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Horsepower and Hill climbing, a Rolling Dyno Test and Final Drives.
by Egon Elssner with Bob DeSaussure, October 12, 1995
The big news in GMC motor homes is high ratio final drives. Especially in the Western states where there are real hills and most owners tow some sort of convenience vehicle. There are several new final drives on the market, but the one that has the most attention these days is the 3.42:1, the final drive originally designed by GM specifically for these coaches but never offered, and is now being produced and marketed by Cinnabar Engineering. Three testimonials by GMC owners and an excellent write-up is offered in GMC Motorhome News, Number 5, September 1995. Cinnabar Engineering, Tel.-810-648-2444. The Caspro Power Drive, a 3.5:1 equiv. transmission modification does essentially the same thing. Caspro. Tel.-216-423-0809.
Intended primarily as a tutorial, this report will look at horsepower required to climb hills, add in estimated aerodynamic and rolling losses, give some, not very complete data on a rolling Dynamometer test of a standard 455 cid. coach with a 3.07:1 Final Drive. (F.D.) (this test commissioned by Bob DeSaussure early in 1995), and make a few projections on how increased horsepower or the use of a higher ratio final drive should affect hill climbing performance. Much of what is projected is speculative because of insufficient experimental data, but what data there is seems to support the projections.
Theoretical power needed to lift an object:
Ignoring friction and aerodynamic loss, it take a certain amount of power to pull or push an object up an incline. Straight forward physics gives the horse power needed to pull or push this object (of some given weight [in pounds]) up an incline (a road of constant grade [in %]) at a constant speed (mph). This could be a block of iron sliding up an icy ramp. From the theory we get the follow two tables:
Table 1
For an object that weighs 12,000 pounds (similar to a standard
GMC)
| Grade | 65 mph | 55 mph | 45 mph |
| 8% | 166hp | 141hp | 115hp |
| 6% | 125 | 106 | 86 |
| 4% | 83 | 70 | 58 |
| 2% | 42 | 35 | 29 |
| 0% | 0 | 0 | 0 |
| Grade | 65 mph | 55 mph | 45 mph |
| 8% | 201 hp | 170 hp | 139 hp |
| 6% | 151 | 128 | 104 |
| 4% | 101 | 85 | 70 |
| 2% | 50 | 43 | 35 |
| 0% | 0 | 0 | 0 |
Table 3
Total power required, Coach alone. 12,000 lbs. Includes aero and
tire drag:
| 65 mph | 55 mph | 45 mph | |
| Drag loss: | 40 hp | 30 hp | 20 hp |
Table 4
Total power required, Coach and towed vehicle 14,500 lbs. Includes
aero and tire drag:
| Grade | 65 mph | 55 mph | 45 mph |
| 8% | 206 hp | 171 hp | 135 hp |
| 6% | 165 | 136 | 106 |
| 4% | 123 | 100 | 78 |
| 2% | 82 | 65 | 49 |
| 0% | 0 | 0 | 0 |
Table 5
| Grade | 65 mph | 55 mph | 45 mph |
| 8% | 241 hp | 200 hp | 159 hp |
| 6% | 191 | 158 | 124 |
| 4% | 141 | 115 | 90 |
| 2% | 90 | 73 | 55 |
| 0% | 40 | 30 | 20 |
Nothing in the tables above says anything about engine size, tire size or Final Drive ratio. Even a GMC outfitted with a Volkswagen engine would have to meet these theoretical horsepower requirements.
To put meaning into these tables, the Dyno test data given below indicated that the true wheel horsepower output of a GMC with a standard configuration power train (455 cid and 3.07 Final Drive) probably never exceeds 160 hp in Drive (third gear) at Wide Open Throttle (WOT) due to the power robbing characteristics of the torque converter and other drive line loses, which appear to be on the order of 50 hp.
Dyno testing of a 455 cid. standard GMC with 3.07 Final Drive. The following data was obtained on a rolling Dyno, at sea level, in third gear (D) ** and wide open throttle:
Table 6
| Measured Coach equiv. speed |
20 |
30 |
40 mph |
| Calc. Tire RPM |
228 |
342 |
456 rpm |
| Calc.Tranny input shaft RPM |
754 |
1132 |
1509 rpm |
| Measured Engine RPM [tach.] |
1600 |
2400 |
2600 rpm |
| Rated WOT engine net hp |
100 |
160 |
175 hp |
| Measured Dyno H.P |
40 |
105 |
120 hp |
| Calc. Power loss, Conv.+driveline |
60 |
55 |
55 hp |
| Calc. Converter slip RPM |
846 |
1268 |
1091 rpm |
| Calc Converter ratio |
1.89:1 |
2.12:1 |
1.72:1 |
| Calc. Dyno Torque [wheels] |
921 |
1612 |
1382 ft. lbs |
| Calc. Torque input to F.D |
300 |
525 |
450 ft. lbs. |
| Rated Torque, net, engine output |
|
344 |
350 ft. lbs |
| Calc. Conv. Torque multiplication |
|
1.53 |
1.28 times |
**Some of you will question why the transmission did not downshift to 2nd gear or even 1st! The transmission may have malfunctioned. Even if it did, the test data as measured shows a torque converter loss of about 50 hp over a wide engine rpm range. The 2600rpm, 40mph and 120 hp data should be OK.
We know that an average engine rpm of 2500 rpm on a level road will power a standard GMC (with 3.07 Final Drive) to about 65 mph on a level roadway.
| Coach Speed | 65 mph |
| Engine R.PM | 2500 rpm (estimated) |
| Calc. Tranny input shaft rpm | 2297 rpm |
| Conv. slip & (ratio) | 203 rpm & (1.09:1) Not much |
Obviously, the torque converter, which keeps our coach simple to drive (less gear shifting) also robs a lot of power at WOT (up to 50 hp.). In the extreme case of a maximum load, as in one of the Dyno cases above, the coach speed did not exceed 40 mph with an engine speed of 2600 rpm at WOT. This load is equivalent to driving a standard coach up an 8 % grade at about 40 mph! On level ground, this same 2600 rpm would drive the coach to about 70 mph! Sound familiar? It is. This is the way it was designed to happen.. The torque converter tries to match vehicle hp needs to available engine hp output. This matching is a continuous process depending on throttle position and vehicle needs (speed and grade of the road).
As almost everyone already knows, an accurate accounting of all factors going into a power gain vs. Final Drive Ratio is not possible without extensive Dyno. testing under partial load throttle settings and with extensive instrumentation. It is, however, possible to speculate on performance based on theoretical power needed to climb hills and engine power available.
Let us consider the hp output (ne0 of a stock 455 cid. engine. From the hp/rpm curve of the stock or original, engine as it came from the factory and with standard exhaust system (at WOT):
Table 7
| Engine rpm |
2300 |
2600 |
2900 |
3200 |
| Engine net hp |
140 |
175 |
195 |
210 |
| Gain in hp. per 300 rpm increase |
35 |
20 |
15 |
|
| Less 50 hp drive line loss |
90 |
125 |
145 |
160 |
From the hp output table (Table 7) above, there is a gain of about 20 hp for the 300 rpm increase (from 2600 to 2900). and even more, 35 hp (from 2300 to 2600) at WOT.
Consider the Dyno test numbers at 2600 rpm, 40 mph and 120 bp. Using the 3.07 FD. (Table 6), these numbers, 120 hp and 40 mph almost agrees with the 8% grade data given on the (Coach alone) hill climbing table (Table 4). Remember, the numbers in Table 4 do not depend on the F.D. ratio.
Coach Alone vehicle improvement (with a 20 hp gain): Using hill climbing (total power) data (Table 4); For the 8% grade data, adding 20 hp would shift the operating point 6 mph faster, from 40 to 46 mph. On the 6% line it would add almost 7 mph, from 51 mph to 58 mph. On the 4% line it would add 8 mph, from 64 mph to 72 mph. These gains could come from any improvement in performance, he it more engine hp, higher ratio Final Drive, high flow exhaust, etc.
Coach plus towed vehicle improvement (with a 20 hp gain): From (Table 5): For the 8% grade data, adding 20 hp would shift the operating point 5 mph faster, from 36 to 41 mph. On the 6% line it would add almost 6 mph, from 45 mph to 51 mph. On the 4% line it would add 8 mph, from 58 mph to 66 mph.
Table 8
Estimated Speed increase with 20 hp gain.
| Coach alone: Grade |
8% |
6% |
4% |
| Speed with 3.07:1 Final drive |
40 |
51 |
64 |
| Speed with 3.42:1 Final drive |
46 |
58 |
72 mph |
| Coach plus tow: Grade |
8% |
6% |
4% |
| Speed with 3.07:1 Final drive |
36 |
45 |
58 mph |
| Speed with 3.42:1 Final drive |
42 |
51 |
66 mph |
Early reports on coach performance with the new higher ratio final drives, however, confirm improved hill climbing ability. Some even believe that using the new higher ratio F.D. will improve gas mileage. Noting that the torque converter is overworked and the engine under heavy load due to a poor engine to F. D. ratio match (with the 3.07 F.D.), it seem reasonable to expect better gas mileage with the better matched higher ratio F.D., assuming you don't use the new found hp in a sporty manner.
Incidentally, 2nd gear (S), provides an even better match for the torque converter at typical hill climbing speeds. At a 2nd gear ratio of 1.48:1 the equivalent F.D. ratio (because of transmission gear reduction) for a 3.07:1 F.D. setup would be 4.5:1 and for the 3.42:1 F.D. would be 5.06:1. These higher ratios provide a better match with less work for the torque converter to do, meaning less converter loss with more net engine horsepower available at the wheels.
One last note on engine hp. Reduced atmospheric pressure due to high altitude reduces output hp. on a normally aspirated engine. 3% per 1000 feet seems to be the accepted value. At 5000 feet this would be a 15% reduction. Somewhat compensating is that fact that aerodynamic load is reduced, but this is usually only a minor factor.
It should be noted that WOT is not a desirable mode of operation for any vehicle, especially a heavy coach. In all cases of the Dyno test, WOT operation and max. load resulted in severe torque converter slip and power loss (on the order of 50 hp) for all three runs. This loss is directly converted to heat. At 746 watts per hp. this translates into a power loss, in the drive train, of 37 Kilowatts! Some of this power gets into the radiator cooling water via that little loop called "transmission oil cooler" in the radiator. The rest, and there is a whole lot of it, heats up the transmission oil, which expands and, in severe cases, overflows out the transmission vent pipe where it drips down on the hot exhaust and ignites. Several coaches have caught fire while towing a car up a steep hill while in Cruise Control. This is the equivalent of WOT in the Dyno test. Don't do it! If you put heavy loads on your power train it's a good idea to keep an eye on transmission oil temperature. Reduce power needs by slowing down/gearing down. Above all, avoid WOT and your Cruise Control while towing!
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