Wow - this is a rather complex question. To fully understand
everything, we need to know 1) how cars use gas, 2) how cars climb
hills, 3) what cars have to overcome in order to climb a hill, and 4)
why engines are horribly inefficient
1- How Cars Use Gas
Sounds simple enough, right? Well, yes actually. When you press your
gas pedal, your gas consumption goes up, right? Many people believe
the gas pedal is connected to the fuel pump somehow, but this is
technically incorrect. Instad, the gas pedal somply opens a valve
called the throttle. All this valve does is to allow air into the
engine. The more open it is, the more air enters. So, the term "gas
pedal" is really a misnomer...it's more of an "air pedal". Anyhow, as
the air entering your engine changes, sensors pick up this info on the
fly and adjust your engine gas intake electronically. In older cars,
this was done through a carburator, a rather ingenious device. This
means simply - the further you push your gas pedal down, the more gas
you burn. It does not matter what gear you're in; how fast your
engine is revving, or really anything else. Gas pedal goes down; gas
cunsumption goes up.
2 - How Cars Climb Hills
The only "force" a car can use to climb a hill or to even more for
that matter, is not actually a force, but a torque. I'm sure you know
what torque is, but if not, here we go...torque is a force exerted
about a distance. You grab a doorknob and open a door; voila torque.
Force (you pushing), multiplied by a distance (width of the door) on
the hinges. This is also why if you decide to push the door at
half-width, you have to exert twice as much force than if you had used
the doorknob.
Cars need torque, too. Everybody talks about horsepower. HP this; HP
that. In reality, torque is way more important. HP = torque x rpm.
So, when you see a horsepower rating, you HAVE to look at the RPM.
200 HP @ 6000 RPM is not quite as good as 170 HP @ 4000 RPM. Sure,
you got 30 less horses, but you got way more torque. In a conceptual
sense, torque is what gives you that oomph when you hit the gas. That
"stick to the back of your seat" feeling. You may have heard
Volkswagon's new ad campaign...regardless, torque is good.
There are two ways to get torque on a car. First, have a good engine -
pick the 170 HP engine over the 200 HP engine, for instance. The
second way is a good gearbox or transmission. Now obviously, all cars
have transmissions. A transmission's only job is to convert rpm into
torque and vice versa. The gear ratios are important here. Different
cars will have different gear ratios, which will affect your final
torque output. There's no magic good gear ratio set, because it
depends on what you need your auto for. Sports cars have different
ratios than semi-trucks and so on. Of course, a combination of good
engine and good gearbox is your best bet.
When you start to go from a standstill, like from a red light, here's
what's happening. You start in gear 1; maximum torque, hence maximum
acceleration. As your revs go higher and higher, revs approach red
line (max out) and you have to switch to another gear. Gear 2.
Acceleration isn't as much, but it's not a big deal anymore, because
you're already going at a good rate. You will accelerate to a higher
speed because your revs "reset", but you accelerate more slowly than
you did in gear 1. And this process continues through to gear 4 or 5
or however many your car has.
When it is harder for your car to accelerate, or when you need more
instant power, you actually need more torque. Therefore, when you are
going up a steeper hill, you need more torque.
3 - What Cars Have to Overcome to Climb Hills (and just go)
- inertia (cars at rest want to stay at rest)
- gravity
- drag/friction
- aerodynamic
- rolling
- internal
Gravity is an easy one. Since the shallow hill and the steep hill
rise to the same point, you theoretically use the same energy to get
to the top of the hill, with respect to gravity.
Inertia - not a big deal in your case, because I am assuming you are
not stopping and going repeatedly on this hill but rather maintaining
a relativele constant speed.
Drag - a big (BIG!) one. Your biggest contributor, aerodynamic drag,
goes as velocity squared. Wowza! That means at 40 mph, you're
actually exerting 4x as much force to overcome drag as you are at 20
mph. With current gas prices, That'd better make you think twice when
you want to go that extra 5 mph. However, note that at zero mph
(idling/red light/etc), you are burning gas and getting nowhere.
Therefore, you get 0 mph. At 1 mph, you are going infinitely further,
but only burning a teeeeeny bit more gas. Same with 2 mph...and
3...(and at these speeds, drag is miniscule) Well, sure enough, this
trend does keep ocurring until a point where drag is no longer
miniscule andsignifantly affects your gas mileage. For a typical car,
this point is right about 55 mph. On some of the modern, super
aerodynamic cars, it's 60-65, but 55 is pretty average and is also the
widely accepted standard. This is also why during the 70's gas
crisis, the national 55mph speed limit was enacted.
4 - Why Engines are Horrible Inefficient.
A typical auto gasoline engine is only about 28% efficient. This
means that only 28% of the energy from gasoline goes into moving your
car. The other 72% gets wasted as heat, which is why your engine is
so dang hot after you've been driving it for even a short distance.
Now before you go believing that the auto companies have secret
negotiations with the gas companies, note that this is unfortunately
due to the laws of thermodynamics. I'm not going to get into the
details, but the main issue is time. If we let the gas/oxygen react
over an infinite time period, then we could obtain 100% efficiency.
But, we are Americans; cowboys; cowgirls; we want our power and we
want it now! For this, we must pay a price. In a car, specifically
an engine cylinder, it ends up that the faster you react, the less
efficient is the reaction. This translates to higher revs equals more
wasted gas.
So, let's recap..
1 - You push down on the gas pedal, you burn gas...period
2 - You need torque to move
3 - Drag is a leech
4 - Higher revs = higher gas consumption
All this comes into play regarding your driving habits - perhaps the
single most important factor in determining your gas mileage. Have
you ever noticed that younger drivers almost always get worse gas
mileage than their parents? This is because younger drivers tend to
accelerate like mad from red lights; they don't use their gears
efficiently, and drive fast; all meaning higher fuel comsumption.
For yourself, you need to assess your driving habits. Ask yourself
how you drive up each hill. Are you going up faster one way than the
other? Is your gas pedal all the way down going up the steeper hill?
If so, consider switching to a lower gear (but not too low, because
you'll start to waste gas).
As for your comment regarding the brakes, this is not technically
true. Remember you are not dissipating more heat one way or another.
You are, however dissipating more power, because you are dissipating a
given amount of energy (heat) in a shorter amount of time (recall
power = energy / time). Also, while you use your brakes to slow down,
you are also using your engine to achieve the same result (you've seen
the signs - truckers, reduce gears) -- this is called engine braking.
So, you are dissipating the same amount of heat, just over a different
time period.
Chances are that you get better gas mileage on the gradual hill. This
is because on the steeper hill, 1) you're probably pushing pedal to
the metal, 2) gear is lower for torque, therefore revs are higher, and
3) like me, are probably speeding like a demon up that hill.
As far as an optimal angle of ascent, it depends completely on your
driving habits, engine, and aerodynamic profile.
The best way to test this theory experimentally is to calculate your
gas mileage both ways for your next 5 or 6 trips. Find the average,
and see which is better.
Hope that helps, and if all else fails, buy a hybrid...
Cheers! |
