Help our hosts settle a marital dispute


#1
Ready to help Tom and Ray bring a touch of domestic tranquility back into Alice's marriage? Great! Because they can use all the help they can get in that department.

Here's Alice's question: which is more fuel-efficient: a shorter route over a big hill, or a longer route around said hill? Alice's casting her vote for the round-the-hill route. Her husband? He's an "up and over" kind of guy. And he's a retired engineer -- with too much time on his hands.

You can hear the call -- complete with mileages, altitude and other important algebraic information -- right here.

Is Alice's husband casting his lot with the classic engineering solution that's entirely wrong, as Tommy claims? Is the round-the-hill route better, because of the energy that's lost from braking on the downhill, as Ray claims?

What do you think?

Share your thoughts right here -- and thanks!

#2

In a hybrid or a Suburban? Which hybrid?

That matters. Efficiency of the mode of motive force and the amount of energy needed are variables in the equation. As you might know, internal combustion engines are only about 25% efficient.


#3

In my opinion, over the hill would be the most efficient path, but it would be the wrong route to take for Ray. Having some experience in this matter my observation is that when one disputes an engineering question with one’s spouse, one can either been correct or one can be happy.


#4

While the physics might be fun to figure, in the end your last senetnce says it all. One can be right, or one can be happy.

Except in this case I think it’s the hubby that could use the advice rather than the OP…he should just let her go around the hill without dispute and he’ll have a happier retirement.


#5

IMHO: The difference is HALF a mile (that too over 2 miles!). I don’t see how there can be any significant difference.Even if your car runs 10 miles/gallon, and rate of consumption was identical on both routes, the difference in terms of gallons used would be 1/20th of a gallon ! so, to save a gallon you would have to make at least 20 trips. Even if you make a trip/week, you are saving one gallon over 5 months !

I say if you enjoy the hills or really need to save time (again, I don’t know how much time saving there really is over 2 mi.) go over the hills or else use this opportunity to buy some “grace-points” from Alice! (Such grace-points may be useful for something else).

Apart from that, my answer would have to be re-evaluated depending on the gradient of the hill plus if the distance was well over 20 miles or so.


#6

I think it’s the overall difference of a couple tablespoons of fuel. Then again, I’m no engineer.


#7

Maybe, maybe not. A huge heavy vehicle will take a lot of fuel to pull up the hill, and won’t recoup that energy on the way down. On the other hand, once you get a huge heavy vehicle rolling it takes a lot less to keep it rolling as long as the tires aren’t aggressive. A body in motion tends to remain in motion.

A Prius, on the other hand, would take less energy to haul up the hill and would recoup some of it on the way back down via regenerative braking.

We don’t have enough data to know for sure the answer to the post.

But hubby should chill out and let her take the route she likes.


#8

Low mass/high wind drag vehicles such as motorcycles are also more likely to use less fuel by taking the short hilly route instead of the long level route. It’s no big deal to lift the low mass of a motorcycle up a hill and there is so much wind drag that they seldom need to ride the brakes when going down the hill.

Highly overpowered vehicles also benefit from hilly routes, especially if they are short geared for “performance”. Four stroke gasoline engines naturally have a efficiency drop off at low power. This means an engine that is making 60 horsepower efficiently one third of the time and making zero horsepower the other 2/3 of the time while coasting, may use less fuel than the same engine would consume operating at a continuous 20 hp on a level road.

Me and my wife took a vacation to the Enchanted Circle region of New Mexico a short time ago in a Honda Element AWD automatic. The first leg of the trip was Austin TX to Lubbock TX driving mostly flat roads with the cruise control. We got around 26 mpg.
The second leg of the trip was Lubbock to our next gas stop in Las Vegas, NM using cruise control on mostly flat roads, we got a little over 27 mpg, NM highways only have a 65 mph speed limit.
The next tank of gas was used touring the mountain roads of the Taos region including a visit to Taos Ski Valley, Red River, and many trips along NM 518. This resulted in the best gas mileage I ever obtained with this vehicle, 30.8 mpg. So, don’t assume that hilly roads are bad for gas mileage.


#9

Ray: In my hasty reply I accidentally implied that you needed advice. I’m sorry.
Thank you, the_same_mountainbike.

Alice: Given the data in your question, in my opinion the most fuel-efficient route will be the route through which the engine runs for the least amount of time. In this case, over the hill is the shorter distance. However, i have observed a little known fact that when an engineer and his wife dispute an equation, then the law of physics will change a little bit just for him to make her choice the best choice. They didn’t teach this in school but I think it’s a combination of the golden rule and Newton’s law of action and reaction.


#10

A conclusion is unreachable because of the unmentioned variables that would have bearing on the correct answer: the altitude of the hill relative to the surrounding terrain, and any traffic controls on the ?around the hill? route, such as stop signs and traffic lights, or whether you?re leasing the vehicle and would be subject to an excessive mileage penalty.
In terms of pure physics, the energy required to raise the vehicle to the top of the hill is ??mgh?, or half the mass of the object (vehicle) in grams times the acceleration of gravity (9.81 meters per second squared [or 32.2 feet per second squared]) times the height in meters by which the object (vehicle) is raised.
So, going over the hill requires energy to raise the vehicle in addition to that required to overcome friction, whereas going around the hill requires
energy only to overcome friction.
Again because of the variables at the beginning of this post, perhaps Click and Clack will have to determine whether the energy saved in not raising the vehicle makes up for the energy lost in friction going around the hill.


#11

I think one experiment is worth more than 100,000 forum postings on the internet.

The MPG computer which is included on most cars these days isn’t totally dependable for predicting the quantity of fuel one will need to top off the tank, but its perfectly good for comparing one route to another.


#12

They must have a pretty good or bad marriage if the bone of contention is based on probable wear and maybe a dollars worth of gas. LET IT GO! Take whatever route the driver likes best and fogett about it, duh.


#13

If it’s an 87 Mazda pickup with four cylinders and a manual transmission, there isn’t any difference. I drove for hours up steep hills in low gears and still got 24 MPG for the tankfull. You can see a long way from Tranquilion Peak. I could not see Santa Barbara, but it’s only a 55 minute drive. Don’t stop until you get carrot cake at Nordstrom’s.

What was the question again?


#14

@pleasedodgevan2:

So, you drove uphill for hours? What was your elevation at the summit? “What was the question?” The question was, do you drive up and down a small hill or drive around it. Try to follow along.


#15

Or a pretty GOOD marriage if this is all they can find to debate about.


#16

The shortest way to a point is a straight line.


#17

Going up and down a hill does not a straight line make.


#18

At my house, the rule is: Whoever washes the dishes gets to do it their own way. I think this rule can be easily applied to this problem.


#19

Heaven help those of us who try to conserve gas if we take the advise of our Car Talk experts. After listening to the description of the "hill vs. flat route, I wonder how anyone can feel that the flat route would come close to being as efficient as the hill route. The fact is, the hill hardly qualifies as a hill.
Assuming that both homes are about equal distance from the top of the hill, and the total distance over the hill is 1.5 miles, each home would therefore be 3/4 mile from the top of the hill. The top of the hill is 150 feet higher than each house, so the slope, both up and down is under 4%, which, though I’m not an engineer, I’m sure is not even enough to keep a car rolling at 30 mph. Considering that there is a stop in the flat route, that means that going that route would involve using the brakes twice to stop rather than once, and accelerating up to speed twice. In addition, the route is 25% longer. Driving up the hill requires the engine of the car to operate at higher torque, which is more efficient, since all cars are overpowered and less efficient at lower loads. The slope of the hill being so small makes the over-the hill much more efficient than the flat route. Once you reach the peak of the hill, you can turn the engine off and you will probably coast to a stop right in front of your relative’s house.
In spite of all I have said, though, the most fuel efficient way to get from one house to the other is to take a brisk walk. At 3 MPH, you can go the hill route in 30 minutes, and the flat route in in 40 minutes. Either way, you will be healthier, you will be saving the environment, and you will decrease our dependence on foreign oil.


#20

It costs 25% less to drive 1.5 miles than it costs to drive 2 miles. Let’s not consider only the cost of fuel here. Average cost/mile is between $0.50 and $0.60. The hill route is about 26 cents cheaper. After a dozen trips, you can afford to stop at Starbucks for a Cappuccino.