Speed and RPM in each gear

[Addicted_to_S]

The thread on 2nd Gear Grunt - Initially very flat prompted me to do an Excel spreadsheet on Cooper S speeds at various RPM in each gear, which I've attached here (I hope!) in case anyone’s interested.

I used the Cooper S gear ratios off the MINI2 data section, and I based the sheet on the premise that the maximum speed of 135 MPH would be achieved at redline RPM of 6750 in Vth gear. This may be slightly incorrect, if so please let me know, but I don't think it will be far off.

If you prefer, you can enter any known combination of road speed, RPM and gear you like in the cells so labelled (C11, C12 and C13), and everything else is then calculated from the gear ratios. Initially I tried using 95MPH, 4000RPM and VI gear (an approximate combination I happen to know only too well as Stonk is still running-in), but that gave a theoretical redline Vth gear speed of only 130.9 MPH, which didn't seem right. I figured that the EMS wouldn't permit a 135MPH maximum over redline, hence I used the settings above.

(Note: I've protected the rest of the sheet, so you can't inadvertently change anything else, but the password to unprotect it is not hard to deduce!)

[Addicted_to_S]

Attachment should be here:

[Addicted_to_S]

Oops, I really messed up! This one is the attachment as I meant it to be, with 135MPH, 6750RPM in V gear:

[AidenL]

I downloaded the first one .....the second ones amended ??

And dont worry, you are doing all the hard work !!

[Addicted_to_S]

Well you can see for yourself. That's enough theory for me, I'm off to try it out in practice!

[gowest]

From the 7/02 issue of Car & Driver.

(Gear) (mph/1000rpm) (max test speed)
(1st) (6.1) (41 mph @ 6750rpm)
(2nd) (9.7) (66 mph @ 6750rpm)
(3rd) (12.9) (87 mph @ 6750rpm)
(4th) (15.8) (107 mph @ 6750rpm)
(5th) (19.1) (128 mph @ 6750rpm)
(6th) (23.4) (128 mph @ 5500rpm)

This was on the 205/45/17's, the tallest of the o.e. tire choices. I have been corrected on this, bad memory, the 16" tires are a little taller resulting in the speed at redline in 5th with the 16" tires being almost 1 mph higher than indicated above with the 17" tires.

Based on this info.

In order to get to 135 in 5th it would have been necessary to take the rpm up to 7068 rpm and 70 in 2nd would be 7216 rpm. Where is fuel cut off, anyone? Keep in mind that it's possible, or even likely, your speedometer reads higher than your actual speed and the above info was collected electronically and not based on observations of the speedometer and tack or on theoretical info or data.

A red line shift from, 1st to 2nd drops rpm to 4193 rpm.
, 2nd to 3rd drops rpm to 5121 rpm.
, 3rd to 4th drops rpm to 5488 rpm.
, 4th to 5th drops rpm to 5643 rpm.
, 5th to 6th drops rpm to 5470 rpm.

You can clearly see the large difference between 1st and 2nd (but still well within the power band) relative to all the other gear changes and yet 1st itself is to long for maximum enjoyment. I'd like to see at least a 6% reduction in 1st and 2nd gears with equal spacing from there to the current 6th. What was BMW thinking when they came up with their gear ratios?

[Keith]

It looks like my guess back in October last year was pretty close. In this thread I estimated the speed at 6500rpm in each gear based on the published rattions and tire diameters. I used 6500 because the real red line was not known at that time.
http://www.mini2.com/forum/showthrea...&threadid=1825

[Addicted_to_S]

Quote:

Originally posted by gowest
...the 205/45/17's, the tallest of the o.e. tire choices.

Not according to the FAQ: What should be considered in choosing a wheel and tire package? , which shows the following diameters for the standard packages:

Quote:

+-----------+---------------+---------------+
| Tire Size | Diameter ('') | Diameter (mm) |
+-----------+---------------+---------------+
| 175/65-15 | ... 23.96 ... | ... 608.5 ... |
| 205/45-17 | ... 24.26 ... | ... 616.3 ... |
| 195/55-16 | ... 24.44 ... | ... 620.9 ... |
+-----------+---------------+---------------+

I recalculated the spreadsheet, using just the gear ratios and the diameter of the MCS standard 16" wheel and tire package, see attachment. It was pleasing to find it quite similar to what I had calculated in the earlier spreadsheet, based on the prediction that maximum speed of 135 MPH would come in Vth close to the 6750 RPM redline. You can enter other diameters if you so wish.

Quote:

What was BMW thinking when they came up with their gear ratios?

Maybe VI was geared to give reasonably good fuel economy for motorway driving; V was geared to give the highest possible maximum speed (based on the torque curve characteristics); and IV, III, II and I were geared to have reasonably close ratios, given the requirements for VI and V, which in turn meant that 1 had to be fairly tall ?

[Keith]

Yopu should not need to make assumptions about red line in 5th being max speed. The gear ratios are known as well as the tire diameters so the speed in each gear can be calculated.

[MINIAC]

There are tables on top speed in gears posted in the FAQ on transmission choices.

[gowest]

Addicted, Thank's for pointing out my error on the tire diamater, bad memory on my part, this would result in 5th topping out at another 1 mph. Keith has made the point that, I guess, I only eluded to, that top speed is probably in 6th gear and provided a link to his response to my earlier post as "bluebaru", I forgot my password for that name and just changed user names. (see above memory statement)

[Addicted_to_S]

Quote:

Originally posted by Keith
Yopu should not need to make assumptions about red line in 5th being max speed. The gear ratios are known as well as the tire diameters so the speed in each gear can be calculated.

Indeed Keith, you are right, which is why I posted the revised spreadsheet "mph & rpm2 - cooper s.zip", which makes no such assumptions and is based purely on gear ratios and tyre diameters. But then I looked at your postings back in October where you refer to the RPM per mile value of 855 (for 205/45-17), which I agree is a better basis for calculation. So I made what I hope will be the final version of the spreadsheet "mph & rpm3 - cooper s.zip", in which you can enter whatever RPM/mile value you like. Interestingly the Firestone 195/55-16 shows a very similar RPM per mile value at www.tirerack.com of 854, and I used this value originally as it's the size I have on my S.

I notice that most of the Tirerack RPM/mile values are about 3% greater than what you'd calculate from the overall tyre diameter in inches (63360/[Pi*D]), presumably due to deformation by the weight of the car. Perhaps different wheel/tyre combos differ in the degree of deformation, which changes the story on which give the greatest acceleration or maximum speed?

Thanks for setting me straight on this.