Gear Ratios and BSFC

[deepnsteep]

I'm working on a project outside of my profession and need help with some concepts! I'm trying to figure out the optimal differential ratio as well as transmission options for a given engine and tire size. I've had different vehicles over the years to have problems with these combos that I'd like to avoid in this project. The first is from what I think are big gaps in transmission gear ratios where the engine is revved way up and after shifting is bogged down. The other problem is poor fuel economy from too high of a final gear ratio, which must be caused by being in a 'bad' spot on a bsfc map.

I'm trying to figure out the right transmission to get and confirm that my 3.73 differential ratio is right for a 5.3 l ls engine and 33" tires!

 

[lucky-guesser]

Off-roading you are going to want the biggest ratio (highest torque) you can get. If this is your daily that will be on the highway most of them time you will likely want longer gears than that.

TLDR -- It depends.

 

[GregLocock]

You work out a drive cycle, then you work out what gear you are in every tenth of a second, then you work out the torque needed and then you work out the fuel consumption. I used to have to do that by hand, now you can do it in a spreadsheet.

Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376

http://eng-tips.com/market.cfm?

 

[3DDave]

Greg, any cars using 2-stage gearboxes to close the gaps as is done on bicycles?

Seems like the OP has too large a gap in the transmission and hopes to fix it by changing the multiplier in the rear end.

For any given power output the larger the tires the worse the top end as the torque increase to overcome drag comes at the expense of running higher RPM, ruining gas mileage as the motor is operated off-peak.

 

[GregLocock]

Lots of 4wd have H and L in theirtransfer boxes, and I used to have a TR4 with an electric overdrive.

Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376

http://eng-tips.com/market.cfm?

 

[3DDave]

Sure - but do those fill gaps or just move the entire range?

In OTR tractors the main box has a narrow range and the auxillary shifts it (I believe) to a range that is adjacent but not overlapping.

 

[BrianPetersen]

For the original poster ... the things that also matter which the rest of us don't know, are the weight of the vehicle (for acceleration and hill-climb) and the aerodynamic drag Cd x frontal area (for being able to select an appropriate overall drive ratio in top gear that the vehicle will still pull at highway speed and be able to climb reasonable grades in top gear).

The gaps in gear ratios leading to hunting are largely why everyone is switching to 8, 9, or 10 speed transmissions which simultaneously allow a deep first gear ratio for acceleration off the line and a tall top-gear ratio for highway cruise and still have ratios reasonably closely spaced to mitigate hunting between gears and allow torque converter lock-up all the time in the higher gears, even through gear changes.

Your wheel rolling diameter and axle ratio give 2279 driveshaft revolutions per mile, i.e. 2279 rpm at 60 mph. That's what engine RPM will be when the transmission is in direct drive with the torque converter locked (if automatic).

If your aero situation is not terrible, it will probably pull a 0.65 - 0.70 overdrive (1500-ish rpm at 60 mph). Lots of production pickup trucks with similarly-sized engines have an overall drive ratio somewhere in that range.

Avoiding gear hunting in hilly areas or when hauling large loads has a lot to do with how sophisticated the transmission controls are. I have experienced the uphill bog-down in top gear on cruise control, until the transmission decides to change down, and with an old skool transmission that's a big step and a big increase in revs, and cruise control still has the pedal to the metal, then the truck overshoots the cruise control setting which then backs off the throttle, leading to the transmission controls giving the OK to upshift, followed by bogging down again ... repeat until cresting the hill. The original "tow-haul" pretty much just locked out top gear (4-speed auto) and kept the torque converter locked in 3rd. The controls nowadays infer whether the vehicle will be able to pull the next gear higher before doing the upshift, and avoid the upshift if they realise that it won't be able to do it.

 

[deepnsteep]

Greg, what do you mean by a drive cycle?

I think this page explains what I'm trying to ask. However I'm having trouble applying the concepts in my head to several specific transmissions with specific gear ratios.

https://x-engineer.org/brake-specific-fuel-consumption-bsfc/

Also, I've tried to find a bsfc chart for a 5.3 l engine but haven't found one yet. Does anyone have one to share?

 

[BrianPetersen]

The hi-lo transfer cases on 4x4 vehicles just move the entire gear range. Low is meant for off-road crawling, and there's normally a big ratio gap between hi and lo (like 2.5 or 3.0 to 1).

An overdrive box with a (let's say) 0.75:1 overdrive could be used as a splitter between gears of a wider-ratio main box, but they're not common except in transport trucks. Problem is that the split between direct and overdrive isn't a whole lot different than the usual split between (let's say) 3rd and 4th of a normal 4-speed box.

fun fact, the Chrysler 62TE transmission used in minivans and other vehicles is basically a 4-speed 41TE main box with an extra 2-speed underdrive splitter-box behind it. Main-box 4th (overdrive) + underdrive in the splitter is numerically the same ratio as main-box 3rd (direct) + direct in the splitter, and both are what they call "5th gear" in the 6-speed. There are two slightly different choices for "4th gear" ... one of them is main-box direct ("3rd") + underdrive splitter, the other one is main-box "2nd" + direct splitter. It actually uses both, depending on whether it's upshifting to 4th following the normal upshift sequence, or downshifting to what they call "4th prime" due to driver requesting more acceleration via a downshift from 5th (direct+direct). So, it's a 7-speed, with two of them really close together, so close that it's marketed as a 6-speed.

So, using a splitter, while possible, gets complicated.

 

[BrianPetersen]

"Greg, what do you mean by a drive cycle?"

For example ...

https://www.epa.gov/vehicle-and-fuel-emissions-testing/dynamometer-drive-schedules

As for the BSFC chart, they have general similarities across all engines "of a type", e.g. 4-stroke spark ignition stoichiometric-operation (which yours is). So the best-efficiency condition is probably going to be somewhere near three-quarters of rated torque (drops off very badly at lighter load) at somewhere near half of rated speed (but not very sensitive). So, for best efficiency, you want to run it at almost the lowest RPM that you can get away with so that the torque is (almost) as high as you can get it by dropping RPM.

Problem 1 ... that operating condition may not coincide very well with actual operation. You're never going to get close to it in urban traffic, for example.

Problem 2 ... gearing tall enough to get the RPM low enough to get the torque up near 60% - 80% of rated, may be so tall that the vehicle becomes a lazy dog to drive, and will want gearing down upon the slightest hill, or headwind, or request for acceleration.