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Velocity is measured relative to the road surface, and is constant, therefore acceleration is zero. Force is applied to overcome rolling and frictional resistance and the work to overcome gravity when going uphill.
So since acceleration = zero, mass is constant the only changing parameter is force. And the portion of force applied to create acceleration is zero. The additional force is required to overcome gravity and add potential energy to the vehicle.
When calculating all forces on the car you have to take both +ve -ve acceation into account (in all three dimensions).
I spent many years doing this. Our mechanics lecturer would always say never assume acceleration is zero, even if it appears to be cancelled out.
To clarify a bit, if you are maintaining a constant speedometer speed up a hill then yes, you're using more fuel than if you were maintaining a constant speed on the flat, because you're exchanging chemical energy in the fuel for gravitational potential energy.
On the way back down, assuming the hill isn't so steep that you need to use the brakes, you will be getting that gravitational potential energy back, and won't use as much fuel as on the flat.
The frictional losses in each scenario (hill vs not-hill) will be pretty much identical as they're related to speed vs the road and speed vs the air.
This does change if the hill is much steeper on one side than the other, but as many trips are there-and-back you'll probably get the reverse in the other direction.
Thus I maintain that if you stick to a steady speed on hills (up and down) then they don't overall make a big difference to fuel consumption on the journey as a whole. Obviously it takes more fuel to go up a hill than to drive on the flat, but equally obviously it takes less fuel to go down a hill than it does to drive on the flat.
Regarding the acceleration arguments, I think we're getting a bit into semantics, and both views are correct for slightly different definitions. I have been working on a midway definition, that acceleration means a change in velocity, because I believe that's probably the most common usage.
@Sporky, changing the subject slightly, I believe you and @Hywelg commented on a link I posted about real world emissions from Euro 6 diesels using data from 2014. The fact is that those vehicles are registered as Euro 6 compliant. If Euro 6 diesels are allowed to be driven into cities then those vehicles will be part of that group. Yes some of the new ones in the last couple of years might be better but maybe they need to come up with a new designation for them - or retrospectively remove it from the older ones - which would cause a lot of issues with people who have bought them, and massive legal complications. Realistically, a Euro 6 designation for a diesel means very little in terms of air pollution. I'm not even sure that they are better than the older diesels. The particulates from the older ones aren't as small and don't get absorbed into the body in the same way.
The point that Hywelg made is that Euro6 only came into force in September 2014. That report was published on the 10th of October, so it only applies to a very small proportion of Euro6 vehicles, most of which weren't even on sale at that point. At most they had what, 41 days to do all their testing, all their analysis and publish the report. I believe the word "shonky" can be fairly applied to that.
"Take these three items, some WD-40, a vise grip, and a roll of duct tape. Any man worth his salt can fix almost any problem with this stuff alone." - Walt Kowalski
"Only two things are infinite - the universe, and human stupidity. And I'm not sure about the universe." - Albert Einstein
Yes, I see what you mean. You do get some back on the way down, but not as much as you spend on the way up.
I do not dispute that there being a hill means you use more fuel than if there isn't a hill. I do dispute the idea that going up (and then down) a hill necessarily uses four times as much fuel as being on the flat, which is the assertion with which I originally disagreed.
I also maintain that any attempt at "real world" testing will, of course, be subverted by the manufacturers, because it'll have to be on a fixed regime or consumers won't be able to make worthwhile comparisons. That said, I do think it's worth a more rigorous test than the current one, which makes small turbo engines and hybrids look exaggeratedly efficient.
As I said, I commute across a 'hill' of sorts - an average of a little under a thousand feet up over about 20 miles, then the opposite. Even this small gradient - less than 1% - is enough to make the fuel economy over the first half up to 5mpg worse than over the second half, in either direction. I was actually surprised it made as much difference as that, but I've tracked it several times and it's quite consistent.
"Take these three items, some WD-40, a vise grip, and a roll of duct tape. Any man worth his salt can fix almost any problem with this stuff alone." - Walt Kowalski
"Only two things are infinite - the universe, and human stupidity. And I'm not sure about the universe." - Albert Einstein
Witness the other link which shows that VW 2.0 150ps engines, introduced late 2015, are pretty much bang on the money as regards ACTUAL emisssions. And of course they havn't tested petrol engines with quite the same enthusiasm. Its quite possible they are piss poor too.
Agricultural bullshit, throw it in the bin.
lol,
I'm not locked in here with you, you are locked in here with me.
this is O level maths
a jet engine in a test lab firing at full power kicks a lot more power out than a 2 litre diesel, but nevertheless, acceleration is zero, since its velocity does not change from zero (relative to the planet it is anchored to)
you can't "cancel out" acceleration, you are either accelerating or not
F=ma
For example, on a "rolling road" you are not accelerating, you are just testing the power output of the car against friction, with zero air resistance
You take the net force vector and that determines acceleration. Going up a hill, if you open the throttle, Force is applied forwards, at the tyres' interface with the road. If you put it in neutral, the force is in the direction back down the hill (I'm ignoring the forces keeping you on the ground)
http://www.telegraph.co.uk/science/2017/04/26/toxic-diesel-particles-penetrate-right-heart-scientists-warn/
The newer diesels give off more of these smaller particulates. The older ones were actually better for particulates because the particulates were bigger and didn't get into the body. The problem is they were even worse on NO2.
For those who can't be bothered to read the whole article here are a couple of key paragraphs:
While petrol particles are also able to penetrate the lungs, a petrol engine will throw out roughly 50 times fewer particles than a diesel engine of equivalent size, the researchers said.
The particles are also capable of penetrating the masks worn by some cyclists to avoid pollution.
What worries me is that all the low emissions zones at the moment are proposing to let Euro 6 diesels in for free.
Diesels in cities do not work.