Differential Calculations

[C9]

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 Spicer 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 passenger 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 Spicer 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.

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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


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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....

[tomslik]

biggest problem with swapping tires around is you COULD end up with wheel/tire combos that look like they're off a peterbuilt or a go kart


btw, you want that dust sheild/deflector?
it's sitting on my desk....

[C9]

biggest problem with swapping tires around is you COULD end up with wheel/tire combos that look like they're off a peterbuilt or a go kart


btw, you want that dust sheild/deflector?
it's sitting on my desk....

I think so.

It presses onto the companion flange under the shoulder where it tapers up to the U-joint area does it not?

I have an Inland Empire race-o companion flange and it looks to be larger in the area where - I think - the deflector goes.

I measured it at 1.812.

If that's about right, let me know and I'll send you my address.

Thanks.

[tomslik]

i'll ckeck tonight.
i gotta go out tonight and freeze my.....

[phat rat]

Or you could run a 700R4 with that 3.5 gear and have the best of both. Good launch and 2000 rpm at 70 mph. Got that with my cpe when I changed over from the 396/350 to the 454/700R4 went from 12 -13 mpg at 70mph to as high as 19.2 at 70. Makes a big difference in the gas bill on a trip of any lenght

[1FATGMC]

Here's a few figures I ran while calculating the differences between differential ratio's and tire sizes................Gettin' out there and runnin' em makes it for me.

Nuff said....

What motor is in the '31.  I looked a couple times, but couldn't seem to find that out :cry: .

What transmission now???

Is an overdrive an option.  I don't think I will ever have another one with out overdrive, either stick or auto.  Even the 2700 you are talking about is too high for me if you are running down the highway all day.  BTW I thought the legal limit on the interstates in AZ was 75, am I wrong.

I've heard the argument about gearing for max torque, but that is just too high for mileage unless it might be something with a 10,000# gross weight.  Look at the rpm a vette cruises at in 6th, about 1700 I believe and it will get 25 mpg with a killer motor.

The "getin' out there and runnin' em makes it for me" too .  I once was going to a car show with some guys from Moab.  Here we are on the interstate where it is 75 (I know that for a fact in Utah) and we are running along about 60 with a bunch of supposed hot rods, street rods, customs getting passed by every little econ-box that got anywhere near us.  I mean what is the point in putting a V-8 in something if you just want to run along at 60 .

c ya,

Sum

[C9]

What motor is in the '31.  I looked a couple times, but couldn't seem to find that out :cry: .
455 Buick that's yet to be built.
Should end up at .030 over and 462".



What transmission now???
T-400.


Is an overdrive an option.  I don't think I will ever have another one with out overdrive, either stick or auto.  Even the 2700 you are talking about is too high for me if you are running down the highway all day.  BTW I thought the legal limit on the interstates in AZ was 75, am I wrong.
Right now, OD is not an option.  Maybe down the road a ways.  Several locals have had a difficult time getting their OD automatics to function properly.
75 mph is the max speed limit I've seen.
Seems like there are some 70 mph highways not too far from town.



I've heard the argument about gearing for max torque, but that is just too high for mileage unless it might be something with a 10,000# gross weight.  Look at the rpm a vette cruises at in 6th, about 1700 I believe and it will get 25 mpg with a killer motor.
I understand that gearing at the max torque level is for heavier vehicles, motorhomes, big pickups towing trailers etc.
Course nowadays you get an OD trans in the pickups so running unloaded still returns pretty fair mileage.



The "getin' out there and runnin' em makes it for me" too .  I once was going to a car show with some guys from Moab.  Here we are on the interstate where it is 75 (I know that for a fact in Utah) and we are running along about 60 with a bunch of supposed hot rods, street rods, customs getting passed by every little econ-box that got anywhere near us.  I mean what is the point in putting a V-8 in something if you just want to run along at 60 .

c ya,


Sum

Try the L.A. freeways.  Geez, we were down there in June 2000 for a 6-7 car rod run tour thatDRD57 set up.  Little old ladies in ecnoboxes were sailing past us and we were doing 75-80.  As well as trying to keep up with Utah Don's (otherwise known as OFOF) blown 34 three window  in the Diamond Lane at 90.  Topper was running 83 and having an LAPD motorcycle slide by us with nary a glance....

[phat rat]

Is an overdrive an option. I don't think I will ever have another one with out overdrive, either stick or auto. Even the 2700 you are talking about is too high for me if you are running down the highway all day. BTW I thought the legal limit on the interstates in AZ was 75, am I wrong.
Right now, OD is not an option. Maybe down the road a ways. Several locals have had a difficult time getting their OD automatics to function properly.
75 mph is the max speed limit I've seen.
Seems like there are some 70 mph highways not too far from town.
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I've got just over 30,000 on my 700R4 and it's doing fine. As Sum said the O.D. can't be beat for long hauls. Less wear and tear on the motor and lots better mileage

[C9]

I've got just over 30,000 on my 700R4 and it's doing fine. As Sum said the O.D. can't be beat for long hauls. Less wear and tear on the motor and lots better mileage

Hard to argue with the gas mileage bit.
Lotta times running the long highways it ain't the mileage so much as it is the gas tank capacity.

I've already started down the road toward using the T-400 - meaning I have some of the parts.

One thing I did do with this car was to make a fairly wide trans dropout so I think an automatic OD trans will be fairly easy to put in later on.

[phat rat]

Hard to argue with the gas mileage bit.
Lotta times running the long highways it ain't the mileage so much as it is the gas tank capacity
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Well 16 gals at 12 mpg = 192 mi., 16 gals at 18 mpg = 288 mi so I think mileage over tank size counts for something. Unless you get into large capacity like my truck, 76 gal capacity , of course hauling the travel trailer and getting 7-8 mpg :cry:  still  gives me a range of 500-600 mi.  

[slocrow]

Heck, even the 192 miles means the car can go farther in one stop then I can............... Frank

[phat rat]

Heck, even the 192 miles means the car can go farther in one stop then I can............... Frank

Yes but it takes a heck of a lot less time to P than gas up. And you can P anyplace try gassing up in the middle of nowhere. Sorry but the less stops I have to make for gas the farther down the road I am. That's why I was able to leave the guys I was running with from Sacramento to Tampa at Kingman, run old 66 and catch back up with them in New Mexico. They were stopping every 150-160 mi for gas and I usually run 230-240.  Last spring coming back from Az with the trailer we ran from Albuquerque to Oaklahoma City before gassing up. However we did have to make a pitstop or two along the way, but that doesn't involve getting off the highway and looking for a gas station

[tomslik]

one thing to consider with an OD trans, my 48 chevy got 10 mpg with a 400 turbo and witha 700?









10mpg


engine setup has a LOT to do with everything...

[Crosley.In.AZ]

A 200-4r would bolt to the buick block.  The trans can be expensive to build with stronger parts.

With the light weight of the car i would look at the 200-4r  as an option. Really depends on the application of the car.. racer driver , salt flats , beach (chick magnet)  cruiser .

As T-slik says the setup is important.  too low of RPM & load on the engine the carb will richen stuff up.

My ZZ4 powered 1971  truck was at 10mpg yrs ago... a 700-r4 install did little to help ( 3.08 gear) . A Howell Development 4 barrel TBI fuel injection set up raised the mpg to 11

Last tank of fuel in our VW Jetta was 43.5 mpg

[phat rat]

Cros and T-slick, are these mileage numbers out on the highway or around town? If I'm only running around town mileage is 12-13 as it never gets into OD.  I certainly agree about the low rpm's, I would think with a 3.08 gear you would have to be running 80 mph or better to have a non lugging condition. Just for the record I'm running a 3.42 gear in a 3700# car with a 27" tire. That's 2000 rpm at 70mph