Thinking of new gears? Here are some interesting calcs for you. (long)

Zero Signal

Active Member
Feb 24, 2003
Tucson, AZ
[EDIT: Resurrecting this thread from 2 years ago]

A lot of people have been asking about gears recently, so I thought I would share some calculations I've done to show you what kind of changes you are making to your performance. It's interesting and very simple to do on your own if you want to run your own numbers for different torque curves and ratios.

Most of you can probably skip down a few paragraphs to the interesting part.

First the question is, what exactly are you doing when you change your gears? It's simple, when your motor turns, the gears multiply the torque through the driveline. The first gear in the series multiplies it by that ratio and and the next gear in the series multiplies that multiplied torque once again by the respective gear ratio.

For example: your bone stock 5.0 puts out about 270 ft-lbs of torque at the flywheel @3500rpm. To find the torque at the axles, you simply multiply your motor's torque by the gear ratios between them, so in 1st gear and stock 3.08 rearend, you have [270 ft-lbs x 3.35 x 3.08]= 2785.86 ft-lbs and for second gear you have [270 ft-lbs x 1.99 x 3.08]= 1654.88 ft-lbs and so on unill 5th gear.

Now that you have the torque which is nothing more than torsional force, you want to convert that to a linear force. All you do from this point, is take the torque at the axles and divide by the radius of the tire with units in feet. So with 245/45 17 tires, in 1st gear@3500rpm, your driving force at the pavement aka Tractive Effort is (2785.86ft-lbs)/(1.07ft)=2603.6 lbs. Now, since F=ma, you can see that the tractive effort is directly proportional to your car's acceleration. I won't get into anything else like rolling resistance, drag and mass factor, but the tractive effort will always be directly proportional to the car's acceleration, meaning, the more tractive effort you can put to the ground, the more your car car will accelerate.

Ok ok, that's cake and alot of you already know all that :)

This is what I thought would be interesting. . .

Now that you have the equation for your tractive effort (Te) in terms of your torque and gearing (Te = [Tq x 1st gear x rearend] / [rolling radius]), you can find your Te for each rpm with the gearing you currently run. I used 3.08 for my calculations. Then go ahead and calculate the Te for each rpm with 3.73 gears. You will obviously see a substantial gain in Te. Now the cool part is that you can take the Te you get with 3.73 gears, and using the same equation, but with 3.08 gears, solve for the torque instead. This will give you a new torque number that would give you the same Te as if you kept your stock gears and upgraded something else to give you more torque. You can take this torque and subtract it from your actual torque to get an 'equivalent torque increase'. I did this in the charts below

For this chart, I used the stock dyno sheet for both gears. You can see the equivalent torque increase to the right. It just shows what kind of SOTP gain you will get from a 3.08 to a 3.73 gear. Now when you talk about bang for the buck with real numbers, you can consider the torque increase and compare the cost of the gears to something else that will give you the same torque. The units for the delta torque are in ft-lbs.

Here is the graphical version. You can see how substantial the gains are with the blue being the 3.73's and the black being 3.08. Each curve represents each gear. Where the curve cross is the optimum shift point. You can use the gearing and tire dimensions to find the rpm from the mph at each shift point. But you can use my shift point calculator on my sig page for that. Notice how the gearing makes the curves taller (more acceleration) but shorter, so they won't last as long. The shortened gear will probably be your deciding factor in which gear you want. I chose 3.73 becuase I want to keep it under 2700rpm on the highway and shift at about 12mph from 1st to 2nd on the road.

The green is the rolling resistance + drag force.
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Nevermind, just looked in your profile, Civil. I'm starting out a 4 year Mechanical Engineering major at Michigan Tech.

Can't wait until I'll actually be able to apply all stuff I'm going to learn like you.

Very nice.

I'm pretty much self taught with the car stuff, with an ME major though, you'll learn plenty of cool automotive design.

I put all the common knowledge type stuff in there just for anyone who didn't already know, I figure about 90% of the people know bout the torque multiplication and all that. I mainly wanted to share the graphical part and equivalent torque increase. Hopefully it will anwere some questions and help a couple people out. If just one person finds it usefull, then I'll be happy :)
Zero..... You are my hero. I'm a junior in high school and I've been wanting to be a civil engineer for years now. You jsut sealed my case. Physics and math are so bad ass lol. I just love how you can solve for anything with those 2 things. I can't wait til I can apply everything with that. College is gonna be haaaaard though. Oh well, it'll be worth it. Anyway.... that's awesome.

Can u explain to me how gears improve an elapsed time in the quarter mile or 0-60? The graph shows the car getting up to speed faster than the stock gears would get it up to speed, but the graph dosent plot the two gears against elapsed time. can u make a graph that plots the two against eplapsed time?
Last night I been trying calculate shift points for my Stang , and what ever I change there ,result is same, can somebody try calculate for me I have 94 Stang GT vert 5 speed wirh 3800lb and 3.73 and I run 14.8@93

The shift points will only change according to your torque curve and tranny ratios. The rear-end gear shouldn't change the shift point, only the mph where you shift will chage.

HEY did anyone notice the wierd advertisement that was magicly attatched to the word 'automotive' in my earlier post? wtf??

Goto my sig page, the link to the Excel file is at the bottom.
Zero Signal said:
OH. . .regarding a plot of e.t. . . .That's REALLY difficult to do, alot of people have spent years developing software to estemate e.t.'s based on a myriad of information. That's way out of my league!
may be way out of your league but i remember posting a question about identically modded GT's with 2.73, 3.55, 3.73, and 4.10 gears respectivley....and i remember it being undisputed that with each increment in gears it the car would be significantly faster (from a highway roll, disregarding driver error)

It's good to see someone who actually knows something about automotive design/engineering. Too many people go on hearsay, etc. to make descisions regarding their cars. Bad move.

I too am an ME with a few courses in automotive engineering. My prof was a powertrain engineer with GM back in the 80's. He worked on the Corvette design team. Awesome teacher. Total horsepower junkie. He owned a '71 Camaro drag car, his daily ride was a new WRX, his wife drove the (supercharged and now nitrous injected) Grand Prix GTP (which I saw him drag at the track, 'Kiss Me''Kiss Me''Kiss Me''Kiss Me'ty 60's on FWD). I really felt like a learned from the best.

Education on basic principles will only make it easier for you to build a faster car.
beanplant said:
Zero..... You are my hero. I'm a junior in high school and I've been wanting to be a civil engineer for years now. You jsut sealed my case. Physics and math are so bad ass lol. I just love how you can solve for anything with those 2 things. I can't wait til I can apply everything with that. College is gonna be haaaaard though. Oh well, it'll be worth it. Anyway.... that's awesome.


Remember Shaun, Zero did this on his own, Civil Eng. usually does not cover this type of material.

I am a soon-to-be-graduating Mech. Eng., and we have done stuff in a program called MatLab that can actually plot the speed vs. time of a car. Granted the model was very basic, but the tools are there to enhance the code and use your own variables. We could change the: Power and Torque curves, time between shifts, clutch slippage, mass of vehicle, etc.... It was really cool. If I can dig it back up, I'll post some graphs we came up with.

EDIT: Actually now that I think about, It would be a lot easier for me if I started with a rwhp/rwtq graph instead of the engine characteristics. If someone could post their graph, I bet I could use that to graph their theoretical 1/4 mile time or what have you. I could use an estimated time for shifts and allow for some tire slip in the first half of 1st gear.... hmmmm. Interesting...