argument re: fuel economy - shortest distance vs time

[Voixdelion]

Need help to settle this disagreement I have with my mother, and documented evidence would be required for claims on both sides as to which is more fuel efficient in an automobile:

Mom recently tortured me and my poor injured kitty on the way home from the vet because she was insistent that it was the shortest distance to travel from point A to B (and therefore the most money saved in gas expenses).  This shortest route, however, took nearly twice as long to get home as any of three alternate routes that maybe differed by a few blocks in extra distance to travel in exchange for far less traffic and stoplights because her route took us through downtown streets and shops near MacArthur Park in mid afternoon down a narrow street with short blocks and poor signal synchronicity.  It was also unbearably warm and air conditioning was obviously not allowed in the interest of fuel economy.  With the cat in a screaming panic in his box carrier, and me dying of stress and worry and heat exhaustion, I nearly killed her for refusing to drive at most an extra mile or two to save 20 minutes of mental and physical strain.  

Since the only thing of any value in this argument is $$$ - I would like to convince her that the shortest physical distance does NOT guarantee the most fuel efficiency, especially in the situation where a little more road can mean fewer stops and starts and much less time spent idling at 0 MPH  wasting gas going nowhere.  Isn't the acceleration and overcoming the inertia much more gas guzzling and hard on the vehicle than having a more constant momentum of motion on the highway at  more or less constant speed even if its slowest speed is the top speed on the other route without the starts and stops?    

The total difference in her route and mine is AT MOST 1.6 miles of distance vs MINIMUM 3 to 8 minutes of time when traffic is light or 8 to 15 when it is heavy and a difference in more than 10 possible traffic signals to get stuck at through an area filled with shops, public parks and historical sites, museums, offices, government buildings and courts and schools and entertainment venues like Covention and sports centers and theaters/concert halls vs highway and residences?  

I realize that it depends on the situation of cost in miles to gain in time advantage, but how can one determine mathematically when the tradeoff clearly indicates a better choice than the shortest route in terms of fuel economy (and not to mention wear and tear on the vehicle otherwise as well).  How far is too far to go to save a few minutes?

[hoggy]

'It all depends', but I think you were right.

Moving the car from a standstill is a real drain on the tank.  To get the most of your gas, try to keep the car moving - this might mean slowing down earlier and ambling towards the obstruction in the hope it will go away before you get there.

That said, drive smoothly, but get up to speed reasonably quickly.

If you have a modern car if you take your feet off the pedals and let the engine do the breaking, the flow of gas will stop until you start accelerating again.   It applies in Europe, I don't know about America.

If you want to get adventurous, try coasting out of gear.  It can be a shock to drivers who have been told that the moment you're out of gear you're out of control.  But the only surprise is just how far you can coast.  The car will handle differently, so start with straight lines and work up from gentle corners when the roads are quiet.

Really mad types coast with the engine turned off - I don't like the sound of that myself.

Avoiding traffic is an obvious step.

If this all seems a bit too far - at time of writing this it's £1.34 a litre here ($8.22 a gallon).

Oh, and check your tire pressure!

[Ekaros]

Optimal sweet spot of fuel economy is somewhere at 60-100km/h outside it the consumption rises drasticly. Also if you are not driving an hybrid or some ultra-modern car waiting at lights also uses gas.

I would side here with the rout with less stops and higher average speed...

[Voixdelion]

OKAY, so for sake of the problem at hand,  lets try and make a comparison between time and MPG since she already knows her average MPG per tank is 37 MPG combined highway and city driving, which she then figures as a cost per mile based on gas prices.   If I know the exact distance driven on the two routes and the time it took to arrive home, then I can get an average speed for both routes and use that as a gauge for engine efficiency.   However in order to prove actual cost savings even based on that average I would need to know the difference im fuel efficiency to get a number that would be used to compare costs, right?  OR assign both routes the same efficiency for shortest distance and call her extra minutes 0 MPh and 0 MPG and add the cost of how much GPH used at idle?  Anybody know how long a 95 Integra takes to burn a gallon of gas at idle or how much gas an hour of idling consumes?   I think that still gives her the benefit of the doubt since she would still be accelrating more than me, but perhaps that balances out by the 0 mph minutes  in terms of the calculation for this problem.

Could that work as a formula for measuring the marginal costs per extra mile and being able to see if it works out cheaper to drive further?  My brain has crapped out on this one, but it seems like it cpould suffice as a rough tool fair comparison on the fly.  What do you guys think?

[bytemeavaj]

miles per gallon has no relationship with time.

[Ekaros]

miles per gallon has no relationship with time.

True, gallons per hour

Basicly simple way, try to find some graph of fuel economy near the car. Calculate average speed and go with it. Other one is more complex...

[hoggy]

I find making a tank of gas last as long as possible seems to 'make sense'.  That might include driving less.

[ashort]

And the real difference in the routes to the vet in terms of cash in her pocket for gasoline is probably about 10-15 cents.  Hand her a quarter and tell her to take the shortest route wrt to TIME.  

Less starting and stopping is also much easier on the car and will produce fewer long term repair bills (brakes, oil changes, etc).

Routes chosen by some motivator other than pocket change is almost always the best option.  Choose your route for saving time, or for staying safe.

[ashort]

One thing that pisses me off are the people who drive slower on the highway when the gas prices go up.  Happened alot about 2 1/2 years ago when gas jumped to about 4.15/gallon here (it's 3.55-ish right now).

I think people are starting to do it again, thinking that somehow, magically, they will use a lot less fuel if they drive 54 mph instead of 61.   Someone give me a gun, I can get them gas mileage that approaches infinity.

[ch_123]

I would imagine that if the journey took more time, then that means that the engine is on longer, which means that more fuel is being burned. Unless of course the engine was turned off regularly, which as pointed out above, is not a good thing and probably causes equivalent damage to the environment either way.

A little knowledge is truly a dangerous thing.

[Ekaros]

I would imagine that if the journey took more time, then that means that the engine is on longer, which means that more fuel is being burned. Unless of course the engine was turned off regularly, which as pointed out above, is not a good thing and probably causes equivalent damage to the environment either way.

A little knowledge is truly a dangerous thing.

On other hand force needed to overcome the friction caused by rolling and air increase, is non-linear. So work needed increases as speed increases. Also, the efficiency of engine varies depending on RPM. Also there is gear ration which affects the final out-come...

Fuel economy isn't too clear to calculate as there is lot of factors...

[firestorm]

Just with a difference of only 1.6 miles, there's no doubt that an open road with higher speeds would yield higher fuel economy.  It's possible that wouldn't even change if a hybrid were driven.  A hybrid does better in the city (less fuel used when stopped), but that doesn't change the fact that more energy will be consumed (gas or electric) to accelerate.  

My truck would be an extreme example.  In heavy traffic like you describe, it gets about 13mpg.  It will get 20mpg going a steady 78mph (it would be higher going 60mph.)  

Sedans that we've own (V6 engine) would get about 24 mpg to 31 mpg with mixed driving (i.e. likely less than 24 in pure city driving, and recorded to get 33-34 with steady 70-78mph driving.)

City route:
Truck: 20 miles @ 13 mpg = 1.5 gallons
Car: 20 miles @ 24 mpg = 0.8 gallons

Highway route:
Truck: 20 miles @ 20 mpg = 1 gallon
Car: 20 miles @ 31 mpg = 0.6 gallons (conservative numbers)

OR...
The car could go 25 miles on the same 0.8 gallons of gas used in the city route.  The truck could go 30 miles on the same 1.5 gallons.

I believe a hybrid might come close to breaking even, but you're still sitting in traffic longer, plus the aggravation of dealing with traffic.

Hell, I had a Saturn SL2 (4 cyl engine) with a manual transmission that got 24mpg in stop and go traffic, but 38 mpg with steady 60-70 mph driving.

[Fwiffo]

Using MPG can be misleading. If you're sitting at a stop light, both a hybrid and a regular car are getting zero miles per gallon, but the hybrid shuts its engine off, so it's obviously using a lot less gas.

It makes more sense to measure in gallons per mile (or gallons per 100 miles to make it an easily understood number). It makes it easier to judge the relative difference in fuel economy between different cars. For example, if you don't do the math, it seems like the difference between 20 mpg and 30 mpg was the same as between 30 mpg and 40 mpg. But it's more clear if you look at 5.00 vs. 3.33 vs. 2.50 gallons per 100 miles.

But as others have pointed out, MPG is not a constant anyway. Stop and go traffic completely wrecks it (unless you're driving a hybrid), as does aggressive and high-speed driving. You can save gas from slowing down on the highway; the optimal MPG for most cars is surprisingly low; something like 40 mph.

A Prius actually gets a little better MPG in the city because of the lower average speed. It makes up for the stop and go with regenerative braking and shutting the engine off at stops.

[ashort]

Not a LOT less but less.

I zoom by them Thinking "way to save a quarter, skippy!"

I'll admit that sometimes I do say it out loud.

[Ekaros]

Using MPG can be misleading. If you're sitting at a stop light, both a hybrid and a regular car are getting zero miles per gallon, but the hybrid shuts its engine off, so it's obviously using a lot less gas.

It makes more sense to measure in gallons per mile (or gallons per 100 miles to make it an easily understood number). It makes it easier to judge the relative difference in fuel economy between different cars. For example, if you don't do the math, it seems like the difference between 20 mpg and 30 mpg was the same as between 30 mpg and 40 mpg. But it's more clear if you look at 5.00 vs. 3.33 vs. 2.50 gallons per 100 miles.

But as others have pointed out, MPG is not a constant anyway. Stop and go traffic completely wrecks it (unless you're driving a hybrid), as does aggressive and high-speed driving. You can save gas from slowing down on the highway; the optimal MPG for most cars is surprisingly low; something like 40 mph.

A Prius actually gets a little better MPG in the city because of the lower average speed. It makes up for the stop and go with regenerative braking and shutting the engine off at stops.

True, here we use L per 100km, so idling at stop lights is acctualy infinite consumption.

[jpc]

To the OP:
A trip computer would tell you empirically. There's no need to guess or argue.

[cbf123]

I was just going to suggest that.  Find someone with an ODBC gauge that can show cumulative fuel consumption.  Or just buy one--I've seen them as low as $60.

That'll settle it once and for all.

[Fwiffo]

People can improve their mileage a lot (like 20% easily) by just driving less aggressively. You all know the guy who guns it to pass you just so they can get to that red light 2 seconds before you. Between reasonable driving habits, and not driving a damn tank, you can cut your gas usage in half, without having to resort to an econo-box, carpooling or other dreaded impositions on the McLuxury American lifestyle.

[insert image of Ripster's fat guy lying on the beach]

[ashort]

When people zip by me I say "Way to save 5 seconds *******!" and have my son give them the finger out the rear window as they pass.

touché

:evil:

[Lpb45]

Drop off your mom at the nearest bus stop.

Show Image

This picture is amazing.  TOTORO!!

[BucklingSpring]

miles per gallon has no relationship with time.

`Miles per gallon is always calculated at a given speed.
So there is a correlation between fuel consumption and speed.

Idling engine in an immobile vehicle takes fuel. But the consumption is marginal comparing to what is used to move the vehicle under normal conditions. Of course if it takes you 3 days to do a mile then idling consumption will become important. I recall a guy saying his 4.3litre engine was taking half a gallon per hour when idling.

What is the most demanding is acceleration. A slow steady acceleration and a constant low speed (according to the chart above, 40mph is best) will give you the best mileage.

Back to your case, for the same distance, constant stop and go will take at least 30% more gas than if you do it strait at a constant and relatively low speed. So it means that a highway path less than 30% longer will be more fuel efficient.

[Ekaros]

What is the most demanding is acceleration. A slow steady acceleration and a constant low speed (according to the chart above, 40mph is best) will give you the best mileage.

Back to your case, for the same distance, constant stop and go will take at least 30% more gas than if you do it strait at a constant and relatively low speed. So it means that a highway path less than 30% longer will be more fuel efficient.

Hmm, I have read that best for fuel consumption is quick acceleration... Who knows...

[BucklingSpring]

Hmm, I have read that best for fuel consumption is quick acceleration... Who knows...

That must come from a petroleum company propaganda.

When I floor my car the computer shows up to 50l/100km
Under normal condition it is more like 10l/100km

Do you remember F=MA?
The Force is directly proportional to the Acceleration.
The consumption is tied to the Force.

You're pulling my leg right? Was I candid enough to respond to your statement?

I guess yes :redface:

[Ekaros]

That must come from a petroleum company propaganda.

When I floor my car the computer shows up to 50l/100km
Under normal condition it is more like 10l/100km

Do you remember F=MA?
The Force is directly proportional to the Acceleration.
The consumption is tied to the Force.

You're pulling my leg right? Was I candid enough to respond to your statement?

I guess yes :redface:

But it isn't proportional to either time or distance. So you use same amount of energy to accerelate to same speed:

E=0.5mv^2 so the energy needed is same.

Fast and steady is better than slow and steady. Faster you get in gear the better...

[Voixdelion]

I zoom by them Thinking "way to save a quarter, skippy!"

.

Yes, I agree wholeheartedly that even if it cost more to go my route I would spend the extra few cents and spare myself the aggravation.  The point of the calculation is to show my Mother, who finds comfort in saving more valuable than sanity (particularly MY sanity), that in this case we could both come out ahead.  (I do suppose, however, that it is possible that perhaps she values being right over her own happiness, too.  In which case this is all a moot point... but I would still like to have the proof that she's shooting herself in the foot.  That would make ME happy.)

EDIT>> I suppose a background is in order to clarify the reason I was asking:  We got into a row in the car on the way home due to her obstinate refusal to choose any route other than the miserably jammed one we were taking because she always goes that way - theoretically because it is the shortest distance as the crow flies and therefore the most prudent financial choice.  My mom has a long history of cheap, as opposed to reasonable frugality.  She maintains that it is the reason she now has enough money to NOT be that way, although she still cuts off her own nose to spite her face when it comes to spending and doesn't get it.  Example:  My Dad told me a secret after making me promise I would NEVER tell her the truth about when they bought the new house - she wanted to make the buy without the benefit of the agent (who was a friend of Dad's) for the purpose of saving the commission/fee and ended up paying more for the thing than it would have cost with the friends cut included...THOUSANDS more.  She also went with the unlicensed guy to install her automatic sprinklers despite the fact that even before he started other people in the neighborhood had come looking for him to complain of the lousy job he did (if he even finished it) Then, of course, when the cheapy thing didn't work and I had to redo alot of it at significant expense to her to fix his mistakes, did she learn anything?  Nope.  She instead finds solace by claiming she will never hire another Somoan because they are unreliable.  (*FACEPALM*)

[Ekaros]

Actually his wiki has pulled 700 legs.

And how many of those are yours, or your linking

My concept of Wikis, might be bit more communal than others

[Voixdelion]

But it isn't proportional to either time or distance. So you use same amount of energy to accerelate to same speed:

E=0.5mv^2 so the energy needed is same.

Fast and steady is better than slow and steady. Faster you get in gear the better...

Actually this would only be true to the point where the fuel still continues to feed the acceleration and the excess isn't going unused.  Its possible to flood the engine with too much fuel, so when the rate of fuel being fed into it exceeds the rate at which it can be burned efficiently, that is wasting fuel by accelerating too fast.  

Basically both of you are right on this, I think.

[Ekaros]

Alas, I have found that if you want something done right in America you end up having to do most of it yourself.

But internet is global now, not only in america.

[Ekaros]

Actually this would only be true to the point where the fuel still continues to feed the acceleration and the excess isn't going unused.  Its possible to flood the engine with too much fuel, so when the rate of fuel being fed into it exceeds the rate at which it can be burned efficiently, that is wasting fuel by accelerating too fast.  

Basically both of you are right on this, I think.

Yeah, it's quite complex.

Still, if the route contains lot more stops, then it's worse. De-accerelation is worst thing you can do for fuel economy. Unless it's modern car or you are very good at idling on gear...

[Voixdelion]

Back to your case, for the same distance, constant stop and go will take at least 30% more gas than if you do it strait at a constant and relatively low speed. So it means that a highway path less than 30% longer will be more fuel efficient.

That is very useful info. Where did you get that 30% figure? Is there an authority I can point at somewhere that has that posted (preferably next to a seal from the government or a logo from  some other recognized agency she will respect (like Consumer Reports)?

[Voixdelion]

This is actually an investment in my future to know this, you see.  My mother has not, in the 20+ years I have been licensed, gotten into the passenger seat of my car or allowed me to drive hers with her in it any time we have gone anywhere together.  I hate being in a confined space with no escape from her longer than I have to be and she essentially has me as a captive audience for criticism on the way to dinner or the movies or whatever.  She's retired, so has a lot of time and no significant other so she is not motivated to save a few minutes on a drive of any distance, though I certainly am.  If I can make time equivalent to money in the car, I will be spared considerable grief of great magnitude since she also will be wanting the shortest travel time, though for different reasons. (Her biggest criticisms are always about how cheap I am NOT - She is always of the mind that I have holes in my pockets that money simply falls through - essentially telling me I'm wasting gas (ie MONEY) by taking the longer route home by 1.6 miles because it gets me there quicker.  I can't tell you how much I would LOVE to have concrete evidence that this is untrue)

[Voixdelion]

Maybe not change her opinions of me, but if she thinks its cheaper to get someplace faster even by a few cents, you can bet she'll change her driving routes to save em.  That's good enough for me.  That's a few less minutes I've got to deal with her telling me her opinions of me.

[Voixdelion]

Are you Chinese too?

[BucklingSpring]

That is very useful info. Where did you get that 30% figure? Is there an authority I can point at somewhere that has that posted (preferably next to a seal from the government or a logo from  some other recognized agency she will respect (like Consumer Reports)?

EPA is a decent authority... What car do you drive?

Take any car and look in its specs. Then compare city mileage vs highway.


18 vs 25... Divide 18 by 25 and you get 0.72... That's 28% difference

But if you take a Toyota Echo you'd get 35city/43highway then this is a bit less than 20%...

[ashort]

http://www.fueleconomy.gov/feg/findacar.htm

[BucklingSpring]

http://www.fueleconomy.gov/feg/findacar.htm

Good job! Now he can take his mom on a field trip. :argue:

[BucklingSpring]

How's your mom with Physics?

Note V (velocity) is CUBED!

Show Image

What's all the junk between the "=" and the AV(cubed)... Where did you get this one? I'm having university flashbacks...

[BucklingSpring]

Drag coefficients, area and fluid density

:redface: Of course :redface:

That's why at higher speed air becomes such a critical factor.

It also explain why bananas on the floor are dangerous.

[keyb_gr]

Show Image

^ Only a handful of formulas are clear out of context. This is a measure of power needed to overcome turbulent air resistance, it seems? [EDIT: Yup. U guys r 2 fast.]
If so, it does not include any kind of friction losses in the engine, transmission and wheels, nor any braking losses (which turn motion energy into heat after all). Some of those are hard to model with a simple formula as they are not directly dependent on speed, hence simulation and the resulting mileage vs. speed graphs. It is true that with increasing speed, air resistance starts dominating at some point. (Thus, here in Germany, a speed limit would make more sense than this stupid E10 fuel nobody wants. These 10% of bioethanol not only give reduced fuel efficiency and damage some engines, they also have to be produced somewhere, usually from corn and such. I wouldn't feel inclined to drive up other people's food prices.)

I do have some relatives who are overly thrifty like that, with similar results. Doesn't seem to be an isolated phenomenon. People like that always want to outsmart everyone else, which backfires more often than not.

[J888www]

Not to worry about the cost of fuel, it will soon be very cheap, as soon as the Western World invades Libya, destroy it and steal all the oil.........just like some did to Iraq.
The main question is, under what pretence will they invade......

[Soarer]

it does not include any kind of friction losses in the engine, transmission and wheels, nor any braking losses (which turn motion energy into heat after all). Some of those are hard to model with a simple formula as they are not directly dependent on speed, hence simulation and the resulting mileage vs. speed graphs. It is true that with increasing speed, air resistance starts dominating at some point.

Exactly. The velocity cubed part doesn't actually contribute much, going by these experimental results:



(The curvature is because the y-axis plots fuel economy rather than consumption. Consumption would make the results clearer in this case).

Picking some numbers off the 535i trace at 20 and 10 mpg gives 80 and about 138 mph respectively. This is clearly very far from a cubic relationship, if fact, it's not far from linear!

Overall, I think the most important factor is engine efficiency - this is at it's best only over a small range of RPM. It's impossible to keep within that range in stop-start traffic, so taking a route that allows maintaining a steady speed in a suitable gear makes a large difference. In addition, every time the brakes are applied, momentum is lost, and money is wasted.

How much? Well, say consumption was 25% less on the steady route (it's a reasonable, probably conservative, guess). That means that the steady route could be up to 33% longer and still save money.

Thinking about a similar example where I live, to get across the city by the shortest route is about 5 miles and takes about 30 minutes in daytime, whereas the highway alternative is about 7 miles and 10 minutes. Fuel consumption is probably about the same in either case, but it's a huge difference in time!

[Soarer]

Fail by over-simplification.

In real world vehicles the change in fuel economy is less than the values quoted above due to complicating factors.