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Tech Reference Page #24
Gearing Formulas
Authored by Wes Vann, April 3, 1999
Opening comments;
On this page, I'm going to go into the different formulas that you may want to use in order to set up the gearing on your car.
It's not really a "stand-alone" page, in that you should have the "gearing" data from the transmission pages (I have to add an "automatic transmissions" page). I'd recommend that you print them out and have them handy. The April Car Craft (1999) has a really good listing of what rear-end ratios are currently available!
This is a long "text" page and in it's final format, there will be "jumps" to the desired sections.
Personal thoughts;
1) What I want out of a car is probably different than what you want. Although some of my opinions may be present, don't let it bug you or think it's a personal slam!
2) We are talking about cars with V8 engines here and not some high rpm, narrow power band 4 cylinder. As such, I really don't see any reason for a 6 speed transmission.
3) Any transmission with an overdrive will give you better fuel economy and lower the rpm while on the freeway. That lower rpm means that the engine will last longer! I don't see the need for two overdrives.
4) Currently, this page is geared (sorry) towards manual transmissions. The formulas are still valid for automatics and I may revise or add more info latter.
Things you need know!
1) The formulas don't take into account things like aerodynamics or frictional loss at speed. As such, even if a formula says you can do 200 mph, the engine (or common sense) may say no!
2) The formulas also assume that the tire diameter stays the same at different speeds. If you watch a dragster at launch, you may notice that the tire expands in diameter and that changes the total over-all gear ratio! (My wagon sure doesn't do this!)
Directory; (and future jump point)
Terms I'm going to use;
"circ", this is the circumference of the rear tire measured
in inches.
"diam", diameter of your tire measured in inches.
"RPM", revolutions per minute of the engine (engine speed)
"trans", transmission gear ratio, "0.68" would be an
overdrive ratio.
"rear", rear end ratio, as in "3.31" to one.
"60", this is a correction factor converting hours to 60 minutes.
"63371.4", this is a correction factor converting inches to miles.
"speed", this is the miles per hour you are going
To get the circumference of the rear tire, you could put a mark on your tire toward the bottom, and a mark on the ground adjacent to the tire mark. Then roll the car until the mark is down in the same position. Make another mark on the ground and measure from it to the original mark on the ground. This is the circumference. Or you could use the following formula;
"circ" = 3.14159 x diam
Here is the formula for computing the speed of the car if you know the RPM;
"speed" =
As an example, if you had a transmission with a 0.68 overdrive, 3.31 rear end gears, tires with a 75 inch circumference, and (finally) the engine is turning at 3000 RPM;
"speed" =
Here is the formula for the RPM if you know the cars speed;
"RPM"=
4. the "Launch" or "Top End" formula;
This formula serves two different purposes, and as such could be called "launch" or "top end" depending on what you are after. For simplicity, I'm just going to call it "launch".
If using "first gear" values, the formula will give a "launch" value. The higher the number (larger), the stronger the launch.
If using the transmission "final gear" (fourth, fifth, or sixth?) values, the formula will give a "top end" value. The lower the number (smaller), the better top end speed (for any given engine speed).
This formula does not take into account the tire diameter and just assumes that you are not going to be changing to a different diameter tire. It's not the "over-all" gear ratio, just a number that you can use for comparison purposes!
"Launch"= rear x trans
5. the myth of "I've got to have 4:11's";
One of the things that really bugs me is hearing somebody say that he just has to run 4.11's! I personally think that it's just one of those things that get into peoples minds because they hear about some 60's muscle car that ran them.
We are not in the 60's and a car with 4.11's is not something you would want to drive on the freeway!
The wording should really be that the individual wants "over-all" low-end gearing similar to what an early car with 4.11's had. You have to take into account the transmission gearing!
There are options! You can have your cake and eat it to! (but your wallet will pay for the cake)
Let's get real and use the formulas.
As a "base-line" example, assume a Muncie M22 rock crusher and 4.11 rear gearing (also assume a tire circumference of 75 inches). The M22 had a low gear of 2.20 and a final drive of 1.00. We are going to compute the "launch" value and use it for comparison. We also want to check the engine speed at a legal 65 mph. For fun, we will also check the rpm at an illegal 120. (I'm not telling you it's ok to do 120!)
Launch = 4.11 x 2.20 = 9.04 (it's just a number for comparison, but keep the number in mind!)
RPM (@ 65mph) = (65 x 1.00 x 4.11 x 63371.4) / (75 x 60) = 3762 RPM (pretty high rpm!)
RPM (@ 120mph) = (120 x 1.00 x 4.11 x 63371.4) / (75 x 60) = 6946 RPM (you just blew-up your big block V8 car and got beat by a Honda!!)
Now let's run the numbers using a Richmond 5 speed (Doug Nash) and 3.08 rear gears! The Richmond has a first gear of 3.26 and a final gear of 1.00.
Launch = 3.08 x 3.26 = 10.04 (this is larger than the 9.04 above, and as such you would launch harder!)
RPM (@ 65mph) = (65 x 1.00 x 3.08 x 63371.4) / (75 x 60) = 2819 RPM (mellow, and the Beach Boys can be heard on the 4 track tape player)
RPM (@ 120mph) = (120 x 1.00 x 3.08 x 63371.4) / (75 x 60) = 5205 RPM (that Honda didn't get away and you still have pistons without holes in them!)
Want to get crazy, and still have that mythical 4.11 launch? Let's run the numbers if you put in an "aftermarket" T56 and 3.42 rear gears. The first gear ratio is 2.66 and the final gear (sixth) is 0.62.
Launch = 3.42 x 2.66 = 9.10 (slightly higher than that original 4.11, just about the same launch, a little better)
RPM (@ 65mph) = 65 x 0.62 x 3.42 x 63371.4) / (75 x 60) = 1940 RPM (think about the mileage!)
RPM (@ 120mph) = 120 x 0.62 x 3.42 x 63371.4) / (75 x 60) = 3583 RPM (this is a slower engine speed that the original car had at 65mph!!)
Hey, let's drive to Los Vegas!! But we still have to have that 4.11 feeling! This time it's a GM T56 6 speed and 3.42 rear gears. First gear is 2.66 and final gear (sixth) is 0.50.
Launch = 3.42 x 2.66 = 9.10 (same as above)
RPM (@ 120mph) = 120 x 0.50 x 3.42 x 63371.4) / (75 x 60) = 2890 RPM (Elvis could only dream of this! Now you know why this transmission is popular with the guys that do things like the Power Tour!)
For fun, I plugged the engine speed of 2890 rpm into the "speed" formula and used the gearing from that original "base-line" 60's car. At 2890 rpm, it would only be going 50 miles per hour!!!!
With all that said and done, what you really have to figure out is what "over-all" gear ratio you want for launch. I can't help you out! I don't drag race at all! What I'd recommend is that you just keep your ears open when listening to people that are running a car with similar engine and weight. What rear are they running and also what transmission. What are their 60 ft. times at the quarter mile? Do they "top-out" before hitting the end of the "quarter"?
The rear-end ratios that I quoted are currently available for Chevy 12 bolt rear-ends (as far as I know).
6. "Viper" top end got you down?
A 64 Chevelle wagon is an aerodynamic brick! But let's say that we have ton's of horsepower, don't mind swapping in a Ford rear-end (they have a better selection of rear-end ratios), and just have to do 200mph!
Let's see what can be done, and still not add an "extension" (Gear Venders) overdrive. We could run a GM T56 6 speed, Ford 9 inch rear-end with 2.80 gears, and a 28" tall tire (the other tire values were based on a 25" tall tire, like I have on my wagon).
The tire circumference = 3.14159 x 28 = 88"
RPM (@ 200mph) = (200 x 0.50 x 2.80 x 63371.4) / (88 x 60) = 3361 RPM (do-able!)
Just count on having a lot of horsepower to plow through the wind (and also think about what happens when the car wants to fly!)!!
Have fun!