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Drivetrain => Differentials, Axles & Brakes => Topic started by: elagache on March 22, 2018, 04:22:58 PM

Title: Did I do the math right on computing rear end ratio?
Post by: elagache on March 22, 2018, 04:22:58 PM
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 (http://65gs.com/board/index.php?action=profile;u=922) 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  :thumbsup: or am I off the beam somewhere in these calculations?  :tongue3:

A curious mind would like to know!  :icon_scratch:

Cheers, Edouard  :occasion14:
Title: Re: Did I do the math right on computing rear end ratio?
Post by: TrunkMonkey on March 22, 2018, 05:48:03 PM
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.)

Title: Gasp! College Physics memories! (Re: Math right on computing rear end ratio?)
Post by: elagache on March 22, 2018, 09:13:22 PM
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. :angel4:  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! (http://www.canebas.org/WeatherCat/Forum_support_documents/Custom_emoticons/shocked_crazy.gif)

(*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.  (http://www.canebas.org/WeatherCat/Forum_support_documents/Custom_emoticons/dollar.gif)  I'm getting close to ordering the tires and are about to find out - da' hard way! . . .  :BangHead:

Cheers, Edouard  :occasion14:
Title: Re: Did I do the math right on computing rear end ratio?
Post by: WkillGS on March 22, 2018, 11:01:28 PM
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.
Title: Some compromises and some not! (Re: Math right on computing rear end ratio?)
Post by: elagache on March 23, 2018, 04:31:50 PM
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! . . .  :icon_scratch:  Therefore, I sought the wisdom of Wikipedia:

https://en.wikipedia.org/wiki/Brake_specific_fuel_consumption (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! . . . (http://www.canebas.org/WeatherCat/Forum_support_documents/Custom_emoticons/D'oh.gif)

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  :occasion14:

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!! . . . . (http://www.canebas.org/WeatherCat/Forum_support_documents/Custom_emoticons/travel-trailer-smiley.gif)
Title: Re: Did I do the math right on computing rear end ratio?
Post by: GreatScat1965 on March 23, 2018, 06:23:52 PM
This is a site that is worth saving, it does just about every kind of automotive math.

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

Jerry
Title: Re: Did I do the math right on computing rear end ratio?
Post by: TrunkMonkey on March 23, 2018, 07:55:26 PM
"... it's a Pontiac Performance site."

(http://www.wootmonkey.com/upload/2016/01/15/20160115072726-742770a0.gif) so. multiply everything by four to get Buick numbers...
Title: Oh da' shame! . . . (Re: Did I do the math right?)
Post by: elagache on March 23, 2018, 09:52:28 PM
Dear Jerry, Michael, and mid-60s Buick "mathematicians," . . . . .

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


(http://www.canebas.org/WeatherCat/Forum_support_documents/Custom_emoticons/wink.gif) . . . . Pontiac ??!?  Oh da' shame!! . . . . (http://www.canebas.org/WeatherCat/Forum_support_documents/Custom_emoticons/hiding.gif) . . . . (http://www.canebas.org/WeatherCat/Forum_support_documents/Custom_emoticons/Laughing_LOL.gif)

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. . . . .  :icon_scratch:

Cheers, Edouard  :occasion14:

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

P.P.S. . . . . .

([url]http://www.wootmonkey.com/upload/2016/01/15/20160115072726-742770a0.gif[/url]) so. multiply everything by four to get Buick numbers...


Only by 4!?!?!?!? . . . (http://www.canebas.org/WeatherCat/Forum_support_documents/Custom_emoticons/car_3gears.gif)
Title: Re: Did I do the math right on computing rear end ratio?
Post by: Super65lark on March 31, 2018, 03:57:21 PM
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.
Title: Should be correct ballpark. (Re: Computing rear end ratio?)
Post by: elagache on March 31, 2018, 06:52:08 PM
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 (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!!
. . . . (http://www.canebas.org/WeatherCat/Forum_support_documents/Custom_emoticons/travel-trailer-smiley.gif)

Cheers, Edouard  :occasion14:
Title: Re: Did I do the math right on computing rear end ratio?
Post by: WkillGS on April 01, 2018, 10:16:18 AM
....
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?
Title: Re: Did I do the math right on computing rear end ratio?
Post by: Super65lark on April 01, 2018, 08:56:09 PM
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?
Title: Need to get out of overdrive for grades. (Re: Computing rear end ratio?)
Post by: elagache on April 02, 2018, 01:50:24 PM
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  :occasion14:
Title: Another line of reasoning for 3.08 . . . . (Re: Rear end ratio?)
Post by: elagache on June 13, 2018, 02:17:41 PM
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 10.25:1355 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
Title: Re: Did I do the math right on computing rear end ratio?
Post by: Loren At 65GS on June 19, 2018, 11:39:29 AM

 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
Title: Da' plot thickens . . . (Re: Computing rear end ratio?)
Post by: elagache on June 19, 2018, 02:15:59 PM
Dear Loren and mid-60s Buick owners who find themselves having to thread needles periodically,

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.

Alas, I just asked Mike Tomaszewski to look up what his computer simulation suggested was the RPM for the peak torque and it proposes the peak torque is close to 4000 RPM.  Even Mike thinks that's mighty high.  When the original version of this engine was tested on a dynamometer, the peak torque was around 3500 RPM.  I'm barely there with a 3:08:1.  The safe choice is 3.23:1, but I'm now wondering if I could find another rear end that would give a ratio in the neighborhood of 3.1:1.  I haven't had time yet, but I think I need to get more sophisticated with the math to see if I can thread this needle as precisely as my available choices permit.

Thanks for the feedback though!  :thumbsup:

Cheers, Edouard  :occasion14:
Title: Re: Da' plot thickens . . . (Re: Computing rear end ratio?)
Post by: WkillGS on June 19, 2018, 11:11:58 PM
.....I'm barely there with a 3:08:1.  The safe choice is 3.23:1, but I'm now wondering if I could find another rear end that would give a ratio in the neighborhood of 3.1:1......

I think you are fine with the 3.08. Just try it.
The difference between a 3.08 and a 3.23 is less than 5%.   
Apply that difference to the mph at a specific rpm, and it's only about 3 mph difference.
Title: Da' plot thickens - part deux. . . (Re: Computing rear end ratio?)
Post by: elagache on June 20, 2018, 04:40:00 PM
Dear Loren, Walt, and mid-60s Buick owners who are handy with math,

Okay, I needed to crunch some numbers and fix a silly mistake.  Unfortunately, when I transferred my spreadsheet snippet for computing the wheel diameter, I neglected to realized I needed an extra pair of parentheses.  As a result, my engine RPM estimates were way too high.  Having corrected this, here is the RPM for 3 rear end ratios:

RPM at different speeds and rear end ratios in 3rd
MPH3.08:13.23:13.36:1
35160716861754
55252626492756
60275628903006
70321533713507

All this becomes very important because of how slowly my trust wagon's engine reaches sufficiently high torque.  Here is a graph based on the data Mike Tomaszewski sent me:

(http://www.canebas.org/Automotive/65GS/Forum%20illustrations/Engine%20horsepower.png)

Here is the data upon which the graph was based:

RPMTorque (ft•lbs)Horsepower
2500472225
3000503287
3500544363
4000565437
4500570495
5000547521
5500495518

I'm not sure how trustworthy this computer simulation is for the top numbers.  When the first version of this engine was actually tested on a dynamometer the peak horsepower was only 510 and torque was 540 foot•pounds.  This engine has a slightly milder cam and lower compression ratio, so caveat emptor.

As you can see, the engine doesn't reach 500 foot•pounds of torque until somewhere between 2500 and 3000 RPM.  Thanks to the power of spreadsheets I can easily compute the torque on the axle from the engine torque numbers for the 3 different rear end ratios listed above.  Here is that information in graph form:

(http://www.canebas.org/Automotive/65GS/Forum%20illustrations/Axle%20torque.png)

Here is a table of the same data:

RPM3.08:13.23:13.36:1
2500145415251586
3000154916251690
3500167617571828
4000174018251898
4500175618411915
5000168517671838
5500152515991663

When the actual torque curve is taken into account, it sure seems to me that the minimum rear end ratio that could do this is 3.23:1 if the torque values for the 1965 Sportwagon can be trusted.  If either the criteria from 1965 Electra or 1970 Estate wagon are used, then 3.36:1 is the smallest ratio that would put the torque in the correct ball pack.  Since those cars are full-sized and therefore heavier, perhaps that is excessive.  However, at a bare minimum I've got to aim for the 3.23:1 ratio.

What do you'all think? . . .  :icon_scratch:

Signed curious!

Cheers, Edouard  :occasion14:
Title: Re: Did I do the math right on computing rear end ratio?
Post by: Super65lark on June 20, 2018, 09:13:01 PM
Great graphs Edouard!
I'm curious just cuz, not planning to tow..
But, I agree with your assessment of the 3.23. I don't think you would be a happy camper buzzin the engine any more than that. Did you put quiet mufflers on?
Title: Re: Did I do the math right on computing rear end ratio?
Post by: WkillGS on June 20, 2018, 11:29:22 PM
I would suggest plotting rpm vs speed, with separate curves for the different axle ratios and also in 2nd, 3rd, an O.D. gears.
That would show you the rpm at the various speeds you will be driving at ....
1) normal highway use at 60-75 mph in O.D.
2) pulling a trailer at highway speed, 55-65 mph, while in 3rd gear
3) pulling a trailer up a steeper grade at 45-55 mph, maybe in 2nd gear?

Then select gear ratio to optimize:
I would consider (3) the worst case where you would want max torque near 4000rpm for a short, steep hill.
Condition (2) around 2600-2800 rpm
Condition (1) around 2000-2200 rpm.

And you can adjust effective gear ratio by changing tire diameter.... going from a 26 inch tire to a 28 inch tire is a 7.7% change..... like going from a 3.36 to a  3.10 rear end ratio.

You seem very concerned with maximizing torque to the wheels.... are you guys in California doing 'trailer pull' races up mountain roads? :laughing7:
I think your 430 has more than enough torque to pull a trailer, and you don't need to 'maximize' anything..... just get the rpm's at your planned speeds comfortable.
What weight trailer are you planning on pulling anyway?



Title: Re: Did I do the math right on computing rear end ratio?
Post by: GreatScat1965 on June 21, 2018, 12:22:56 AM
I've been loosely following this thread. It seems that the final drive ratio has been narrowed down to three ratios. 3.08,3.23 and 3.36. I'm not even going to try to discuss the merits of any particular gear ratio but the 3.36 gear set requires a different 3rd member than the other two. 3.23 and numerically smaller use one carrier and 3.36 and numerically larger use another. That may or may not have some bearing on your final decision.  :dontknow:


Jerry
Title: Re: Did I do the math right on computing rear end ratio?
Post by: Dr Frankenbuick on June 21, 2018, 07:43:05 AM
Edouard, I agree with Walt.  Use the gear that is most comfortable for you. There is more than enough power for any of the gears under consideration. 

Let me illustrate with my 28' RV:  It has a Gross Vehicle Weight, GVW,  of 14,000 LBS (meaning maximum load with people, fuel, water and things).  It has a Gross Combined Weight Rating, GCWR, of almost 18,000 LBS (weight of above and the weight of what is being towed).  It has the Ford Triton V10 engine (410 CI) on a E450 chassis.  This is the platform most commonly used in Class C RVs up to 35' in length for the last 15 years. Chevy also has a cutaway van platform used for RVs, but it is much less popular.  So, the heart of this behemoth makes a maximum of ............wait for it ............ 310 HP and roughly 425 FT LBS.  This is 50 FT LBs less than you are making at 2500 RPMs at probably two times any Gross Vehicle Combined Weight you would carry. This affords you the opportunity to choose from any number of gears that are economical and/or just plain comfortable for you. 

We will be in California with said vehicle in less then a month.  We are going to Yosemite, Redwood and Sequoia.  I am not sure where you are at in relation, but I would not turn down a race up hill if it is your desire! 
Title: Re: Did I do the math right on computing rear end ratio?
Post by: Buick_65 on June 21, 2018, 11:32:59 AM
IMO you want 2500-3000 at 60mph.  Any less and its a dog, any more and your mileage will tank and it will be buzzy at HWY speeds. 
Title: Re: Did I do the math right on computing rear end ratio?
Post by: 35chevcoupe on June 21, 2018, 04:21:18 PM
Edouard ,    Interesting topic so I did some calculating also . A couple more things to consider is how sticky the tires are and the brand or octane rating of the fuel you are using .
I already worked the numbers on my car and with sticky tires and REALLY GOOD FUEL its just perfect for the 3.90 gears i,ll be running .  :evil6:
Title: Definitely a thick plot! (Re: Computing rear end ratio?)
Post by: elagache on June 21, 2018, 05:44:16 PM
Dear Iain, Walt, Jerry, Good Dr., Todd, John, and mid-60s Buick owners interested in a twisted plot!

Great graphs Edouard!


Oh da' shame! (http://www.canebas.org/WeatherCat/Forum_support_documents/Custom_emoticons/hiding.gif)  All this data analysis, including graphs, are being done with Microsoft Excel when I have been a diehard Mac guy since 1988! (http://www.canebas.org/WeatherCat/Forum_support_documents/Custom_emoticons/Mac_emoticon.gif)

. . . . Did you put quiet mufflers on?


I got the quietest free flowing mufflers available according to the local experts: Dynomax Super Turbo.

http://www.dynomax.com/mufflers/super-turbo-mufflers (http://www.dynomax.com/mufflers/super-turbo-mufflers)

Once things settle down, I'm going to bring Biquette to a muffler shop recommended by my friend with the 1957 Bel Air.  Both these cars are members of the family and his Bel Air was also too loud, so perhaps this shop can also do something to reduce the noise.

What weight trailer are you planning on pulling anyway?


Okay, so lets revisit this topic briefly.  Early in this project I came across Author Throckmorton's epic 3000 mile journey with his 1965 Buick Special pulling a trailer carrying his 1968 GS:

https://gmcguy.shutterfly.com/pictures/622 (https://gmcguy.shutterfly.com/pictures/622)

At some point in this exercise he got on a truck scale and found his consist was 10,000 pounds.  So this was the proof of concept.  The trailer I'm dreaming about is a Airstream 24 tradewind from the mid-60s.  Here is an example from 1966:

https://www.airstream.com/wp-content/uploads/archive/9b5f2c98992b8fb9.pdf (https://www.airstream.com/wp-content/uploads/archive/9b5f2c98992b8fb9.pdf)

More likely is a 23 trailer from the 1970s.  There are more plentiful and after the oil crises are probably among the lightest trailers Airstream ever built.  Here are the specifications for the 1975 models.  The twin axle Safari was about 3500 pounds.

https://www.airstream.com/wp-content/uploads/archive/ef2f40c978cc1dc7.pdf (https://www.airstream.com/wp-content/uploads/archive/ef2f40c978cc1dc7.pdf)

Here is an example of a trailer on Airstream classified ads that has been gutted and is ready for a restoration:

http://www.airstreamclassifieds.com/ads/1971-airstream-safari-23-colorado/ (http://www.airstreamclassifieds.com/ads/1971-airstream-safari-23-colorado/)

You seem very concerned with maximizing torque to the wheels.... are you guys in California doing 'trailer pull' races up mountain roads? :laughing7:
I think your 430 has more than enough torque to pull a trailer, and you don't need to 'maximize' anything..... just get the rpm's at your planned speeds comfortable.


Well, I'm not trying to maximize torque exactly.  Instead I'm trying to make comparisons between my wagon and Buick recommendations from their 1965 and 1970 tow guides.  That's what this post is trying to explain:

http://65gs.com/board/index.php/topic,3925.msg28955.html#msg28955 (http://65gs.com/board/index.php/topic,3925.msg28955.html#msg28955)

As it turns out, I had an error in the calculations associated with that previous posting that I was now trying to correct.  For example, if you compare the operational speed of the 1970 Estate wagon at 55 mph with the Buick recommended rear end ratio of 3.23:1 - the engine is within 6% of maximum torque.  In that previous posting, I paid no attention to the RPM where Biquette's engine would actually make the same torque as the 1970 Estate wagon.  It turns out that at 3.08:1 the engine isn't anywhere close to putting out the same torque as the 1970 Estate wagon.  The idea here is to compare apples with apples and try to use Buick's own recommendations as best as I can related them to my wagon.

Let me illustrate with my 28' RV:  It has a Gross Vehicle Weight, GVW,  of 14,000 LBS (meaning maximum load with people, fuel, water and things).  It has a Gross Combined Weight Rating, GCWR, of almost 18,000 LBS (weight of above and the weight of what is being towed).  It has the Ford Triton V10 engine (410 CI) on a E450 chassis.  This is the platform most commonly used in Class C RVs up to 35' in length for the last 15 years. Chevy also has a cutaway van platform used for RVs, but it is much less popular.  So, the heart of this behemoth makes a maximum of ............wait for it ............ 310 HP and roughly 425 FT LBS.  This is 50 FT LBs less than you are making at 2500 RPMs at probably two times any Gross Vehicle Combined Weight you would carry. This affords you the opportunity to choose from any number of gears that are economical and/or just plain comfortable for you. 


Alas, I assume that your Ford Triton V10 engine has an RV cam in it.  That means it makes that 425 ft•lbs of torque very close to idle.  So it can handle a much heavier load.  However, I assume it is a real dog on the freeway.  You may remember this very old thread on Team Buick where you talked me out of trying to go with an RV cam for this engine:

https://www.teambuick.com/forums/showthread.php?20059-The-quot-epic-quot-430-rebuild-caper!&p=78108#post78108 (https://www.teambuick.com/forums/showthread.php?20059-The-quot-epic-quot-430-rebuild-caper!&p=78108#post78108)

This is where things get potentially interesting.  If you look at the torque graphs above, this engine is probably very close to the engine in the 1970 Estate wagon at about the same RPM ~2800.  However, while the Estate wagon is maxed out at 510 ft•lbs, my wagon's engine will produce still more torque and horsepower as the RPM increases.  So your advice back then may be paying some benefits now.  With a heavy trailer, my wagon should still be more nimble and that should help in passing on the freeway.

We will be in California with said vehicle in less then a month.  We are going to Yosemite, Redwood and Sequoia.  I am not sure where you are at in relation, but I would not turn down a race up hill if it is your desire! 


Well, Yosemite is a long way from the San Francisco Bay Area and it wouldn't exactly be a fair race since - I don't have the trailer yet! . . . (http://www.canebas.org/WeatherCat/Forum_support_documents/Custom_emoticons/travel-trailer-smiley.gif)


I would suggest plotting rpm vs speed, with separate curves for the different axle ratios and also in 2nd, 3rd, an O.D. gears.
That would show you the rpm at the various speeds you will be driving at ....
1) normal highway use at 60-75 mph in O.D.
2) pulling a trailer at highway speed, 55-65 mph, while in 3rd gear
3) pulling a trailer up a steeper grade at 45-55 mph, maybe in 2nd gear?


I might still try to do this, but I don't really have enough data points to make any clear conclusions.  I need to write all this stuff up and send it to Mike Tomaszewski for his advice.  Alas, it is a royal pain to convert Excel data into forum formats and converting this stuff to fit an email is basically starting the same process over again.



And you can adjust effective gear ratio by changing tire diameter.... going from a 26 inch tire to a 28 inch tire is a 7.7% change..... like going from a 3.36 to a  3.10 rear end ratio.


Unfortunately, I can go with any taller tires than I have.  The spare tire well is limited to tires that are 26.4"

IMO you want 2500-3000 at 60mph.  Any less and its a dog, any more and your mileage will tank and it will be buzzy at HWY speeds. 


That's what I have to do anyway to reach 500 ft•lbs of torque with this engine.  At 60 mph the engine is at 2890 RPM with a 3.23:1 gear and 3006 RPM with a 3.36:1 gear.

Edouard ,    Interesting topic so I did some calculating also . A couple more things to consider is how sticky the tires are and the brand or octane rating of the fuel you are using .
I already worked the numbers on my car and with sticky tires and REALLY GOOD FUEL its just perfect for the 3.90 gears i,ll be running .  :evil6:


(http://www.canebas.org/WeatherCat/Forum_support_documents/Custom_emoticons/wink_smile_triangle.gif) . . . . . Really?  So how do you manage to burn the tires on the trailer? . . . . . (http://www.canebas.org/WeatherCat/Forum_support_documents/Custom_emoticons/Laughing_LOL.gif)

That should be enough amusement for you'all to keep you busy for a while!  :laughing7:

Cheers, Edouard  :occasion14:

P.S. Here is a listing on eBay for a 1978 Airstream 23 foot travel trailer that is all together:

https://www.ebay.com/itm/1978-Airstream-Safari-23-travel-trailer/292613199713 (https://www.ebay.com/itm/1978-Airstream-Safari-23-travel-trailer/292613199713)

This one might be a decent candidate for a restoration.
Title: Re: Did I do the math right on computing rear end ratio?
Post by: Dr Frankenbuick on June 22, 2018, 05:47:02 AM
Edouard,

I don't have any graphing software currently, but here are the RPM/TQ data points for the truck/RV Triton: 1000/358, 1500/375, 2000/392, 2500/392, 3000/417, (3250/425), 3500/417, 4000/408, 4500/358, 5000/225. You have (lots) more TQ at all data point and there is only 700 RPM difference between their peak TQ points.  The TQ to spare is the reason I think you can get away with any of the rear gears mentioned. 

Also,  consider you are only a downshift away from peak torque any time you need it. The RV does not run at peak TQ on the highway. The big Allison transmission lets it run in OD on flat roads until it hits a hill. Then it shifts down to roughly peak torque until it crests the hill.  It does not pick up speed well on the highway regardless of terrain, but it will maintain 65 or 70 MPH nicely.  I am confident you and a trailer would leave me in your wake any time you wanted.  :icon_salut:

I am the only one in the family that has been to the Pacific.  So, we have to break through to the coast at some point.  We will be coming from Crater Lake to the Sacramento area.  I think we have to do it somewhere between those two points.    :dontknow:   

Steve   
Title: Seems Buick was too conservative back then. (Re: Computing rear end ratio?)
Post by: elagache on June 22, 2018, 06:14:56 PM
Dear Good Dr. and mid-60s Buick owners with a flare for numbers,

I don't have any graphing software currently, but here are the RPM/TQ data points for the truck/RV Triton: 1000/358, 1500/375, 2000/392, 2500/392, 3000/417, (3250/425), 3500/417, 4000/408, 4500/358, 5000/225. You have (lots) more TQ at all data point and there is only 700 RPM difference between their peak TQ points.   


Okay, so I decided to take another angle on this problem.  I decided to compute the axle torque for two modern tow vehicles: the 2018 Chevy Tahoe and the 2018 Ford Expedition.  Moreover, since I could find a torque graph, I decided to read off the graph the torque at the highway speeds.  The graphs are available from Automotive Catalog:

http://www.automobile-catalog.com/ (http://www.automobile-catalog.com/)

Here is the link to the information on the 2018 Chevy Tahoe:

http://www.automobile-catalog.com/car/2018/2496560/chevrolet_tahoe_2wd.html (http://www.automobile-catalog.com/car/2018/2496560/chevrolet_tahoe_2wd.html)

Here is the link to the information on the 2018 Ford Expedition:

http://www.automobile-catalog.com/car/2018/2593595/ford_expedition_xlt_max_4x4_3_5l_v-6_ecoboost.html (http://www.automobile-catalog.com/car/2018/2593595/ford_expedition_xlt_max_4x4_3_5l_v-6_ecoboost.html)

Obviously this meant computing the RPM for a given speed, but this could be done with wheel size.  I assumed the transmissions would be locked up so I made no allowance for transmission slip.

Once I computed the engine RPM at the various speeds, I made my best guess of the torque from the graphs.  Here is the results for the Chevy Tahoe.  I computed the last 3 gears of the 6 speed transmission since it is hard to tell what the computer would do when towing:

Estimated axle torque for 2018 Chevy Tahoe (tow capacity: 6600 pounds)
Tow capacity of 8600 pounds with 3.42 rear end ratio

Estimated torque in 6th (ft•lbs)
MPH3.083.42
55709787
60761845
70879976

Estimated torque in 5th (ft•lbs)

MPH3.083.42
55875971
609431047
709771085

Estimated torque in 4th (ft•lbs)

MPH3.083.42
5510001110
6010681186
7011061228

Even in 4th (no overdrive) the greatest torque is only 1228 ft•lbs.  More importantly, the engine is well below its maximum torque of 383 ft•lbs @ 4100 RPM.

I now suspect that the Buick tow guides of 1965 and 1970 were unusually conservative because towing heavy loads was still somewhat novel and gas was cheap.  The Ford Expedition is even more weird because it has a 10 (yep 10) speed transmission!!  I again computed 3 of those gears 7th to 9th:

Axle torque for a 2018 Ford Expedition

Estimated torque in 9th

MPH3.16
551002
601060
701165

Estimated torque in 8th

MPH3.16
551136
601193
701249

Estimated torque in 7th

MPH3.16
551215
601288
701318

The Ford Expedition gets the closest to the torque numbers that Buick proposed, but 1318 ft•lbs isn't even as high as what Buick suggested for the 1965 Sportswagon.  So I now more fully agree with your pronouncement:


The TQ to spare is the reason I think you can get away with any of the rear gears mentioned.


So I need to go back and look at my numbers and compare them to these modern vehicles.  The other issue is how well the engine will perform at low RPMs.  It may be asking too much to run the engine below a certain RPM for these sorts of loads.  Still, there is absolutely no reason to choose a rear end ratio above 3.23:1.

I am the only one in the family that has been to the Pacific.  So, we have to break through to the coast at some point.  We will be coming from Crater Lake to the Sacramento area.  I think we have to do it somewhere between those two points.    :dontknow:   


I'm in the San Francisco East Bay which is about 90 minutes from Sacramento depending on the traffic.  Unfortunately, the family health situation is such that I cannot be away from the house for very long periods of time.  It might end up being a hit or miss situation depending exactly on the timing.

Thanks for the offer though.

Cheers, Edouard
Title: Surprise ending! (Re: Computing rear end ratio?)
Post by: elagache on June 24, 2018, 06:21:42 PM
Dear mid-60s Buick owners with a knack for numbers,

Where we last left this baffling numerical conundrum, it appeared that 2018 Chevy Tahoe basically guaranteed that a 3.08:1 rear end ratio would work just fine for my trusty wagon.  Still, the matter could resolved with more precision, so I went ahead and crunched the numbers.  This time I started by giving myself a more complete estimate of the torque and power curves for Biquette's engine:

(http://www.canebas.org/Automotive/65GS/Forum%20illustrations/Comparing%20axle%20torque/Biquette's%20engine%20power%20torque.png)

I wouldn't bet my life on these numbers but it was good enough for the next step.  I went back to my calculations of the engine RPM at different highway speeds.  I then looked up the torque on the graph for that given RPM.  So I could now graph the torque on the axle at various speeds and compare that to the Tahoe.  For a start here is the comparison with Biquette's engine in overdrive:

(http://www.canebas.org/Automotive/65GS/Forum%20illustrations/Comparing%20axle%20torque/Axle%20torque%20in%20overdrive.png)

That would suggest if I wanted to always stay in overdrive that I would want a 3.08:1 rear end ratio, but that would be silly.  So let's look at the graph with the transmission downshifted to 3rd:

(http://www.canebas.org/Automotive/65GS/Forum%20illustrations/Comparing%20axle%20torque/Axle%20torque%20in%203rd.png)

In third, even the 2.78:1 rear end ratio is always providing more axle torque than the Chevy Tahoe at highway speeds.  Since that is the rear end ratio that's there now and I'm happy with the car's performance - why would I change anything?

I have one more graph to explain to illustrate how conservative Buick was in the 1965 and 1970 towing guides.  I went through the same process of computing the engine RPM at highway speeds for the 1965 Sportswagon, 1965 Electra 225, and 1970 Estate wagon.  Then I looked up the engine torque from the curves on automobile catalog com:

http://www.automobile-catalog.com/ (http://www.automobile-catalog.com/)

So that allowed me to compute the axle torque that was being generated by those cars when equipped as Buick recommended for towing a class-III load.  Here is a graph comparing the Tahoe, Biquette in 3rd, Sportwagon, Electra, and Estate wagon:

(http://www.canebas.org/Automotive/65GS/Forum%20illustrations/Comparing%20axle%20torque/Biquette%20vs%20old%20tow%20guides.png)

Biquette compares with the Sportwagon, but the full-sized Buicks are expected to produce much more axle torque to handle a class-III load.  They are producing over 50% more torque than the Tahoe!  I don't understand why Buick was so conservative in those days, but clearly I shouldn't have attempted to make comparisons based on those guides - they were way overboard!

So, I think I'm going to just leave the present 1964 Tempest rear end that is in Biquette for now.  Eventually I'll have to find a stronger rear end that can be fitted with a differential that is 2.78:1.  That could be something of a problem since that isn't the sort of gear that performance enthusiasts are likely to be looking for!

Thanks for your support!  :hello2:

Cheers, Edouard  :occasion14:
Title: Re: Did I do the math right on computing rear end ratio?
Post by: Super65lark on June 24, 2018, 06:41:43 PM
I think my head is still spinning from all these graphs and numbers :help:
But.... I use a TH350 with no overdrive & 2.78 gears, and down the freeway is a pleasure with gobs of torque.

I guess you'll just have to hook up the trailer and see how it goes!
Title: Obviously . . . . (Re: Computing rear end ratio?)
Post by: elagache on June 24, 2018, 09:57:39 PM
Dear Iain and mid-60s Buick owners who survived college, . . .

I think my head is still spinning from all these graphs and numbers :help:


(http://www.canebas.org/WeatherCat/Forum_support_documents/Custom_emoticons/wink_smile_triangle.gif) . . . . Obviously, you never received a degree from the University of California, Berkeley . . .  (http://www.canebas.org/WeatherCat/Forum_support_documents/Custom_emoticons/scholarly_teacher.gif)

Somehow I did and still managed to make a complete recovery!! . . . . (http://www.canebas.org/WeatherCat/Forum_support_documents/Custom_emoticons/Laughing_LOL.gif)

But.... I use a TH350 with no overdrive & 2.78 gears, and down the freeway is a pleasure with gobs of torque.


I'm sure that you do enjoy that, but you just - might - enjoy a big block with overdrive just a little bit - more!! (http://www.canebas.org/WeatherCat/Forum_support_documents/Custom_emoticons/car_3gears.gif)

I guess you'll just have to hook up the trailer and see how it goes!


Certainly sounds like a good bit of advice.  Just one small problem . . . . still haven't located the trailer yet! . . . (http://www.canebas.org/WeatherCat/Forum_support_documents/Custom_emoticons/travel-trailer-smiley.gif)

Cheers, Edouard  :occasion14:
Title: Re: Did I do the math right on computing rear end ratio?
Post by: GreatScat1965 on June 25, 2018, 07:23:52 AM
Edouard,

Hi all, as previously mentioned I've been loosely following this post. Not to throw a monkey wrench in all the calculations, but since the transmission doesn't have a tow/haul feature(Computer Controlled Logic) aren't you supposed to tow in Drive not OverDrive? I was always told the transmissions would overheat and/or damage the converter towing in OD. At least that is what it said in the owner's manuals for my early GM cars and trucks. I'd consider consulting your trans builder and inquire with them.

Jerry
Title: Taken reasonable precautions (Re: Computing rear end ratio?)
Post by: elagache on June 25, 2018, 09:21:25 AM
Dear Jerry and mid-60s Buick owners with towing aspirations,

Hi all, as previously mentioned I've been loosely following this post. Not to throw a monkey wrench in all the calculations, but since the transmission doesn't have a tow/haul feature(Computer Controlled Logic) aren't you supposed to tow in Drive not OverDrive?

I've also been very cautious about the transmission.  It is a TH200-4R hardened by California Performance Transmission and it has its own transmission cooler.  In actual practice I would pay careful attention to how the car is performing and downshift to 3rd whenever there is any concern about overloading the transmission.  Even so, when the road is flat it should be possible to stay in overdrive and save some gas.

Cheers, Edouard  :occasion14:
Title: Final twist in da' plot! (Re: Computing rear end ratio?)
Post by: elagache on July 01, 2018, 06:03:13 PM
Dear mid-60s Buick owners who are handy with figures,

I sent my analysis on the rear end ratio to Mike Tomaszewski at TA-Performance and got this response.

Quote
The 3.08 will not be noisy at all, and I wouldn't think the 3.23 would be much more noticeable. If the trans has a over drive gear in it I would myself be putting in the 3.23


So I thought the matter over and realized I would have made an important mistake if I stuck with a 2.78:1 rear end ratio.  Biquette has smaller tires right now.  Her new taller tires would force the engine to spin even more slowly than it does now.  I'm greedy but not that greedy.  So basically, I need to jump at least one notch to 3.08:1.  So this has been considered a safe choice for a long time, so I could have just stopped there, but I looked into a few more things.  As it turns out, with the taller tires, the engine RPM will only increase by 7% with a 3.08:1 rear end ratio.  So basically guaranteed to be the same noise level.  I can't complain about that!  Moreover that small change has some significant benefits.  If I redo the comparison graph between the 2018 Tahoe, 1965 Sportwagon, Biquette in 3rd, 1965 Electra, and 1970 Estate wagon, Biquette compares much more favorably with the full-sized cars:

(http://www.canebas.org/Automotive/65GS/Forum%20illustrations/Comparing%20axle%20torque/Biquette%20vs%20towing%20guides%20308.png)

That certainly should be enough torque to handle a class-III load!  I did one more comparison.  I used the horsepower graph to estimate the horsepower in overdrive and in 3rd:

(http://www.canebas.org/Automotive/65GS/Forum%20illustrations/Comparing%20axle%20torque/Horsepower%20at%20highway%20speed.png)

I think this graph settles any question of attempting to tow in overdrive.  The engine isn't producing enough power even with the 3.23:1 rear end ratio.  However in 3rd it is a different story.  Even with the 3.08:1 ratio, the engine is over 200 horsepower cruising at all highway speeds.  So if the need came to pass a truck even with the trailer, there is the horsepower to at least make the attempt.

So I think this matter is settled!  3.08:1!  :thumbsup:

Thanks for your support! (http://www.canebas.org/WeatherCat/Forum_support_documents/Custom_emoticons/thanks_sign.gif)

Cheers, Edouard  :occasion14:
Title: Hemming's Thomas A. DeMauro thoughts on (Re: . . rear end ratio?)
Post by: elagache on July 20, 2018, 11:02:57 AM
Dear mid-60s Buick owners who want their car's to run "just right!"

This morning on the Hemming's Blog, Thomas A. DeMauro offers his own thoughts on what rear end ratio to choose:

https://www.hemmings.com/blog/2018/07/19/gearing-for-go-or-no-do-you-prefer-high-revs-or-low-revs/ (https://www.hemmings.com/blog/2018/07/19/gearing-for-go-or-no-do-you-prefer-high-revs-or-low-revs/)

Nothing surprising here, but another quick read with a bit of food for thought.

Cheers, Edouard