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Old 09-04-2014, 11:16 PM   #1
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Math question for acceleration

So if my 0-60 time is 6.3 sec with 3.21 gears - changing nothing else EXCEPT gear ratio to 4.88 - what would my 0-60 be?

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Old 09-04-2014, 11:22 PM   #2
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I don't think anyone will be able to answer that. You can't assume 34% faster (due to the 34% change in ratio) due to the torque curve of the engine and other dynamics.

You can assume it will be quicker to 60 though. And...if you are getting 6.3 sec good for you. Mine does not seem that fast with 3.73

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Old 09-04-2014, 11:23 PM   #3
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Im not sure you could come to an accurate number using a formula. I could be wrong. I would think there would be to many variables.
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Old 09-05-2014, 03:56 AM   #4
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This sounds like a homework assignment so you will have to check the validity of the equations.

For this to apply you literally have to assume "everything" is constant which is not realistic. However here is one simplistic approach.

You need to solve the old F=ma equation and V = V0 + at

Solving for t: t = (V-V0)/a

Then from F = ma -> a = F/m = (Efficiency factor x engine torque x gear ratio) / (mass x tire radius)

Everything is constant so you get
a = Constant x gear ratio

Th acceleration with old gears is proportional to the acceleration with the new gears since everything is constant

a(old)/(gear ratio(old) x C) = a(new) / (gear ratio(new) x C)

a(new) = ( a(old) x (gear ratio (new) )/gear ratio (new)

Plug in the values making sure all units are dimensionally correct

Then plug in the resulting value of a(new) into:

t (new) = (V-V0)/a(new)

If all your units are right you will get your new 0-60 time in seconds
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Old 09-05-2014, 12:13 PM   #5
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Those simple formulas would work nicely if acceleration was constant. But acceleration varies , not simply with time, but with engine speed, transmission ratio, and vehicle speed (accounting for aerodynamic drag). Changing axle ratio changes the relationship between speed and rpm, which in a complicated way changes the relationship between acceleration and time, the speed and time at which you must shift gears, etc. Then you also have to account for the time it takes to shift gears and the deceleration that happens then due to friction and air resistance.

No simple calculation. It requires a simulation that uses the torque curve of the engine and all the most significant specs about the vehicle (weight, drag-area coefficient, gear ratios, tire size, etc).
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Old 09-05-2014, 06:57 PM   #6
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Quote:
Originally Posted by allenoffroad2009 View Post
So if my 0-60 time is 6.3 sec with 3.21 gears - changing nothing else EXCEPT gear ratio to 4.88 - what would my 0-60 be?
After much calculating, my results are; slower

I know, its amazing anyone could figure it out..
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Old 09-05-2014, 07:15 PM   #7
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It also depends on if your gearing adds a shift to the 0-60 run...which can actually slow it down.
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Old 09-05-2014, 09:49 PM   #8
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Originally Posted by UselessPickles View Post
Those simple formulas would work nicely if acceleration was constant. But acceleration varies , not simply with time, but with engine speed, transmission ratio, and vehicle speed (accounting for aerodynamic drag). Changing axle ratio changes the relationship between speed and rpm, which in a complicated way changes the relationship between acceleration and time, the speed and time at which you must shift gears, etc. Then you also have to account for the time it takes to shift gears and the deceleration that happens then due to friction and air resistance.

No simple calculation. It requires a simulation that uses the torque curve of the engine and all the most significant specs about the vehicle (weight, drag-area coefficient, gear ratios, tire size, etc).
I complete agree, changing the gear ration completely changes shift points and the relationship with the torque curve. But given the amount of information provide making that assumption is the only way to get a rough approximation and the OP stated he was OK with assuming "everything" else was constant. However, it doesn't necessarily require a simulation. It does require the applied torque curve; meaning the portion of the torque vs RPM curve applied for each gear, applying each section to the equations and summing up the times.

The more assumptions you replace with real data values the better the result becomes. Either way it's a bit of an exercise in futility.
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Old 09-06-2014, 12:27 AM   #9
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It might be faster, it might be slower, or even the same. <--I have a knack for always being right. ��
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Old 09-06-2014, 05:35 AM   #10
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That would require one spectacular equation.
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Old 09-06-2014, 12:09 PM   #11
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It's gonna be slower 0-60mph, I can tell you that with a lot of mathematical hokus-pokus..

Sure, we could get into shift points-torque curves-converter stall speeds-blah,blah,blah-but...

With no other changes, this vehicles performance was optimized for 3.21 & not 4.88, that gives 3.21 gearing all the advantage it needs..

I can also tell you with 4.88's you'll be making a lot more pit stops (fuel)..
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Old 09-06-2014, 12:24 PM   #12
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Wallace Racing has many calculators. I'm sure you can find your answer here.

Wallace Racing - Automotive Calculators

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Old 09-06-2014, 12:41 PM   #13
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I use to use this on my HP but when it died I went to a mac. But it is really accurate if you plug in all the variables. Drag Racing Software & Formulas
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Old 09-06-2014, 02:24 PM   #14
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Quote:
Originally Posted by allenoffroad2009 View Post
So if my 0-60 time is 6.3 sec with 3.21 gears - changing nothing else EXCEPT gear ratio to 4.88 - what would my 0-60 be?
So I'm going out on a limb and predicting you'll shave at least .2 seconds off your 0-60 with 4.88's... maybe more.

Typically a lower gear ratio will get you there quicker.

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Old 09-06-2014, 04:03 PM   #15
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Originally Posted by ASE_MasterTech View Post
It's gonna be slower 0-60mph, I can tell you that with a lot of mathematical hokus-pokus..

Sure, we could get into shift points-torque curves-converter stall speeds-blah,blah,blah-but...

With no other changes, this vehicles performance was optimized for 3.21 & not 4.88, that gives 3.21 gearing all the advantage it needs..

I can also tell you with 4.88's you'll be making a lot more pit stops (fuel)..
Don't believe that is true. People change the gears (and nothing else) in fbodies and it greatly improves 0-60 times.
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Old 09-07-2014, 01:58 AM   #16
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Originally Posted by Lammy View Post
Don't believe that is true. People change the gears (and nothing else) in fbodies and it greatly improves 0-60 times.
Ok.. 3.21 stock vs 4.88 non-stock? with no other changes? no shift point change/no stall speed change? really??
Please provide some proof/support for this rebuttal..
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Old 09-07-2014, 02:16 AM   #17
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Originally Posted by m998dna View Post
So I'm going out on a limb and predicting you'll shave at least .2 seconds off your 0-60 with 4.88's... maybe more.

Typically a lower gear ratio will get you there quicker.

.
The only thing lower gears do (racing wise) is pull you out the 'hole' quicker..

After that short 50ft, EVERYBODY wants to be taller (higher geared)..

That's a fact....
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Old 09-07-2014, 03:13 AM   #18
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Quote:
Originally Posted by ASE_MasterTech View Post
The only thing lower gears do (racing wise) is pull you out the 'hole' quicker..

After that short 50ft, EVERYBODY wants to be taller (higher geared)..

That's a fact....
But that's what he's trying to do.. get out of the hole quicker to improve his ET from 0-60.. not changing anything but gears. He didn't say 1/8th or 1/4 mile run..

He has a five speed with OD... how taller can you get? Nothing changes except front and rear diff gears.

With exception to Fuel or Alcohol classes that use progressive clutches, most drag cars run highly built two or three speed transmissions with a high stall converters.. GM Powerglide, 727 Torqueflite or Ford C6..

Then there are those that will install a Jerico transmission.

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Old 09-07-2014, 09:43 AM   #19
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Also remember that engine torque output along the RPM is NOT linier.
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Old 09-08-2014, 12:18 AM   #20
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Quote:
Originally Posted by ASE_MasterTech View Post
The only thing lower gears do (racing wise) is pull you out the 'hole' quicker..

After that short 50ft, EVERYBODY wants to be taller (higher geared)..

That's a fact....
If that was a fact, everyone would just upshift after 50 feet ...
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Old 09-08-2014, 01:00 AM   #21
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If that was a fact, everyone would just upshift after 50 feet ...
Why are you drag racing a jeep?
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Old 09-08-2014, 01:35 AM   #22
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Quote:
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Why are you drag racing a jeep?
Jeeps are pretty quick... ever seen one run?

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Old 09-08-2014, 09:50 AM   #23
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Why are you drag racing a jeep?
I am not, but the physics involved in drag racing also apply to discussions about gearing, tire size, towing, diesel vs gas, etc.

Do you always jump into conversations and ask the last guy to post why he is talking about a topic that was introduced long before he posted in the thread?
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Old 09-08-2014, 11:56 AM   #24
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4.56s made a huge difference in my acceleration. 60 foot 0-60 and 1/4 mile. Engine is in its powerband more.

As long as you are not just spinning off the line lower gears are better for acceleration.

However, my buddys f-body took a hit in the quarter mile. He went from 3.73 to 4.10 and lost a tenth. He was traction limited off the line though. And were talking 11.9 sec vs 12.0.
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Old 09-08-2014, 12:01 PM   #25
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Quote:
Originally Posted by ASE_MasterTech View Post
It's gonna be slower 0-60mph, I can tell you that with a lot of mathematical hokus-pokus..

Sure, we could get into shift points-torque curves-converter stall speeds-blah,blah,blah-but...

With no other changes, this vehicles performance was optimized for 3.21 & not 4.88, that gives 3.21 gearing all the advantage it needs..

I can also tell you with 4.88's you'll be making a lot more pit stops (fuel)..
Acceleration will be faster, absolutely no question. However, the big issue is whether it'll be fast enough to offset the new shifting. Being "optimized" for a gear ratio is BS. It's optimized for that ratio for fuel economy reasons, not acceleration.
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Old 09-08-2014, 05:29 PM   #26
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Acceleration will be faster, absolutely no question. However, the big issue is whether it'll be fast enough to offset the new shifting. Being "optimized" for a gear ratio is BS. It's optimized for that ratio for fuel economy reasons, not acceleration.
Ok, so I guess everybody can throw their ProCal's away.. I mean who really cares about minor speedo errors or slightly less fuel economy?
Oh yeah, that's right, there's those shifting issues with larger tires (& likewise shorter gearing) with autos.. maybe I'll keep my ProCal, it really does make a difference for me (& only 33 to 35's, go figure).

Am I the only one who read the OP's original question & absorbed the "no other changes" statement?
I agree 4.88's will pull harder & seem 'quicker'.. but with "no other changes", 3.73's will deliver faster 0-60 (even if it's only by a 10th)
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Old 09-08-2014, 08:55 PM   #27
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Quote:
Originally Posted by allenoffroad2009 View Post
So if my 0-60 time is 6.3 sec with 3.21 gears - changing nothing else EXCEPT gear ratio to 4.88 - what would my 0-60 be?
Quote:
Originally Posted by ASE_MasterTech View Post
Ok, so I guess everybody can throw their ProCal's away.. I mean who really cares about minor speedo errors or slightly less fuel economy?
Oh yeah, that's right, there's those shifting issues with larger tires (& likewise shorter gearing) with autos.. maybe I'll keep my ProCal, it really does make a difference for me (& only 33 to 35's, go figure).

Am I the only one who read the OP's original question & absorbed the "no other changes" statement?
I agree 4.88's will pull harder & seem 'quicker'.. but with "no other changes", 3.73's will deliver faster 0-60 (even if it's only by a 10th)
Actually I did ... read it and absorbed it. He said he ran 0-60 in 6.3 sec. with 3.21 gears..

The OP is discussing ET not MPH... so Faster isn't necessarily a consideration in this discussion, Quicker (ET) is the goal. That means 4.88s with a 5-speed OD will get him 0-60 quicker than 3.21s assuming he dosn't hit a power pole first.

I checked with a GAI and confirmed my assumption..

The only real way to find out, if the OP comes out of hiding and installs those 4.88s and proves he can shave .2 sec off his ET. He also will need to learn how to launch his Jeep with 4.88s.

Until he does that, this is all a bunch of bench racing..



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Old 09-08-2014, 09:10 PM   #28
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It also depends on if your gearing adds a shift to the 0-60 run...which can actually slow it down.
This is the best point that has been made in this thread. The acceleration you gain from improved gearing has got to offset the extra time you spend shifting. If you shift from 2-3 with your current gears at 65 mph and you gear down so that shift is now at 55 mph, chances are good your 0-60 will be a bit slower. Overall, your Jeep will probably still be a bit quicker, say if you ran a full 1/4, and faster to 55 mph, but not to 60.
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Old 09-08-2014, 09:40 PM   #29
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Actually I did ... read it and absorbed it. He said he ran 0-60 in 6.3 sec. with 3.21 gears..

The OP is discussing ET not MPH... so Faster isn't necessarily a consideration in this discussion, Quicker (ET) is the goal. That means 4.88s with a 5-speed OD will get him 0-60 quicker than 3.21s assuming he dosn't hit a power pole first.

I checked with a GAI and confirmed my assumption..

The only real way to find out, if the OP comes out of hiding and installs those 4.88s and proves he can shave .2 sec off his ET. He also will need to learn how to launch his Jeep with 4.88s.

Until he does that, this is all a bunch of bench racing..



.
Huh??
ET's (Elapsed Time) are comparing distance vs time (1/4 mile-etc..) to determine speed.. not to measure time vs speed (how much time 0-60MPH??)..
What the f**k are you talking about?? you're making no sense at all..
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Old 09-08-2014, 10:13 PM   #30
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There are many variables to consider when trying to improve a 0-60 ET baseline... however, assuming the OP allowed the trans to upshift on its own, using Auto Stick, I would hold the shift at 55 and bounce it off the rev limiter first. This motor makes HP through 6,500 RPM.

With 4.88s he will not see a typical drop in RPMs during the upshifts as he sees with 3.21s. With 4.88s the motor remains in the HP / torque curve longer.

Assuming he has 32" tires and NAG1, ~60 MPH...

3.21s.. engine is at 1,618 RPM.
4.88s.. engine is at 2,460 RPM.

The HP/ torque curve below indicates at final drive he will never hit the rev limiter with 4.88 gears.

Again, all bench racing...

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