This posting is all about how a REASONABLE computer model can be created for important bus performance attributes, even when the data available is incomplete or rough.
What I was trying to do was to see if I could answer a few basic questions about the likely fuel mileage performance of the 1979 Eagle conversion bus I recently acquired as the new fulltiming home for me and my wife. Specifically, I wanted to know:
- What fuel mileage is likely given this bus’s engine, driveline, and weight?
- How much does the fuel mileage change as cruising speed is increased?
- What is the highest sensible cruising speed, assuming a really nicely engineered highway with high speed limits? (We have a 200 mile section of I-10 in Texas that is posted at 80 mph speed limit, if fuel cost is not an issue!)
- Was the fuel consumption I experienced on the maiden voyage, from where I bought it in Florida, back home to Texas, typical of what I should expect?
Here is the data I currently have available, or have been told:
- The engine in the bus is a Detroit Diesel 8V71 with supercharger but no turbo or intercooler
- The engine HAS been modified from its original as-delivered state of tune (272 hp at 2100 rpm). I know this for several reasons:
o The dealer I bought it from says it is in “318 hp” tune now
o I have seen 85 mph on the speed when my attention wandered on the interstate
o A 40 foot, 34180 pound bus with 8” roof rise, mechanical “always driven” fan, add-on power steering, and only 272 hp can’t go that fast
o The speedo was tested versus interstate mileage markers and the error is minimal
o I have invoices paid by the prior owner that show size “N65” injectors, which are consistent with the 318 versus 272 hp tune
- The factory as-delivered gearing was 3.73, and there is no documentation to suggest that the gearing was ever altered
- Per the Toyo tire website, my 11R24.5 M147 bus tires turn 478 revolutions per mile
- My bus has the the Allison HT740 automatic transmission, and I was able to get the gera ratios for that transmission from several different sources
- The fact that the bus hits 85 mph, with the transmission, gearing, and tires it has means that the engine governor speed, originally 2100 rpm, had to have been altered, since that requires doing 2526 rpm at 85 mph with the stock 3.73 gearing, and would require 2275 rpm at 85 mph with even the nominally available 3.36 gearing found on some Eagle buses.
- The bus’s carefully measured maiden voyage encompassed 74 hours, covered 1149 odometer miles, consumed 230.5 GROSS gallons, including the fuel used to run the generator for 63 of the 74 hours, and despite the discovery late in the voyage that the air filter badly needed replacing (it actually started to collapse during the last hour or so on the road!)
- I have, courtesy of several members of this forum, Detroit Diesel data and graphs that provide the power, torque, BSFC, governor speeds, and injector sizes for a huge number of V71 engine variants, and that include data on versions governed to 2500 and even higher engine rpm
- I have a copy of the Caterpillar booklet “Understanding Coach / RV Performance”, which includes a lot of data and charts on road and wind resistance versus speed, engine cooling fan power consumption, the effect of highway grades, and generator fuel consumption.
Is this enough to build a reasonably useful and reasonably accurate computer model? As it turns out, yes!
Below are 2 charts of data. They differ in one significant assumed parameter: The first one assumes the as-delivered rear axle gearing ratio of 3.73, while the second one explores what would happen if the axle ratio were to be changed to 3.36 (a commonly suggested “improvement” for those who want better fuel mileage from their buses). Let me walk you through them.
The first data line shows the gear ratio, either 3.73 or 3.36.
The next line shows the assumed weight of diesel fuel, which varies by ambient temperature and by formula changes, but averages 7.15 lb per gallon, which is what I assumed here.
Then, I list the gear ratios within the 4-speed Allison HT740 automatic transmission on my bus.
The first column of data then shows speed in miles per hour.
The 2nd column shows the lowest gear that can be used at that speed.
The 3rd column shows the corresponding engine rpm at that speed. This is calculated for each MPH row by using the axle ratio, Allison gear ratio, and tire revs/mile.
The “BSFC” column shows the “brake specific fuel consumption”. That is an engineering term that measures how many pounds of fuel are used by a specific engine per horsepower-hour produced. For most gasoline cars, the BSFC ranges from 0.4 to 0.6. For diesel buses, it ranges from as high as 0.45 for some engines at certain operating rpm, to as low as 0.35 for other engines at their optimal engine rpm for best fuel efficiency. The more modern 5-stroke, electronically controlled engines tend to run closer to the 0.35 number, while my 30 year old Detroit Diesel, high rpm, 2-stroke engine NEVER gets better than just above 0.40, and is as bad as 0.46 at unfavorable engine rpm. What does a BSFC of 0.40 mean? It means that the engine will burn 0.4 pounds of fuel per hour for each horsepower produced.
So, for example, if we needed 150 hp to run at 55 mph under certain highway conditions, the engine would be burning fuel at the rate of 150 x 0.40 = 60 pounds per hour. That 60 pounds per hour would in turn translate to 60/7.15 = 8.4 gallons per hour. THAT would in turn translate to 55 MPH / 8.4 gallons/hr = 6.6 mpg. This is just a fictitious example, but it shows you how the math works.
The “HP req’d at wheels” column shows the total horsepower required (road friction plus air resistance), at the WHEELS of the bus, AFTER all frictional and accessory drive losses have been deducted from the “gross” power output of the engine at that road speed. This means NET power required AFTER driving the engine cooling fan, the power steering, the alternator, and the bus AC (mine doesn’t have bus AC), and after all frictional losses through the transmission and rear axle. This data comes from the Caterpillar booklet, and specifically assumes a bus of 34,000 pounds, with frontal cross sectional area of 90 sq ft, and a coefficient of drag = 0.60.
The “Fan HP” column approximates (!!) the power diverted from the wheels to instead drive the engine cooling fan. This is a surprisingly BIG number on any bus, and a particularly big number on any bus where the fan is ALWAYS driven in direct proportion to engine rpm (like on my bus). Some modern buses have hydraulically driven fans, which can run at speeds NOT proportional to engine rpm, or can even be entirely “turned off” by the electronic control system, and such fans use a lot less power since they only run when the electronic control systems know they are NEEDED. I had to approximate the fan numbers for my bus, since Detroit Diesel does not provide them, so I used the values from the Cterpillar booklet with one deviation: Caterpillar normally runs its mechanically driven fans at about 1.25 times engine rpm, but I checked my actual Detroit Diesel bus installation, and mine runs at engine rpm (driven pulley size = driver pulley size, and miter box ratio appears to = 1 to 1).
The “HP req’d total” column simply adds the fan hp to the hp required at the wheels to give a TOTAL hp that the engine must produce after all internal, transmission, and accessory losses and diversions.
The “HP avail” column uses the engine rpm calculated in the 3rd column, and “looks up” what power the engine produces at that rpm, according to Detroit Diesel. Here, I ran into a significant need for a reasonable set of assumptions and approximations, since my engine is (a) modified in its tune and (b) appears to be governed to 2500 rpm or higher.
This is not as hard to resolve as you might imagine. First, power is simply torque at any given rpm multiplied by the rpm, and divided by a numerical constant to convert it into “horsepower” (as opposed to say “watts”). The formula is in fact:
HP = Torque x RPM / 5252.
Thus IF torque was constant over an RPM range, if you increase the RPM from 2100 to 2500, you would get 2500/2100 = 1.19 times as much power. However, torque is NOT constant over an rpm range for most engines, and in fact, on the Detroit Diesel 8V71, it is FALLING in the rpm range from 2100 to 2500. However, we can reliably estimate it by using 2 different methods, and taking the more conservative to be, if anything, a bit pessimistic.
The first method is to study the Detroit Diesel charts (good for getting yourself to sleep when you have insomnia!), and noting that for engine variants where everything is the same (including injector sizes) except for governor speed, the engines produce on average 13% more power when spun to 2500 versus 2100. With the 318 engine variant, that leads you to about 1.13 x 318 = 359 hp.
The second method is to manually “extrapolate” the falling, curved shape torque curve to 2500 rpm, and then calculate the power at 2200, 2300, 2400, and 2500 rpm based on that extrapolated curve. With the “318” engine version, that leads you to about 338 hp.
Let’s conservatively assume the 338 hp versus the 359 hp. That way, our model will, if anything, UNDERestimate versus overestimate what we should expect our bus to be able to do. That leads to the numbers you see in the “HP avail” column.
In the “MPG” column, we simply take the BSFC, multiply by “HP req’d total”, divide by 7.15 to convert from pounds of fuel to gallons, and divide into MPH to get MPG.
The next column, “HP for hills & accel” simply takes the available power, subtracts the total power required to run down the highway and turn the cooling fan, and shows you how much power is left over to handle uphill grades, headwinds, and acceleration for passing other vehicles. I regard this number to be as important as the MPG number, since a bus that gets great fuel mileage but cannot climb even moderate hills or fight reasonably foreseeable headwinds, is not going to be much good.
The last column adds in the fuel mileage impacts of running the generator while driving down the highway. The Caterpillar booklet says that 0.5 gallon per hour is a reasonable assumption for a moderately (not fully) loaded generator, and that is what I have used.
Let’s look now at some of the findings and predictions that this modeling produces.
First, note that if my engine was still governed to 2100 rpm, 3rd gear could not be engaged at much above 50 mph. With a 2500 rpm governor, it can be engaged to about 60 mph, when necessary to help climb a steep grade. This means that with the higher governor setting, assuming the Allison can be configured to shift at the higher road speed, I would have a better chance of maintaining a speed closer to that of cars and light trucks when climbing a 60 mph highway hill in traffic.
Note also that running a Detroit Diesel 8V71 at low rpm does NOT improve BSFC, but rather hurts it significantly. In fact, the best BSFC occurs at around 1900 rpm. This is very different from modern 4-stroke electronically managed engines, which Caterpillar states achieve their best BSFC at around 1400 to 1500 rpm.
Note how HIGH the power requirements are for pushing a bus down the highway at elevated speeds. Basically, the power required increases roughly proportionately to the CUBE of the speed, since air resistance is the largest component of total resistance at highway speeds. Note that a “stock” 272 hp engine would have no chance of driving the bus to 85 mph – even before allowing for the power diverted to run the cooling fan. In fact, a 272 hp engine output would not even be sufficient to hit 80 mph.
Note how the MPG falls swiftly as speed increases. To illustrate dramatically the difference, I appear to have the choice of achieving 8.4 mpg at 55 mph, or getting to my destination a lot faster by suffering with a 5.3 mpg average at 75 mph – a 37% degradation in fuel mileage in order to go 36% faster. This is not that awful, but is only this “good” because the BSFC on this specific engine is actually EQUAL at either 55 mph or 75 mph, because the 8V71 likes high rpm!
To compare 2 slightly more likely scenarios, I can get 7.5 mpg at 60 mph or 5.9 mpg at 70 mph. That’s a 27% fuel mileage improvement for going 14% slower.
The numbers in the “HP for hills & acceleration” column are pretty compelling. “Reserve power” for hills and acceleration falls off noticeably beyond 70 mph, while being quite impressive at 60 mph.
Note the “skewed” effect of running the generator on the fuel mileage – its impact is far greater at lower speeds than at high speeds. This is simply because the generator fuel consumption rate is basically CONSTANT regardless of road speed, so the faster you drive over any given distance, the less time the generator has to run to keep the AC and other conveniences running. Note that for this reason it is WILDLY inaccurate to say that the generator costs you “x” miles per gallon, where “x” is any fixed number. It’s just not so.
There’s another set of numbers UNDER the main table, which is labeled as “Sums (area under the curve0” and as “Averages”. This is merely a simple and graphic way to try to measure the ENTIRE AREA under the curve for each of the columns, or the average for each column. These numbers only take on significance when you compare them for the “3.73” gearing versus the “3.36” gearing. THAT is interesting in the extreme.
Note that the “area under the curve” and the “average” for “HP available”is 6.3% higher with the 3.73 gearing versus the available 3.36 gearing. In other words, the bus would feel 6.3% weaker with 3.36 gearing than with 3.73 gearing. Those of you who are hotrodders will understand that a 6.3% difference is BIG – readily detectable in the “seat of the pants”.
Much more surprising is that the fuel mileage average with 3.36 gearing is NOT appreciably better than with 3.73 gearing. It is in fact projected at only 6.6 mpg versus 6.4 mpg, averaged across the 55 to 85 mph range. That 0.2 mpg difference is pretty inconsequential. Note that at 55 and 60 mph, it is only 0.1 mpg different, which is even less consequential. For this I should give up 6.3% of my usable power?
The case for the 3.73 becomes even stronger when you look at the hp available for hills and acceleration. There, the 108 hp average with 3.73 gearing is 12.5% better than with the 3.36 gearing. That kind of difference makes a bus feel like an entirely different bus!
Conclusion: Numerically lower gearing is NOT always a good way to get better mileage. In fact, with this “high rpm” 2-stroke Detroit Diesel engine, it could be argued to be precisely the WRONG thing to do.
There’s one more point to address: how truly accurate and real world is this “modeling”, which is after all based on a combination of incomplete or approximate data from different sources, coupled with some reasonable assumptions and extrapolations?
Well, now that you ask, it IS pretty accurate.
Remember that earlier I said that the maiden voyage for my bus encompassed 74 hours (Monday early morning through Thursday mid morning), covered 1149 odometer miles, consumed 230.5 GROSS gallons, including the fuel used to run the generator for 63 of the 74 hours, and despite the discovery late in the voyage that the air filter badly needed replacing. Let’s examine this data and compare to the modeling projections.
My trip was done trying to maintain 73 mph wherever possible. Naturally, I had to reduce the speed where the speed limit on the interstate was lower, and I did run into traffic briefly at a few points on the trip. I also found myself doing 80 to 85 mph sometimes, when my attention on speed briefly wandered. I also did have a significant headwind for a few hours on the first day on I-10. But, the vast majority of the trip was done at the 73 mph, and the majority of the trip was done under wind conditions that did not represent a significant adverse load. And yes, there were hills, but not an unusual number of them – certainly nothing like a mountainous area that would seriously skew the mpg results.
IF we incorrectly ignore the generator hours, we calculate mpg for the trip at 1149 miles / 230.5 gallons = 4.98 mpg. However, if we take into account that the generator ran for 63 hours, and assume that Caterpillar is accurate in estimating 0.5 gallons / hour, then the generator consumed 63 x 0.5 = 31.5 gallons of the fuel. That means that the engine consumed 199 gallons. That means the ACTUAL fuel mileage was 1149 / 199 = 5.8 mpg.
Looking at our table for the 3.73 gearing, we see that at 70 mph, the model predicts 5.9 mpg, and that at 75 mph it predicts 5.3 mpg.
I’d say that the model is in reasonable agreement with the actual measured results.
Note that if I had been willing to drive at 60 mph, I could have achieved 7.5 mpg.
I’m looking forward to doing MORE modeling, and learning many more things.