Axle Gearing: How to choose the ratio

[Scott Brady]

For years, people (and many still do) chose axle gearing based on a simple chart. For a 33" tire, you install 4.10 gears, for 35" tires, you install 4.56 gears, etc.

Gearing selection is significantly more complex than that, and is based on engine peak torque (not HP), tire diameter, final drive ratio, desired performance attributes (economy or acceleration), etc.

So I thought is would be helpful to start a thread on exactly how to select an axle ratio.

Step 1: Determine peak torque RPM. For example, the 3.4L Tacoma V6 generates peak torque at 3,600 RPM.

Step 2: Determine tire diameter (32.6" or whatever).

Step 3: Determine overdrive ratio. For the Tacoma automatic, it is .705:1. The remainder is used, so for the calculation it would be 1-.705= .295. The calculation uses the multiplier 1.295

Step 4: Determine maximum desired cruising speed in MPH. This is not desired top speed, but cruising speed. For me, it is 80 mph

Step 5: Determine if you want power or economy. If you want power than multiply your peak torque RPM by .85. If you want economy, multiply your peak torque RPM by .75. (Example: Power= 3,600*.85= 3,060)

Step 6: Calculate required ratio:

Formula=

Gear Ratio = RPM x Tire Diameter x overdrive ratio remainder
MPH x 336

So for the examples above:

1. 3060 x 32.6= 99756

2. 80 x 336= 26880

3. 99756/26880= 3.711

4. 3.711 * 1.295= 4.81

4.81 is the desired axle ratio. 4.88 is a typical production ratio, and would be ideal.

Here is another example: peak torque= 3,200 rpm, tire diameter=30.8, overdrive=.80, desired cruising speed=75 and the owner prefers power over economy.

1. 2720 x 30.8= 83776
2. 75 x 336= 25200
3. 83776 / 25200 = 3.33
4. 3.33 * 1.20 = 3.98 ratio

Last example: My truck: peak torque= 3,600 rpm, tire diameter=33.2, overdrive=.705, desired cruising speed=75 and I prefer power over economy.

1. 3060 x 33.2= 101592
2. 75 x 336= 25200
3. 101592/25200= 4.03
4. 4.03 * 1.295 = 5.22 ratio

How does your vehicle equate?

[articulate]

Not to be a tweaker, but is the formula supposed to look like this?
http://www.markdstephens.com/images/formula.jpg

So, if I'm using 4 beautiful BFG AT 265/75r 16 tires on my Frontier, I come up with the following ratios:
Power = 5.01
Economy = 4.42

(according to BFG, this tire measures a full 32"...)

4.88 would be nearly an exact meet-me-in-the-middle solution, as well as a popular axle ratio. Very interesting.

So, where's the formula that gives us $1200 for the re-gear? :sunflower

Cool stuff!

Mark

[Scenic WonderRunner]

I found this link below useful when I was upgrading from my stock 225 tires to my 31" / or. There were some other good calculator Links I used......when I find them I will add them here.

I have 31x10.50x15 tires (Cooper All Terrains....but hey!.....they were practically free!).....I have an Auto with Overdrive.....so at 65mph with O/D on.....I'm only turning 2,450 RPM.....with Factory Stock 4:10 Gears.

Scott..........I'm not saying your formulas are not perfect or correct............I'm sure they are dead on! I'm just sharing links that I had found (quick look) when I was trying to decide on tires but really didn't know anyone to ask. It would be interesting to compare your "Dead ON" Formulas to the chart Links.....and see if they really know what they are talking about.



Gear Ratio & Tire Size Chart (http://www.4lo.com/calc/geartable.htm)<~this one is great because it helps you decide between Better Gas Mileage to More Power.


Axle Ratio/Tire Size Calculator 1.1 (http://www.4crawler.com/4x4/4LoCalc.shtml)

[Scott Brady]

Thanks Mark, that is exactly how the calculation should look. I will use your cool image from now on.

I put together this method a few months ago after doing some research. There were no good calculators for determining the correct gear ratio based upon engine torque and driving style. So, this was my attempt.

[pskhaat]

Okay, so this might be an anomoly, but in my imaginary world I have a Toyota FJ60 that has a gasser 4.2 I6 (2F) engine in it that peaks torque at 1800 RPMs and I'm in it for power, if I want to run 35" tires @75mph and final drive ratio (tranny) in 4th is 1.0 I come up with a ratio of 2.125.

Is my maths correct? In the case for low torque engines like the Toyota 2F and diesels, there may need to be a sliding scale or factor applied.

Now this all said, that FJ60 performs best stock with 3.73s at 55mph and IMO simply wasn't made for comfortable highway speeds :)

[articulate]

Okay, so this might be an anomoly, but in my imaginary world I have a Toyota FJ60 that has a gasser 4.2 I6 (2F) engine in it that peaks torque at 1800 RPMs and I'm in it for power, if I want to run 35" tires @75mph and final drive ratio (tranny) in 4th is 1.0 I come up with a ratio of 2.125.

Is my maths correct? In the case for low torque engines like the Toyota 2F and diesels, there may need to be a sliding scale or factor applied.

Now this all said, that FJ60 performs best stock with 3.73s at 55mph and IMO simply wasn't made for comfortable highway speeds :)
Isn't the FJ60 an "older" one? Back in the day, weren't normal highway speeds 60 mph or so?

On one of Mark's (Senor Scenic) links, there is this simple formula, too:
http://www.4lo.com/images/geartire-formula.gif
This one assumes you want to have similar performace to factory specs, and is a simple proportional guage: if your tires go up so much, then your gearing goes down so much.

Scott's version - as we all expected - is far more advanced and likely produces a much lower gear ratio than in the simpler formula above; well, excepting pskhaat's machine. MAN! I could eat at Brady's table-o-knowledge any day of the week... :chowtime: The thinking never ends with this guy.

Anyway, I believe I've found another fine line between geeky and hardcore. Back when that FJ60 first came out, there was a vast difference between geeky and hardcore. Now these two are interchangeable - if not the same :)


Cheers,
Mark

[Scott Brady]

Okay, so this might be an anomoly, but in my imaginary world I have a Toyota FJ60 that has a gasser 4.2 I6 (2F) engine in it that peaks torque at 1800 RPMs and I'm in it for power, if I want to run 35" tires @75mph and final drive ratio (tranny) in 4th is 1.0 I come up with a ratio of 2.125.

Is my maths correct? In the case for low torque engines like the Toyota 2F and diesels, there may need to be a sliding scale or factor applied.

Now this all said, that FJ60 performs best stock with 3.73s at 55mph and IMO simply wasn't made for comfortable highway speeds :)

Your math is correct. The formula is intended to focus on the greatest efficiency of the motor. So, either you would have to sacrifice efficiency by reving the motor above peak torque, or 75mph is not really feasible with the combination you indicated. I do not remember ever driving at 75 mph in my 60. :elkgrin:

BUT, having said that, I will look at including the actual torque number, but then it would have to be adjusted by the curb weight (to factor a torque value per pound).

I have to do some work :)

[flyingwil]

There is also an article on this in the April edition of Four Wheeler Magazine. However, the above posts, have better information! Way to go guys!

[DaveInDenver]

Yeah, pskhaat, I get the similar results when I run this with my truck. The 22R-E torque peak is 140 lb-ft at 2800 RPM. I want power, 75 MPH is plenty for me , I have 0.85 overdrive in the W56 tranny and run 33x9.50 BFG (so I use 32.6").

The formula says I should use 3.56:1 ratios. No way a 22R-E is going to move a truck down the highway in 5th gear on 33" tires with 3.56 gears.

But if I use the HP peak of 115 HP at 4800 RPM, I get a 6.07:1 ratio. I went with 5.29 with my 33" tires and I think that's pretty decent. At least 5.29 does accomplish 75MPH without much fuss.

Since HP is calculated by:

HP = torque (lb-ft) x 2 x pi * RPM

Using HP is taking torque, but adding time. Since it's not instantaneous force (torque is just force through an angle), but the rate of sustained force that moves the vehicle, I think using HP can make more sense.

But also using torque and not HP deals only with the rolling resistance (which is basically constant at all speeds) of the truck, not the aerodynamic drag (which is exponential with speed). Starting a truck from a dead stop (or overcoming an obstacle) requires immediate torque, but keeping it moving at some speed is power (i.e. sustained force over time). Since you gear a truck to put the engine in the right RPMs to move the truck on the road, I'd think it's available HP that is going to determine how easily it is to move your your lifted brick moves down the road through the air.

Mixing in efficiency is whole new game. That point is probably no where near either the HP or torque peaks. My guess is that you want to pick some number between peak torque and peak HP to use as the engine's peak performance point. That's probably the skew that's needed, to determine how much to skew between the torque and power. What the number is going to be different for all engines, so the bias needs to be built in at steps 1 and 5 in the original calculations.

Sorry, just thinking out loud. Feel free to ignore if it's total bunk.

[Scott Brady]

Great post Dave. As the variables are considered, my formula appears to only work with a modern DOHC V6 :mad:

So, it will be fun to consider other options of calculating the result.

[DaveInDenver]

Yeah, Scott, what's curious is that the R motors are SOHC, aluminum heads, etc. They are positively modern compared to the 2F in the FJ60, so why exactly the results for my '91 (with EFI, even) and pskhaat's Cruiser jived rather than with your 5VZ is a bit baffling. Most likely I think it's the overdrive ratio.

I'm not sure there's a perfect absolute formula here. At least, I think you need more variables to make it more universal, probably including more engine characteristics or different variable for stick and automatic. You need to use internal losses, which for the engine is going to be implicitly accounted for in the HP numbers anyway. I do think using HP is the key over torque, though. Just curious, why do you specifically use torque and not HP?

I was messing with your formula a little.

If you completely remove the 0.75 and 0.85 RPM multipliers for performance verses mileage, my results are 4.16 & 7.14. No help there.

If I use the mileage multiplier I get 3.12 and 5.36. That last one is interesting because it used 0.75 x HP peak and produced almost the exact ratio I ended up using. Not sure if that's not just coincidental, though. But still it sparked an idea...

My thought was those fraction of peak modifiers. Those are the key to the formula I think.

I wondered what would happen if you use 0.65 (MPG) & 0.75 (power) of peak HP? So, I did that.

I found that when I use 75MPH top speed, peak horsepower RPM, a 0.65 multiplier (for economy) and 29" tires that I get 4.13 ratio. Which is incidentally the ratio that Toyota put in my truck from the factory with the original tires (225/75R15 is about 28.5).

Feeling lucky, I put my current parameters through (32.6" tires, left top speed at 75MPH) and it gives me 4.64 for mileage and 5.36 for power. Again, pretty cool, since the charts all tell me to use 4.56 with 33" tires to retain stock gearing and I used 5.29 and feel like I'm driving a Japanese Power Wagon.

Finally, I put in your parameters (32.6", 0.705 OD, 80MPH top speed) and left the HP peak at 4800 (the 5VZ-FE had a peak of 190 HP at 4800 RPM) and it pops out 4.90 for mileage and 5.65 for power. The multipliers were still 0.65 and 0.75.

Tweaking the multipliers to 0.64/0.74 gives me the ratios of 4.57 and 5.28 for a 5-speed at 75MPH. If I use 0.60/0.70 for your truck with the 0.705 overdrive automatic, I get 4.82 and 5.63 for 75MPH and 4.52/5.28 for 80MPH.

Interesting, eh?

[Scott Brady]

I do think using HP is the key over torque, though. Just curious, why do you specifically use torque and not HP?


Typically, modern engines operate at their greatest efficiency at 80% of peak torque. Torque (rotating mass and force) has a greater influence on sustained speed than HP does. HP is an RPM tool (watts), especially in a DOHC gas motor, where the RPM band is much wider than a diesel.

So, I am of the opinion that torque is the most critical asset of a motor (for our purposes) as it is the turning force of the engine (ft-lb or N-m). :)

[Scott Brady]

But, yeah, that's my point. Dynamometers don't measure HP, they measure torque and RPM, leaving HP to be calculated from that. Calculated pwer is completely dependent on measured torque.

Well said, and the reason I choose not to refer to HP, as torque is the true unit of measure we are most interested in.


BTW, the definition of torque is not force through a rotating mass, but actually a force at a point through a lever arm (a vector and an angle). Power is produced by applying a torque through a rotating shaft. The rotational speed of the shaft is RPMs and that's where the time component comes in. That eventually translates to work by applying the power to the wheels and actually moving the truck.

Thank you for the additional detail. The rotating mass of the motor is what generates the torque, which is measured as force (which you indicate in the lever comment above). That is why I referred to the rotating mass, not as the unit of measure, but as the physical action.

As you mention, HP is a calculated measurement:
http://www.straightdope.com/mailbag/Equation1.gif

A foot pound of torque is defined as the twisting force necessary to support a one pound weight on a horizontal bar (which has no weight), one foot from the fulcrum.


So engineers determine how much power is required to do something and then design an engine or motor that generates enough torque at some desired operating RPM to do that. It's all interdependent.

I'm wondering where the 80% of torque peak comes from? Has this got to do with the volumetric efficiency at some RPM? I honestly don't know, just asking.

As you mention, a vehicle motor is designed for a specific task and operating range. So I took the liberty to assume (:p ) that peak torque would provide the greatest performance within that range (reasonable), but not necessarily the greatest efficiency (not all of the energy is required for cruising). Cruising at 80% (2,880) of peak torque (3,600 rpm) for my Tacoma 3.4L generates the greatest MPG, and leaves a range of about 1,000 rpm's for climbing and passing. After 1,000 rpms above 2,880 the torque band drops considerably, and I am only left with (time or RPM) in the power equation, but force dips...

[pskhaat]

As to the HP vs Torque debate, a factor that can be generically used (and multiplied by something to scale out) is the stroke/bore ratio. An overstroked engine will live better on lower revs and generate lower torque curve vs an overbored engine which can pump the RPMs and have it's torque higher in the RPM range.

2F = 102mm/94mm = ~108.5%

Which could somehow be used as a multiplier to raise/lower the gear ratios. But we always have the anomolies like this:

22RE = 89mm/92mm = ~96.7%

Which means the gears would be even lower against intuition on the 22RE. Okay, let's keep on going. Maybe the rated torque/hp max:

2F = 3600rpm/1800rpm = 2
22RE = 4600rpm/3400rpm ~= 1.35

Combine them linearly and get a correction factor of

2F ~= 2.17
22RE ~= 1.31

For the orignal posts where the 2F was listed at 2.125 with the correction factor comes ~4.61 for the 2F (not bad). For the 22RE listed at 3.56 is ~4.66 (not bad).

Thoughts on the correction factor of:

(stoke * HP peak) / ( bore * Torque peak)

[flywgn]

Here's a link to a site I've used for a couple of years.

http://www.4lo.com/calc/gearratio.htm

Allen

[DaveInDenver]

Just got back to the computer and read the last couple of posts. Don't really have anything to add at the moment (be sure that I'll reread them and let it bounce around the noodle for a while, tho), but just wanted to say that this is pretty interesting and a neat thread. I like the idea that others around go to the same over analysis to figure out something like gear ratios! :-)

[Hornito]

"Cruising at 80% (2,880) of peak torque (3,600 rpm) for my Tacoma 3.4L generates the greatest MPG, and leaves a range of about 1,000 rpm's for climbing and passing."

Hey Scott, how did you determine this? I can see how this would apply to inclines, but it would seem that 2000-2500 rpm would be more economical. I regeared to 4.56 with the AT, V6, 33's and moderate gear/armor, and on a flat piece of hwy I can do 75 at about 2300 rpm in OD. Are you suggesting that 488s would result in better fuel economy at the same speed?

Thanks!

Hornito

"Alcohol: the cause and solution to all of life's problems."

H. Simpson

[Scott Brady]

80% of peak torque is ideal for a DOHC motor in a heavily loaded truck. I worked from by ideal cruising speed back (70 mph or so), along with tire size to determine the appropriate gearing.

DOHC motors (most gas motors for that matter) are not efficient when they are being lugged down.

I gained about 2-3 mpg back by going to 5.29 gears, as the motor is back operating in the power band.

HTH.

[Shovel]

heh, this is something that was discussed at almost comical length on Vmag back in the 90s.. I think it was most simply put that 2000 rpm with your foot 3/4 into the gas pedal is less efficient than 3000 rpm with your foot only halfway in :Mechanic:

[DaveInDenver]

Hey Scott, how did you determine this? I can see how this would apply to inclines, but it would seem that 2000-2500 rpm would be more economical. I regeared to 4.56 with the AT, V6, 33's and moderate gear/armor, and on a flat piece of hwy I can do 75 at about 2300 rpm in OD. Are you suggesting that 488s would result in better fuel economy at the same speed?

Don't confuse the engine speed where you're consuming the least amount of gas as the most efficient engine speed. Efficiency is a measure of fuel consumption against power produced. So while you are consuming less fuel at 2000RPM than 3500RPM, the engine is also producing less power. If your engine makes sufficient power through its power band that at a lower RPM it can use a lower RPM and still move the truck. The engine isn't running at it's most efficient RPM, but it's also consuming less fuel and so your economy will be fine.

It's hard to visualize, but look at it this way with a generic engine (apparently a diesel).

At 1000RPM it makes 100ft-lb and burns 1 ounce/min, that's 19HP and 19HP per ounce per min
At 2000RPM it makes 125ft-lb and burns 2 ounces/min, that's 48HP and 24HP per ounce per min
At 3000RPM it makes 150ft-lb and burns 3 ounces/min, that's 86HP and 29HP per ounce per min
At 4000RPM it makes 135ft-lb and burns 5 ounces/min, that's 103HP and 21HP per ounce per min

So the most efficient point is at 3000RPM, since you are making the most power per fuel burned. If the job required 50HP to produce the work, then 2000RPM would be fine and you'd consume less fuel. If the job required 75HP to produce the work, then the engine will consume more fuel but still be within its efficiency curve. If the job took 105HP, the engine might still do it but burn a ton of gas. Since the real work done is measured at the wheels, the idea of gearing is to put the engine at it's optimal speed to produce sufficient power to do the work. What that ideal gearing is depends on how fast you want to go, how much reserve power you want to keep, etc.

[TeriAnn]

DOHC motors (most gas motors for that matter) are not efficient when they are being lugged down.


Sometimes there's something good to be said about old school. Low tech V8s like to cruise in the mid 2000 RPM area and usually achieve their best fuel mileage there. From the factory they tend to have a wide power band and plenty of power to push most trail rigs. I personally am a fan of wide power bands & reserve power. My 302 Ford V8 does all that just fine. If I need more low end torque there is always a stroker kit. Being a law abiding slow poke who prefers to drive past filling stations, I tried to set my gearing for maximum economy at 65 MPH.

The charts & formulas you have been sharing don't really lend themselves well to Land Rovers which is why I thought I would inject my two cents worth into this thread. Also Land Rover engines are old school technology (designed in the mid 1950's) with fairly wide power bands.

The high range of a Land Rover transfer case is an under drive which varies by model and engine used. There are just a few R&P ratios available for Land Rover axles (3.54:1, 4.1:1, 4.7:1, 4.75:1 (much stronger than the 4.7:1) and I think someone has come up with another around 3.9:1). As modifiers there are a couple overdrives available that can split all gears and Ashcroft Transmissions offers a hi ratio transfercase conversion for the Series transfercase that is an overdrive in high range but does not affect low range ratios.

Here's some ratio charts for Land Rover gearboxes & transfer cases (http://www.expeditionlandrover.info/gear_ratio.htm)

Here are some ratio charts for gearboxes commonly used with Land Rover engine swaps (http://www.expeditionlandrover.info/gearboxSwap.htm)

To figure a Land Rover's axle ratio you need to multiply your gearbox ratio times your transfercase ratio times your R&P ratio. I like to plug the axle number into the bottom calculator on this web page. (http://www.csgnetwork.com/multirpmcalc.html)

I found the stock Series Land Rover low range first gear ratio (40.7:1) to be too tall for most rock crawling and many climbing situations. Having 8 years experience with a 70:1 ratio I have found it to be too low for anything but the most technical rock crawling situations (with 33.3 inch dia tyre). At this time I'm leaning towards somewhere around 55:1 as being the best overall low range ratio for use in many different situations with 32 - 34 inch dia tyres. That low range ratio seems to fit Land Rovers well.

My advice to Land Rover folks in general is to pick a gearbox, transfercase and R&P that best anchors a low range first gear near 55:1 and high gear for best economy at normal highway cruise and fine tune with the tyre diameter. Most Land Rover folks are concerned about fuel economy as 15 - 16 MPG is the highway norm for Series rigs and aspired to by coiler owners.

[DaveInDenver]

Sometimes there's something good to be said about old school. Low tech V8s like to cruise in the mid 2000 RPM area and usually achieve their best fuel mileage there. From the factory they tend to have a wide power band and plenty of power to push most trail rigs.
I don't know that this is a uniquely V8 characteristic, but rather a displacement and size question. Old, big displacement inline engines share a lot of the same characteristics, low RPM torque peak, etc. As the displacement goes up, the bore and/or stroke increase and that has as much or more to do with the performance of the engine as does the piston configuration.


My advice to Land Rover folks in general is to pick a gearbox, transfercase and R&P that best anchors a low range first gear near 55:1 and high gear for best economy at normal highway cruise and fine tune with the tyre diameter.

This is good advice. You gear the axles so that you are comfortable on the highway and the tranny/xfer low-range are geared for off highway. Too often people try to get lower crawl ratios by putting very low gears in the axles and I think that is short sighted. BTW, I run a 45:1 low-low and think your 55:1 is not unique to Rovers. I think this turns out to be a pretty good ratio for a lot of trucks.

[ntsqd]

The way I figured out what ratio would be ideal for the Ballena Negra was to find what the stock tire specs were. Then I worked out what kind of RPM that resulted in at the various speeds I tend to drive.
I then worked things backwards using my new tire size.

The base for my approach was a reasonable assumption that GM's engineers knew the engine & trans combo better than I do & would have set up the axle ratio and tire size combos such that the engine would be at or near it's best BSFC at legal highway speeds.

[ntsqd]

Optimizing mpg at cruise speeds was my goal for the Ballena Negra.
One must keep in mind that if the engine is operating at it's best BSFC RPM that it is going to get the best mileage it possibly can at that vehicle speed, regardless of any other factors. Those other factors do have a subtractive effect, but changing the RPM in either direction will result in an MPG loss.

In re-reading this I realize that I should define BSFC. It stands for "Brake Specific Fuel Consumption." It's units are typically lbs-hr/HP. In an SI engine best BSFC occurs at the torque peak RPM. I suspect this to be true of diesel engines too, but I can't state it with certainty.

Were towing or hill climbing ability my goal I would still use the same process, but then after finding the stock equivalent gear ratio I would look at the available ratios one to two steps lower (higher numerically). If you're looking for tow capability then you would want to use the towing package ratio for comparison, if available. If this mod is made I would then still operate at the best BSFC RPM and accept that cruise speed would be reduced.

The reason behind my approach is that finding torque & HP curves for OE engines in light duty vehicles has not proven to be all that easy to come by. Finding the stock tire size & axle ratio combos is.

[DaveInDenver]

The reason behind my approach is that finding torque & HP curves for OE engines in light duty vehicles has not proven to be all that easy to come by.
An aside, ExPo-member Brian McCamish has aggregated them for several small Toyota engines.

http://www.brian894x4.com/Hiluxengines.html