Effect of hills on bus top speed!
Posted: Tue Jun 30, 2009 3:23 pm
I have modified a computer model that I built a decade or more ago to model cars and trucks, to handle buses, and have been running "what if" simulations on it. One of the simulations I have run is the effect of hills (gradients) on the top speed and INSTANTANEOUS (while on the hill) fuel mileage of the bus.
It turned out to be pretty interesting, and I thought I'd share the results in case they help someone else understand their bus better.
First some explanatory notes abut assumptions and error possibilities:
I assumed my bus, which weighs 34,180 pounds with 130 gallons (930 lb) of diesel fuel aboard and 50 gallons (418 lb) of water in the fresh water tank.
I assumed a 175 lb driver, even though that's less than I weigh, in the interests of copying the car road test magazines who apaprently assume the average driver is 175 pounds, and make sure their driver plus ballast weighs exactly that.
I assumed my 3.73 gearing, and my Allison HT740 4-speed transmission.
I know my 8V71 engine with blower but no turbo is not stock, because it has larger injectors and the governed speed is something like 2500 rpm now, and it produces more power than a stock 8V71 as installed in a 1979 Eagle does. But, its the bus and engine I have, so live with it!
I assumed coefficient of friction as published in the Caterpillar booklet "Understanding Coach / RV Performance".
I photographed the front of my bus from exactly straight ahead, and counted squares to determine the frontal area.
Finally, I noted that the model predicted a top speeed of 84 mph for my bus. I have never tried consciously to run at top speed , but I have noted in past postings that I have seen 85 mph on the speedo, and that the speedo is reasonably accurate.
The way to look at the following results is to look at the TREND versus the specifics of my bus. I suspect many other buses would be reasonably SIMILAR in their performance on grades.
All that said, here we go:
In the following table, I have listed the following columns:
% Grade - this is the official measure of the steepness of a gradient on a highway. 0% is flat. 6% is the maximum gradient allowed on Interstate highways. A negative gradient means DOWNhill.
Top speed: Is the top speed my bus can hit n the grade.
HP req'd: Is the horsepower that the model says is required to maintain that speed on that gradient. Note that the bus may NOT be able to get to the speed that corresponds to the peak engine power simply because the transmission ratios might prevent it (e.g. 4th is too high and 3rd is too low). Instead, the bus gets to the speed that the combiantion of engine power and gearing enable.
MPG: This is the INSTANTANEOUS fuel mileage while climbing that grade at that speed. If the grade is short, the effect on AVERAGE fuel mileage will be modest. If the grade is long, or there are MANY such grades, the effect might be pronounced.
Gear: This is the gear that MY bus would be at, on that grade, with the engine and transmisison and rear axle ratio it has.
% Grade - Top Speed - HP req'd - MPG - Gear
0% - 84 mph - 307 hp - 4.6 mpg - 4th gear
1% - 76 mph - 314 hp - 4.2 mpg - 4th gear
2% - 67 mph - 304 hp - 3.9 mpg - 4th gear
3% - 61 mph - 314 hp - 3.5 mpg - 4th gear
4% - 54 mph - 310 hp - 3.0 mpg - 3rd gear
5% - 46 mph - 284 hp - 2.8 mpg - 3rd gear
6% - 42 mph - 299 hp - 2.5 mpg - 3rd gear
-1% - 85 (gov) - 244 hp - 5.9 mpg - 4th gear
-2% - 85 (gov) - 166 hp - 8.6 mpg - 4th gear
Note:
- How much the top speed falls as the grade increases
- How much the mpg falls as the grade increases
- How much the mpg increases on downhills
- How a downhill might not enable higher top speed simply because the engine is governed to an rpm lower than the hill would allow (Although, a steep enough hill can allow the engine to exceed the givernor speed, can't it?)
Note also how much POWER is required to climb hills, and therefor how much HEAT is being produced. To put the power required into perspective, my specific bus requires about 140 hp to cruise at 60 mph on a flat road. Compare this to the hp numbers in the table above on grades!
Yes, my primitive model DOES also predict wide open throttle acceleration and cruising fuel mileage. Those topics will be covered in future postings.
In the meantime, I ned to know if I have made any serious errors. If any of you more experienced bus owners see anything that looks odd in the numbers, post here or PM me. I want to see if I can get a reasonably accurate model that can hopefully answer real world questions as they arise.
It turned out to be pretty interesting, and I thought I'd share the results in case they help someone else understand their bus better.
First some explanatory notes abut assumptions and error possibilities:
I assumed my bus, which weighs 34,180 pounds with 130 gallons (930 lb) of diesel fuel aboard and 50 gallons (418 lb) of water in the fresh water tank.
I assumed a 175 lb driver, even though that's less than I weigh, in the interests of copying the car road test magazines who apaprently assume the average driver is 175 pounds, and make sure their driver plus ballast weighs exactly that.
I assumed my 3.73 gearing, and my Allison HT740 4-speed transmission.
I know my 8V71 engine with blower but no turbo is not stock, because it has larger injectors and the governed speed is something like 2500 rpm now, and it produces more power than a stock 8V71 as installed in a 1979 Eagle does. But, its the bus and engine I have, so live with it!
I assumed coefficient of friction as published in the Caterpillar booklet "Understanding Coach / RV Performance".
I photographed the front of my bus from exactly straight ahead, and counted squares to determine the frontal area.
Finally, I noted that the model predicted a top speeed of 84 mph for my bus. I have never tried consciously to run at top speed , but I have noted in past postings that I have seen 85 mph on the speedo, and that the speedo is reasonably accurate.
The way to look at the following results is to look at the TREND versus the specifics of my bus. I suspect many other buses would be reasonably SIMILAR in their performance on grades.
All that said, here we go:
In the following table, I have listed the following columns:
% Grade - this is the official measure of the steepness of a gradient on a highway. 0% is flat. 6% is the maximum gradient allowed on Interstate highways. A negative gradient means DOWNhill.
Top speed: Is the top speed my bus can hit n the grade.
HP req'd: Is the horsepower that the model says is required to maintain that speed on that gradient. Note that the bus may NOT be able to get to the speed that corresponds to the peak engine power simply because the transmission ratios might prevent it (e.g. 4th is too high and 3rd is too low). Instead, the bus gets to the speed that the combiantion of engine power and gearing enable.
MPG: This is the INSTANTANEOUS fuel mileage while climbing that grade at that speed. If the grade is short, the effect on AVERAGE fuel mileage will be modest. If the grade is long, or there are MANY such grades, the effect might be pronounced.
Gear: This is the gear that MY bus would be at, on that grade, with the engine and transmisison and rear axle ratio it has.
% Grade - Top Speed - HP req'd - MPG - Gear
0% - 84 mph - 307 hp - 4.6 mpg - 4th gear
1% - 76 mph - 314 hp - 4.2 mpg - 4th gear
2% - 67 mph - 304 hp - 3.9 mpg - 4th gear
3% - 61 mph - 314 hp - 3.5 mpg - 4th gear
4% - 54 mph - 310 hp - 3.0 mpg - 3rd gear
5% - 46 mph - 284 hp - 2.8 mpg - 3rd gear
6% - 42 mph - 299 hp - 2.5 mpg - 3rd gear
-1% - 85 (gov) - 244 hp - 5.9 mpg - 4th gear
-2% - 85 (gov) - 166 hp - 8.6 mpg - 4th gear
Note:
- How much the top speed falls as the grade increases
- How much the mpg falls as the grade increases
- How much the mpg increases on downhills
- How a downhill might not enable higher top speed simply because the engine is governed to an rpm lower than the hill would allow (Although, a steep enough hill can allow the engine to exceed the givernor speed, can't it?)
Note also how much POWER is required to climb hills, and therefor how much HEAT is being produced. To put the power required into perspective, my specific bus requires about 140 hp to cruise at 60 mph on a flat road. Compare this to the hp numbers in the table above on grades!
Yes, my primitive model DOES also predict wide open throttle acceleration and cruising fuel mileage. Those topics will be covered in future postings.
In the meantime, I ned to know if I have made any serious errors. If any of you more experienced bus owners see anything that looks odd in the numbers, post here or PM me. I want to see if I can get a reasonably accurate model that can hopefully answer real world questions as they arise.