Who Is Right, Who Is Wrong? Theoretical Math Challenge!!

This. I have a gauge that measures injector pulse width. They never shut off completely when coasting in gear. They drop to about 1.9 ms when coasting in gear (measured in a 20ms pulse width, 20 meaning the injectors are firing 100% of the time and 0 meaning they're off). So they're on and pumping gas about 10% of the time when coasting. While coasting in neutral, they are about 2.0ms. Coasting in gear uses a tiny bit less fuel but you also get engine braking which reduces how far you can coast.

 

Think about what the energy losses are for each option.
Friction (wind, road)
Gravitational potential energy for the height

I think going over hill will require more fuel than driving on flat ground because the hill is a longer distance traveled by the vehicle, thus more friction is experienced.

For the second situation, i think the steeper hill will require less fuel than the less steep hill because the vehicle will incur less resistance due to friction of the whole distance traveled.

In both situations gravitational potential change can be neglected because the net result will be equal for both vehicles.

My results are assuming the engine is running at the same level of efficiency(not mpg, but fuel-> energy) regardless of the incline.

 

http://physics.stackexchange.com/questions/6220/can-a-car-get-better-mileage-driving-over-hills

 

As far as I can tell, people who live in mountainous/hilly areas (up and down driving just as you're suggesting), get less mpg than those who live in flat lands. It's pretty self explanatory.

 

for engines designed to turn off injectors...incorrect.

you do not need fuel to keep engine turning and alternator providing power...
in some specific circumstances...inertia and gravity provide the power

some Hondas do this, and others...
engine will be driven from the transmission keeping alternator turning and power on
if engine speed is <>1200 rpm or higher and no throttle input

some PZEV's turn off injectors 100% at specific speeds and conditions such
as off ramps and downhills, and will restart fuel when rpm's drop.

 

Whats for lunch on this flight?

 

btw, your injector shuts off on the other 3 cycles, Wink~

 

Looks like I need to move to Kansas.

 

...i'd presume this analysis would need some further analysis on the "rules of the game"

1) does the vehicle have to maintain a constant speed? a) over the flat route, and b) going up the hill?

2) w/out knowing the answer to the previous question, ...what transmission is involved and what "gear" are we "in" and what "speed" are we going?

3) does the vehicle going up hill have to stay above a minimum speed, or can it be allowed to slow down to a near stop at the crest, before being allowed to coast downhill? i.e. an uphill "coast" of sorts...

4) what is the slope of the hill? this could determine what "gear" is needed, especially if the "uphill coast" notion is deemed not allowed..

...so in summary, i don't see a way to formulate an analytical solution to this w/out more boundary conditions and specific performance characteristics for the vehicle... if so it might make a good calculus problem...

...depending on the slope of the hill, the intial speed, the characteristics of the vehicle, assume the flat route is taken at a constant initial speed, etc. ...the "uphill coast" method (i.e. start w/ initial speed at bottom of hill, and use just enough to make it to clear the crest, ...allowing speed to slowly fall off along the way..) might be feasible?...?...? but that is just my guess

 

LOLWUT.

The title says "Theoretical"....lol I can't provide all the variables. Constant speed in both routes, gear would obviously change up hill.

 

This is why you don't ask engineers 'theoretical' questions

 

Oh man , ain't that the truth , I can ask the PEng that does the structural / seismic work for me a yes or no question and get a minimum 10 minute answer

 

We're good at those

In his defense though, if you had given proper initial information and proper parameters, you would receive a simple yes or no answer

 

No no no , it's like this :

" Do you want me to epoxy the rebar pins you've drawn on your plan into the existing concrete ? "

Blah blah blah blah blah

 

that's right! ..."closed-form" solutions yield "definitive answers"... any analytical solution requires that there be at least as many equations as unknowns.. anything else kinda leaves ya guessing

 

In theory, the coasting you do downhill can be done on flat ground as well.

In practical terms, you will not notice a difference because the distance driven on your home street should be a very small percentage of your overall driving. The difference may well be within the gas pump certification tolerance.

 

I was wrong.

I was watching my Ultragauge more closely the last couple of days, and the only time it goes into open loop (once up to operating temperature) is under moderately firm braking.
I'm assuming it's the decel that triggers it.

And on a number of road trips I've monitored my trip-avg MPG and on longer grades I typically drop about 0.2 to 1 MPG by the time I hit bottom on the other side. There is certainly an increase on the way down, but not enough to offset the increase on the way up.

In a perfect world with no wind or rolling resistance, only gravity, you could theoretically get a balance, but not in the real world.

 

I just think its funny you live on Broke Back Mountain!
My bad, it says Brokebank Mountain.

 

Also consider the trip up up and over the hill is longer than the same trip on a flat (essentially the hill is two sides of a triangle vs the long side in the flat run)