need math equation for determining rpm/gear ratios

[dustyroads]

Anyone know the mathematical (algebraic?) equation to determine engine rpm based on ring/pinion ratios and tire circumference?

For instance, in my case looking to see what rpm I'd run if going to larger tire. I know my transmission gear ratios, differential gearing and can get tire circumference just don't know the equation for experimenting.

Thanks in advance!

edit: i meant to say tire diameter not circumference. Whoops!

 

[OneEyeJack]

The answer to your problem is Google. Enter "engine rpm calculator" for the search.

Try this.

 

[Leo99]

http://www.advanced-ev.com/Calculators/TireSize/

 

[dustyroads]

That was quick. Thanks OneEyeJack and Leo99! Both very helpful.

 

[dustyroads]

Once upon a time I knew the equation and actually did the math. I should've known there would be a "plug and play" system on the interweb.

 

[ARCOgraphite]

Gotta learn longhand.

In the end, You will need to convert "inches per minute" to get MpH.

(Pi*D) is your circumference. The vehicle will move this circumference as a distance over time at any specific engine tachy readout - if you had a 1:1 final drive and a 1:1 R&P ratio.
Now, Just divide (reducing speed result) by the final drive to get roads speed in inches per min. Now simply convert this to obtain MpH

Can you figure it out from here? It always good to do the brain exercise once in a while. The happily jump on the Google calc for expediency

 

[Jetronic]

why not add ordetract the difference in tyre size?

doubling tyre size halves the rpm for a given speed.

 

[exranger06]

Originally Posted By: dustyroads

edit: i meant to say tire diameter not circumference. Whoops!

No, you had it right the first time. The tire diameter won't tell you anything. You need to know the tire circumference. However, the tire diameter is useful to figuring out the circumference. Diameter * PI = circumference.

This is how I do my calculations:

Engine RPM divided by transmission gear ratio = driveshaft RPM. Driveshaft RPM divided by axle ratio = wheel RPM.
Wheel RPM times tire circumference (in inches) = vehicle speed in inches per minute.
Vehicle speed (in/min) divided by 12 = vehicle speed in ft per minute.
Vehicle speed (ft/min) divided by 5,280 = miles per minute.
Vehicle speed (mi/min) times 60 = vehicle speed in miles per hour.

I made my own calculator in Excel using these equations. I can plug in different tire sizes and gear ratios and figure out engine RPM at various speeds.

 

[dustyroads]

Thanks ARCO and exranger. I do like to work things out with pencil and paper (and maybe a calculator) as opposed to all things internet.

When I was a teen (late 1980's) I had a subscription to 4wheel & Off Road magazine. In an edition of that mag, I saw a very simple equation for this thread's subject. It did in fact use tire diameter in inches, not circumference.

I used it for my 79 chevy blazer as a teen and later on with my F150's. Unfortunately, it's been too long since I used the equation and I've forgotten it.

 

[dustyroads]

Originally Posted By: dustyroads


When I was a teen (late 1980's) I had a subscription to 4wheel & Off Road magazine. In an edition of that mag, I saw a very simple equation for this thread's subject. It did in fact use tire diameter in inches, not circumference.





I don't mean to drag this thing out, but yes my forgotten equation did involve 3.14 along with inches diameter. As (PI) was mentioned by ARCO and exranger.

Thanks again for all replies...very helpful!

 

[TiredTrucker]

RPM x 60 / (Tire RPM x Trans Gear Ratio x Diff Ratio)

Tire RPM is revolutions per mile per the tire manufacturer data on the tire in question.

Example: 1800 X 60 / (637 x .67 x 4.10) = 62 mph

 

[dustyroads]

Originally Posted By: TiredTrucker
RPM x 60 / (Tire RPM x Trans Gear Ratio x Diff Ratio)

Tire RPM is revolutions per mile per the tire manufacturer data on the tire in question.

Example: 1800 X 60 / (637 x .67 x 4.10) = 62 mph


That will work great! I know what rpm I'd like to achieve at certain speeds and I can match up a tire to meet my goals.

That's much closer to the equation I was thinking of and very simple. Thank you sir!

 

[punisher]

Quick point- You need to use rolling diameter (2X roll radius), not the listed tire diameter. Roll radius= axle center to road surface.

 

[Jetronic]

Originally Posted By: exranger06
Originally Posted By: dustyroads

edit: i meant to say tire diameter not circumference. Whoops!

No, you had it right the first time. The tire diameter won't tell you anything. You need to know the tire circumference. However, the tire diameter is useful to figuring out the circumference. Diameter * PI = circumference.

This is how I do my calculations:

Engine RPM divided by transmission gear ratio = driveshaft RPM. Driveshaft RPM divided by axle ratio = wheel RPM.
Wheel RPM times tire circumference (in inches) = vehicle speed in inches per minute.
Vehicle speed (in/min) divided by 12 = vehicle speed in ft per minute.
Vehicle speed (ft/min) divided by 5,280 = miles per minute.
Vehicle speed (mi/min) times 60 = vehicle speed in miles per hour.

I made my own calculator in Excel using these equations. I can plug in different tire sizes and gear ratios and figure out engine RPM at various speeds.


since pi is a constant, diameter tells you just as much as circumference...

 

[exranger06]

Originally Posted By: Jetronic
Originally Posted By: exranger06
Originally Posted By: dustyroads

edit: i meant to say tire diameter not circumference. Whoops!

No, you had it right the first time. The tire diameter won't tell you anything. You need to know the tire circumference. However, the tire diameter is useful to figuring out the circumference. Diameter * PI = circumference.

This is how I do my calculations:

Engine RPM divided by transmission gear ratio = driveshaft RPM. Driveshaft RPM divided by axle ratio = wheel RPM.
Wheel RPM times tire circumference (in inches) = vehicle speed in inches per minute.
Vehicle speed (in/min) divided by 12 = vehicle speed in ft per minute.
Vehicle speed (ft/min) divided by 5,280 = miles per minute.
Vehicle speed (mi/min) times 60 = vehicle speed in miles per hour.

I made my own calculator in Excel using these equations. I can plug in different tire sizes and gear ratios and figure out engine RPM at various speeds.


since pi is a constant, diameter tells you just as much as circumference...

I know. I said that in my last post. But what you really want is circumference. Diameter just gives you a way to figure out the circumference.

 

[ARCOgraphite]

If tire is off the car you can measure circumference with a string (mark it at overlap point) and then lay the string out on a steel tape measure - this way might be more accurate for the shade tree.