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

[elagache]

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! 

Cheers, Edouard 

[WkillGS]

.....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.

[elagache]

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

MPH	3.08:1	3.23:1	3.36:1
35	1607	1686	1754
55	2526	2649	2756
60	2756	2890	3006
70	3215	3371	3507

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:



Here is the data upon which the graph was based:

RPM	Torque (ft•lbs)	Horsepower
2500	472	225
3000	503	287
3500	544	363
4000	565	437
4500	570	495
5000	547	521
5500	495	518

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:



Here is a table of the same data:

RPM	3.08:1	3.23:1	3.36:1
2500	1454	1525	1586
3000	1549	1625	1690
3500	1676	1757	1828
4000	1740	1825	1898
4500	1756	1841	1915
5000	1685	1767	1838
5500	1525	1599	1663

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? . . . 

Signed curious!

Cheers, Edouard 

[Super65lark]

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?

[WkillGS]

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?
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?

[GreatScat1965]

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. 


Jerry

[Dr Frankenbuick]

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! 

[Buick_65]

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. 

[35chevcoupe]

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 . 

[elagache]

Dear Iain, Walt, Jerry, Good Dr., Todd, John, and mid-60s Buick owners interested in a twisted plot!

Great graphs Edouard!

Oh da' shame!   All this data analysis, including graphs, are being done with Microsoft Excel when I have been a diehard Mac guy since 1988!

. . . . 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

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

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

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

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/

You seem very concerned with maximizing torque to the wheels.... are you guys in California doing 'trailer pull' races up mountain roads?
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

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

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! . . .

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 . 

. . . . . Really?  So how do you manage to burn the tires on the trailer? . . . . .

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

Cheers, Edouard 

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

This one might be a decent candidate for a restoration.

[Dr Frankenbuick]

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. 

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.       

Steve   

[elagache]

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/

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

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

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)

MPH	3.08	3.42
55	709	787
60	761	845
70	879	976

Estimated torque in 5th (ft•lbs)

MPH	3.08	3.42
55	875	971
60	943	1047
70	977	1085

Estimated torque in 4th (ft•lbs)

MPH	3.08	3.42
55	1000	1110
60	1068	1186
70	1106	1228

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

MPH	3.16
55	1002
60	1060
70	1165

Estimated torque in 8th

MPH	3.16
55	1136
60	1193
70	1249

Estimated torque in 7th

MPH	3.16
55	1215
60	1288
70	1318

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.       

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

[elagache]

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:



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:



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:



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/

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:



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! 

Cheers, Edouard 

[Super65lark]

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

[elagache]

Dear Iain and mid-60s Buick owners who survived college, . . .

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

. . . . Obviously, you never received a degree from the University of California, Berkeley . . . 

Somehow I did and still managed to make a complete recovery!! . . . .

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!!

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! . . .

Cheers, Edouard