 | 52.0 | 67.8
3250 : 15.5 | 25.7 | 36.5 | 46.4 | 56.3 | 73.4
3500 : 16.7 | 27.7 | 39.4 | 50.0 | 60.7 | 79.0
3750 : 17.9 | 29.7 | 42.2 | 53.6 | 65.0 | 84.7
4000 : 19.1 | 31.7 | 45.0 | 57.1 | 69.3 | 90.3
4250 : 20.3 | 33.7 | 47.8 | 60.7 | 73.7 | 96.0
4500 : 21.5 | 35.6 | 50.6 | 64.3 | 78.0 | 101.6
4750 : 22.7 | 37.6 | 53.4 | 67.9 | 82.3 | 107.3
5000 : 23.9 | 39.6 | 56.2 | 71.4 | 86.7 | 112.9
5250 : 25.1 | 41.6 | 59.0 | 75.0 | 91.0 | 118.6
5500 : 26.3 | 43.6 | 61.9 | 78.6 | 95.3 | 124.2
5750 : 27.5 | 45.5 | 64.7 | 82.1 | 99.7 | 129.9
6000 : 28.7 | 47.5 | 67.5 | 85.7 | 104.0 | 135.5
6250 : 29.9 | 49.5 | 70.3 | 89.3 | 108.3 | 141.1
6500 : 31.1 | 51.5 | 73.1 | 92.9 | 112.7 | 146.8
6750 : 32.3 | 53.4 | 75.9 | 96.4 | 117.0 | 152.4
7000 : 33.5 | 55.4 | 78.7 | 100.0 | 121.3 | 158.1
7250 : 34.7 | 57.4 | 81.5 | 103.6 | 125.7 | 163.7
7450 : 35.6 | 59.0 | 83.8 | 106.4 | 129.1 | 168.2