Figuring out my engine RPM

I guess I should thank my junior high school algebra teacher for this

story. So Thank You Mr. Kumbe, even though I did think you were quite a

strange fellow!

After about 7 years I finally pulled my '66 Chevelle out of my

brother's garage (well, he is actually co-owner but that's another

story). A bad radiator and a slipping Powerglide brought it to rest and

it was finally time to get it going again. With a new cooling system

installed I brought the car over to Foothill Transmission in Pasadena

for a transmission swap. A TH-350 with a shift kit and 1800 stall

converter was installed and I was good to go! It felt like a totally

different car. After I drove it around for a while I remembered I never

quite figured out what my engine RPM's were (crusing at 60MPH) since

this car doesn't have a tachometer (yet).

I found the following formula on the internet:

MPH =       RPM x Tire Diameter (in inches)

___________________________________

Rearend Gear Ratio x 336

After 10 minutes of head scratching and almost just forgetting about it

my mathematical sense re-awakened. I hope my algebra is correct. Here

goes! --->

assuming 3.08 Gears in my '66 Chevelle cruising at 60MPH

AND

x = RPM

60 = x * Tire Diameter (in inches)

______

1034.88 (3.08 x 336)

Now I needed to do some algebra to isolate the RPM variable. --->

multiplied both sides by 1034.88

this brings the formula to:

62092.8 = x * Tire Diameter (in inches)

then, dividing variable "Tire Diameter" on both sides

brings the formula to:

62092.8

_______    = x

Tire Diameter      <--- now I have my adjusted formula

Oh wait, now I had to calculate how tall my tires were. This is the “Tire Diameter” in the formula. Of course you could just take a measuring tape to your tires but you should understand the math behind tire sizes.

In my case :

My Chevelle with 14" rims and 215/70 R14 tires:

215/70 R14 is the tire size as printed on my tires. Most people get very confused here. Here is the breakdown :

215 is the tire width in millimeters. The 70 means each sidewall (top and bottom) is 70% of the width of the tire, or 215 millimeters in my case. R just means Radial and 14 means a 14 inch tire and rim.

Converting sidewall mumbo-jumbo to height in inches: That’s 70% of 215 millimeters (150.5 mm) multiplied by 2 for each sidewall (301 mm), converted to inches, then adding in the rim diameter (14 in).

Hint: If you visit http://www.google.com and type in 301 mm to inches, for example, Google will automatically calculate the conversion for you.

Once again, in my case:

(combined sidewall height + rim) --->

11.85 + 14 = 25.85 inch tall tire

Now I finally plugged it in the formula:

62092.8

_______ = 2402 RPM

25.85

Now I know what RPM my 350 engine is cruising at!

So now I was curious how a different tire size would affect my RPM's...

I decided on three possible tires sizes using 16" rims.

Here are the calculations:

==================================================

With rear wheel 245/50 R16 tire

9.65 + 16 = 25.65 inch tall tire

62092.8

_______ = 2421 RPM

25.65

==================================================

With rear wheel 265/50 R16 tire

10.43 + 16 = 26.43 inch tall tire

62092.8

_______ = 2349 RPM

26.43

==================================================

With rear wheel 295/50 R16 tire

11.61 + 16 = 27.61 inch tall tire

62092.8

_______ = 2249 RPM

27.61

I guess you could say that 17 years later I finally had fun with algebra. I am such a fuckin’ geek!

,

Zuma