Thứ Bảy, 25 tháng 2, 2017

How does final drive affect acceleration? part 1

Unabomber 03-03-2007 01:48 PM

How does final drive affect acceleration?
If one goes from 205/55-16 tires to 205/30-16 tires, their final drive on a WRX goes from stock 3.90 to apparent 4.02. This is a 3% change. Does this mean that they will see 3% faster acceleration in every gear at every RPM? On paper it does, but I'd like to see if someone has a differing opinion or theory. In theory, if someone was running 12.9 in the quarter mile, just by switching tires, they'd run a 12.5 in a perfect world using this 3% theory. Your input is appreciated.
dcpatters 03-03-2007 01:58 PM

I would say yes. By decreasing the tire diameter effectively increases engine RPM in each gear; as you indicated changing the final drive ratio. Basically, the car should accelerate faster at any given RPM in any gear.

As for decreasing 1/4 times by 3%, hhhhmmm.... I suppose if a 4.02 ratio is what the car needed to get through the gearbox and into the powerband, then again yes.
Patrick Olsen 03-03-2007 02:06 PM

I'm too lazy to really think about this right now, but I think the answer is YES, you would be accelerating 3% faster in every gear at every RPM. However, it's worth noting that you would [i]not[/i] be accelerating 3% faster at every [i]speed[/i].

And if one is looking for 1/4mi improvements by changing gearing there's always the possibility that the shorter gears will end up forcing you to make an extra shift, which ruins everything.
speedyHAM 03-03-2007 03:33 PM

I have a feeling this will turn into a long and useless thread.

Your change in tires will result in a 3% gain in acceleration assuming the rotational intertial of the tires is the same and nothing else changes. That will not result in a 3% better 1/4 mile time.

Assuming acceleration is constant (which it isn't) gives your average acceleration for a 12.9 second 1/4 mile time as 15.86 feet/second^2. Increasing this by 3% gives 16.34 feet/second^2. If you calculate the 1/4 mile time based off that acceleration [B]you get a 12.71 second time[/B]. You might actually get a better rotational intertia with the smaller tires which would help your time just a little bit more.

The equation for calculating a time to a cover a distance is d=d0 + Vt +1/2at^2.
SuperWRXSTi 03-03-2007 03:42 PM

The first thing that pops into my mind when I saw this was this: Correct me if I'm wrong but, yes your tires will spin faster in acceleration but, with the smaller tire you won't cover as much ground in one rotation of the tire as you would with a bigger tire.

And speedyHAM, unless your in highschool or college I can't believe you still know that formula. I have been using it all year for problems in my high school physics class. Thats cool that you still know/use it.
speedyHAM 03-03-2007 04:07 PM

I am a foutain of useless knowledge. (I had to look it up)
shemoves 03-03-2007 04:38 PM

Edit...well dang, I should've read more than just the title. I think you should get the biggest tires possible and attach a bunch of those little home-rocket motors to them...that'll make 'em spin :lol:

Seriously though, it would not work that easily as there are other variables to consider. You will hit redline quicker...could be good or bad depeniding on what your power band looks like. They will be easier to spin at launch (could be good or bad). It will take less power to turn them...

Hmm, I wonder if you may have found something...

\/ This was my original post

The higher the FD is = more fun (somewhat subjective), more acceleration, "more" torque, more shifting, high-rpm while cruising, lower gas mileage, lower top speed.

As far as terminology goes, a high FD is considered 'short,' whereas effectively 'longer' gearing can be obatained by lowering the FD #.
GTScoob 03-03-2007 04:44 PM

[QUOTE=shemoves;17246257]Using the same gears, a tranny with a FD of 4.44 will have great acceleration, but a generally low speed at redline. A tranny with a 3.9 FD, won't have as good accel. as the 4.44, but will be going faster at redline.

The higher the FD is = more fun (somewhat subjective), more acceleration, "more" torque, more shifting, high-rpm while cruising, lower gas mileage, lower top speed.

As far as terminology goes, a high FD is considered 'short,' whereas effectively 'longer' gearing can be obatained by lowering the FD #.[/QUOTE]
Agree completely, nobody else in the area has the same setup as me to easily compare my 4.44 tranny to a 3.9 WRX tranny. Its a lot of fun to drive but I'm not sure if its necessarily any quicker, spools the turbo quicker but thats also because the engine is at a higher rev for any given speed.
WRXBob 03-03-2007 05:03 PM

The engine will only supplies so much torque/ horse power at a certain RPM. If you load the engine with higher gear ratio like 3.9 or 3.7 compares to 4.44 your car top speed will occurs at a lower RPM but you will not go any faster at top speed and it will takes longer for the car to reach that speed. With lower gear ratio the engine will spin quicker to the red line and generates faster acceleration from 0 to top speed. The trick is to have a gear ratio that matched with your engine torque out put characteristic and its RPM range. As for the original question, I put 205-45-16 in my WRX and the car has much quicker acceleration, but the car looks funny.
Counterfit 03-03-2007 05:28 PM

[QUOTE=shemoves;17246257]I think you should get the biggest tires possible and attach a bunch of those little home-rocket motors to them...that'll make 'em spin :lol: [/quote]
:lol:
[quote]The higher the FD is = more fun (somewhat subjective), more acceleration, "more" torque, more shifting, high-rpm while cruising, lower gas mileage, lower top speed.[/QUOTE]

I think there would actually be more torque at the wheels due to the multiplication of it by the gears. I think someone who's more experienced in this could explain better.
remowgn 03-03-2007 06:46 PM

Yes, changing the final drive will make your car faster, and it doesn't matter what method you go about doing this. Back in the 60's and 70's, some car manufacturers would have up to 5 different options for rear axle ratios- from 2.72:1 all the way up to 4.85:1! You can also back this one up in gran turismo by playing with the FD and gear ratios to your heart's content.

If you're not anywhere close to requiring another shift, any increase in gear ratio is going to help your 1/4 mi times and trap speeds. This is of course ignoring issues like wheelspin in first gear, which may become a problem with more torque multiplication.
Homemade WRX 03-03-2007 06:57 PM

[QUOTE=speedyHAM;17245845]I have a feeling this will turn into a long and useless thread.

Your change in tires will result in a 3% gain in acceleration assuming the rotational intertial of the tires is the same and nothing else changes. That will not result in a 3% better 1/4 mile time.

Assuming acceleration is constant (which it isn't) gives your average acceleration for a 12.9 second 1/4 mile time as 15.86 feet/second^2. Increasing this by 3% gives 16.34 feet/second^2. If you calculate the 1/4 mile time based off that acceleration [B]you get a 12.71 second time[/B]. You might actually get a better rotational intertia with the smaller tires which would help your time just a little bit more.

The equation for calculating a time to a cover a distance is d=d0 + Vt +1/2at^2.[/QUOTE]

gotta love dynamics...I am going to dread the FE but am done in may :banana:
regardless, this would be the most simple way of determining the gains and ignoring individual gears and inertia and considering all other variables as constants...
Unabomber 03-03-2007 09:38 PM

[QUOTE=speedyHAM;17245845]I have a feeling this will turn into a long and useless thread.

Your change in tires will result in a 3% gain in acceleration assuming the rotational intertial of the tires is the same and nothing else changes. That will not result in a 3% better 1/4 mile time.

Assuming acceleration is constant (which it isn't) gives your average acceleration for a 12.9 second 1/4 mile time as 15.86 feet/second^2. Increasing this by 3% gives 16.34 feet/second^2. If you calculate the 1/4 mile time based off that acceleration [B]you get a 12.71 second time[/B]. You might actually get a better rotational intertia with the smaller tires which would help your time just a little bit more.

The equation for calculating a time to a cover a distance is d=d0 + Vt +1/2at^2.[/QUOTE]

This was the variable that I knew was out there, thank you for refreshing me on it as I've been thinking of the reason forever. You are right about the endless debate though and I think this answer is good enough for me. I'm hoping to use this in a post about final drive conversion/tire changes/what it does to power/what it does to transmission sometime soon and this is the final piece of the puzzle I need. Mercy buckets! :)
Crazyhippy 03-04-2007 12:49 AM

Taking it one step farther, since the tires can only transfer so much tq to the road, the smaller tires will show less tq to the trans. Less load on the motor (ignoring the revs as you drive @ speed)

255/20r16's for everyone!!
cowapult 03-04-2007 04:26 AM

speedyHam has a good analysis, but it's actually even worse than that.

What people don't realize is, you'll have 3% more acceleration in every gear, but you'll also have to up-shift 3% sooner (at 3% lower speeds) - which EXACTLY cancels out improvement. Think of 2nd gear as being made up of a 3% lower ratio most of the way, except the last bit of 2nd gear is now in a much higher ratio (3rd gear!). Average them together and you're still in the same boat. However, you might get a smaller advantage depending on the situation. It might help the launch/starting point to have your first gear higher or lower, but as you run through the gearbox, the advantages and disadvantages cancel out. You might get an advantage in autocross/rallycross where you simply stay in one gear. But, if you're rowing through many gears, there's no advantage at all.

The right way to look at it would be to see how the gears affect your use of the power band. Changing ratios should be used to maximize the time you spend in the highest parts of the power band while also thinking about not spending too much time shifting a lot.
Davenow 03-04-2007 08:21 AM

I know in the mazdaspeed miatas, once you get them past about 210whp, they seem to accelerate faster through 1-3 with 3.90 rear end gears than they do with the stock 4.11s. I dont know if thats because it doesnt just blister the tires through 1st and 2nd, but from what I have seen, its true. It seems they do anyway.

It could also be the fact that the uber short gearing, isnt quite as uber short anymore once you do it.

But my WRX was definately faster in the 1/4 with slightly smaller diameter tires. And foresters were faster because of the lower gearing as well.
hotrod 03-04-2007 09:15 AM

It is a little more complex than everyone is making it but on a first order approximation, yes it will improve acceleration ---- [b] to a point[/b]

It will generally make the car "quicker" but your trap speed will not change as much as your ET, since it is mostly determined by your engines power output.

1. As your total gear reduction goes up ( ie 4.44 vs 3.90 ) your max accelerative thrust will go up in exact proportion to the gear change.

2. Your inertial weight will also go up in proportion to the gear ratio. The engine has to accelerate faster to create a given acceleration rate at the wheel so the effect of the moment of inertia (rotating weight) of the entire drive train including the engine will be magnified. Light weight engine parts and drivelines, clutches are your friend here.

3. As your time in each gear drops due to the higher acceleration rate, the sensitivity to how quick you shift goes up. If you take a full second to shift from low to second, that does not mean much if your driving a 1922 whippet which takes 15 seconds to top out in low. It becomes very important if the car hits red line in low gear in 1.6 seconds.

4. Frictional losses will go up with the higher surface speeds in all your gears so that will work against the effect of lower gears.

5. gearing through the traps will strongly effect the total benefit to lower gears. If by lowering the effective gear ratio you can now run through the traps pulling hard in 4th instead of riding the rev limiter in 3rd or lugging in 4th you will go faster for the quarter mile. If the gear change makes you need to shift one more time, it may not help much.


6. Power is useless if you can't get it to the ground, if your gearing change is too big you will no longer be able to hook off the line and will actually lose time spinning through low and maybe second. At that point you need more tire to take advantage of the gear reduction.

In general small changes will improve your short time and make slight improvements in trap speed. Go too far and the negatives will cancel out the benefits. There is not one ideal drag gearing, in fact top end teams know what gear gives them the best ET and what other gear gives them the best MPH. They are seldom the same.


On moderate power cars the 4.44 gears would be a good thing, on a higher power car, the 4.11 or the 3.90's may actually give better times, by not blowing the tires off during the launch.


Larry
Unabomber 03-04-2007 06:00 PM

Thanks Larry! I didn't think to PM you on this and I'm glad you came here.

Here's some more dork information that I just came upon. Using [url=http://www.wallpaperinstaller.com/scooby/flywheel.xls][u]this excel spreadsheet[/u][/url] and futzing with the numbers for my car, we come up with these values:

3.90 final drive with stock 205/55-16 tires:

Geff..............mal,fly,rot.......... (kg)......M (kg)....M (lbs)
M1 (1st gear)... 13.4706.......77.9667....54.33...119.78
M2 (2nd gear)... 7.5933........24.7740...20.11....44.34
M3 (3rd gear)... 5.3274........12.1946....12.02....26.50
M4 (4th gear)... 3.7908.........6.1744.....8.15.....17.96
M5 (5th gear)... 2.8782.........3.5594.....6.46.....14.25

3.90 final drive with 205/45-16 tires (4.16 apparent final drive):

Geff..............mal,fly,rot.......... (kg)......M (kg)....M (lbs)
M1 (1st gear)... 13.4706......89.1616....61.54....135.66
M2 (2nd gear)... 7.5933.......28.3312...22.40.....49.38
M3 (3rd gear)... 5.3274.......13.9455....13.15.....28.98
M4 (4th gear)... 3.7908........7.0610.....8.72......19.21
M5 (5th gear)... 2.8782........4.0705.....6.79......14.97

In effect, the smaller diameter tires act like a lightweight flywheel. In this case, the 205/46-16 tires give the values of a 13lb flywheel. True or are my conclusions wrong?
hotrod 03-04-2007 06:31 PM

I don't have time to dig through that spread sheet ( the last time I messed with any of that was more that 3 decades ago ) but it looks reasonable.

You are however only looking at one end of it. The lighter smaller tires will reduce the cars enertial weight, but the higher rpms and acceleration rates will make all the upstream parts like differentials, transmission gears, flywheels, drive shafts, engine pulleys etc. look heavier. Many years ago Jim Hall the racing engineer, did a very interesting article in as I recall Sports Car Graphic magazine. He discussed this issue and due to inertial effects he suggested that a driver shift out of the lower gear a bit sooner than simple area under the power curve calculations indicated because as he put it --- when you shift from low to second gear the change in rotating enertia makes the car appear about 100# lighter after the shift than before the shift. This was all due to the very high rates of acceleration the engine and drive train must achieve in low gear to do anything useful.

You also have the question of gearing effeciency which drops as the ratios get higher for similar reasons ( very rapidly spinning gears throwing around more lubricant in the transmission etc.)

When I ran my best times in my WRX on the stock turbo here at altitude I was running very short tires (equivalent final drive about 4.30:1). They made a very noticable difference in drivability -- the car was much easier to ease off the line at traffic lights and to be in slow stop and go traffic as low gear no longer wanted to stall the car at low engine rpms. It also put me well into 4th gear instead of having to choose between riding the rev limiter in 3rd and shifting to 4th and having essentially no acceleration.

That is one of the reasons I have the only stock turbo WRX to trap over 100 mph up here at this altitude. The nearest trap speed for a stock turbo is almost 3 mph slower in the quarter (some of that is due to car weight) but I would attribute about 1/2 the difference in trap speed to the better gearing, and rpm band through the traps.

Larry
Homemade WRX 03-04-2007 10:46 PM

[QUOTE=Unabomber;17248400]This was the variable that I knew was out there, thank you for refreshing me on it as I've been thinking of the reason forever. You are right about the endless debate though and I think this answer is good enough for me. I'm hoping to use this in a post about final drive conversion/tire changes/what it does to power/what it does to transmission sometime soon and this is the final piece of the puzzle I need. Mercy buckets! :)[/QUOTE]

If you want I will have a dyno collection soon of 4.44 vs. 4.11 and hopefully 3.9 on the same car, same tune, same dyno, same corrections...
RWD makes it easy...now if I could just keep from blowing R160s up all the time:(


Larry, everything you stated is true but most adress going to taller rings and not smaller tire diameters...as for what is ideal comes down to each car's powerband/torque curve and the gearing in the transmission (making this fixed as changes here are quite pricey)...time in gear, while in the torque curve, rules all as well as being able to stretch the last gear without having to shift...the reason the 6-speeds suck for straight line and any car with a good torque curve...I'll have to find an SAE paper I have on this for you...or Ron

as for frictional and intertial losses, those are calculations that still get debated one way or the other...yes intertial and friction become and issue but which outweighs the other...similar to high rev's for cfm gain vs frictional losses.... One thing you may have overlooked are the larger housings to accompany the larger ring gears...I know the 4.44 housing I've been running stands about 3/4" taller than my 4.11 housing ;) more iron
hotrod 03-05-2007 02:26 AM

[quote]as for frictional and intertial losses, those are calculations that still get debated one way or the other...[/quote]

Which is why most folks are well served by the old racers rule of thumb, -----

[B][I]"Keep adding gear until the car slows down"[/I][/B]

Not very sophisticated but it usually works pretty well. In most cases it is a matter of ---- keep adding gear until you can't put enough tire under it to hook the power.

This is where most folks screw up in racing --- they only think about power. When you become traction limited on acceleration --- spend your money on the suspension before you add any more power. More power when you are traction limited will only make matters worse!

That's why sometimes a race car will run better lap times on a sick engine.

Larry
aps2fast4u 03-05-2007 10:44 AM

great info here guys, keep up the good data!

Homemade, I can't wait to the the dyno comparisons. That should give a good look at the diff. in powerband and HP through RPMs
Porkchop-WRX 03-05-2007 05:20 PM

I'm also intrested in seeing a dyno comparison but I'm going to have to agree that this will improve your 1/4 mile time and general acceleration. WRX shifts into 4th at the track no matter what and a 3% increase will put us no where near the end of 4th.
Homemade WRX 03-05-2007 07:54 PM

well, my 3.90 comparison will be no good now...skipping the r160 and going straight to r180...tired of killing 160s...
Gonz 03-06-2007 10:52 PM

[QUOTE=Unabomber;17245266]If one goes from 205/55-16 tires to 205/30-16 tires, their final drive on a WRX goes from stock 3.90 to apparent 4.02. This is a 3% change. Does this mean that they will see 3% faster acceleration in every gear at every RPM? On paper it does, but I'd like to see if someone has a differing opinion or theory. In theory, if someone was running 12.9 in the quarter mile, just by switching tires, they'd run a 12.5 in a perfect world using this 3% theory. Your input is appreciated.[/QUOTE]

That would be nice. If I can follow your math correctly, then I would expect a 2.73 geared Mustang running 15.1 in the quarter would run 9.6 seconds in the quarter mile by going to a 3.73 gear.

that's obviously rediculous. In reality, you might get a low 14 seconds out of that change. A 4 or 5 % improvement.

(even if you give the first car unlimited traction, and it could run a 14.0, the modded car would have to run UNDER 9 seconds for the ET to shorten by the same amount as the gear ratio)

Maybe I didn't do the ratios correctly, (very possible) but I think the improvement is not going to be equal to the change in gear ratio. It's still well worth it for the drag strip. Changing gears is one of the best bang for the buck.
hotrod 03-06-2007 11:18 PM

The improvement would be in the [b]rate of acceleration[/b] while under power (shifts would still be coasting) not in the ET.


Your 15.1 mustang would drop to something like 15.1x.97 = 14.647 ---- probably not quite that entire drop, more like a couple tenths.

Larry
djpast 06-05-2007 12:12 PM

would this put any more strain on the transmission or rear differential?
RRR-K2 06-05-2007 07:37 PM

[QUOTE=djpast]would this put any more strain on the transmission or rear differential?[/QUOTE]
In theory, smaller tires should put [I]less[/I] strain on them as with a smaller tire there would be less inertial mass to move...though I do believe that, all other things being equal, a smaller diameter "wheel" has more (inertial) rolling resistance. :rolleyes:

Matt Kennedy
[URL="http://www.RockyRoadRacing.com][U][COLOR=DarkRed]www.RockyRoadRacing.com[/COLOR][/U][/URL]

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