Help with some final drive math
 

Hello again,

This being laid up with a broken foot is giving me way too much time to think.

I was looking for an article about how to figure out final drive ratios and ran across this on a website.....

"Because transmissions are comprised of several gear choices, the transmission allows the vehicle to accelerate quickly with lower gears and to maintain a cruising rpm using higher gears. In the '60s and '70s, most transmissions offered three or four gears with a 1:1 high gear. Using a TH400 as an example, First gear is 2.48:1, Second gear is 1.48:1, and Third gear is 1:1. Multiplying the 2.48 First gear by the 4.10 rear axle results in a final drive ratio of 10.16:1 (2.48 x 4.10 = 10.16). For most street performance applications, a 10:1 final First gear ratio is usually considered optimal. The disadvantage of operating a 4.10:1 axle ratio on the street with a 1:1 high gear is excessive freeway engine speed.

Fortunately, today's transmissions frequently utilize Overdrive high gears in the neighborhood of 0.70:1, which allow reduced engine speeds. Combine these overdrive transmissions with a 4.10 axle ratio and you have a fuel-friendly final drive ratio of 2.87:1 (4.10 x 0.70 = 2.87) in high gear. A TH200-4R overdrive automatic utilizes a First gear of 2.74, a Second of 1.57, a Third of 1.00, and a 0.67 Overdrive. With this transmission's First gear ratio of 2.74 combined with a 3.73 axle ratio, the final drive ratio >> yields a 10.22 (2.74 x 3.73 = 10.22). In overdrive, the final drive ratio equates to a Bonneville-ready 2.49:1."

I'm assuming what they mean by "Bonneville ready" is that it will really accelerate and by "fuel friendly" they mean better than at 1:1 in third. But is a 2.87 final drive really fuel efficient? I have no clue in this area.

Using the formula above, I figured my final drive as this

(rear gear) x (OD gear) = final drive
3.73 x 0.79 = 2.94 final drive

I have been thinking about a rear gear change and the math brings me....

3.45 x 0.79 = 2.73

and

3.27 x 0.79 = 2.58

What I don't know is how my new tire size affects this number.

My stock tires are:

225/70/15
approx. 27.5" diameter
approx. 745 rev / mile

The new ones are:

235/75/15
approx. 28.9" diameter (+5%)
approx. 710 rev / mile (-5%)

To figure the final drive with the new tire size do I adjust the stock final drive by that same 5% ?

What I am wondering is this.....

If I can adjust by the 5% difference in tire size I think this is what I come up with for final drive numbers.....

3.45 x 0.79 x .95 (5% reduction from 100%) = 2.59

and

3.27 x 0.79 x .95 = 2.45

Interestingly enough, the stock 3.27 and the tire size adjusted 3.45 final drives are nearly the same. And the tire size adjusted 3.27 final drive is slightly taller than the "Bonneville ready" final drive from the original post.

What these numbers mean I don't know. Can anyone shed some light for me?

Gear Ratio Calculator
By bonny ready they mean its geared to hit 300 in overdrive or some high speed. But yeah pretty much towing capacity will go down and will make you question if you're really driving a truck anymore, but the lower the rpm the better the fuel economy.

Yes. The tire is like another gear in effect.

I don't tow anything and only use the bed for light loads. Home remodeling supplies and household stuff if one of my kids moves or gets married. I'd rather have the bed and not need it much than not have it and need it sometimes.

So, effective gearing will also depend on tire size and engine torque/HP.

Consider this:

Honda K20 engine = 200HP, 2 liters, ~142ft-lbs of torque
Honda K24 engine = 200HP, 2.4 liters, ~170ft-lbs of torque

The K24 and K20 produce the same peak horsepower. The K24 does it at 20% lower RPM by having 20% more torque from its 20% large displacement. Therefore, to have the same power in every gear, it could have a 20% taller final drive. It would feel the same as the K20.

Or, in other words, the K24 at 2500rpm "feels" the same as the smaller K20 engine if that's spinning at 3000rpm, gearing adjusted by 20%. Both engines would have almost identical driving characteristics.

~

The engine I'm putting in my Insight is from a 2008 TSX. The TSX transmission has a very short 4.764 final drive in part because the K24 is a very high revving engine and Honda wanted it to feel "sporty", but also because the TSX has relatively large 215/50r17 tires, which have an 80" circumference, and a very tall 0.659 6th gear. This results in ~2700rpm @ 65mph in 6th gear, and a very short 15.5:1 ratio in 1st gear.

Moving this engine to my Insight, which has smaller 70.5" circumference wheels, results in ~12% shorter effective gearing due to the change in tire size alone. Highway RPM goes up to 3075rpm because the tires are smaller, and each turn of the engine takes the car less distance.

To compensate for this, I'm replacing the 4.764 final drive with a custom-made 3.4 final drive - absurdly tall for a 4 cylinder. I'm also replacing the 0.659 6th gear with an even taller 0.647.

4.764 x 0.659 = 3.14
3.400 x 0.647 = 2.20

Transmission gearing will be 42% taller, or from a different perspective, RPM will be 30% lower in every gear. However, the tires are 12.2% smaller which partially negates this. So, effectively I'm getting 24.7% taller gearing if I include the the difference in tire size, or 21% lower RPM in every gear.

With the smaller tires, 3.4 final drive and 0.647 6th gear, I can expect 2140rpm @ 65mph. If I change to 185/65r14 tires, which are ~5% larger, I can expect ~2040rpm at 65mph.

So I can effectively get the 3.27 rear gear advantage with the taller tires and the 3.45 rear gear. This may have just made my choice for me. The 3.27 with the taller new tires may be too much gear from a stop. My everyday drive may be 80% highway and 10% freeway, but it is broken up by a couple of small towns. And my weekend driving is nearly all in town. If I go with the 3.45 and taller tires and see an FE improvement, I can switch to a 3.27 and go back to a lighter stock size tire when I wear out the current tires. I've only got about 5k miles on them now.

Yep, that's how it works.

Be aware that taller tires are heavier and have more of that mass farther from the center of rotation, and thus will impact city fuel economy a bit differently (more) because of increased rotating mass - it effectively makes your truck a lot "heavier". However, 5% bigger tires will affect RPM in the same way that 5% taller gearing does, and will be effectively identical on the highway (all else equal) where you won't be accelerating and decelerating.

From another thread of mine, my rpm numbers with the 3.45 look similar to your final numbers Ecky.

2270 rpm / 55 mph / 4th gear (1:1)
2127 rpm / 65 mph / 5th gear (.79)
1793 rpm / 55 mph / 5th gear (.79)*

*about 80% of my daily work commute

For what it's worth, my Insight has a 1.0L engine. It has a 3.208 final drive and 0.710 5th (top) gear. With its default tire size the engine is turning at 2217rpm @ 65mph, and 1875rpm @ 55mph. That works out to approximately 4.5% shorter than your truck's gearing. Pretty close indeed, and my new engine/transmission will be even closer.

Another important factor, it weighs 1850lbs, and has 66ft-lbs of torque. That works out to around 71ft-lbs of torque per ton.

With the IMA in place (which I've removed) it had 90ft-lbs of torque. That works out to 97ft-lbs per ton as the target Honda was aiming for.

With the IMA, the car was spunky and fun. Without, it's pretty slow, but accelerates fine if you wring it out.

Your truck weighs in at ~3100lbs (?) and 135ft-lbs of torque (?), best I could find. That works out to ~87ft-lbs of torque.

Or, in other words, you have about 25% better power to weight than I do right now ;) but I'd consider your gearing to still be quite tall.

EDIT: If you have a 3.45 right now, to have similar gearing to my Insight (in terms of power to weight, ability to accelerate in each gear) you'd need a 2.76 final drive.

My current rear gear is a 3.73 giving me a tire adjusted final of 2.80

Oh Deer weighs in at 3100# and the 2.3l Duratech had 143 hp and 154 ft/lbs of torque according to the internet.

What's your tire size? I'll run some numbers.

Tire size and all my math are in the first few posts but they are 235/75/15

Just want you to have all the numbers I came up with.

So, I'm going to duplicate some math here, and it's to help me wrap my head around everything.

My Insight:
FD - 3.208
1st gear - 3.266
5th gear - 0.710
Tires - 165/65r14
Weight - 1850#
Torque - 67ft-lbs
Power to weight - 72ft-lbs/ton

Your truck:
Current FD - 3.73
Proposed FD - 3.45 and 3.27
1st gear - 3.72
5th gear - 0.79
Tires - 235/75r15
Weight - 3100#
Torque - 154ft-lbs
Power to weight - 99ft-lbs/ton


Comparatively speaking,

With your 3.73 FD, your RPM in 1st and 5th gear are almost identical to my Insight's. You have 42% better power to weight in 1st gear, and 37.5% in 5th gear, taking tire size into account.

With a 3.45 FD, you'd have 31% better power to weight in 1st gear, and 26% better power to weight in 5th.

With a 3.27 FD, you'd have 25% better power to weight in 1st gear, and 20% better power to weight in 5th.

Taking tire size into account, to have the same power to weight in 1st gear (and thus effectively equally "tall" gearing) you'd need 2.63 final drive. To have the same power to weight in 5th gear, you'd need a 2.71 final drive.

Or, in other words, even with a 3.27 FD and bigger tires you'd still have considerably more power in every gear than I do. I'll admit that I could do with a slightly shorter first gear without the IMA to help, but it's very drivable.

Totally up to you just how tall you go.

Thanks for making my decision hard again. :p

Based on Ecky’s work, you’d about be able to get away with a 3.08 FD and still accelerate as well as a G1 Insight, but at much much lower RPMs...

Which is to say not very fast at all. :turtle:

I just don't want to be too slow. The little towns I pass through lead directly into two lane blacktop with few if any safe passing zones. Slowing down other drivers also on their way to work could result in someone trying to pass in a sketchy area. I can't control other drivers but I don't want to make a bad situation worse if you know what I mean.

Any idea on how slow I might be from a dead stop with the 3.27? After reading all this great information, I am again leaning towards that. Unless it's still going to be a turtle.

I can probably improve acceleration by freeing up some usable hp with an e-fan and maybe an aluminum drive shaft. Building a hybrid M5OD-R1/HD transmission would definitely help but be pretty expensive.

A hybrid R1/HD trans? The only different variation of the M5OD-R1 that I know of is the one behind the 4.0V6, which has a taller 1-3 gear...

You got any more info?

That's the one. If I read this article right, it's a remote possibility for my truck. When I win the lotto that is. LoL

How to replace a M5OD-R1 with a M5OD-R1HD

Basically, in terms of power to weight, your 5th gear is like my 3rd gear (closer to my 3rd than 4th). If I want to accelerate like you can in 5th right now, I downshift to 3rd. If I want to accelerate like your 3rd gear, I downshift to 2nd. I just have 2 more gears on top of your 5th gear for economy, while effectively having not as many choices in the middle.

My car still scoots in 1st and 2nd. I can just leave it in 1st and 2nd much longer.

EDIT: So it would be somewhat akin to your new gearing being something like:
1.25st gear
2.5nd gear
3.75rd gear
5th gear
6.5th gear

My only concern with taller gearing personally would be whether you'd go past the point where you can no longer reasonably use 5th gear, but I don't think you'd be anywhere near that with a 3.27. Maybe with a 3 or less.

My 2 cents.

I always take too slow as an opinion coming from owning a 2400lb civic with low compression with a CX trans that spun like 2100 in 5th at 70 lol

2100 rpm in 5th at 70 mph is somewhere near both the 3.27 and the 3.45


3.27 = 2151 rpm (55 mph/4th gear)
1700 rpm (55 mph/5th gear)
2016 rpm (65 mph/5th gear)

3.45 = 2270 rpm (55 mph/4th gear)
1793 rpm (55 mph/5th gear)
2127 rpm (65 mph/5th gear)

My Ranger at 3100 lbs would be slow then? If I'm reading you and Ecky right it sounds like a bit of a balancing act.

One perspective is that RPM is really just the number used to determine the relationship between engine torque and vehicle weight. If you have a heavier vehicle but the same engine, you'd need more RPM for it to drive the same. Conversely, if you put a bigger engine in your vehicle, you need to reduce RPM for it to feel the same, and for the engine to be similarly loaded. But, this is why you have a set of different gears to choose from. And you can't directly compare RPM of your truck to that of a Civic in a given gear.

Lowering RPM has a very similar effect on economy and feel to downsizing the engine.

EDIT: A great example is the 2018 Corvette. It weighs 3600# - more than your truck. Its rear axle ratio is 2.41. 8th gear is a very tall 0.65. It has big tires - 20 inch rims, in fact. In top gear it's able to cruise along at 1330rpm @ 65mph. It's a very fast car, but some have reported seeing upwards of 40mpg on the highway despite having a monstrous supercharged 6.2L engine. It can still accelerate well in lower gears, but it's nice top have that top gear and tall final drive for relaxed, efficient cruising.

I see what you are saying Ecky, but a Corvette has more torque than my Ranger. Even with the really tall rear gear it has no problem getting up and moving from a dead stop. I'm assuming that it's lower gears are rather short and with 8 gears to go through, the transition from short lower gears to really tall FD must be mechanically easy.

I only have a couple of gears before I make the jump to 1:1 and then to FD. I really want the 3.27, but I guess it's fear of the unknown and the cost involved to find out if it was a bad idea. But the flipside to that argument is going with the 3.45 and finding out I would have been fine with the 3.27 and pining about having to pay for the same swap all over again.

Now my head hurts too.

I'm good at making people's heads hurt. :D

Seems to me you can either:

1) Go with the safe 3.45, and worry you might have saved more fuel with the taller gear, or...

2) Go with the less safe 3.27, and risk feeling like your truck accelerates too slowly.


I expect the 3.27 will be fine, personally, but I also have very low expectations on how a vehicle should accelerate.

You’re overthinking it... get the 3.27FD, and if it feels too slow, then go for some mods that free up power(alum drive shaft, clutch fan delete, tune, etc)... find some light weight wheels to swap on for an extra kick...

I like this idea.

Even better, OP could downsize tires just a little next time they're up for replacement. That would help tremendously. Double whammy of increasing RPM, and greatly reducing unsprung/rotating mass.

I got a suggested mod list...(got me dreaming cause I had two Rangers)

3.08FD
205/65 tires on 15x7”RPF1
Alum driveshaft
Clutch fan delete
87oct tune(for enabling e-fan)

And then do a 4/5 drop and clean up the aero... 45mpg anyone?

For the most part you wanna stay in max bsfc and produce the lowest horsepower needed to propel the car at x speed.. The civic was between 1750-2150 max output per g of fuel. Even the LS1 is something like 36% efficient at 2000 rpm at 70 mph which is fantastic and why like half the ls1 cars get 30 mpg on the interstate with their 0.50 6th gears. Even the new c7 corvette went more extreme and went to a 0.40 7th speed. But yeah you can always shift down. With the civic if I went to 4th it brought the rpms up to like 3000 and you could pass like how you used to.
For the most part most 4 cylinder cars have aaaabout the same bsfc chart. Look up the thread on here to make your decision. I mean if your towing a trailer it will make a big difference. But if you aren't.... wind a gear out a lil longer.
I feel like this is the ranger club. I also had a two rangers. 99 4.0 towing pack. 06 3.0. etc... :D

I think when I graduate I'm going to get another ranger with a clean body and a long bed to Kubota diesel swap. Have you considered a diesel swap? haha

I never calculate with gear ratios and final gear drives and tires. Too much math.

I see how much RPM per MPH, and base the result on my experience with other vehicles.

Depending on the engine size, a 1.4 liter turbo engine or 1.8liter NA engine really can't take much lower than running at 2,5k RPM at 80MPH; while this is easy for any 1.6l turbo, 2.0 liter NA or more.
Those are my preferred, and most optimal gear ratios.
2.5k RPM at 60MPH for a 1.6 liter turbo hatchback or sedan results in ~40MPG avg, 50 hwy.


I once ran a my Honda Rebel 250 motorcycle at 3k RPM at 45MPH just fine. Down from 4.5k RPM. That's a drop of 33%. For such a tiny engine it ran quite low in RPM.
If I could have, I would have ran it at a 35% lower than stock ratio, but hardware wise, I wasn't able to modify the bike to go any lower in RPM. Otherwise I'd have done it.