Differential Calculations

Here’s a few figures I ran while calculating the differences between differential ratio’s and tire sizes.
With the aim being how a 3.25 or 3.50 diff for the 31 roadster compares against the 3.70 diff in my 32 roadster.

What folks forget sometimes is you can make fairly large changes in the overall rear axle ratio by simply swapping tire size.
And if you don’t make too large of a diff ratio change and run a similarly sized tire - not too much larger or smaller in diameter than the tire used for the base comparison - you may not have gained much.

Tires involved in these calculations are the 29" tall tires on the 32 and the 28" tall tires on the 31.
Interestingly, the 28" tall tire is about the same height as the 8.20 x 15 bias plies that were popular back in the day.
The 8.20 wasn’t too much of a change over the 6.70 x 15 tires that came stock on 50 Shoeboxes, but if you ran the stock 3.78 diff gear's (from memory, so bear with me here) the 8.20's could drag things down a bit.

Shoeboxes that had overdrive transmissions ran (factory installed) 4.10 diff gears so the jump to the larger diameter tire didn’t drag these cars down too much.
Even so, the bigger tires which took more effort to turn and had more traction helped to a considerable degree in breaking the decidedly weak Shoebox driveline stuff.

One thing that was a saver here was when we swapped an OHV engine in and utilized the stronger transmission that either came with the engine or a different brand transmission that bolted to - factory bellhousing or aluminum aftermarket adapter - the engine did the trick most times.
The weak link then was the Shoebox rear axle.
These things seemed to break axles at the least provocation.

That problem solved when we discovered that the Ford and Merc 49 to about 54 or so ****er rear axles out of station wagons were a bolt-in.
A bonus with these was to find an overdrive car because the diff ratio in those was 4.27.
Another plus were the 11" brakes as vs the standard p***enger car 10" brakes.

Along with this swap, other than the low ratio which added a lot to the car’s performance capabilities we learned about brake balance.
A few highway type panic stops where the car tried to switch ends had us going back to the junkyard and grabbing the 11" front drum brakes off the station wagons.
It made for an excellent brake system and the hot setup was to install Velvetouch linings.
Velvetouch linings were favored in aircraft and the circle burner gang used em in their race cars as well.
With the lining being made of Sintered (finely ground) metal and a ceramic binder baked in a very hot oven - over 1000 degrees for a specific amount of time - made for a fairly fade-proof brake shoe for highway and mountain driving as well as drag racing.
Never had a Velvetouch lining fade.
Raybestos - brand name - ‘hard’ linings worked fairly well in the street performance venue as well.
Their ‘soft’ linings had an easier pedal, but wore faster and faded easier.

The ****er rear axles were fairly bulltproof all things considered.
Especially so for the power levels we were running - which was around 250 horsepower for mildly built overheads and the stronger street runners were pumping out about 300 horsepower.
Not much horsepower when compared to the engines of today, stock or built, but it was enough power to get the job done most times and considering the lightweight cars the engines were in, things worked out pretty well.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The formulas used for these calculations are the standard ones for figuring percentages as well as an old standard.

The old standard being:

TD x RPM divided by AR x 336
TD = Tire Diameter
RPM = you know this one . . . and if you don’t, maybe you’re in the wrong place.
AR = Axle Ratio
336 = K or the constant

Like any other math formula if you have enough knowns you can solve for the any of the unknowns.

And like always, there’s an easy way to do things as well as some shortcuts.
To make life easy, use 1000 RPM when you do the TD x RPM bit.
That will give you a constant for that particular diff ratio and you can do some basic math to find MPH at a particular RPM and better yet to find the RPM for a particular MPH.

RPM at highway speeds is what most of us are concerned with.
We don’t want to end up with an engine spinning 3800 RPM at moderate highway speeds.
Nor do we want it running too low on the RPM scale and lugging.

I’ve always heard and it seems to hold true for heavier vehicles is that you should gear for the desired highway speed at the engines RPM rating for maximum torque.
In the case of our hot rods some estimates will have to be made, but it won’t make too much difference since hot rods are fairly lightweight compared to one ton pickups, motorhomes and the like.
Best to err on the lower side as far as RPM values go.

First up are some comparisons between the available ratio’s - which are 3.25, 3.50 and 3.70.

The first set of figures are for 28" tires and the second set is for 29" tires.

Surprisingly, there’s more of a difference in RPM levels with only a 1" change in tire diameter than I originally thought.


1K = 1000 RPM.


28" Tires
3.25 Diff
25.6 mph per 1K RPM

3.50 Diff
23.8 mph per 1K RPM

3.70 Diff
22.5 mph per 1K RPM

RPM @ 65 MPH
3.25 = 2539 RPM
3.50 = 2731 RPM
3.70 = 2888 RPM


3000 RPM = MPH
3.25 = 76.8 MPH
3.50 = 71.4 MPH
3.70 = 67.5 MPH

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

29" Tires
3.25 Diff
26.5 mph per 1K RPM

3.50 Diff
24.6 mph per 1K RPM

3.70 Diff
23.3 mph per 1K RPM


RPM @ 65 MPH
3.25 = 2452 RPM
3.50 = 2642 RPM
3.70 = 2789 RPM


3000 RPM = MPH
3.25 = 79.5 MPH
3.50 = 73.8 MPH
3.70 = 69.9 MPH


Percentage Difference Between Ratio’s
3.50 - 3.70 = 5%
3.25 - 3.70 = 12%
3.25 - 3.50 = 7%


Percentage Difference Between 28" & 29" Tires
The 28" tire is 96% of the height of the 29" tire.
The 29" tire is 103% of the height of the 28" tire.

To make life - and calculations - easy, just use 4% as the difference between them.



All these figures are predicated by use of a transmission with no slippage and a one to one ratio in high gear.
Toss in a high stall converter and the values will change.
Even so, the figures are useful and come close enough to real world automatic transmissions as used by most of us.

As is obvious, use of a 3500 RPM stall converter means that in most highway driving with a reasonable differential ratio, you’ll never reach full lock-up and the converter will be slipping.
A slipping converter makes heat and could be one reason why the engine overheats at highway speeds and especially so when climbing long grades.
In some cases a low stall converter will help cure the overheating at highway speeds problem.

A converter with say, 2400 RPM stall in a light car locks up fairly well at 65 MPH on level ground, but it will still slip a bit on grades.
Keep in mind too that a 2400 RPM - or other figure - is somewhat arbitrary.
A small engine may stall a 2400 RPM rated converter at 2000-2200 RPM and a bigger - read more torque -engine running the same converter may stall at 2800 RPM.


So . . . with the 32 running 29" tall tires with a 3.70 diff and doing fairly well on the highways, you can see why I chose the 3.25 diff to go along with the 31's 28" tall tires.

Driving the 32 in Sunny California, a lot of it was in-town and not too many trips over 200 miles.
Now that I’m living in even Sunnier Arizona with it’s long desert highways and speed limits set at 70 MPH on many of them, along with the need to travel longer distances it’s easy to understand why the desire for a lower engine RPM level during long drives.

It kinda bugs me to see the 32's big engine (462" Buick) sitting at 3000 - 3200 RPM for long periods.
Just running the figures in my head - the above were done by a calculator - it looks like the 31 will be cranking off 70 MPH at about 2700 RPM.
An entirely livable figure and it will work well performance-wise if you consider the 31 will weigh about 2200# and with the big engine built more for torque than RPM, pulling away from stoplights and up freeway on-ramps shouldn’t be a problem.

Kinda fun methinks . . . and if it wasn’t fun why would we be building the cars we do?

Sittin’ around the Saturday night rod run isn’t what it’s all about in my book.

Gettin’ out there and runnin’ em makes it for me.

Nuff said....

 

Ow...my..head..hurting...the...pain....

Intesting...would this be worthy of a Tech article? powers that Be.??

 

GOOD INFO that you posted. In case every one doesn't have a photo graphic memory, NHRA.com website has many handy formulas. Easier to remember when needed.

 

True, but memorizing the basic formula allows for calculations in the field.

You know . . . when you're at March Meet and having a beer with your pals and the BS and questions start flying....

 

Man, I have been going through all of this trying to map out my next project. I already have a rear end with 4.10 gears set up. I'm most likely going with an automatic.

So weighing rear tire size, overdrive ******, Gear Vendors, etc. is driving my crazy. Who knows if a 700r4 or 200-4roverdrive ****** will even hold up to decent power in a heavier car? Adding up the dollars in each scenario and weighing in stip performance and highway cruising becomes quite a jigsaw puzzle!

 

Here's the formula I keep handy up in my noggin for when I need to figure out a new gearing/tire combo:

1/2 tire height X 1000
____________________ = MPH @ 1000 RPM

final drive ratio X 168


Example: 28" tall tire, 3.23 rear gear (no overdrive)

14000
_________ = 25.7997936 MPH @ 1000 RPM

542.64


To find speeds in each transmission gear, just multiply the rear gear ratio by the trans gear ratio to get the final drive number to plug into the formula.

 

I did this chart a few years ago for our club newsletter. It seems the computer genius can't get the gear ratio columns aligned with the correct speed column, but the info is otherwise correct.

Cruise Speed Gear Ratio and Tire Size Charts

RPM at 60 MPH by tire o.d. and overall gear ratio

2.20 2.50 2.80 3.00 3.25 3.50 3.70 3.90 4.11 4.30 4.57 4.89 5.00 5.13

24 1850 2102 2354 2522 2732 2943 3111 3279 3456 3615 3842 4111 4204 4313
25 1776 2018 2260 2421 2623 2825 2986 3148 3317 3471 3689 3947 4036 4141
26 1707 1940 2173 2328 2522 2716 2872 3027 3190 3337 3547 3795 3880 3981
27 1644 1868 2093 2242 2429 2616 2765 2915 3072 3214 3415 3655 3737 3834
28 1585 1802 2018 2162 2342 2522 2666 2811 2962 3099 3293 3524 3603 3697
29 1531 1740 1948 2087 2261 2435 2574 2714 2860 2992 3180 3402 3479 3569
30 1480 1682 1883 2018 2186 2354 2489 2623 2764 2892 3074 3289 3363 3450
31 1432 1627 1823 1953 2115 2278 2408 2539 2675 2799 2975 3183 3255 3339
32 1387 1576 1766 1892 2049 2207 2333 2459 2592 2711 2882 3084 3153 3235
33 1345 1529 1712 1834 1987 2140 2262 2385 2513 2629 2794 2990 3057 3137

RPM at 80 MPH by tire o.d. and overall gear ratio

2.20 2.50 2.80 3.00 3.25 3.50 3.70 3.90 4.11 4.30 4.57 4.89 5.00 5.13

24 2466 2803 3139 3363 3643 3924 4148 4372 4607 4820 5123 5482 5605 5751
25 2368 2690 3013 3229 3498 3767 3982 4197 4423 4628 4918 5263 5381 5521
26 2277 2587 2897 3104 3363 3622 3829 4036 4253 4450 4729 5060 5174 5308
27 2192 2491 2790 2989 3238 3488 3687 3886 4095 4285 4554 4873 4982 5112
28 2114 2402 2690 2883 3123 3363 3555 3747 3949 4132 4391 4699 4804 4929
29 2041 2319 2598 2783 3015 3247 3433 3618 3813 3989 4240 4537 4639 4759
30 1973 2242 2511 2690 2915 3139 3318 3498 3686 3856 4098 4385 4484 4601
31 1909 2170 2430 2604 2821 3038 3211 3385 3567 3732 3966 4244 4339 4452
32 1850 2102 2354 2522 2732 2943 3111 3279 3456 3615 3842 4111 4204 4313
33 1794 2038 2283 2446 2650 2854 3017 3180 3351 3506 3726 3987 4076 4182

Notes:

1. These speeds ***ume no converter slip.

2. For an overdrive transmission, remember that the overall ratio is the rear end gear ratio times the overdrive. For example: 4.57 rear end gear with .67 overdrive in fourth gives about 3.04 overall.

3. Further, note that a combination where the tire size and the gear ratio are the same (3.00 gear, 30 inch tire) gives almost exactly 2000 rpm at 60 mph (3000 at 90). I have found this to be a good rule of thumb.........

 

good tech,where's Paul?

 

huh, so that's why those 2.75s are so nice on the road with 27" tires.

A list of commonly used tire sizes and their actual diameter would be handy

 

Hey there~ I made up an Excel spreadsheet for calculating RPM vs. Tire size vs. Gear ratios. It works well. If you have Excel on your computer and you want me to email you the Spreadsheet PM me with your email addy And I'll send it out. Jaysin

 

I got one of these Isky old school computers.

 

Here is a link that has a bunch of handy calculators including differential:

http://www.speedworldmotorplex.com/calc.htm

 

All the calculators and stuff are nice and I use different ones in other applications.

The main thing I wanted to point out here is using percentages to make comparisons between tire sizes, gear ratios and combinations thereof.

 

Please save this!

It MUST be tech worthy.


BTTT