transmission questions *engineering based not dumb..*

so right now i'm looking at some possibilities of gear my car and all that good stuff. make the gear ratios to be the most efficient and the most drivable to my preference. since i wanna get a 6 spd transmission and be able to run up to 7.5k rpms *will be looking later into how that'll be obtainable* and also getting taller tires. but ne ways to start off with my investigation i had some problems finding the equation since i was missing the final drive ratio which completely threw everything off. but thx to my observations i saw how far i was off and was able to figure out what it was...*with alittle help from my dad.

i was on the internet looking for equations for gear ratio's that'll translate into how fast a vehicle will travel in what gear at what rpm and i was quite disappointed...and being the math wiz *and someday engineer* i decided to figure this out for myself so i came up with the equation. i actually feel kinda like a flippin idiot for taking so long becuz its such a simple equation.

velocity = (time conversion * crank rpms * tire height * pi) / (distance conversion * gear ratio * final drive ratio)

so for those of you that are already lost we'll do first gear, tire height will be in inches, and we want miles per hour so..

(60*6500*23"*pi)/(63360*3.545*3.944)

60 being how many minute are in an hour, 63360 being how many inches are in a mile. *btw this is manual*

*pull out the calculator*

1st gear redlined = 31.81 mph

so for the manual transmission will give me these numbers for each gear redlined

1st = 31.81mph
2nd = 57.77mph
3rd = 88.38mph
4th = 116.137mph
5th = 147.797mph
reverse = 33.834mph...lol

and since no body i know has been able to redline 5th gear, but some have gotten to 120mph which means you would be at approx 5.3k rpms

so as for the auto transmission

1st = 40.328mph
2nd = 73.104mph
3rd = 115.944mph
4th = 166.347mph
reverse = 50.41mph...lol

ok so what i want from you guys is to give me some input of what you've gotten speed wise when you redlined each gear so i can make sure that my formula is correct *cuz i simply refuse to look on the internet for the equation cuz i wanna figure it out for myself... which i still feel disappointed becuz figuring this out was...embarrassingly ez

my auto 3rd gear doesnt go past 108-109.

so then how fast did you get 3rd gear going. and was it actually at redline?

the automatic trans shifted itself at that speed with my foot all the way to the floor.

i have a manual, and 3 gear at redline is about 125km/h-130km/h

Your numbers look correct.
Go to:

http://www.cyberstangs.com/autocalc/calc_mphvsgear.php

I'm using 185/60R14 as the tire size, manual gear ratios:
3.545,1.952,1.276,0.971,0.763
Final gear ratio 3.944.
It doesn't give accurate #'s like you, but the graph values look to match well. The thing I like about the graph is that it tells you the new RPM after you shift gears and what rpm is needed if you wanted to rev match.

The STOCK car is DRAG LIMITED to ~110 mph on flat surface, no wind, stock tire + tire pressure. Anything to increase HP/torque and lower drag and rolling resistance will increase that top speed. I haven't seen anything to say that the car is electronically speed limited.

thx for the input. since all of these numbers *mostly upper gears* are only really obtainable in a place void of all resistance/friction/gravity. and that is a good idea to look into at what rpm's the gears match. i think it'd actually be fairly ez to figure out and i'm gonna look into making the graph for myself...since this equation was too ez...and ne more input would be appreciated. and for those that don't have stock tires just simply take measuring take and get the height.

which i was hearing something interesting from my dad is that by getting a tire thats taller it'll give you better fuel efficiency assuming that he tire isn't heavier*. since every revolution will yield more distance. lol if we find the right gear ratio's and overall wheel/tire height we might be able to match stuff like civic and corolla's.

You should expect to pay more than the car is worth (new) for a 6spd (sequential or not), LSD (might as well, the tranny is out, and you're spending big bucks anyways), and custom gear set.