Re: 5th gear upgrade. .70 ratio!
In regards to the rpm discussion, I certainly agree with the conclusion of lower rpms being better as long as the car can maintain speed relatively efficiently. My questions would be regarding some theoretical purely conjecture for discussion limits, namely:
You're in luck! I was just working up a spreadsheet for my 2005 Passat GLS TDI Wagon (5-speed automatic (Tiptronic)), so I have the numbers for that. I've assumed standard air density, temperature, sea level, 0% grade, etc. Your results may vary.
1) At say 50-60mph, how much hp/torque is needed to simply maintain speed on a flat?
Needed horsepower at a given speed is a function of rolling resistance, air resistance, gradient (if any), and transmission/other losses. Here's what I calculated for the Passat:
35 mph - 7.2 bhp
50 mph - 13.9 bhp
60 mph - 20.7 bhp
70 mph - 29.7 bhp (more than 2x required power for 50 mph, and more than 4x required power for 35 mph)
2) What is the lowest rpm that can provide this hp/torque?
RPM is dependent on road speed, wheel/tire size and gearing only. For the gearing on the Passat (5th gear - 1:0.74; and final drive - 1:3.10 = 1:2.29 gearing in 5th), and Continental ContiTouring Contact CH95 205/55R16 tires (listed at 834 revs/mile at tirerack.com), I calculated the following:
35 mph - 1,116 rpm
50 mph - 1,594 rpm
60 mph - 1,913 rpm
70 mph - 2,232 rpm
3) Would idle injection fuel quantity provide this sufficient hp/torque in 5th gear? If it does then the most efficient cruising rpm would be the ecu programmed in-gear low limit, somewhere around 1000rpm. Considering the TDI's compression this may well be the case.
Yes sufficient torque is available. Torque for a given horsepower and speed has to take into account rpms. Here are the torque values and equivalent BMEP values based on the power and RPM figures above (Passat TDI has a 1,968 cm3 displacement = ~2.0L). I also show an estimate of the % of maximum available torque used.
35 mph - 34 ft.-lbs./ 2.9 bar (24%)
50 mph - 46 ft.-lbs./ 4.0 bar (21%)
60 mph - 57 ft.-lbs./ 4.9 bar (23%)
70 mph - 70 ft.-lbs./ 6.0 bar (29%)
The estimated specific fuel consumption (SFC) as measured in grams/kilowatt-hours (I used the fuel map published on page 5 in the second of 2 reports in this EPA document:
www.epa.gov/OMSWWW/reports/adv-tech/420r04002.pdf and very slightly adjusted it to match the torque curve for the 2.0L TDI) for the given BMEPs and RPMs shown above is as follows:
35 mph - 291 g/kW-h
50 mph - 289 g/kW-h
60 mph - 270 g/kW-h
70 mph - 246 g/kW-h
The engine is running more efficiently at 70 mph. But it also has to perform a lot more work. Multiplying the SFC by the power needed gives the following fuel consumption rates in grams/second and liters/hour (based on a specific density for diesel fuel of 856 grams/liter):
35 mph - 0.435 g/sec; 1.83 l/hr
50 mph - 0.834 g/sec; 3.51 l/hr
60 mph - 1.154 g/sec; 4.85 l/hr
70 mph - 1.516 g/sec; 6.38 l/hr
This is equivalent to the following fuel efficiency figures:
35 mph - 72.5 mpg; 3.25 l/100km
50 mph - 54.0 mpg; 4.36 l/100km
60 mph - 46.8 mpg; 5.03 l/100km
70 mph - 41.6 mpg; 5.66 l/100km
As a note: considering that the car is rated by the EPA at 38 mpg highway and the EPA automatically deducts 22% from the tested figure (= 48.7 mpg tested figure) to arrive at the published figure, these calculations look to be pretty reasonable.
4) What would the mimimum possible fuel consumption be in 5th gear just above idle? Idle fuel consumption is something less than 1 Liter/hour if memory serves, but that is out of gear, I'd guess the increased gearbox/drivetrain friction and wind resistance would double that, so perhaps 2 L/hour is possible? Assuming 50mph that works out to a theoretical low limit of 100mpg.
See above. At 35 mph (~1,100 rpm) in 5th gear, fuel consumption is 1.83 l/hr = 72.5 mpg = 3.25 l/100km
5) What would the 5th gear ratio have to be for 50mph to be equal to 1000-1100rpm in 5th? I understand this would be quite impractical but no less interesting for the sake of discussion. Looking at the table I think it is about .5?
Depends on specific gearing. Given the final drive ratio on the Passat of 3.10:1, a 5th gear of 0.50:1 would get you 1,077 rpms at 50mph.
Rik