Need some help with the math
 

This is just an idea I had regarding tire size and gear ratio.

Let's say that my Ranger has a stock rear end with 3:73 gears and stock 225/70/14 tires. If i wanted to keep my stock tires and go to a taller gear ratio I could change to a 3:45 just by swapping in another rear end. But let's say I need new tires anyhow. Is there a tire size that would give me the same (3:45) gear ratio or would it be so large that it just wouldn't fit in the wheel well? If there is a size that actually would give the desired results then you could fix the speedo at the same time by changing to a 3:45 speedo gear.

Something like taller tire (x)+3:73 gear=stock tires+3:45 gear.

Also swapping the rear end for better gears would mean more energy used from each stop sign/light. Would the loss be relatively the same if you changed the gear ratio by changing tire size instead of changing rear end gears?

Something like:

if stock tires+3:73 gears uses (=) a certain amount of energy (E)
and stock tires +3:45 gears uses (=) more energy (mE), then does a taller tire (x)+3:73 gears use more/less/same energy as stock tires+3:45 gears?

I guess what I am getting at is: is there an advantage to changing the final drive ratio with the tires rather than rear end?

For my driving situation the ultimate would be a rear end swap to 3:45's but I was wondering if there was a tire size that I could go to that would make the equation look like this:

Stock tires+3:31 gears=taller tires (x)+3:45 gears

I am planning a change to 3:45's, but when my tires DO wear out I would love to switch to a tire that would give me the equivalent of the 3:31 gear ratio. That is, if such a tire exists. Then all I would have to do is switch the speedo gear to a 3:31 and my speedo would be in sync and I would have effectively raised my final drive ratio again.

Is there a simple formula like:

Tire size(TS)+Rear Gear(RG)=Final Drive

or

Tire Diameter(TD)+Rear Gear(RG)=Final Drive

If there is then I could play around with different tire sizes and gearing to see what options are out there.

Thanks for the help.

Do both.
That is what I am likely going to end up doing.
I went with 2-3 inch taller tires back in 2008 and at some point I would like to go from a 3.08 rear to 2.73 rear gear also.

If you had 225/70/14 that is a 26.5 inch tire, 3.73 rear end, drove 65mph and had an over drive of 0.7 you would be turning 2152rpm.

If you only changed your rear end to 3.45 gears you would drop your 65mph engine speed to 1990rpm

Keeping the 3.73 and only switching tire size to 29 inch tires would drop engine speed at 65mph down to about rpm 1966rpm.

Going to 3.45 gears and 29 inch tires will drop engine speed at 65mph down to 1819rpm.

Keeping 3.73s and going to 30 inch tires will drop engine speed at 65mph down to 1901.

...the equation:

MPH = [ 60 / (G×A) ]×[ RPM / rpm ]

where:

MPH = vehicle speed, miles-per-hour.
RPM = engine speed, revolutions-per-minute.
rpm = tire speed, revolutions-per-mile [get from tire dealer]
60 = conversion constant, minutes-per-hour.
G = gear ratio of top gear, ie: 1.00:1 or 0.69:1, etc.
A = axle or final drive ratio, ie: 3.55:1 or 3.07:1, etc.

Also remember that a taller tire is going to be heavier (more mass), so acceleration will be more sluggish, and might load your engine more heavily. If you are aware of this it shouldn't affect you unless you do all-city driving, in which case you wouldn't be asking this question.
Just something to be mindful of.

Also you will have less multiplied tq available. When climbing hillsect what you used to climb easily might require a down shift and slowing down. Same with towing /hauling.

Going up in wheel diameter is probably the easiest way to do this. It is often hard to find tires with the same width as your original ones that have a very tall "aspect ratio". Much easier to find tires for larger wheels that have a larger overall diameter and fewer revs per mile.

It looks like what you want is a tire that is (3.73 / 3.45) times as big. That's about a 1.08 multiplier. Look up your current tires on a site like tirerack.com and see what the revs-per-mile figure is. Then search around for tires that have a revs-per-mile figure that is about 0.92 (1/1.08) times the current figure.

-soD

This might be of help to you:

Tire size calculator

Can someone double check my math
 

Thank you all for the help and information.

My drive to work is 60 miles one way on 2-lane blacktops with the occasional stop sign or light. I know there will be some loss when taking off from stop signs/lights, but I think I can make up for it with the longer stretches at 55 mph.

Using soD's math and the tire size calculator from Smurf, these are the numbers I am coming up with.

My stock tires (225/70/14) come in at 764 rev/MILE. If I wanted to go from my 3:73's to 3:45's by only changing tire size then,using soD's math, I would need to find a tire that comes in at 703 rev/MILE. (764x.92)

From the tire calculator these are my choices:
215/75/16 at 703 rev/MILE
225/75/15 at 713 rev/MILE

If I do the rear gear swap to 3:45 and want to get to 3:31, then using the same process I take 3.45 divided by 3.31 and get 1.04 as a multiplier. Using soD's math again I am now looking for a tire that comes in at 733 rev/MILE compared to my stock tires at 764 rev/MILE. (764x.96)

Using the tire size calculator again these would be my options:
225/70/15 at 736 rev/MILE
215/75/15 at 728 rev/MILE
195/75/16 at 733 rev/MILE

If someone could double check my math and I did it right, then I will have to take the next step and research which tire sizes are available from which companies and their overall weight and cost.

Thank you all again for all the help.

I have a 95 S10 with 3.73s, and the kid that owned it before me bumped from 215/75 15s (728 revs per mile) stock to 225/60 16s (757 revs per mile).

Trying to achieve a 3.43 ratio would mean ~688 revs per mile. Taking my 225/60 16s to 225/75 16s gives me 689 revs per mile. Good 'nuff.

With 225/75 16s and 3.73s, I could then swap in actual 3.43 ring&pinion, which would then give me 633 revs per mile. Now we're talkin.

Smurf gives a good example to consider:

A) You can use taller tires/rims to reduce engine speed in highest gear, but that entails bigger/heavier tires (more rotational mass) which may/maynot hurt final mpg results depending upon how many start/stop cycles you have to endure because additional 'rotational' weight (heavier tires) *hurts* acceleration but isn't a problem once you're at speed.

B) You can change the axle (RWD) or final-drive (FWD) gearing ratio, which does NOT increase rotational mass (good thing), but entails mechanical change out of parts, which isn't trival to those who are non-mechanically inclined...and, it's a more permanent type task.

C) ALTERNATIVE "trick" -- temporarily swap TWO tires/rims(*) only on the speed-measuring axle to test/measure the actual engine reduction & increased MPG that you get. Then, if you get results you like, actually do the axle/drive-ratio swap. DIY using decent junkyard parts and the total axle cost & installation is often LESS than four new tires & rims.

(*) NOTE - select "new" size tire/rims that most closely match the "new" axle/drive-ratio 'revolutions-per-mile' (like Smurf mentions) that you plan to install.

• New tires/rims is quickest and easiest route, and easiest to UN-do if you don't like the results; but, might not be the cheapest.

• New axle/drive-ratio is more difficult to both do & UN-do, but allows you to keep & use the tires/rims you already have (if you wish).

• Alternative "test" provides a quick-n-dirty "middle-ground" way to firsst test the results BEFORE doing the more permanent mechanical change-out.


Just a few things to mull over before actually spending your money.