Rational Powertrain Selection
This discussion
will examine an engineering based approach to the selection of
engine size, transmission, and ring & pinion ratio. We will base
this on a Cobra replica, but it is applicable to any car.
The examples will be based on optimizing a
Cobra for street use. The same procedure can be used for racing
with a simple modification that I will discuss later. All numbers
given in the examples are corrected to a 2,400 lb car. So, when you
see numbers for a 3,200 lb C6 Corvette, the actual numbers have been
divided by 3,200 lbs and then multiplied by 2,400 lbs to get an
equivalent power to weight number that can be directly compared to
the Cobra. The HP and Torque numbers have also been corrected from
Net to Gross to allow for comparison.
We first need to have a short discussion on
Torque and HP. The measure of actual force available to accelerate
the car is Torque. HP is Torque multiplied by RPMs and is just a
mathematical construct. The HP number was developed to take into
account the fact that if one engine was making 300 ft/lbs of torque
at 3,000 RPM and another was making 300 ft/lbs of torque at 6,000
RPM, the 6,000 RPM engine could be geared down 2 to1 compared to the
3,000 RPM engine and the double gearing would produce an output of
twice the torque. However, if both engines are geared the same, the
actual force produced would be the same even though the HP figure
for one would be twice the HP of the other.
Remember: Torque is the actual force we are
working with, the HP number only indicates how high in RPM the
engine is able to hold its torque as it revs out.
OK, now that we have that out of the way…
To begin with, Cobras, like all light
high-powered cars, are traction limited. You can easily build more
motor than you can possibly hook up. Therefore, we begin with
finding how much torque the tires have the traction to handle.
I have done a number of surveys of cobra
owners, and the numbers come out as follows. (Note: These numbers
are approximate! Differences in front to rear weight distribution,
road surface and temperature, etc. will modify the actual values.
Consider these Ballpark numbers. Also, these numbers are
torque at the tires and not to be confused with engine torque).
15” Street Tires (Yokohama Avid S/T, etc.) ---
2,300 ft/lbs
17” Top Quality Street Tires (BFG g-Force,
Goodyear GS-D3, etc.) --- 2,800 ft/lbs
I do not have sufficient information to
accurately predict the numbers for Drag Radials or DOT Race tires.
I would estimate them to be in the area of 3,100 ft/lbs, but that is
just an estimation.
For a car driven on the street, the critical
gear is second. Second gear is good for 70 to 80 MPH in most cars,
optimizing for higher speeds is unrealistic for street use since you
will spend 99% of your time within that speed range. For racing,
optimizing for third gear would probably be better, so long as you
don’t end up with so much torque in second that you spin the car off
into the weeds every couple of laps because you can’t control it.
The formula for finding torque at the tires is
very simple. You take the flywheel torque for the engine, multiply
it by the ring and pinion ratio, and then multiply that by the
transmission ratio for the gear in question.
Example, a 347 making 420 ft/lbs of torque at
the flywheel, with a 3.54 R&P and second gear in a TKO trans (1.89):
420 x 3.54 x 1.89 = 2,810 ft/lbs of torque at
the tires.
Notes:
1 – This is the peak torque number, through
most of the RPM band, the actual torque will be less.
2 – to estimate the torque of any street
engine, use the following formulas. (HP can vary tremendously, but
torque remains in a very small range for all naturally aspirated
engines.) For factory engines with stock iron cylinder heads,
multiply displacement by 1.1. For engines with high performance
aftermarket aluminum cylinder heads, multiply displacement by 1.2.
Here are some numbers for reference:
(Note: These are all Gross HP and Torque
ratings. All production cars after 1973 were rated Net HP and
Torque, which is the Gross number minus all losses from the exhaust
system, intake system, and accessory drives. A rough approximation
of Gross HP and Torque can be obtained for newer engines by
multiplying the Net number by 1.1).
|
Ford street engines with modern aluminum heads: |
| 306 |
390 HP @ 6,000 |
370 ft/lb @ 4.800 |
| 331 |
410 HP @ 5,900 |
400 ft/lb @ 4,800 |
| 357 |
430 HP @ 5,800 |
430 ft/lb @ 4,700 |
| 383 |
450 HP @ 5,700 |
460 ft/lb @ 4,600 |
| 408 |
470 HP @ 5,600 |
490 ft/lb @ 4,500 |
|
Ford factory engines with stock heads: |
| 289 Hi-Po |
271 HP @ 5,800 |
314 ft/lb @ 3,400 |
| 289 Race |
385 HP @ 6,750 |
340 ft/lb @ |
| 302 / 5.0L |
280 HP @ 5,200 |
325 ft/lb @ 4,000 |
| 302 Boss |
320 HP @ 5,800 |
330 ft/lb @ 4,300 |
| 351 Cleveland |
300 HP @ 5,400 |
380 ft/lb @ 3,400 |
| 351 Boss |
330 HP @ |
370 ft/lb @ 4,000 |
| 390 4-bl |
375 HP @ 6,000 |
427 ft/lb @ 3,400 |
| 390 3 x 2-bl |
401 HP @ 6,000 |
430 ft/lb @ 3,500 |
| 428-CJ |
360 HP @ 5,400 |
460 ft/lb @ 3,200 |
| 428-Shelby |
390 HP @ 5,200 |
470 ft/lb @ 3,700 |
| 427 4-bl |
410 HP @ 5,600 |
475 ft/lb @ 3,400 |
| 427 2 x 4-bl |
425 HP @ 6,000 |
480 ft/lb @ 3,700 |
| 427 Race |
480 HP @ 6,500 |
510 ft/lb @ 3,700 |
Next let’s look at transmission ratios.
Here are the ratios for both modern and
historical transmissions.
| Transmission Gear Ratios |
| |
1st |
2nd |
3rd |
4th |
5th |
| T5 |
3.35 |
1.99 |
1.33 |
1.00 |
0.68 |
| T5 (non-standard) |
2.95 |
1.99 |
1.33 |
1.00 |
.068 |
| TKO 600 |
2.87 |
1.89 |
1.28 |
1.00 |
0.82 |
| Toploader WR |
2.78 |
1.93 |
1.36 |
1.00 |
-- |
| BorgWarner WR T-10 |
2.56 |
1.91 |
1.48 |
1.00 |
-- |
| Muncie M20 |
2.52 |
1.88 |
1.46 |
1.00 |
-- |
| Toploader CR |
2.32 |
1.69 |
1.29 |
1.00 |
-- |
| Borg Warner CR T-10 |
2.20 |
1.66 |
1.31 |
1.00 |
-- |
| Muncie M21 |
2.20 |
1.64 |
1.28 |
1.00 |
-- |
| C4 / C6 |
2.46 |
1.46 |
1.00 |
-- |
-- |
We now have sufficient information to make a
selection.
As I stated before:
The formula for finding torque at the tires is
very simple. You take the flywheel torque for the engine, multiply
it by the ring and pinion ratio, and then multiply that by the
transmission ratio for the gear in question.
Example, a 331 making 400 ft/lbs of torque at
the flywheel, with a 3.54 R&P and second gear in a TKO trans (1.89):
400 x 3.54 x 1.89 = 2,676 ft/lbs of torque at
the tires.
(If you are using larger tires, like 275/60-15,
you would need to multiply the final number by .957 (26.7 divided by
27.9) to correct for the larger diameter tires.)
Here are some examples of actual numbers:
Note: There are gear ratio numbers in
parenthesis for the original cars and the CR Toploader examples.
The original cars used tires that were about 27.75” diameter and
that had the effect of changing the effective gear ratio to that
shown in parenthesis. If you are using a 275/60-15 rear tire, these
would be correct. If you are using a 295/50-15 or similar modern
size tires, the numbers shown for the T5 and TKO would be correct:
The first column is the first gear ratio.
Second column is the second gear ratio. Third column is the HP
(Remember these numbers are corrected to a 2,400 lb equivalent
weight). The next three columns are the speed in first, second, and
top gear @ 6,000 RPMs. The last column is the RPMs @ 60 MPH.
Original Cobras:
2.32 1.69 HP 1st 2nd
4th @ 60
289 @ 3.73 (3.65): 2,950
2,150 300 55 75 127 2,850
289 FIA @ 3.73: 3,150
2,300 420 64 88 148 2,850
390 @ 3.54 (3.41): 3,350
2,450 400 59 81 137 2,650
427 @ 3.54 (3.41): 3,550
2,600 400 59 81 137 2,650
427 Comp @ 3.54: 3,900
2,850 465 64 88 148 2,650
CR Toploader:
2.32 1.69 HP 1st 2nd
4th @ 60
306 @ 3.54 (3.39): 2,900
2,100 390 59 81 138 2,650
331 @ 3.54 (3.39): 3,150
2,300 410 59 81 138 2,650
357 @ 3.54 (3.39): 3,400
2,450 430 59 81 138 2,650
383 @ 3.54 (3.39): 3,600
2,650 450 59 81 138 2,650
408 @ 3.54 (3.39): 3,850
2,800 470 59 81 138 2,650
T5: 3.35 1.94
HP 1st 2nd 5th @ 60
306 @ 3.27: 4,050
2,350 390 42 72 219 1,650
306 @ 3.54: 4,400
2,550 390 39 66 201 1,800
306 @ 3.73: 4,650
2,700 390 37 63 192 1,900
TKO:
2.87 1.89 HP 1st
2nd 5th @ 60
347 @ 3.27: 3,900
2,600 420 49 74 171 2,150
347 @ 3.54: 4,250
2,800 420 45 68 158 2,300
347 @ 3.73: 4,500
2,950 420 43 65 150 2,400
393 @ 3.54: 4,800
3,150 460 45 68 158 2,300
Historical:
1st 2nd HP 1st
2nd 4th @ 60
LS-6 Chevelle:
WR @ 3.54: 3,000
2,250 300 50 68 129 2,800
WR @ 3.73: 3,150
2,350 300 48 65 123 2,950
WR @ 3.91: 3,300
2,450 300 46 62 117 3,100
66 427 Vette:
CR @ 3.54: 2,900
2,150 350 59 78 129 2,800
WR @ 3.54: 3,350
2,450 350 50 68 129 2,800
65 327 Vette:
WR @ 3.54: 2,650
1,950 280 50 68 129 2,800
65 4.2 XKE: 3,000
1,650 250 43 74 129 2,800
Modern Cars:
1st 2nd HP 1st 2nd
Z06:
3,600 2,400 430 61 91
Viper:
3,400 2,300 410 59 88
Ford GT:
3,500 2,300 430 61 93
C-6:
3,400 2,400 340 50 72
Ferrari 612:
3,450 2,400 350 48 69
BMW Z4 M: 3,350
1,950 280 38 66
Mustang GT: 2,900
1,750 235 39 65
BMW Z4: 2,500
1,450 215 36 63
For the modern cars, note how closely the
torque numbers are grouped for the higher HP cars. This is what the
engineers at the auto companies have found is the optimum. Because
Cobras are much lighter and use proportionally much wider tires for
their weight, they can make slightly higher values work.
One of the main reasons the original cars
worked was the close ratio toploader transmission that reduced the
torque to manageable levels in first and second gear. In our
examples, you can see that a 306 with a T5 and 3.54 R&P is making
4,400 ft/lbs of torque in first gear compared to an original car
with a 427 and 3.54 R&P that made 3,350 ft/lbs. In second gear they
are nearly the same at 2,550 ft/lbs and 2,600 ft/lbs respectively.
Where this is made up is in the speed the car
reaches in each gear. The T5 car only reaches 39 MPH @ 6,000 RPM in
first gear, where the Toploader car reaches 59 MPH @ 6,000 RPM.
Since the T5 car can’t possibly hook up 4,400
ft/lbs of torque, it is no faster up to 39 MPH than the Toploader
car, but from 39 to 59 MPH the toploader car is still in first and
making it’s full 3,350 ft/lbs to the T5 cars’ 2,600 ft/lbs in second
gear.
Once you know what type of tires you will be
using, and therefore the maximum torque you can hook up, you can run
the numbers with different engine sizes, transmissions, and ring &
pinion ratios to find the combination that gives you the desired
level of torque in second (or for racing, third) gear. This will
give you a non-guesswork method for optimizing your car to fit its
intended use.
Kevin McGowen
April 05, 2007
