RoyJ wrote:
Here's a fun question, what if we "sand-bagged" the PSD with an Aisin 6 speed?
The be fair, I used a 4.10 rear end vs the 3.31 on the 10 speed. Surprise the overall 1st gear ratio becomes nearly identical, so performance is strictly down to gear gap:
The thrust tells us something really interesting:
The Aisin is only able to hit 3rd gear, but the final thrust (and therefore overall gear ratio) is almost an exact match to 4th on the 10 speed. This means given enough time (big enough hill), the Aisin truck will reach the same speed.
Sure enough, my raw data says @ 200 seconds, the Aisin truck hits 44.7 mph, @ 2752 rpm and 475 hp. That's 1 mph faster.
At 190 seconds into the race, the 10 speed has covered 3493 meters, and the Aisin 3494. So the Aisin passed the 10 spd by 3 feet at 3 min 10 sec. It was quite a bit behind at the start.
Comparing the acceleration or even hill climbing traits of a 3.31 10 speed to that of a 4.10 6 speed really needs to be shown in light of comparing the fuel economy in high gear between the two set ups. In order to obtain similar cruising fuel economy the two transmissions would have to be set up with similar final drive ratios .... with final drives equal the advantage of the 10 speed would be revealed comparing acceleration and heavy pulling performance.
RoyJ wrote:
Here's a fun question, what if we "sand-bagged" the PSD with an Aisin 6 speed?
The be fair, I used a 4.10 rear end vs the 3.31 on the 10 speed. Surprise the overall 1st gear ratio becomes nearly identical, so performance is strictly down to gear gap:
The thrust tells us something really interesting:
The Aisin is only able to hit 3rd gear, but the final thrust (and therefore overall gear ratio) is almost an exact match to 4th on the 10 speed. This means given enough time (big enough hill), the Aisin truck will reach the same speed.
Sure enough, my raw data says @ 200 seconds, the Aisin truck hits 44.7 mph, @ 2752 rpm and 475 hp. That's 1 mph faster.
At 190 seconds into the race, the 10 speed has covered 3493 meters, and the Aisin 3494. So the Aisin passed the 10 spd by 3 feet at 3 min 10 sec. It was quite a bit behind at the start.
Comparing the acceleration or even hill climbing traits of a 3.31 10 speed to that of a 4.10 6 speed really needs to be shown in light of comparing the fuel economy in high gear between the two set ups. In order to obtain similar cruising fuel economy the two transmissions would have to be set up with similar final drive ratios .... with final drives equal the advantage of the 10 speed would be revealed comparing acceleration and heavy pulling performance.
Here's distance vs time for both trucks:
Conclusion - if you have a 10 spd racing against your buddy with a 6 speed, time the race to 70 sec, you'll be at 1143m, with him at 1102m. Then say "told ya should've waited, beat your by 120 feet"
If you have the 6 spd, race him to 190 sec, where you pass him and say "told ya a 10 spd is waste of money" ๐
Conclusion - if you have a 10 spd racing against your buddy with a 6 speed, time the race to 70 sec, you'll be at 1143m, with him at 1102m. Then say "told ya should've waited, beat your by 120 feet"
If you have the 6 spd, race him to 190 sec, where you pass him and say "told ya a 10 spd is waste of money" ๐
Here's a fun question, what if we "sand-bagged" the PSD with an Aisin 6 speed?
The be fair, I used a 4.10 rear end vs the 3.31 on the 10 speed. Surprise the overall 1st gear ratio becomes nearly identical, so performance is strictly down to gear gap:
The thrust tells us something really interesting:
The Aisin is only able to hit 3rd gear, but the final thrust (and therefore overall gear ratio) is almost an exact match to 4th on the 10 speed. This means given enough time (big enough hill), the Aisin truck will reach the same speed.
Sure enough, my raw data says @ 200 seconds, the Aisin truck hits 44.7 mph, @ 2752 rpm and 475 hp. That's 1 mph faster.
At 190 seconds into the race, the 10 speed has covered 3493 meters, and the Aisin 3494. So the Aisin passed the 10 spd by 3 feet at 3 min 10 sec. It was quite a bit behind at the start.
The be fair, I used a 4.10 rear end vs the 3.31 on the 10 speed. Surprise the overall 1st gear ratio becomes nearly identical, so performance is strictly down to gear gap:
The thrust tells us something really interesting:
The Aisin is only able to hit 3rd gear, but the final thrust (and therefore overall gear ratio) is almost an exact match to 4th on the 10 speed. This means given enough time (big enough hill), the Aisin truck will reach the same speed.
Sure enough, my raw data says @ 200 seconds, the Aisin truck hits 44.7 mph, @ 2752 rpm and 475 hp. That's 1 mph faster.
At 190 seconds into the race, the 10 speed has covered 3493 meters, and the Aisin 3494. So the Aisin passed the 10 spd by 3 feet at 3 min 10 sec. It was quite a bit behind at the start.
Here's the speed vs time output. My gear shifts are 200ms, during which I assigned an arbitrary 50hp (difficult to estimate engine output during clutch pack switch-over):
So @ 60s, our rig reaches 43.4 mph. At 120s, 43.8 mph, which is pretty max our V-max climbing this grade. This happens at 2881rpm in 4th, hp is 464.
Here we can see the gross thrust, before aero, tire, and gravity drag vs speed. Think of this as "drawbar pull" on a tractor:
17.67 kN, or 3971 lbs. Also in 4th of course.
So @ 60s, our rig reaches 43.4 mph. At 120s, 43.8 mph, which is pretty max our V-max climbing this grade. This happens at 2881rpm in 4th, hp is 464.
Here we can see the gross thrust, before aero, tire, and gravity drag vs speed. Think of this as "drawbar pull" on a tractor:
17.67 kN, or 3971 lbs. Also in 4th of course.
4x4ord wrote:
^^^ I figure a Ram towing a typical 20,000 lb toy hauler should get around 9 mpg at 62 mph. If you use the BSFC map that we have and figure the Cummins will be running in the 205 g/kwhr area of the bsfc map we can come up with the kw required to tow a 20k trailer at 62 mph. 9 miles per gallon is 22182 grams of fuel per hour. 22182/205 = 108 kw or 145 HP. From there you should be able to come up with what you think are reasonable numbers for surface area, rolling resistance and coefficient of drag.
(Keep in mind that the calculated power requirement is at the crankshaft so rear wheel hp would only be about 123 to 125 hp.)
I'm trying the Powerstroke with 10 spd first, as it's a real combo and we can calibrate against real life performance.
First the curve fitting based on your numbers, a 5th order poly provides near exact fit, with R^2 of 0.9998:
I re-calculated hp using the equation in the last column, and numbers are near perfect to the input.
For the model, I used a mass of 43,500 lbs, full GVW of an F450. Cross section area of 75 sq ft, based on J2807's max for travel trailers. I guessed a Cd of 0.80. Tire diameter based on 245/75R17, and tire coefficient of 0.015. I'm starting out full throttle on 7% grade, as a "torture test".
The model uses a column for each gear, each row is 0.1s time step. Based on initial launch rpm (2000), it uses the hp curve to calculate final net thrust: gross thrust minus air drag, tire drag, and gravity. Net thrust calculates instant acceleration, which gets ups the new starting speed for the next 0.1s time step:
