Did I do the math right on computing rear end ratio?

[elagache]

Dear mid-60s Buick caregivers who are handy with facts and figures,

One of the problems that has frustrated me on my grand scheme to use my trusty wagon to tow a vintage travel trailer was figuring out what differential to use to obtain sufficient torque for the job without forcing the engine to spin so much as to waste fuel.  Lucky for me Ken Klassen had located a genuine 1965 Buick towing guide and shared with me some of the data.  Within that guide is a rear end ratio recommendation for towing a class-3 load (5000 lbs.) with a Buick Sportwagon of 3.90:1.

According to the Team Buick reference section, the Buick 300 cid V-8 with 10.25:1 compression ratio had a maximum torque of 365 ft•lbs.  I wanted to know what was the torque on the axle, so I multiplied the engine torque by 3.90 and got: 1424 ft•lbs.

Now my trusty wagon has a Buick big-block engine capable of a nominal 500 ft•lbs of torque.  That's a lot more than the Buick 300.  So by my thinking, I shouldn't need as extreme a rear end ratio to still be able to comfortably pull a class-3 load.  So I divided 1424 ft•lbs by the engine 500 ft•lbs and that gives me a ratio of amazingly: 2.85:1

Just to be conservative, I decided to check what would the axle torque using the rear end ratio that Biquette came with 3.08:1.  That works out to: 1540 ft•lbs.  It seems to me that I should be fine with a 3.08:1 rear end ratio even if I could manage to get my hands of a mid-sized vintage travel trailer.

This all seems reasonably clear to me, but just in case.  Have a assessed the situation correctly  or am I off the beam somewhere in these calculations? 

A curious mind would like to know! 

Cheers, Edouard 

[TrunkMonkey]

Yes.

Flywheel torque x gear ratio = *pounding pavement gets. (minus any parasitic nibbling on your horses by the hungry transmission)

(*Multiply by .25 to see what the tire store gets.)

[elagache]

Dear Michael and mid-60s Buick armchair physicists, . . .

Flywheel torque x gear ratio = *pounding pavement gets. (minus any parasitic nibbling on your horses by the hungry transmission)

Thanks, I thought I was in the safe zone.   Although I have to admit to my horror, it dredged up memories of how I was solving problems while getting my Bachelor's degree in Physics!  Worse still, what I remember still worked!

(*Multiply by .25 to see what the tire store gets.)

Well, there was a possible issue of the tires I'm planning to buy being larger or smaller and that would effect the final torque.  However, I'm trying to get tires as close to the height of the spare tire well and that's the size of the tires that were used on the Sportwagon.  So I assume those effects are negligible.

On the other hand there is the question of how much money the tire store is going to get for those super-deluxe tires with all that rubber.    I'm getting close to ordering the tires and are about to find out - da' hard way! . . . 

Cheers, Edouard 

[WkillGS]

I don't have an answer, but recommend you do more research.
I'd think engine rpm at your desired speed should be optimized, then chose the rear gear that keeps it in that ideal rpm range.
I'm vague on the details, but search bsfc (Brake Specific Fuel Consumption). I believe it's included in a dynometer report..... that should identify your best rpm range for the most efficient operation.

Also consider the stall speed of your transmission torque converter. You don't want a high-ish stall stall speed that is higher than your cruise rpm.... or it will be constantly slipping. Does your trans have a lock-up converter? That should help.

For tires, Discount Tires Direct often has some great sales. You just missed their eBay special, $100 off a purchase of $400 or more (ended 3/19). Cooper Cobras are a popular choice for 60-series radials, at a much better price than the BFG T/A's.

[elagache]

Dear Walt and mid-60s Buick seekers of "harmony" over optimization.

I don't have an answer, but recommend you do more research.
I'd think engine rpm at your desired speed should be optimized, then chose the rear gear that keeps it in that ideal rpm range.
I'm vague on the details, but search bsfc (Brake Specific Fuel Consumption). I believe it's included in a dynometer report..... that should identify your best rpm range for the most efficient operation.

Never heard of it! . . .    Therefore, I sought the wisdom of Wikipedia:

https://en.wikipedia.org/wiki/Brake_specific_fuel_consumption

Very interesting concept!  Not only that but the formula isn't too complicated and I might be able to get data from the electronic fuel injection system to compute it to some approximation.

Not only that, I did check the only dynamometer data I have for this engine which goes all the way back to the Jim Weise version.  Alas, Jim started collecting data at over 3000 RPM, I want to keep the engine under that.  What data I do have the engine is quite steady.  The value varies from 0.538 at 3,200 RPM to 0.509 at 4,900 RPM.  Since this engine has been changed quite a bit including a modified cam to increase low-end torque, I think I'll have to compromise and allow other considerations to decide on this RPM.  The goal here is to travel long distances and that makes the cabin noise level also very important.  Even if I end up using a bit more gas, I'm better off being comfortable otherwise the whole project is futile.

Also consider the stall speed of your transmission torque converter. You don't want a high-ish stall stall speed that is higher than your cruise rpm.... or it will be constantly slipping. Does your trans have a lock-up converter? That should help.

I believe the stall converter is reasonably low, but alas this is a California Performance Transmission from the days when they didn't sell lock-up torque converters.  Of course about 2 years later not only they did but they now sell a neat little controller to engage the lock-up converter!  Just my luck! . . .

For tires, Discount Tires Direct often has some great sales. You just missed their eBay special, $100 off a purchase of $400 or more (ended 3/19). Cooper Cobras are a popular choice for 60-series radials, at a much better price than the BFG T/A's.

I'm sure I could have saved a ton of dough on the tires if . . . . . . . I wasn't absolutely stubborn as a mule that Biquette have whitewall tires.  I don't what tires she came with from the Fremont factory.  When we bought her second-hand, she had "plain-jane" black-wall tires.  That sure was dull and dreary.  She has had white-wall since her first tire change with us I believe.  So I just bit the bullet and ordered all 4 tires from Diamond-back tires.  After all, I've had to make plenty of compromises on this project, at least the tires can be what I want!

Cheers, Edouard 

P.S. I'm in luck!  Diamond-back even makes white-wall tires for trailers!  So I can get matching tires for the vintage travel trailers.  Now all I need is a travel trailer to put them on!! . . . .

[GreatScat1965]

This is a site that is worth saving, it does just about every kind of automotive math.

http://www.wallaceracing.com/Calculators.htm

Not only will it figure out your tire size to gear ratio engine RPM and speed if it's an automatic car there's even a torque converter slip calculator. FYI it's a Pontiac Performance site. 

Jerry

[TrunkMonkey]

"... it's a Pontiac Performance site."

_{so. multiply everything by four to get Buick numbers...}

[elagache]

Dear Jerry, Michael, and mid-60s Buick "mathematicians," . . . . .

"... it's a Pontiac Performance site."

. . . . Pontiac ??!?  Oh da' shame!! . . . . . . . .

Seriously, whenever possible, I try to figure out the math and create a solution using something like a spreadsheet.  My Dad in his day would do calculations that took tens of pages by hand and get the results right.  I'm not that good, but I try to understand the mathematics enough that I can decide if the result makes any sense or not. . . . . 

Cheers, Edouard 

P.S. That doesn't mean I always can mind you!!! . . . .     

P.P.S. . . . . .

_{so. multiply everything by four to get Buick numbers...}

Only by 4!?!?!?!? . . .

[Super65lark]

A few thoughts Edouard:

1. The 300 4V for 1965 had 355lb. Ft. Torque. 355 Wildcat.
2. Are you still running the switch-pitch? I think you said gunky now have overdrive?
3. In 1965 speed limit was 55 and now for your towing I'm thinking 65mph?

I think you're well on your way but just a few thoughts I had.

[elagache]

Dear Iain and mid-60s Buick owners who like a lot of torque.

1. The 300 4V for 1965 had 355lb. Ft. Torque. 355 Wildcat.

Hmm, I got my torque value from this Team Buick reference page:

https://www.teambuick.com/reference/300-340_engine_specs.php

It does list it a 10 foot•pounds over the Buick decal.  Any comments from the other experts?

2. Are you still running the switch-pitch? I think you said gunky now have overdrive?

My wagon has a hardened TH200-4R transmission with built-in overdrive from California Performance Transmission.  It should be beefy enough to cope with the 500+ foot•pounds of torque that her Buick blg-block engine is capable of.

3. In 1965 speed limit was 55 and now for your towing I'm thinking 65mph?

The speed limit shouldn't be a factor because cruising doesn't require either a lot of torque or horsepower.  In the mountains, I'll have to slow down, but that's the nature of the grades.  My main reason for trying to solve the problem this way was to estimate how low of a rear end ratio I could use and still generate the torque that Buick recommended for the load I'm planning to haul someday.

I think you're well on your way but just a few thoughts I had.

Actually, I'm short one key ingredient . . . . . the trailer!! . . . .

Cheers, Edouard 

[WkillGS]

....
I'd think engine rpm at your desired speed should be optimized, then chose the rear gear that keeps it in that ideal rpm range.
....

I still recommend this^^
With the overdrive ratio of 0.69, 3.08 rear, and 27" tall tires, you're looking at 1719 rpm at 65 mph. That's well below the engine torque peak and the engine will be struggling.  You could leave it in 3rd gear and be turning 2490 rpm..... the engine would be much happier there while pulling a heavy trailer.

Therefore:
3.08 gear @ 65-75 MPH: 1719- 1984 rpm in OD, and 2491- 2875 in third gear.
Even dropping to a 2.93 gear would give an rpm range of 1635-1887 in OD and 2370-2735 in third gear  at 65-75 mph.

Or step up to a 3.90 gear and turn 2177 to 2512 rpm at 65-75 mph while in OD.

With such a big difference between 3rd gear (1.0) vs OD (0.69) there isn't a perfect rear gear.... either your spinning the engine a little fast (2500 rpm +) while towing in third gear, or your OD rpm is so low you're at about a fast idle at 70 mph!
A 2.93-3.08 looks to be a good compromise, depending on tire size.
What size tires did you end up getting?

[Super65lark]

Smart thinking Walt.
I am thinking here it would be best to go with the taller gear, right? Otherwise you woud be putting extra stress on the expensive transmission.

Edouard you are planning or already use a trans cooler too?

[elagache]

Dear Walt, Iain, and mid-60s Buicks owners with an eye for towing,

With the overdrive ratio of 0.69, 3.08 rear, and 27" tall tires, you're looking at 1719 rpm at 65 mph. That's well below the engine torque peak and the engine will be struggling.  You could leave it in 3rd gear and be turning 2490 rpm..... the engine would be much happier there while pulling a heavy trailer.

Therefore:
3.08 gear @ 65-75 MPH: 1719- 1984 rpm in OD, and 2491- 2875 in third gear.
Even dropping to a 2.93 gear would give an rpm range of 1635-1887 in OD and 2370-2735 in third gear  at 65-75 mph.

Or step up to a 3.90 gear and turn 2177 to 2512 rpm at 65-75 mph while in OD.

With such a big difference between 3rd gear (1.0) vs OD (0.69) there isn't a perfect rear gear.... either your spinning the engine a little fast (2500 rpm +) while towing in third gear, or your OD rpm is so low you're at about a fast idle at 70 mph!

When pulling the trailer, Biquette would definitely have to come out of overdrive whenever these is any sort of grade.  So indeed I would want to have the engine close to its peak torque in 3rd gear.  That way if I need to climb up I-80 in the Sierras, the car will have the torque to cope with the heavy load.  It definitely won't be as pleasant, but the engine will get the job done.  On the other hand when loafing downhill, being close to idle isn't so bad and after all, the car will be driven without the trailer as well.

A 2.93-3.08 looks to be a good compromise, depending on tire size.
What size tires did you end up getting?

I stuck with the final recommendations on the tire thread I started here years ago:

Front: P215/65-R15
Rear: P235/60-R15

Edouard you are planning or already use a trans cooler too?

Transmission cooler is already installed.

Cheers, Edouard 

[elagache]

Dear mid-60s Buick caregivers who are handy with facts and figures,

As Walt pointed out earlier, a rear end ratio of 3:08:1 is about the best match for towing given operating RPM considerations.  However, I was worried as to whether or not, the engine would have enough torque to handle a reasonably heavy load.  To answer this question, I got my hands on the 1965 and 1970 Buick towing guides.  These provide Buick's recommended rear end ratios for towing as much as a class-III (5000 pound) trailer.  With this I was able to compute the torque that Buick was expecting to generate at the axle for that class-III load.  I have three examples: 1965 Sportwagon, 1965 Electra 225, and 1970 Estate wagon.  When I crunch the numbers this is what I get:

Nominal torque of Biquette's big-block:	530 ft•lbs
Biquette's original rear end ratio:	3.08:1
Torque on axle:	1632 ft•lbs
Computing rear end ratio to tow a class-3 load based on 1965 Sportwagon
Maximum torque of a Buick 300 cid V-8 10.25:1	355 ft•lbs
Recommended rear end ratio for a class-3 load:	3.90:1
Torque on axle:	1385 ft•lbs
Computing required rear end ratio to tow a class-3 load based on 1965 Electra 225
Maximum torque of a Buick 425 cid V-8:	465 ft•lbs
Recommended rear end ratio for a class-3 load:	3.58:1
Torque on axle:	1665 ft•lbs
Computing required rear end ratio to tow a class-3 load based on 1970 Estate wagon
Maximum torque of a Buick 455 cid V-8:	510 ft•lbs
Recommended rear end ratio for a class-3 load:	3.23:1
Torque on axle:	1647 ft•lbs

With a 3.08 rear end ratio, Biquette would generate 15% more axle torque than the Sportwagon.  Biquette would be generating 2% less torque than the Electra and only 1% less than the Estate wagon.  Since both those cars are heavier, it seems to me that I'm in the ballpark.  Does anybody see something out of whack in these estimates?

The same curious mind would like to know!

Cheers, Edouard

[Loren At 65GS]

 Looks to me as if the 3.08 would work well. You still have plenty of torque and you are not drag racing while towing.

Worse case is a rear gear change once you have the opportunity to test the 3.08 gears under towing  conditions.

 Just my .02 worth,
  Loren