help: need the formula!

[XOC]

Can someone (Bob??) please (re)post the formula that relates engine RPM, gear ratio, diff. ratio, and tire size to vehicle speed? It would be so very appreciated!

TIA!

[Prairieman]

here you go:

RPM = MPH x Gear Ratio x 336
Tire Diameter



here's a site "geared" toward the bigfoot off road set, but has a simple RPM, Ratio, Tire Size matrix


www.superlift.com (http://)


from the Prairie,
Brad

[Prairieman]

whooops...

the words "tire diameter" should be to the right of the equal sign to denote the denominator on the right side of the equation.





"I need to work on a proper sig"


from the prairie,

[Bob ///M3]

Tell me what information (and scenarios) you are looking for and I will give you the results.

Bob ///M3



Originally posted by 98m3/2
Can someone (Bob??) please (re)post the formula that relates engine RPM, gear ratio, diff. ratio, and tire size to vehicle speed? It would be so very appreciated!

TIA!

[XOC]

Well, I am actually on the verge of getting a Euro 6-speed! (woohoo :D) and I want to figure out what the best diff ratio would be to get the best tradeoff between acceleration, top-speed, and gas mileage. I think, from what I've heard, the 1st 5 speeds of the 6-speed are the same as that of the 5-speed, and the 6th is .83 I think. I just wanted to be able to figure out what the theoretical top speeds would be and so on.

Oh so I am considering a 3.38, 3.46, 3.73, and 3.91.

Thanks Prairieman for the formula, I will play with it. If you have any more insights Bob that would be great.

Thanks! :)

[XOC]

Oops, looking again at the formula above, it doesn't account for diff ratio. So does it assume a diff ratio of 1:1 or ???

Also I'm not sure if diff ratio is engine:wheel or wheel:engine. I guess if I play I might be able to infer which one it is. Hmmm ..... Actually if the higher number diff ratio gives better acceleration, it should be the ratio of driveshaft(engine) to wheel spin, right?

[Bob ///M3]

The following is "ground speed" in mph versus "engine speed" in RPM based on the following information for the '96 thru '99 M3:

Transmission gearing:

1st Gear - 4.20
2nd Gear - 2.49
3rd Gear - 1.66
4th Gear - 1.24
5th Gear - 1.00
6th Gear - 0.83 *

* Note: 6th Gear was calculated for Euro versions. The Euro version M3 has slightly different transmission gears in 1st (4.23), 2nd (2.51) and 3rd (1.67) gears which makes less than 1 mph difference compared to the U.S. version M3.


Final Drive Gearing:

Stock '96-'99 gearing: 3:23 to 1**

** Note: The '95 model M3 has a 3:15 to 1 Final Gear Ratio.


Rear (Drive) Tire Diameter:

245/40 X 17" (24.72" Diameter)

Note: Depending on rear tire diameter size, the calculations will be different.



Figures will be "RPM" in 500 rpm increments followed by "Speed" beginning with 1st gear and so on.

1st Gear:

1,000 rpm - 5 mph
1,500 rpm - 8 mph
2,000 rpm - 11 mph
2,500 rpm - 14 mph
3,000 rpm - 16 mph
3,500 rpm - 19 mph
4,000 rpm - 22 mph
4,500 rpm - 24 mph
5,000 rpm - 27 mph
5,500 rpm - 30 mph
6,000 rpm - 33 mph
6,500 rpm - 35 mph
7,000 rpm - 38 mph
7,500 rpm - 41 mph
8,000 rpm - 43 mph


2nd Gear:

1,000 rpm - 9 mph
1,500 rpm - 14 mph
2,000 rpm - 18 mph
2,500 rpm - 23 mph
3,000 rpm - 27 mph
3,500 rpm - 32 mph
4,000 rpm - 37 mph
4,500 rpm - 41 mph
5,000 rpm - 46 mph
5.500 rpm - 50 mph
6,000 rpm - 55 mph
6,500 rpm - 59 mph
7,000 rpm - 64 mph
7,500 rpm - 69 mph
8,000 rpm - 73 mph


3rd Gear:

1,000 rpm - 14 mph
1.500 rpm - 21 mph
2,000 rpm - 27 mph
2,500 rpm - 34 mph
3,000 rpm - 41 mph
3,500 rpm - 48 mph
4,000 rpm - 55 mph
4,500 rpm - 62 mph
5,000 rpm - 69 mph
5,500 rpm - 75 mph
6,000 rpm - 82 mph
6,500 rpm - 89 mph
7,000 rpm - 96 mph
7,500 rpm - 103 mph
8,000 rpm - 110 mph


4th Gear:

1,000 rpm - 18 mph
1,500 rpm - 28 mph
2,000 rpm - 37 mph
2,500 rpm - 46 mph
3,000 rpm - 55 mph
3,500 rpm - 64 mph
4,000 rpm - 73 mph
4,500 rpm - 83 mph
5,000 rpm - 92 mph
5,500 rpm - 101 mph
6,000 rpm - 110 mph
6,500 rpm - 119 mph
7,000 rpm - 129 mph
7,500 rpm - 138 mph
8,000 rpm - 147 mph


5th Gear:

1,000 rpm - 23 mph
1,500 rpm - 34 mph
2,000 rpm - 46 mph
2,500 rpm - 57 mph
3,000 rpm - 68 mph
3,500 rpm - 80 mph
4,000 rpm - 91 mph
4,500 mph - 101 mph
5,000 rpm - 114 mph
5,500 rpm - 125 mph
6,000 rpm - 137 mph
6,500 rpm - 148 mph
7,000 rpm - 159 mph
7,500 rpm - 171 mph
8,000 rpm - 182 mph


6th Gear *(Euro version)

1,000 rpm - 27 mph
1,500 rpm - 41 mph
2,000 rpm - 55 mph
2,500 rpm - 69 mph
3,000 rpm - 82 mph
3,500 rpm - 96 mph
4,000 rpm - 110 mph
4,500 rpm - 123 mph
5,000 rpm - 137 mph
5,500 rpm - 151 mph
6,000 rpm - 165 mph
6,500 rpm - 178 mph
7,000 rpm - 192 mph
7,500 rpm - 206 mph
8,000 rpm - 219 mph


Please note I have included data up through 8,000 rpms! This is so anyone who has aftermarket performance software, which increases the rev limiter, will have the necessary information up through and beyond the new limits.

Also of interest, one can determine what the rpm will be when downshifting into a lower gear so as not to redline the engine and cause damage. This information can also be used to determine at what rpm the engine speed was "if" there happened to be a mis-shift on a downshift if you knew what speed you were traveling.

It is assumed that everyone knows our M3s should not be operated at the upper most limits of the rpms which I have listed and it is also assumed that everyone knows our M3s will not approach the upper limits of the ground speeds (mph) which I have listed due to aerodynamic drag!

Lastly, if you happen to have a tire and wheel combination which does not have a 24.72" diameter, the above calculations will be different.

I will furnish information based on the other Final Drive Gearing ratios you wanted in a separate post on this thread.

Bob ///M3

[Bob ///M3]

The following is "ground speed" in mph versus "engine speed" in RPM based on the following information for the '96 thru '99 M3:

Transmission gearing:

1st Gear - 4.20
2nd Gear - 2.49
3rd Gear - 1.66
4th Gear - 1.24
5th Gear - 1.00
6th Gear - 0.83 *

* Note: 6th Gear was calculated for Euro versions. The Euro version M3 has slightly different transmission gears in 1st (4.23), 2nd (2.51) and 3rd (1.67) gears which makes less than 1 mph difference compared to the U.S. version M3.


Final Drive Gearing:

3:38 to 1


Rear (Drive) Tire Diameter:

245/40 X 17" (24.72" Diameter)

Note: Depending on rear tire diameter size, the calculations will be different.



Figures will be "RPM" in 500 rpm increments followed by "Speed" beginning with 1st gear and so on.

1st Gear:

1,000 rpm - 5 mph
1,500 rpm - 8 mph
2,000 rpm - 10 mph
2,500 rpm - 14 mph
3,000 rpm - 16 mph
3,500 rpm - 18 mph
4,000 rpm - 20 mph
4,500 rpm - 22 mph
5,000 rpm - 27 mph
5,500 rpm - 29 mph
6,000 rpm - 31 mph
6,500 rpm - 33 mph
7,000 rpm - 36 mph
7,500 rpm - 39 mph
8,000 rpm - 41 mph


2nd Gear:

1,000 rpm - 9 mph
1,500 rpm - 13 mph
2,000 rpm - 17 mph
2,500 rpm - 22 mph
3,000 rpm - 26 mph
3,500 rpm - 31 mph
4,000 rpm - 35 mph
4,500 rpm - 40 mph
5,000 rpm - 45 mph
5.500 rpm - 49 mph
6,000 rpm - 52 mph
6,500 rpm - 58 mph
7,000 rpm - 61 mph
7,500 rpm - 67 mph
8,000 rpm - 70 mph


3rd Gear:

1,000 rpm - 13 mph
1.500 rpm - 20 mph
2,000 rpm - 26 mph
2,500 rpm - 33 mph
3,000 rpm - 39 mph
3,500 rpm - 46 mph
4,000 rpm - 53 mph
4,500 rpm - 60 mph
5,000 rpm - 66 mph
5,500 rpm - 73 mph
6,000 rpm - 79 mph
6,500 rpm - 87 mph
7,000 rpm - 92 mph
7,500 rpm - 101 mph
8,000 rpm - 105 mph


4th Gear:

1,000 rpm - 17 mph
1,500 rpm - 26 mph
2,000 rpm - 35 mph
2,500 rpm - 44 mph
3,000 rpm - 53mph
3,500 rpm - 62 mph
4,000 rpm - 70 mph
4,500 rpm - 80 mph
5,000 rpm - 88 mph
5,500 rpm - 98 mph
6,000 rpm - 105 mph
6,500 rpm - 114 mph
7,000 rpm - 123 mph
7,500 rpm - 133 mph
8,000 rpm - 140 mph


5th Gear:

1,000 rpm - 22 mph
1,500 rpm - 33 mph
2,000 rpm - 44 mph
2,500 rpm - 54 mph
3,000 rpm - 65 mph
3,500 rpm - 76 mph
4,000 rpm - 87 mph
4,500 mph - 95 mph
5,000 rpm - 107 mph
5,500 rpm - 119 mph
6,000 rpm - 131 mph
6,500 rpm - 141 mph
7,000 rpm - 152 mph
7,500 rpm - 163 mph
8,000 rpm - 174 mph


6th Gear *(Euro version)

1,000 rpm - 26 mph
1,500 rpm - 39 mph
2,000 rpm - 52 mph
2,500 rpm - 66 mph
3,000 rpm - 79 mph
3,500 rpm - 92 mph
4,000 rpm - 105 mph
4,500 rpm - 118 mph
5,000 rpm - 131 mph
5,500 rpm - 144 mph
6,000 rpm - 157 mph
6,500 rpm - 171 mph
7,000 rpm - 184 mph
7,500 rpm - 197 mph
8,000 rpm - 210 mph


Please note I have included data up through 8,000 rpms! This is so anyone who has aftermarket performance software, which increases the rev limiter, will have the necessary information up through and beyond the new limits.

Also of interest, one can determine what the rpm will be when downshifting into a lower gear so as not to redline the engine and cause damage. This information can also be used to determine at what rpm the engine speed was "if" there happened to be a mis-shift on a downshift if you knew what speed you were traveling.

It is assumed that everyone knows our M3s should not be operated at the upper most limits of the rpms which I have listed and it is also assumed that everyone knows our M3s will not approach the upper limits of the ground speeds (mph) which I have listed due to aerodynamic drag!

Lastly, if you happen to have a tire and wheel combination which does not have a 24.72" diameter, the above calculations will be different.

I will furnish information based on the other Final Drive Gearing ratios you wanted in a separate post to this thread.

Bob ///M3

[Bob ///M3]

The following is "ground speed" in mph versus "engine speed" in RPM based on the following information for the '96 thru '99 M3:

Transmission gearing:

1st Gear - 4.20
2nd Gear - 2.49
3rd Gear - 1.66
4th Gear - 1.24
5th Gear - 1.00
6th Gear - 0.83 *

* Note: 6th Gear was calculated for Euro versions. The Euro version M3 has slightly different transmission gears in 1st (4.23), 2nd (2.51) and 3rd (1.67) gears which makes less than 1 mph difference compared to the U.S. version M3.


Final Drive Gearing:

3:46 to 1


Rear (Drive) Tire Diameter:

245/40 X 17" (24.72" Diameter)

Note: Depending on rear tire diameter size, the calculations will be different.



Figures will be "RPM" in 500 rpm increments followed by "Speed" beginning with 1st gear and so on.

1st Gear:

1,000 rpm - 5 mph
1,500 rpm - 8 mph
2,000 rpm - 10 mph
2,500 rpm - 14 mph
3,000 rpm - 15 mph
3,500 rpm - 18 mph
4,000 rpm - 20 mph
4,500 rpm - 22 mph
5,000 rpm - 26 mph
5,500 rpm - 28 mph
6,000 rpm - 30 mph
6,500 rpm - 33 mph
7,000 rpm - 35mph
7,500 rpm - 38 mph
8,000 rpm - 41 mph


2nd Gear:

1,000 rpm - 9 mph
1,500 rpm - 13 mph
2,000 rpm - 17 mph
2,500 rpm - 22 mph
3,000 rpm - 26 mph
3,500 rpm - 30 mph
4,000 rpm - 34 mph
4,500 rpm - 38 mph
5,000 rpm - 43mph
5.500 rpm - 47 mph
6,000 rpm - 51 mph
6,500 rpm - 55mph
7,000 rpm - 60 mph
7,500 rpm - 64 mph
8,000 rpm - 68 mph


3rd Gear:

1,000 rpm - 13 mph
1.500 rpm - 18 mph
2,000 rpm - 25 mph
2,500 rpm - 32 mph
3,000 rpm - 37 mph
3,500 rpm - 45 mph
4,000 rpm - 51 mph
4,500 rpm - 57 mph
5,000 rpm - 64 mph
5,500 rpm - 70 mph
6,000 rpm - 77 mph
6,500 rpm - 83 mph
7,000 rpm - 90 mph
7,500 rpm - 96 mph
8,000 rpm - 102 mph


4th Gear:

1,000 rpm - 17 mph
1,500 rpm - 25 mph
2,000 rpm - 34 mph
2,500 rpm - 43 mph
3,000 rpm - 51mph
3,500 rpm - 60 mph
4,000 rpm - 68 mph
4,500 rpm - 77 mph
5,000 rpm - 86 mph
5,500 rpm - 94 mph
6,000 rpm - 103 mph
6,500 rpm - 111 mph
7,000 rpm - 120 mph
7,500 rpm - 128 mph
8,000 rpm - 137 mph


5th Gear:

1,000 rpm - 21 mph
1,500 rpm - 32 mph
2,000 rpm - 43 mph
2,500 rpm - 53 mph
3,000 rpm - 64 mph
3,500 rpm - 74 mph
4,000 rpm - 85 mph
4,500 mph - 95 mph
5,000 rpm - 106 mph
5,500 rpm - 117 mph
6,000 rpm - 128 mph
6,500 rpm - 138 mph
7,000 rpm - 149 mph
7,500 rpm - 159 mph
8,000 rpm - 170 mph


6th Gear *(Euro version)

1,000 rpm - 25 mph
1,500 rpm - 38 mph
2,000 rpm - 51 mph
2,500 rpm - 64 mph
3,000 rpm - 77 mph
3,500 rpm - 90 mph
4,000 rpm - 102 mph
4,500 rpm - 115 mph
5,000 rpm - 131 mph
5,500 rpm - 141 mph
6,000 rpm - 154 mph
6,500 rpm - 167 mph
7,000 rpm - 179 mph
7,500 rpm - 192 mph
8,000 rpm - 205 mph


Please note I have included data up through 8,000 rpms! This is so anyone who has aftermarket performance software, which increases the rev limiter, will have the necessary information up through and beyond the new limits.

Also of interest, one can determine what the rpm will be when downshifting into a lower gear so as not to redline the engine and cause damage. This information can also be used to determine at what rpm the engine speed was "if" there happened to be a mis-shift on a downshift if you knew what speed you were traveling.

It is assumed that everyone knows our M3s should not be operated at the upper most limits of the rpms which I have listed and it is also assumed that everyone knows our M3s will not approach the upper limits of the ground speeds (mph) which I have listed due to aerodynamic drag!

Lastly, if you happen to have a tire and wheel combination which does not have a 24.72" diameter, the above calculations will be different.

I will furnish information based on the other Final Drive Gearing ratios you wanted in a separate post to this thread.

Bob ///M3

[Bob ///M3]

The following is "ground speed" in mph versus "engine speed" in RPM based on the following information for the '96 thru '99 M3:

Transmission gearing:

1st Gear - 4.20
2nd Gear - 2.49
3rd Gear - 1.66
4th Gear - 1.24
5th Gear - 1.00
6th Gear - 0.83 *

* Note: 6th Gear was calculated for Euro versions. The Euro version M3 has slightly different transmission gears in 1st (4.23), 2nd (2.51) and 3rd (1.67) gears which makes less than 1 mph difference compared to the U.S. version M3.


Final Drive Gearing:

3:91 to 1 (I'm skipping the 3.73 since you will be able to figure out closely what the results would be.)


Rear (Drive) Tire Diameter:

245/40 X 17" (24.72" Diameter)

Note: Depending on rear tire diameter size, the calculations will be different.



Figures will be "RPM" in 500 rpm increments followed by "Speed" beginning with 1st gear and so on.

1st Gear:

1,000 rpm - 5 mph
1,500 rpm - 7 mph
2,000 rpm - 9 mph
2,500 rpm - 11 mph
3,000 rpm - 13 mph
3,500 rpm - 16 mph
4,000 rpm - 18 mph
4,500 rpm - 20 mph
5,000 rpm - 23 mph
5,500 rpm - 25 mph
6,000 rpm - 27 mph
6,500 rpm - 29 mph
7,000 rpm - 31mph
7,500 rpm - 34 mph
8,000 rpm - 36 mph


2nd Gear:

1,000 rpm - 8 mph
1,500 rpm - 11 mph
2,000 rpm - 15 mph
2,500 rpm - 19 mph
3,000 rpm - 22 mph
3,500 rpm - 26 mph
4,000 rpm - 30 mph
4,500 rpm - 34 mph
5,000 rpm - 38mph
5.500 rpm - 41 mph
6,000 rpm - 45 mph
6,500 rpm - 49mph
7,000 rpm - 53 mph
7,500 rpm - 56 mph
8,000 rpm - 60 mph


3rd Gear:

1,000 rpm - 11 mph
1.500 rpm - 17 mph
2,000 rpm - 23 mph
2,500 rpm - 28 mph
3,000 rpm - 34 mph
3,500 rpm - 45 mph
4,000 rpm - 46 mph
4,500 rpm - 51 mph
5,000 rpm - 57 mph
5,500 rpm - 63 mph
6,000 rpm - 68 mph
6,500 rpm - 74 mph
7,000 rpm - 79 mph
7,500 rpm - 85 mph
8,000 rpm - 91 mph


4th Gear:

1,000 rpm - 15 mph
1,500 rpm - 23 mph
2,000 rpm - 30 mph
2,500 rpm - 38 mph
3,000 rpm - 45mph
3,500 rpm - 53 mph
4,000 rpm - 61 mph
4,500 rpm - 68 mph
5,000 rpm - 76 mph
5,500 rpm - 83 mph
6,000 rpm - 91 mph
6,500 rpm - 98 mph
7,000 rpm - 106 mph
7,500 rpm - 113 mph
8,000 rpm - 121 mph


5th Gear:

1,000 rpm - 19 mph
1,500 rpm - 28 mph
2,000 rpm - 38 mph
2,500 rpm - 47 mph
3,000 rpm - 56 mph
3,500 rpm - 66 mph
4,000 rpm - 75 mph
4,500 mph - 84 mph
5,000 rpm - 94 mph
5,500 rpm - 103 mph
6,000 rpm - 113 mph
6,500 rpm - 122 mph
7,000 rpm - 132 mph
7,500 rpm - 141 mph
8,000 rpm - 150 mph


6th Gear *(Euro version)

1,000 rpm - 23 mph
1,500 rpm - 34 mph
2,000 rpm - 45 mph
2,500 rpm - 57 mph
3,000 rpm - 68 mph
3,500 rpm - 79 mph
4,000 rpm - 91 mph
4,500 rpm - 102 mph
5,000 rpm - 113 mph
5,500 rpm - 124 mph
6,000 rpm - 136 mph
6,500 rpm - 147 mph
7,000 rpm - 159 mph
7,500 rpm - 170 mph
8,000 rpm - 181 mph


Please note I have included data up through 8,000 rpms! This is so anyone who has aftermarket performance software, which increases the rev limiter, will have the necessary information up through and beyond the new limits.

Also of interest, one can determine what the rpm will be when downshifting into a lower gear so as not to redline the engine and cause damage. This information can also be used to determine at what rpm the engine speed was "if" there happened to be a mis-shift on a downshift if you knew what speed you were traveling.

It is assumed that everyone knows our M3s should not be operated at the upper most limits of the rpms which I have listed and it is also assumed that everyone knows our M3s will not approach the upper limits of the ground speeds (mph) which I have listed due to aerodynamic drag!

Lastly, if you happen to have a tire and wheel combination which does not have a 24.72" diameter, the above calculations will be different.


Bob ///M3

[XOC]

Whoa Bob thank you so much. This is exactly what I was looking for! :jump:

[Bob ///M3]

I'm glad I could help you Lee.

Bob ///M3