Help with some final drive math

[hat_man]

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.

[hat_man]

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% ?

[hat_man]

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?

[hayden55]

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.

[California98Civic]

Originally Posted by hat_man

... What I don't know is how my new tire size affects this number. ... To figure the final drive with the new tire size do I adjust the stock final drive by that same 5% ?

Yes. The tire is like another gear in effect.

[hat_man]

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.

[Ecky]

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.

[hat_man]

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.

[Ecky]

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.

[hat_man]

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