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Transmissions, Gearing and RPM

2nd Gen Dakota Tech 1997 - 2004 Dodge Dakota Tech - The ultimate forum for technical help on the 2nd Gen Dakota.

Transmissions, Gearing and RPM

  #11  
Old 01-12-2014, 02:12 AM
Blacknights
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Adding onto what you said and theoretically, I've done the math. With a 3.00 first gear, 2.40 low ratio transfer case, 4.56 differential, 1.25 foot radius tire, a 4.7L's torque (300 ft. lbs). You have the strength to drive a quad cab vertically, 90 degrees up a slope. In second you might start gaining some speed. Anyone want to try this out?

(300 ft. lbs*3*2.4*4.56)/1.25= 9,849 lbs of torque
(300 ft. lbs*1.73(second)*2.4*4.56)/1.25=5,679 lbs of torque
 
  #12  
Old 01-12-2014, 06:37 PM
magnethead
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Torque is rotational force, it becomes thrust at the tangent of the tire. And while numerically the thurst-to-weight ratio may exceed 1:1, a vehicle can't pull itself vertically because you would lose Mu, the traction coefficient. There would have to be a pressure bar going through and behind the wall to keep 100% traction between the tires and wall. The reason indycars can do it is that they have wing down force gluing the tires to the surface.
 
  #13  
Old 01-12-2014, 09:49 PM
Blacknights
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Yes I understand, and however even though I don't know the proper term for it. I understand the principle. I was speaking all in terms of fun and games, I mentioned "theoretically" in the beginning. I mean it would be kind of awesome to be driving vertically at 10 mph. In 12 minutes (Okay longer considering the shift to 1st after about 8,000 ft) you'd be at skydiving height
 
  #14  
Old 01-16-2014, 02:05 AM
magnethead
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The following data is based on video taken this week. Runs were made on the street, not exceeding the speed limit.

Run 1.
1500 rpm....0 mph
2000 rpm....5 mph
2500 rpm.....15 mph
3000 rpm......20 mph
3500 rpm......24 mph
4000 rpm......28 mph
4500 rpm......31 mph
5000 rpm......35 mph
3400 rpm......40 mph
3800 rpm.....47 mph
2200 rpm.....47 mph

Run 2:
1500 rpm.....0 mph
2000 rpm.....5 mph
2500 rpm.....15 mph
3000 rpm.....20 mph
3500 rpm.....25 mph
4000 rpm.....28 mph
4500 rpm.....31 mph
5000 rpm.....35 mph
3500 rpm.....41 mph
2200 rpm....45 mph
 
  #15  
Old 01-16-2014, 02:23 AM
magnethead
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NOTE: The following data is erroneous. My tires check out at 29.75", but for anybody on 4.10's with 32's, have at it, though your numbers likely won't match.

35 MPH / 5000 RPM = 7 MPH per 1,000 RPM

35 MPH = (5000 / 2.74 * Y / 4.10 ) * (32" * 3.141591 / 12 * 60 / 5280)
35 MPH = 445.07 * Y * 0.0952
35 MPH = 42.37 * Y
35 / 42.37 = Y
0.8260 = Y

40 MPH = (3400 / 1.54 * Y / 4.10 ) * (32" * 3.141591 / 12 * 60 / 5280)
40 MPH = 538.49 * Y * 0.0952
40 MPH = 51.26 * Y
40 / 51.26 = Y
0.780 = YY

That's a lot of slip!

47 MPH = (2200 / 1.00 * Y / 4.10 ) * (32" * 3.141591 / 12 * 60 / 5280)
47 MPH = 536.59 * Y * 0.0952
47 MPH = 51.08 * Y
47 / 51.08 = Y
0.920 = Y
 
  #16  
Old 01-16-2014, 09:21 PM
magnethead
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NOTE: The following convertor data is erroneous, though MPH/RPM data is correct. My tires check out at 29.75", not the 32" I thought they were.

Did a 45-75 run video today. Hard to get out of the 45MPH sped limits, have to get on the highway...so I did.

1500 rpm......45 mph
4000 rpm......50 mph
4500 rpm......57 mph
5000 rpm......63 mph
3250 rpm......69 mph
3500 rpm......72 mph
3750 rpm......78 mph

45 mph @ 1500 RPM = 30 MPH per 1,000 RPM (4th gear)
50 mph @ 4000 RPM = 12.5 MPH per 1,000 RPM (2nd gear)
63 mph @ 5000 RPM = 12.6 MPH per 1,000 RPM (2nd gear)
69 MPH @ 3250 RPM = 21.2 MPH per 1,000 RPM (3rd gear)
78 MPH @ 3750 RPM = 20.8 MPH per 1,000 RPM (3rd gear)

Now combine that with yesterday's 0-45 MPH data:

1500 rpm....0 mph
2000 rpm....5 mph
2500 rpm.....15 mph
3000 rpm......20 mph
3500 rpm......24 mph
4000 rpm......28 mph
4500 rpm......31 mph
5000 rpm......35 mph (top of 1st gear)
3400 rpm......40 mph
3800 rpm.....47 mph
<break between runs>
4000 rpm......50 mph
4500 rpm......57 mph
5000 rpm......63 mph (top of 2nd gear)
3250 rpm......69 mph
3500 rpm......72 mph
3750 rpm......78 mph (3rd gear)

And now you have a WOT RPM/MPH map for 4.10's with 29.75ish inch tires and a fairly loose street/strip convertor

I used excel to grab these numbers for convertor slip.

2000 rpm....5 mph = 29.5% drive
2500 rpm.....15 mph = 70.8% drive
3000 rpm......20 mph = 78.8% drive
3500 rpm......24 mph = 80.9% drive
4000 rpm......28 mph = 82.6% drive
4500 rpm......31 mph = 81.3% drive
5000 rpm......35 mph = 82.6% drive
3400 rpm......40 mph = 78.0% drive
3800 rpm.....47 mph = 82.0% drive
4000 rpm......50 mph = 82.9% drive
4500 rpm......57 mph = 84.0% drive
5000 rpm......63 mph = 83.5% drive
3250 rpm......69 mph = 91.4% drive
3500 rpm......72 mph = 88.6% drive
3750 rpm......78 mph = 89.6% drive

And the lone datapoint for 4th gear-

1500 rpm......45 mph = 89.1% drive (note: convertor should have been locked 1:1, but it may be because my tires aren't quite 32, so that would skew alot of this data) <-- BINGO
 
  #17  
Old 01-17-2014, 06:40 PM
magnethead
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problem. Tires measure out at 29.75 in back and 29.5 up front. So I'll have to re-do a lot of the math for 29.75 instead of 32. As hard as I hit the fenders and cut tread blocks, could have sworn they were in the 30's.
 
  #18  
Old 01-17-2014, 10:04 PM
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re-correcting data (starting from up front). I am leaving the original posts in case somebody with 4.10's and 32's comes humming along.

----------------------------------------------------------------

I'm going to extend this a touch, just to see if Hank's numbers and my numbers match. Keep in mind I have the weakling 3.9.

Horsepower 175 hp @ 4400 rpm
Torque 230 ft. lbs. @ 3200 rpm
Bore x Stroke 3.91 x 3.31 in.

2175 rpm = 1200/(2x3.31/12)

4th gear with convertor locked up:
= (2175 / 0.69 / 4.10 ) * (29.75" * 3.141591 / 12 * 60 / 5280)
= 768.82 * 0.0885
= 68.04 MPH

3rd gear with convertor locked up (tow/haul mode):
= (2175 / 1.00 / 4.10 ) * (29.75" * 3.141591 / 12 * 60 / 5280)
= 530.48 * 0.0885
= 46.95 MPH

2nd gear with convertor unlocked (20% slip assumed)
= (2175 / 1.54 * 0.8 / 4.10 ) * (29.75" * 3.141591 / 12 * 60 / 5280)
= 275.578 * 0.0885
= 24.39 MPH


Now lets go run back through that with the 3.55's and 29.0" tires my truck left the assembly plant with:

4th gear with convertor locked up:
= (2175 / 0.69 / 3.55 ) * (29.0" * 3.141591 / 12 * 60 / 5280)
= 887.93 * 0.08627
= 76.61 MPH

3rd gear with convertor locked up (tow/haul mode):
= (2175 / 1.00 / 3.55 ) * (29.0" * 3.141591 / 12 * 60 / 5280)
= 612.67 * 0.08627
= 52.86 MPH

2nd gear with convertor unlocked (20% slip assumed)
= (2175 / 1.54 * 0.8 / 3.55 ) * (29.0" * 3.141591 / 12 * 60 / 5280)
= 318.27 * 0.08627
= 27.46 MPH

So based on that, Chrysler likely felt it would be better to lug the motor with tall gearing and keep the throttle most of the way open. Basically, the ideal situation would be OD off at 55MPH, or OD on at 75 MPH, and pick whatever you want in between because it's a parabolic curve (actually probably closer to 3rd or 5th degree).

With the regear/bigger tire, I didn't really make the losses too great for either 55 or 75 MPH. 29.0 -> 29.75" = 2.5% loss and 3.55 -> 4.10 = 15% gain, so I really gained 12.5% of torque.

This is why I say I wish they made 4.30's for our trucks. Since most of this section's trucks are on 30-32" tires, the 4.30 reallocates the entire system.

4th gear with convertor locked up:
= (2175 / 0.69 / 4.30 ) * (29.75" * 3.141591 / 12 * 60 / 5280)
= 733 * 0.0885
= 64.870 MPH

3rd gear with convertor locked up (tow/haul mode):
= (2175 / 1.00 / 4.30 ) * (29.75" * 3.141591 / 12 * 60 / 5280)
= 505.81 * 0.0885
= 44.76 MPH

2nd gear with convertor unlocked (20% slip assumed)
= (2175 / 1.54 * 0.8 / 4.30 ) * (29.75" * 3.141591 / 12 * 60 / 5280)
= 262.76 * 0.0885
= 23.25 MPH

4th gear with convertor locked up:
= (2175 / 0.69 / 4.30 ) * (32" * 3.141591 / 12 * 60 / 5280)
= 733 * 0.0952
= 69.78 MPH

3rd gear with convertor locked up (tow/haul mode):
= (2175 / 1.00 / 4.30 ) * (32" * 3.141591 / 12 * 60 / 5280)
= 505.81 * 0.0952
= 48.15 MPH

2nd gear with convertor unlocked (20% slip assumed)
= (2175 / 1.54 * 0.8 / 4.30 ) * (32" * 3.141591 / 12 * 60 / 5280)
= 262.76 * 0.0952
= 25 MPH


4.30's with a 32" tire moves the economy state to right there at 70 MPH, which is the actually traveled speed of most interstates. The trade off is a pretty steep loss at 55 MPH.

But that's okay. 4.30's don't exist for our axles.

4th gear with convertor locked up:
= (2175 / 0.69 / 4.56 ) * (29.75" * 3.141591 / 12 * 60 / 5280)
= 691.26 * 0.0885
= 61.17 MPH

3rd gear with convertor locked up (tow/haul mode):
= (2175 / 1.00 / 4.56 ) * (29.75" * 3.141591 / 12 * 60 / 5280)
= 476.97 * 0.0885
= 42.21 MPH

2nd gear with convertor unlocked (20% slip assumed)
= (2175 / 1.54 * 0.8 / 4.56 ) * (29.75" * 3.141591 / 12 * 60 / 5280)
= 247.78 * 0.0885
= 21.93 MPH

Now we have some pretty big moves. 4th gear isn't so bad, but we just can't get close to a 55 MPH economy number.

One more time.

4th gear with convertor locked up:
= (2175 / 0.69 / 4.88 ) * (29.75" * 3.141591 / 12 * 60 / 5280)
= 645.93 * 0.0885
= 57.16 MPH

3rd gear with convertor locked up (tow/haul mode):
= (2175 / 1.00 / 4.88 ) * (29.75" * 3.141591 / 12 * 60 / 5280)
= 445.70 * 0.0885
= 39.45 MPH

2nd gear with convertor unlocked (20% slip assumed)
= (2175 / 1.54 * 0.8 / 4.88 ) * (29.75" * 3.141591 / 12 * 60 / 5280)
= 231.53 * 0.0885
= 20.49 MPH

4th gear doesn't look so bad anymore, does it? Be alot of RPM, but probably good fuel mileage too for the innercity commuter. Wouldn't want it on the highway, though.

Chrysler engineers win other than 4.88.


Which is more important: having the rpms near this 1200 foot per minute
speed for the pistons, or having the throttle in the 65-75% open range?
Answer: it is more important to be in the 70% throttle range and you should
slow down the rpms to get there. There is not much change in efficiency
when piston speed drops from 1200 down to 800 ft/minute but there is a big
change in efficiency when the throttle goes from 70% open to 40% open.

Why?

Imagine that you have a disassembled engine in front of you. Put a loose
piston in a bore and pull it down against the friction of the rings. It won't
be very hard. Now imagine that same piston in the bore has the top of the
bore sealed off and has a vacuum sucked of 12 inches of Mercury.
12 inches of vacuum is about 6 psi of negative pressure. If the piston is
4.00 inches in diameter it has an area of about 12.5 square inches
(remember pi R squared but most cherry pies are round?)
6 pounds per square inch times 12.5 square inches = 75 pounds would be
required to pull the piston down - you probably couldn't do it with the grip
of just a couple fingers! An engine running with a high vacuum in the intake
manifold has to do just this, and for eight cylinders!


-------------------------------------------



Part 2: Because we don't drive bleeping Priuses!

[Footnote: This data is pretty limited to my build only, but the data can be processed similarly for any other setup]

I do have this video from 2011. I'm not sure if it's before or after the re-gear, so lets find out.


40 MPH @ 5,000 RPM in first gear = 8 MPH per 1,000 RPM

40 MPH = (5000 / 2.74 * 0.8 / X ) * (29.75" * 3.141591 / 12 * 60 / 5280)
40 MPH = 1459.85 / X * 0.0885
40 MPH = 129.20 / X
129.20 / 40 = X
3.22 = X

So it was with the stock 3.55 gears. But since 3.22 is unequal to 3.55, the convertor efficiency is off. Let's figure it out.

40 MPH = (5000 / 2.74 * Y / 3.55 ) * (29.75" * 3.141591 / 12 * 60 / 5280)
40 MPH = 514.03 * Y * 0.0885
40 MPH = 45.50 * Y
40 / 45.50 = Y
0.8791 = X


Now for second gear.

I'm going to call it being 3150 at the fallback @ 45 MPH, for 14.28 MPH per 1,000 RPM.

45 MPH = (3150 / 1.54 * Y / 3.55 ) * (29.75" * 3.141591 / 12 * 60 / 5280)
45 MPH = 576.18 * Y * 0.0885
45 MPH = 50.99 * Y
45 / 50.99 = Y
0.883 = X

And for the top of second gear:
4,000 RPM @ 60 MPH, for 15 MPH per 1,000 RPM.

60 MPH = (4000 / 1.54 * Y / 3.55 ) * (29.75" * 3.141591 / 12 * 60 / 5280)
60 MPH = 731.66 * Y * 0.0885
60 MPH = 64.75 * Y
60 / 64.75 = Y
0.9266 = X

[footnote 2: The rest of this is pending newer footage]

Since that video, I've added Methanol Injection, a high-stall convertor, 4.10 gears, 1.7 roller rockers, E-fan mod/clutch fan delete, and SCT 94 octane tune.

If you are into math and almost-calculus, I refer you here: https://dodgeforum.com/forum/racing-...the-track.html

otherwise, continue with abbreviated version below:

On the night of that video, I 60'd in the 2.70 even range.

60 feet divided by 2.7 seconds = average speed of 22.22 feet per second.

That divided by 2.7 seconds again is an average acceleration of 8.230 feet per second squared. (verify: 60 divided by 2.7^2 = 60/7.29 = 8.230)

60 feet divided by 2.3 seconds squared = an average acceleration of 11.342 feet per second squared.
Now let's jump ahead to the reverse engineering part.

32,096.162 poundals divided by 3400 pounds = 9.44 feet per second squared (an improvement of 1.21 feet per second squared)

60 feet divided by 9.44 feet per second squared = 6.35 seconds squared.

square root of 6.35 is 2.52 seconds

So the gears alone will put me from a 2.7 to a 2.52 second 60 foot time.
Thanks to my form of archiving (and keeping every time slip for the truck) -> https://dodgeforum.com/forum/2nd-gen...-the-dako.html

[Footnote: the atmosphere was significantly different for the following run data, so it's hard to compare them]

Stock,
2.678 | 7.676 @ 46.00 | 11.798 @ 58.94

with only the SCT and 180 stat, best pass was
2.684 | 7.565 @ 47.10 | 11.574 @ 60.30

with 180 stat, SCT, clutch fan delete, 1.7 roller rockers, 4.10 gears, best pass was
2.610 | 7.282 @ 48.95 | 11.132 @ 62.90

After adding the high stall convertor and methanol,
2.460 | 7.7073 @ 48.86 | 10.920 @ 62.37

Let's focus on the 60 foot. The quicker the sixty, the quicker the run.

2.678
2.684
2.610
2.460

That's quite the bit of a difference. But the math above said I would go from a 2.70 to a 2.52 with the gear change. I only got to the low 60's, about half that change. Why? Because I was losing torque multiplication through the torque convertor. By going to a deeper gear, I removed load from the convertor, tightening it up, lowering it's stall/hydraulic lock-up RPM. So even though I was getting more torque multiplication through the rear gears, I was losing it through the torque convertor.

I needed a looser torque convertor that would multiply torque for a longer period of time. So I got one and put it in. Not only did I hit that target 2.52, I passed it and hit 2.46 (but I will also attribute some of that to the methanol and Hemifever's tune to suit it).

I passed it so hard, I've run into traction problems. Being an open diff, the right rear tire is no longer staying attached to the track. I have no doubt that I can get into the low 2.40's once I get hooked up. The goal is to get into the 2.10's-2.20's-2.30's to break into the 9's.

I'm going to do it by manipulating the effective ratio.

By going from a 29.75" AT to a 26.5" DOT slick, I'm reducing the diameter and therefore circumference by 11%. I'm taking the effective ratio from 29.75" @ 4.10:1 to 26" @ 4.69:1.

In an ideal world, that's 11% increased torque = 11% thrust. In an ideal world, 11% gain in thrust = 11% gain in 60ft. 11% gain takes a 2.46 sixty to a 2.18 sixty. But we don't live in an ideal world.

The trade-off in changing the effective ratio, is now I have other things to consider. Instead of making big torque at little RPM like a V8, I'm taking advantage of the V6 making mediocre torque at high RPM. The smaller tire doesnt go as far per rotation, so RPM goes up. Higher driveline RPM + high torque RPM = I'm closer to the torque number.

= (3200 / 2.74 * 0.8 / 4.10 ) * (29.75" * 3.141591 / 12 * 60 / 5280)
= 227.88 * 0.0885
= 20.17 MPH

= (3200 / 2.74 * 0.8 / 4.69 ) * (29.75" * 3.141591 / 12 * 60 / 5280)
= 199.21 * 0.0885
= 17.63 MPH

= (3200 / 2.74 * 0.8 / 4.10 ) * (26.5" * 3.141591 / 12 * 60 / 5280)
= 227.88 * 0.0788
= 17.96 MPH

(For an apples to apples comparison, I'm going to neglect convertor torque multiplication)

230 ft-lb * 2.74 * 3.55 = 2,237 ft-lb / (1.24 ft) = 1,804 pound-force thrust
230 ft-lb * 2.74 * 4.10 = 2,584 ft-lb / (1.24 ft) = 2,084 pound-force thrust
230 ft-lb * 2.74 * 4.10 = 2,584 ft-lb / (1.10 ft) = 2,349 pound-force thrust
230 ft-lb * 2.74 * 4.69 = 2955 ft-lb / (1.24 ft) = 2,383 pound-force thrust

That's just due to round-off error.

The problem I now face, is that I have now once again removed load from the torque convertor, so it will tighten up again. But that's okay, for for this reason: since the engine RPM will be higher, I will want it to hydraulically lock up to maximize the amount of torque passed through at the torque peak.

The idea of a looser torque convertor is that the engine can be closer to the powerband (an arbitrary point between the torque RPM peak and the HP RPM peak) with the driveline locked, so that the engine is already nearly making peak power the instant that the brakes are released. Then you want it to hydraulically lock as quick as possible to transfer the power peak into the driveline. Between those two points, torque multiplication occurs inside the torque convertor, as much as 2.5:1 at the asymptote to the not-locked stall point.

Another issue that must be dealt with is gear choice vs rev limiter. With the 26" tire (Excel helped me greatly here), I'll be around 34 MPH at the rev limiter in first gear, 61 MPH at the top of second gear, and 94 MPH at the top of third gear.

Why is that important? Because I'm already going through the 1/8" traps against the high side in 2nd gear with the 32" tires. No question I'll be using third gear on the 26.5" tire. Also, 94 MPH high side in third gear is up to an 9.00 @ 76 MPH 1/8 mile pass or 14.00 @ 94 MPH 1/4 mile pass. I have to consider the ability to do 1/4 mile because it may crop up now and then. I don't think I will ever get that fast with this motor, but you never know. 76 MPH will be around 4,000 RPM in third.

So there you have it. How gearing, tire size, and torque convertors all play together on top of what Hank said in that other thread.


-----------------------------


5 MPH / 5000 RPM = 7 MPH per 1,000 RPM

35 MPH = (5000 / 2.74 * Y / 4.10 ) * (29.75" * 3.141591 / 12 * 60 / 5280)
35 MPH = 445.07 * Y * 0.0885
35 MPH = 39.39 * Y
35 / 39.39 = Y
0.889 = Y

40 MPH = (3400 / 1.54 * Y / 4.10 ) * (29.75" * 3.141591 / 12 * 60 / 5280)
40 MPH = 538.49 * Y * 0.0885
40 MPH = 47.66 * Y
40 / 47.66 = Y
0.840 = Y

That's a lot of slip!

47 MPH = (2200 / 1.00 * Y / 4.10 ) * (29.75" * 3.141591 / 12 * 60 / 5280)
47 MPH = 536.59 * Y * 0.0885
47 MPH = 47.49 * Y
47 / 47.49 = Y
0.99 = Y

(The convertor locks up 1:1 in OD, so for all round-off purposes....it's correct)


--------------------


I used excel to grab these numbers for convertor slip.

2000 rpm....5 mph = 31.7% drive
2500 rpm.....15 mph = 76.2% drive
3000 rpm......20 mph = 84.6% drive
3500 rpm......24 mph = 87.0% drive
4000 rpm......28 mph = 88.9% drive
4500 rpm......31 mph = 87.4% drive
5000 rpm......35 mph = 88.5% drive
3400 rpm......40 mph = 83.4% drive
3800 rpm.....47 mph = 88.2% drive
4000 rpm......50 mph = 89.2% drive
4500 rpm......57 mph = 90.3% drive
5000 rpm......63 mph = 89.9% drive
3250 rpm......69 mph = 98.4% drive
3500 rpm......72 mph = 95.3% drive [aero drag comes into affect]
3750 rpm......78 mph = 96.3% drive

And the lone datapoint for 4th gear-

1500 rpm......45 mph = 95.9% drive (should have been locked 1:1 in 4th gear. )
 
  #19  
Old 01-17-2014, 10:05 PM
magnethead
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Here is my 45-75 run:

 
  #20  
Old 01-17-2014, 10:36 PM
magnethead
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This will be not for the faint of heart. Welcome to Automotive calculus.

I had a friend offer me a set of 40-pass 26" DOT slicks off of his old tire rack (he does land speed stuff now, not so much drag racing), I just have to find a set of 15" dak/dur wheels to put them on. That just saved me about $400 in my endeavor. haha

derived from https://dodgeforum.com/forum/racing-...the-track.html


So I did a google search for dakota time slips, and came across a certain site that has a very convenient timeslip database, some with pictures. I established that it basically takes a 2.20-2.30 60 foot to run low 10's. So I thought about that for a second.

Average 60 foot time is currently 2.46-2.50. I'll use 2.50 for following calculations since it's nice and round.

60 feet divided by 2.5 seconds = average speed of 24 feet per second.

That divided by 2.5 seconds again is an average acceleration of 9.6 feet per second squared. (verify: 60 divided by 2.5^2 = 60/6.25 = 9.6)

60 feet divided by 2.3 seconds squared = an average acceleration of 11.342 feet per second squared.

How to make up that much acceleration?

Lets say the rolling radius of a tire is 14" (1.166 ft), first gear is 2.74, rear is 4.10.

T = Torque (Tau)
F = force
D = distance
R = radius
A = linear (tangential) acceleration
a = angular acceleration (alpha)
m = mass

T = F x D
F = m x A

T = m x A x D (yes, I know that spells MAD..but you have to be to enjoy this stuff!)

A = r x a

since R = D when talking Torque of a tire,

T = m x A x R

since A = R x a,

T = m x R x R x a

T = m x r^2 x a

Thus, Torque is directly related to Mass, Radius, and Angular Acceleration

To improve acceleration, we are to assume that mass will stay the same, and radius will stay the same. Thus, Torque must increase.

---

Hang with me here:

T = m x r^2 x a
T' = m x r^2 x a'

T/a = m x r^2
T'/a' = m x r^2

T/a = T'/a'

That's a basic ratio. I hope you're still with me. This won't be so basic.

Go back to this:

T = F x D
F = m x A

Force: 4200 pounds x 9.6 fps^2 = 4200 x 9.60 pound-feet per second squared = 4200 x 9.60 poundals

The tires are the only thing accelerating the vehicle, to the tires must be providing a tangential force of 4200 x 9.6 poundals

Torque is force times radius (distance)

T = 4200 x 9.6 poundals TIMES 1.166 feet (14" tire rolling radius)

T = 4200 x 9.6 x 1.166 poundal-feet

32.174049 poundal-feet = 1 foot-pound of torque

4200 x 9.6 x 1.166 = 47,013.12 poundal feet = 1,461.212 foot-pounds of torque

So that says that based on that guestimated weight, I'm making an average of about 1,461 foot-pounds of torque at the axle shaft.

Now let's bring the gears into the equation:

1,461 / 4.10 / 2.74 = 130 foot-pounds of torque.

I bet you're going, "That aint right!" And it's not- that's ignoring any torque multiplication going on in the torque convertor, plus I under-balled that weight [though not by much]. Even with being an average value, it shouldn't be that low. The V6 is supposed to be rated at 225 ft-lb of torque, so I'm off by about 42.5%.

Anywho, everything in this world is relative anyways. So we'll go with it, and now work everything backwards with the smaller tires.

130 * 2.74 * 4.10 = 1,461.212 foot pounds

1,461.212 * 32.174049 = 47,013.12 poundal-feet (no change to this point)

47,013.12 poundal-feet divided by 1.04 feet (rolling radius) = 45,204.923 poundals (was 40,320)

45,204.923 poundals divided by 4200 pounds = 10.76 feet per second squared (an improvement of 1.16 feet per second squared)

60 feet divided by 10.76 feet per second squared = 5.58 seconds squared.

square root of 5.58 is 2.36 seconds

So the tires alone will put me from a 2.50 to a 2.36 second 60 foot time.

Database says that a 2.36 will put me in the range of 10.05 to 10.20 1/8 mile time, leaned more towards the 10.10-10.20 range.

I found a timeslip on that database from a 4.7 tuned durango with the following:

60- 2.346
330- 6.602
1/8- 10.163 @ 69.06
1000- 13.261
1/4- 15.931 @ 83.98

Remember, with the 26" DOT slicks, I'll be 94 MPH at the top of third gear. So to run that slip above, I'd probably be around 4500 RPM or so.
 

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