Between the speedometer reading low and using different size tires, I wanted to figure out how to calculate the true speed of my MCS based on RPM. Hopefully this is correct. If not, let me know and I'll edit the post with corrections.

Here is how I built up the equation:

Engine RPM
---------- = turns per minute of the axel
gear ratio

Let's add the tire:

Engine RPM * tire circumference (in inches)
------------------------------------------ = inches per minute
gear ratio

Now let's convert this from hours to minutes and inches to miles. Multiply the top times 60 to get hours, multiply the bottom by 63360 (the number of inches in a mile) to get miles.

Engine RPM * tire circumference (in inches) * 60
------------------------------------------------ = mph
gear ratio * 63360

Plug in an engine RPM value, your tire circumference and then the gear ratio of the gear you want. You can get the tire info from the TireRack web page. They list the tire diameter. The circumference is just 3.145 * diameter.

In the picture are the results for my car and tire combination at various RPMs. Gear ratios for a 2006 MCS were taken from the sales catalog. I put the formula in a spreadsheet so I can easily change tires size and/or RPM and see the results.
*Obviously that 150mph in 6th gear is limited by the computer, aerodynamic drag and horsepower

 

wow my head hurts, im gettin out of school tomorrow so i already lost alllllll my knowledge of math

 

Hmmm... never really thought much about this before - I wonder how/if tire deformation under load impacts it's "effective" circumference somehow - I guess the tire has a definite distance around the tread, and somehow this whole tread comes in contact with the pavement during one revolution... so maybe not...

 

As an engineer, I try to look for different ways to look at problems. I have a GPS unit that reads-out the actual speed based on global positioning. It does confirm based on my changed tire size, speedo error, etc. that my speedo is about 4 mph fast. Give it a try. I like your chart.

 

Tire deflection does cause the actual rolling circumference of the tire to be less than the circumference computed from the measured tire diameter.

A common trick to finding the actual circumference is to put a drop of oil on the thread and then roll the car through a few tire revolutions. The distance between the oil marks on the pavement is the actual rolling circumference.

Most of us just calibrate our speedometers to find out what the error is (either by GPS or by timing mile markers on the freeway), and then apply the appropriate adjustment factor to the indicated speed. Typically the speedo reads 5% or so high, but there are many variables.

- Mark

 

GPS, baby. GPS.
Note that axel RPMs will change over time - tire diameter changes by 1/2" (8/32 x 2) from new tires to fully worn.

 

and also, some tires increase in diameter slightly at high speeds
(pretty small effect with most steel belted radials, however).

 

Agrred with Markjenn. To be truly acurate you would have to take different measurments of the tire at different temps Then run them off as averages anyway. Go with GPS. As far as having your speedo calibrated. I haven't done mine and it's almost 4 miles per hour off acording to GPS and roadside radar.

 

MINI2 FAQ has this all http://www.mini2.com/forum/faq.php?f...speed_in_gears

R * 60 * 3.14159 * (W * P / 100 * 2 / 25.4 + D) / 12 / 5280 / G

 

Is there gonna be a test? :impatient

 

I'm running 215x40/17 and compared to my GPS my speedo shows that I'm going about 2 MPH faster than the GPS. Thats about right given the 215X40s are slightly smaller in diameter that the 205X40s. So, when my Speedo shows 75MPH I'm really doing 73MPH.

 

I only know what I've read around here, but supposedly the speedo reads 2-3 mph fast (for practical reasons because any error you want to be on the high end, and for "nanny" reasons of keeping you driving a little slower).

 

Speaking as an ex phsics and mathematics instructer yu have done a geat job. now the dreaded, but. You need to use the measured diameter, ie from the hub center to the ground as the car sits on the ground.

Aint math fun!!!

Motor on

 

One more variable... air pressure.

I didn't think this was a factor until I was calibrating my electronic bicycle speed/distance on board calculater.

I have a flat, straight stretch of highway shoulder that has been measured with a tape to exactly one mile. The sensor measures how many revolutions of the front wheel.

By changing the tire pressure, you get different results.

Just wanted to throw another wrench into the mix.

YD

 

You have to remember, too, that the tach isn't calibrated, and reading precisely is hard. That'll introduce some amount of error. Speedometers have an amount of error too.

Significant digits-it does no good to use pi to 5 or 6 digits when one of the inputs can be 2 or 3% off. (phsics (sic) and mathematics don't teach this?) The extra digits don't make anything more or less precise than the least precise input to the equation. And hub to ground would be radius, not diameter...

I'd always used those travelling radar readouts set up by police to get a better idea of my true speed (don't have a GPS but that works too).

 

I measured lack of calibration in my tach in my last car. Haven't been bored enough in my mini yet, but the old tach wasn't any better than the last mini.

GPS is ideal, but otherwise, time yourself going past milemarkers with cruise control on. I have found milemarkers apparently positioned after a 3 martini lunch, but most are good and you can check for consistency. There is measurement technique to consider as well, but you can get this down on a long trip. You just need to be consistent. Now you have one indicated speed and one real speed. In my experience, the guages are consistently off by X%, so you can just find your indicated speed, add or subtract X%, and there you are. This will also let you find real RPM from indicated RPM.

Something to do on long car trips.

 

Thanks for all the comments. When I did this, I was looking to be accurate, but not so accurate as to account for tire wear or tire deformation (and I thought I was sick.) I also did not find where it was done before (that would have made things easier though ) ... and I don't have a GPS.

Actually this started when I showed a friend a video clip from a track day I attended. He asked how fast I was going and I said I didn't know. In the clip I shifted from 3rd to 4th. If I did it according to plan, that would have been about redline in 3rd. So the next obvious question was, what is my top speed in 3rd gear. That led me to this little exercise. Once I had the chart I thought of comparing the calculated speed to what the speedometer shows to see the amount of error. Another thought was to compare my summer and winter tires for speed difference (once I had the data, why not play around?) ... and there you have it.

So with all that said and done, how much do you thing (plus or minus) my version of the calculation is off from true speed?

 

As a designer who can't understand math, I use the nav's sophiscated satellite whachamameamitlocator to calculate my Absolute postulation (with a lime twist) added to my son's indominabole vector divided by my hamster's half life to tell me my actual speed...

 

as in fast, faster, fasterer, and whoa nellie???

 

Is the differential a 1:1 ratio? The gear ratio is typically given out of the the tranny, not the final drive.

 

So with all that said and done, how much do you thing (plus or minus) my version of the calculation is off from true speed?[/quote]


You are very close . No more than 3-4%. You may think that is alot, but for what you are doing it is fine. Besides as you go from one tire to the next, using the same method, your error will be the same, 3-4%. That mean that your error is basically a wash. Don't worry about it.

Math should be fun, so don't sweat . You are cool

Motor on from the ol man

 

Math??? You won't catch me in here!

 

If you don't have a GPS and want to calibrate your speedo using mile markers, here's a good trick: Set the cruise control to 60 mph, and watch the 2nd hand on your watch to see how many seconds it takes to go between markers. If your speedo is accurate, it will take 60. The neat trick is that the number of seconds you are off from 60 is approximately your speedo error in mph. For example, if it takes 64 seconds on average to do a mile, it means your speedo is reading about 4 mph low. There is a small error as you get further away from 60 seconds, but within typical speedometer errors, this method is accurate to within 0.5 mph or so.

You get more accurate results if you do this over several miles. For the math to be easy, just do 10 miles. The total error in seconds divided by 10 is your speedo error in mph. So if it takes 10 minutes, 34 seconds to do 10 miles, then your error is 34/10 or 3.4 mph and you were actually doing 60-3.4 or 56.6 mph. (There is a small error and it's actually 56.782 mph, but close enough for government work.)

- Mark

 

And do it on a very flat stretch of road, since cruise control does not respond instantly to hills, however slight.

 

Typically, but a MCS is not typical....

The 6 speed transmission has two different final drive ratios. It is more like two separate 3-speed transmissions, therefore MINI posts the overall ratios.

Rawhyde