Ken's corner #7: Gear ratios

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Ken's corner #7: Gear ratios

Postby ken.lagarec on Sun Apr 11, 2004 5:32 am

OK, so you're running in an auto-cross going down a fast slalom after a hairpin in first gear and a few turns before the end, you're hitting the rev limiter: so what do you do? Keep it in first and just let it bounce off, knowing you won't gain any speed or go into second, loose some time because of the shift and loose torque, but have the ability to gain some speed before the end? Or say you're on a track, reaching the end of a 1/4 mile straight and you're topping out third gear, shy of your braking point. Do you stay in third and wait for your braking point or shift to fourth, barely gain any speed and then downshift back to third under braking. Both these situations and many others illustrate the importance of proper gearing for optimal performance. These examples illustrated case where the top of the gear was reached too early. As another example, you can have a corner on a track where you're coming through the apex really high in one gear, meaning you'll need to shift up during the acceleration. Not the best situation, But if you went through the corner in the higher gear, you're acceleration might be sluggish until you get to your engine powerband. What you really need for that corner is a gear in between the two...

When a transmission and differential convert the rotation of the engine into rotation or the wheels, they multiply the number of turns by a factor which is the product of the tranny gear ratio and the differential gear ratio. On a 240 with a KA, the tranny gear ratios are (1st to 5th) 3.321, 1.902, 1.308, 1.000 and 0.759 and the final drive (differential) gear is 4.083. That means the total gearing is (1st to 5th) 13.6, 7.8, 5.3, 4.1 and 3.1 and top speeds at redline (6400 rpm) are 55, 97, 140, 184 and 242 km/h for a 225/50r16 tire.

So who cares what the gearing is? Won't the car go just as fast anyway? Well, no. The engine will always produce the same amount of power, whatever the gear and that same power will be distributed to the wheels. So baring losses in the drivetrain that are speed sensitive, if you make 100 hp in 1st, you'll make 100 hp in 5th. BUT, the amount of torque applied to the wheels is equal to the torque at the flywheel multiplied by the gear ratio. So if the engine produces 100 ft.lbs of torque at 500 rpm, the torque at the wheels in 1st will be 1360 ft.lbs but only 310 ft.lbs in 5th. This explains why you easily can burn rubber in 1st, but not in 5th...

So that's the first thing: Wheel torque gets multiplied by the gearing. So for pure acceleration, you'll want larger gear ratios. The fairly high 13.6 gearing in 1st coupled with good low-end torque is what gives the 240 a really good kick off of the line.

What about top speed? Well, obviously, if you have really high gear ratios, you will reach redline at lower speeds than if you had lower gear ratios, which means your top speed will be limited. Notice that the 240 is limited to 242 km/h (if redline is 6400 rpm). Even if you put a 1000hp KA in there, if it was still limited to 6400 rpm, you could never go past 242 km/h with your existing gear set. But put a 3.69 final drive in there, and suddenly, top speed is now 268 km/h! In 3rd, these speeds would be 140 and 155 km/h. So in the track example we had before, if you topped out 3rd at 140 before running out of straightaway, then by putting a diff with a slighty lower gear ratio, you would maybe accelerate out of the corner a little slower, but you could accelerate longer in the lower gear, possibly improving your times. The other important aspect is for fuel economy: engines comsume less at lower rpms, typically because friction losses increase with rpm. To go 100 km/h in 5th, a 240 is at ~2650 rpm. With a 3.69 final drive, you would be at 2400 rpm, probably getting better fuel economy. That's usually why 5th gear is put so low on many cars.

So top speed is increased by using a lower gear ratio, as is fuel
economy.


So why are six-speed boxes becoming more common? Well, by having more gears, you can start off by having a high gear ratio to get good acceleration, but you have enough gears to end up with an overdriven 6th gear that still provides good fuel economy. And they don't have to be spaced out soo much that you feel like you just went into economy mode when you shifted from 3rd to 4th...

In an ideal world where you build a car for every circuit (that is, not taking into account specific target speeds for specific corners), you want the following: as you go up from gear to gear, you want to fall back into the powerband of your engine. Check out the following graph. It shows a KA engine's power as a function of vehicle speed in all 5 gears (this is a modified engine):
Image

Notice that when you reach redline in 1st and you shift to 2nd, you end up with a lot less power. 2nd to 3rd should be done at redline, but shifts from 3rd to 4th, and up should actually be done before redline to get the most power out of the engine. So the top gears are well matched but the first ones definitely aren't. If you were on a track or at an auto-cross where most speeds were between 55 and 65 km/h, you'd be forced to run in second when the engine is producing only 100-120 hp instead of above 150!

So let's play around with the gearing: putting a lower ratio on the final drive won't improve the spacing of the gears. It just stretches erverything out to higher speeds:
Image

In this second case, I've kept the same first and last gears and final drive, but I've changed 2nd, 3rd and 4th to improve the spacing. Believe me, this car would be alot more responsive in the low gears, but there would be a sacrifice in fuel economy because of the shorter gears:

Image

You can also imaging that with 6 gears, you could space them out quite a bit with a lower final drive ratio and pop a gear between 1st and 2nd to fill the gap. You can also imaging the compromises needed in making a 4 gear set with decent fuel economy...

In addition to the gearing in the tranny and diff, the tires will affect the force exerted on the ground, and hence the acceleration. The torque produced by the wheel on the ground is the product of the force by the wheel radius. What actually pushes the car forward is the reaction force produced by the ground on the tire. This reaction force is, by Newton's first law for those who really want to know, exactly opposite to the force produced by the tire on the ground. Confused? Too bad... Anyway, so we know the torque from the engine dyno and the gearing. To calculate the force, just divide the torque by the wheel radius. This means that putting a wheel/tire with a larger diameter will actually reduce the force pushing the car forward... This is why auto-crossers always try to find smaller wheels to fit the cars. That's also why people who put oversized wheels feel their car is slower: it probably is! A wise(!) man once told me: for the auto-cross, use the smallest wheel diameter you can fit on your car. For the track, find the biggest brakes you cn fit under your wheels. And if that's not enough, get bigger wheels!

Last point: putting larger diameter tires will slow you down, not just because of the weight. That's why small, low-powered cars don't have 20" wheels!

And that brings me to the last point: naming conventions. And this is where it gets confusing:
Gear 1 is a low gear number. Gear 5 is a high gear number.
Gear 1 has a high gear ratio. Gear 5 has a low gear ratio.
A gearset with high gear ratios (normally due to the final drive) is known as a short gearset. A gearset with low gear ratios (normally due to the final drive) is known as a tall gearset: short gears good for low speed spririted driving, tall gears good for high speed cruising.

So when you talk to someone about gears, be sure you're one the same page: saying the high gears is confusing: do you means high numbers as in 4 and 5 or high gear ratios as in 1 and 2. Martin once wanted to break a beer bottle over my head because of this type of confusion.

Again, I hope this helped someone out there. Sorry for the length, I feel like I've written much but there is so much more that can be said. I hope it will come out in the questions or comments you have.

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Postby Norgad on Sun Apr 11, 2004 2:50 pm

Wow!! Great Ken's Coners!!! Now I know how to adjust my things with Grand turismo 3 when I must adjust the gear ratio! :P lolll

But seriously, Really great Ken!!! :)
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Postby KukL on Sun Apr 11, 2004 7:05 pm

Awsome Ken, thank you very much. This has been really educational ;-)
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Re: Ken's corner #7: Gear ratios

Postby Jonweir on Tue Apr 13, 2004 1:22 pm

ken.lagarec wrote:Confused? Too bad...


LOL!

Excellent work Ken.
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Postby Biz on Thu Apr 15, 2004 8:28 pm

Great Post Ken!

I've got questions:

Can you actually modify these gear ratios? - by changing "hardware" or "software" in your car?

Are the gear ratios in a 240 optimize for the power output it has stock?

As for wheel size discussion, drag racing: small diameter but wide rubber(perpendularly to the diameter)?

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Postby Black Madgic on Fri Apr 16, 2004 12:28 am

Biz,
I don't know of any company names, but there has to be companies out there that manufacure different gear sizes. In ALMS and GT series and anything and everything above that, they can change the gear ratios in their transmissions by swapping out gears.

I don't see how software could change your physical gear ratios.... :?
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Postby red98s14 on Fri Apr 16, 2004 12:41 am

Black Madgic wrote:I don't see how software could change your physical gear ratios.... :?


A CVT is software controlled.
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Postby Nismo on Fri Apr 16, 2004 12:47 am

Black Madgic wrote:Biz,
I don't know of any company names, but there has to be companies out there that manufacure different gear sizes. In ALMS and GT series and anything and everything above that, they can change the gear ratios in their transmissions by swapping out gears.

I don't see how software could change your physical gear ratios.... :?


OS Giken, Mines and Tomei have 3 or 4 gear sets for the 240sx depending if your doing drag, track, dori, you name it.

Plug and play for SR or KA.

Good read Ken... Thanks!
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Postby Black Madgic on Fri Apr 16, 2004 1:43 am

red98s14 wrote:
Black Madgic wrote:I don't see how software could change your physical gear ratios.... :?


A CVT is software controlled.


Yes all the new ones are older ones are not. I was thinking of the gears in a 240 transmission.

Thanks Alex, I figured there must be some companies out there that make them for the 240, I just wasn't sure who.
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Postby ken.lagarec on Fri Apr 16, 2004 3:18 am

Biz wrote:Great Post Ken!

I've got questions:

Can you actually modify these gear ratios? - by changing "hardware" or "software" in your car?

Are the gear ratios in a 240 optimize for the power output it has stock?

As for wheel size discussion, drag racing: small diameter but wide rubber(perpendularly to the diameter)?

Biz


1. Gear ratios requires a hardware change. Very expensive so it's not really a normal option. However, changing the differential gearing is not uncommon, as Martin did on his race car (I think). Quaife also sells gear sets for the Silvia. Compare:

Stock: 3.321 1.906 1.308 1.000 0.759 (KA and SR are the same but turbo has 3.692 final drive, NA has 4.083)
S15 6sp: 3.626 2.200 1.541 1.213 1.000 0.767 (3.692)
Quaife: 2.762 1.961 1.533 1.212 1.000 0.790

So: a converted 240sx with SR engine/tranny and stock diff will be quicker than a JDM silvia...
Quaife gear ratios are meant for race situations so 1st gear is not as high, and all gears are very closely spaced so you're always in the powerband when shifting, even if you have a narrower power band. This means 1st gear might actually be useful in a hairpin turn. With the 240sx gearing, even a slow hairpin turn puts you at high revs, making it pretty much useless.


2. Not entirely. The dyno charts shown above are for a moded engine with pdm cams. It changes the power curve slightly but not completely. You can see that 1st gear has a much too high ratio, which is there to give it good acceleration. With a turbo'ed car, a lower ratio for 1st gear would be much more useful. The other gears seem to be adequately spaced. A lot of gear selection in a production car has to do with noise in the car at conventional city driving speeds and things like that, not always ultimate gearing.

3. Drag racing: a lot about drag racing tires has to do with getting traction more than just having power to the wheels. Too small tires will overheat easier and might not be effective. Also, the problem with small wheels/tires is that you run out of gears quicker: you might get 10% more torque running tires 10% smaller, but you will also have to shift at a speed that's 10% lower, meaning more shifts in the end. More gears in a tranny also typically makes them more fragile... These are then obvious reasons why you can't go with a tire that is too small. Of course you want a tire that is wide. But wide tires also increase drag and at high speeds, wind drag becomes a huge factor, so there's a compromise there too: narrower tires offer less traction, but better aerodynamics (this was the reasoning behind the 4 small wheels on the 6 wheel Tyrell: same grip but better aero).

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Postby Nismo on Fri Apr 16, 2004 1:09 pm

http://www.osgiken.co.jp/pro_gear/nissan.html 8)

Gonna have to make a correction above. Tomei uses OS gears to upgrade trannies and Mines only does the software upgrades.
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Postby MRWmotorsports on Wed May 05, 2004 7:33 pm

Hey Ken you got the "high" and "low" gear terminology backwards again.. he says searching for a beer bottle :twisted:

BTW.. yes indeed I changes the diff gear in the stock car to a 4.625, LOWER than the stock 4.083.

Why is it lower? Well a gear ration is just that, a ratio, so although it's decsribed as a 4.625, that shoudl really be 4.625 to 1 or 4.625:1, what this really means is that you need to turn the driveshaft 4.625 times to turn the wheels once.

Stock gear = 1 / 4.083 = .244917
New gear = 1 / 4.625 = .216216

Which one is lower? That's my thoery and I'm sticking to it.. othewise I've got to re-learnr everything I've learned about gearing and I'm too old for that shit :-)

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Postby frostman on Wed May 12, 2004 9:34 pm

I have finally now had a chance to read your post here. I must say that this was very informative. Just one thing I noticed though. Going from lets say a 4.11, to a 3.55 axle ratio will not always give you better fuel economy in top gear. In my experiences with both the 240, and my new sentra, I have found that at 120 kmh and 100 kmh I got better gas mileage using 4th gear. I believe it has something to do with where the engine is making torque, and how much power is being transferred to the ground, in comparison as to how much power is needed to keep the forward momentum. basically what i8 mean is that the engine is being forced to consume more fuel at lower rpm's to create the power to move, where as at the higher rpm, the engine is making more power and not having to have the throttle open as much. I drive from Toronto to petawawa almost every weekend, and usually let the cruse do the work for me. Plus when I am in 5th some times I can really feel the engine lugging up hills. I thin this is common since to most of us, but just wanted to see if my uneducated guess was correct.
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Postby Black Madgic on Thu May 13, 2004 1:15 pm

Frosty,
Your logic is correct for the fuel consumption being higher at lower rpm's. At lower rpm's for some (more than likely most) engines are consuming more fuel than they do higher in the rpm band (I am referring to say 1500 vs 2500 rpm).
Part of this has to do with keeping the engine running. More fuel (to a point) keeps the engine running. When the engine is out the low end of the optimum rpm range most ecu's are programmed to dump more gas into the engine to keep it running. Same goes for outside the higher end of this optimum range.
Edit: There are other reasons for this. Each manufacturer has their own reason for doing stuff like this. I just can't recall what they are exactly. It's been a while since I was in the dyno lab.
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Postby red98s14 on Fri Dec 08, 2006 7:19 pm

Resurrecting this thread, cause I found something interesting today while poking around the SCCA Improved Touring board. (new info to me at least)

R200 diffs are used in the front of many Nissan 4x4's

1989, and similar, Pathfinders have either 4.375 or 4.625 ratios.

V6 pickups (not 1996 or 1997) have a 4.375.

2001 and newer Xterras and Frontiers have a 4.63 or 4.9 available

Anyone looking to use a lower final drive for better acceleration (trade-off lower top speed) can likely get a ring & pinion from one of these at a better price than aftermarket.

Many of the IT guys change their final drive depending on which track they're running.
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