[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.
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.