had my 230sl 3.75 converted to a 3.27 rear end...

[jharkin]

...and i also had new motor mounts, subframe mounts and transmission mount, as well as new rubbers on the rear springs and new bushings in the trailing arms.
the 3.27 certainly quiets it down on the freeway (thanks Dan), with only minor loss of power or pick up in 2nd and 3rd when on local roads. for me though the most notable differences are how much more solid she feels now as well as how much nicer she handles. she doesn't lean nearly as much in turns, and a lot of vibration noise is gone, and some odd clunks have disappeared too
now i have to figure out how to calculate true speed - my speedo in in KPH and my tires are 185/70/15, so using the miata.com tire chart, i calculated my speed in miles is .58 of my speed in kilometers, but my speedo has a nervous bounce between 80 and 110. my tac is rock solid at any speed, so i was wondering if anyone had an idea how to
compute speed in mph using tac readings? e,g., at 110kph on my speedo, it means i'm doing 64mph, but the tac is around 3700. from what i've read here, i should be doing 70mph. any ideas are welcome... 

[Cees Klumper]

Hi John - easiest way to get to true MPH is to take along a portable navigation system. Sure-fire way to get to very accurate readings.

[jharkin]

thanks cees; using tomtom, 3400 on tac = 70mph

[gugel]

Something doesn't add up here.  Given your tire size of 185/70-15 and a rear end of 3.27, I calculate that 3400 on the tach should be about 76 mph.   Or 3100 on the tach should be about 70 mph.  Is there a typo here somewhere, or did I miscalculate?

Chris

[jharkin]

  i used my TomTom to get the mph speed and had a friend with me recording the tach rpm and the TomTom speed readings.
at 2000 rpm, mph was 40
at 2400 rpm, mph was 49
at 2600 rpm, mph was 52
at 3000 rpm, mph was 60
at 3500 rpm, mph was 72
based on those measurements, i guestimated 3400 for 70mph.
maybe my tach is off?
i'm really interested in what formula you used to get mph using tire size and tach reading.

[gugel]

First, the number of tire revolutions per mile must be determined.  The Tire Rack usually gives this directly for tires they sell, but they don't have any of size 185/70-15.  So I took the average for a number of tires of size 185/70-14, getting 858 rev/mi.  Dividing this into 5280 (feet per mile) gives a tire circumference of 6.15 feet, or 73.85 inches.  Dividing this by pi gives a wheel diameter of 23.5 inches.  Your wheel diameter is an inch larger, or 24.5 inches, giving a wheel circumference of 77 inches, or 6.417 feet.  Dividing this into 5280 gives about 823 tire revolutions per mile.

One can also calculate this directly:  the width of the tire is 185 mm, so the height of the sidewall is this times the aspect ratio .7, or 129.5 mm.  The sidewall appears both above and below the wheel, so the wheel diameter is 2 times 129.5 mm + 15 inches, or 2 x 129.5 mm + 381 mm, which is 640 mm, or 25.2 inches.  Note that this is larger than the 24.5 inches above, because there is some give in the sidewall.  That is, the effective sidewall height is  120.65 mm, or about 93% of the calculated value.  (This percentage is consistent with that for other tire sizes I've calculated).  In any case, I'll use the above figure of 823 revolutions per mile.

With a 3.27 rear axle, the engine revolves 3.27 times for each tire revolution.  Multiplying this by 823 tire revolutions per mile gives 2691 engine revolutions per mile.  At 3500 rpm, the car speed is then 3500/2691 miles per minute, or 78 miles per hour.  By these figures, a car speed of 72 mph works out to 3229 engine rpm.  If you instead use the calculated tire circumference, this works out to 800 tire revolutions per mile and a car speed of just over 80 mph, which is even farther away from your number of 72.

Your tach might indeed be off -- you could check it using any cheap tuneup tachometer.  I also calculated whether severely underinflated tires could result in your numbers, but that works out to a sidewall height of just 96.7 mm, or about 80% of normal, which would hardly go unnoticed.

Chris

   

[Benz Dr.]

I should paid more attention in math class.....

[jharkin]

i don't know if it makes any great difference but there was 30 psi in all 4 tires.
i'll look into the tach issue.
btw, are you familiar with http://www.miata.net/garage/tirecalc.html
john

[glenn]

How about measuring he circumference of the tires with a tape- once off the ground and once on the ground?

[gugel]

ibtw, are you familiar with http://www.miata.net/garage/tirecalc.html
john

Yes, but I tried to use it the other day and got this message from my McAfee SiteAdvisor:

"When we tested, this site attempted to make unauthorized changes to our test PC by exploiting a browser security vulnerability. This is a serious security threat which could lead to an infection of your PC."

This may be a false alarm of some sort, or a glitch in my own computer configuration, but it scared me away nonetheless.

Chris

[J. Huber]

Slightly wide of thread but has anyone ever tested their speedometer ratio using the Palo Alto Speedometer test on their website?

I recently had my speedometer refurbished and it came back kind of goofy. Looks good and works but the speedometer is now considerably off. For example, with my 3.75 -- I used to run about 3700 at 110KPH (or about 68-70MPH). Now -- I when at same revs, I am at 130+KPH. My tach is very close to my hand held tach, and unless some leprechauns changed my axle to a 2.75 in the middle of the night-- my speedo is off. PAS suggested I use their "test" before I send it back... Just wondered if anyone has done this...

[jharkin]

chris,
i just realized i misquoted my tire size . they are 185/70/14, not 185/70/15.
would that make a significant difference in your calculation?

[ejboyd5]

Yes, 14" vs. 15" would make a difference.  While I appreciate the math exercises engaged in by others, you must be aware that many of these calculations are based upon assumptions rather than actual measurements (tire diameter, for instance).  When you add the variations introduced by a string of calculations, any answer arrived at will be an estimate at best.  Your tach is probably right on target and the easiest speed correlations you will get will come from the GPS.  For truly accurate readings, multiple runs through a measured mile are hard to beat and require nothing but a stopwatch.

[gugel]

chris,
i just realized i misquoted my tire size . they are 185/70/14, not 185/70/15.
would that make a significant difference in your calculation?

I suspected that when I asked about a possible typo. 

Yes, it makes a difference, and now the calculations can be based on the actual number of wheel revolutions per mile from the Tire Rack, rather than on estimations of those values.  The Rack offers quite a few tires of that size, with rev/mi ranging from 850 (General) to 893 (Michelin), with the average being 861.3.   For an engine speed of 3500 rpm and and a 3.27 rear end, the corresponding car speeds are 75.6 mph to 71.9 mph, with an average of 74.6 mph.  Conversely, at 72 mph the corresponding engine speeds are 3335 rpm to 3504, with an average of 3380.  Your figures of 72 mph at 3500 rpm are within that range, so your tach is probably pretty accurate. 

BTW, the above calculations are too simple to introduce errors.  For example, for a tire rotating 850 times per mile, the calculation is
mph = 60 x rpm / (850 x 3.27), or inversely, rpm = (850 * 3.27 * mph) / 60.  The variability comes from the wide range of actual sizes that manufacturers offer for a single nominal size.  And I was probably wrong that a difference between actual and calculated revolutions/mile for a tire stems from sidewall give -- rather it stems from the difference between actual and specified tire sizes. 

Chris

[gugel]

John,

How much of a job was it to replace the rubbers on the rear springs and the bushings in the trailing arms?  I'm thinking of doing that to my car one of these days.

Incidentally, I went ahead and used a spread sheet to compute all the speed and rpm ranges corresponding to your observed values, based on the data from the Tire Rack, so I may as well give the results:  

    Observed                           Calclulated mph (range)      Calculated rpm (range)

at 2000 rpm, mph was 40           41.1 to 43.2                    1853 to 1947
at 2400 rpm, mph was 49           49.3 to 51.8                    2270 to 2385
at 2600 rpm, mph was 52           53.4 to 56.1                    2409 to 2531
at 3000 rpm, mph was 60           61.6 to 64.8                    2780 to 2920
at 3500 rpm, mph was 72           71.9 to 75.6                    3335 t0 3504

From this, it does look like your tach may be reading a bit high, but of course I don't know just what kind of tires you're using.

Chris

[jeffc280sl]

http://www.corral.net/tech/gearcalc.html

This program and others like it take inputs like tire size, rear axle ratio, final transmission gear ratio and rpm and will compute mph.  You can input mph and the program will compute rpms.  If you prefer you can input rpm and mph and it will compute rear axle ratio.

[jharkin]

hi Chris,
thanks for the info.
since i had a mechanic do all the work as part of the axle conversion, I'm afraid i have no idea how much work is involved in replacing the spring rubbers and the trailing arm bushings.
this video will give some info. or you could contact  Jim Villers who makes the presentation.
http://video.google.com/videoplay?docid=6010922069310307017&hl=en talks about shocks and springs
John

[JimVillers]

John .... Good job and good comments. 

With my changing rear end ratios and tires, I have noticed a couple of items.  As you said, on the Interstate, the engine is quieter and the car feels very solid and total lack of "stress".  On the other hand, I spend a lot of time in 2nd and 3rd when driving local roads.  Were the car was very comfortable at 40MPH in 4th, I need to be in 3rd. 

It is a total different feel that seems to match the modern roads and driving styles (faster).

[gugel]

http://www.corral.net/tech/gearcalc.html

This program and others like it take inputs like tire size, rear axle ratio, final transmission gear ratio and rpm and will compute mph.  You can input mph and the program will compute rpms.  If you prefer you can input rpm and mph and it will compute rear axle ratio.

Nice, useful program!  However, it doesn't take into account that manufacturers -- particularly Michelin -- typically produce tires whose diameter is a bit smaller than the specified size.  And of course it doesn't take tread wear into account.  A new tire typically has 8 or 9 mm of tread depth.  After 4 mm is worn away, the speed of John's car, for example, would be about 1 mph less at 70 mph for the same engine rpm.

Chris

[lurtch]

Hello All - - we have a very interesting thread going on here. I going to suggest "dumbing-it-down" a little?

Why can't we use a simple equation like this:

stock ratio ( 3.75 )  divided by   replacement  ratio ( 3.27 )  gives an overdrive factor  of 1.147

As seen in my photo:  indicated MPH  ( 60 )   times   1.15    would equal   69 MPH

This method seem to correlate well with Chris's spreadsheet values and John's data recordings.

Larry in CA

[jharkin]

great shot, but how much did the auto-pilot cost?   

[gugel]

Hello All - - we have a very interesting thread going on here. I going to suggest "dumbing-it-down" a little?

Why can't we use a simple equation like this:

stock ratio ( 3.75 )  divided by   replacement  ratio ( 3.27 )  gives an overdrive factor  of 1.147

As seen in my photo:  indicated MPH  ( 60 )   times   1.15    would equal   69 MPH

This method seem to correlate well with Chris's spreadsheet values and John's data recordings.

Larry in CA

Good suggestion (and neat photo!) but one still needs to establish the speed vs rpm before the conversion.  From your photo, it looks like your car either has a 4.08 rear axle, or your tires are of relatively quite small diameter.  Or perhaps your speedometer reads slow (mine does).  What size tires are you using? 

For example, my car has a 3.75 rear axle and 205/70-14 Bridgestone tires (814 revolutions per mile), and an engine speed of 3400 rpm results in a car speed of 67 mph.  The diameter of the tires is very close to that of the original 185/80-14 tires.

Chris