Naked Science Forum
Non Life Sciences => Technology => Topic started by: Somes J on 05/08/2011 09:05:43
-
Something I was wondering about. I was doing some calculations on how much energy different types of vehicles consume, and I got a result that surprised me.
For big trucks, I found an estimate of 5-6 MPG on the internet, divided the energy content of a gallon of diesel fuel by that, and then corrected for a ~45% efficiency. For the cars I divided the battery energy content of the Nissan Leaf by its range to get miles/joules. To check my results I tried doing an estimate for an electric truck with a battery as big in proportion to its (fully loaded) weight as the Nissan Leaf and I got more energy required for a given range than with the 5-6 MPG based calculation.
I'm wondering if this is an artifact of my calculation (could easily be, it was just not very precise amateur work), or if there's some kind of genuine economy of scale for big vehicles that I stumbled on. I did a little searching on the internet and found that air resistance is a very significant factor in energy efficiency at high speeds (over half the power demand at 65 mph - see pg. 5 (http://www.rvtechlibrary.com/engine/MPG_Secrets.pdf)) and its partially proportional to the vehicle's frontal area. A fully loaded big rig certainly is going to have more frontal area than a car, but I doubt it would have 25 times the frontal area (proportionate to how much heavier it is). If the car is 1.5 X 2 m (4.5 X 6 ft) and the truck is 3 X 3 m = (9 X 9 ft) the truck is going to have 3X the frontal area, nowhere even remotely close to 25X.
Is there an actual economy of scale in energy with big long vehicles like trucks because of this? Does anybody have any idea how to actually calculate how big of a difference this factor would make to energy consumption of a large truck vs. a regular sized car?
Thanks.
PS, I hope it's not a problem that I posted this to a couple of other message boards I frequent, I was told that was discouraged here but I really prefer to post questions like this to a couple of different boards in order to heighten the chances of getting an enlightening answer. I will cease to do so in the future if it is a problem.
-
In terms of your maths, I'm not going to stop & check it, but the claims you are making would not seem unreasonable. I would say that 45% fuel efficiency is perhaps a little high for a Diesel lorry in real world operation, but in general, yes, agreed.
Is there a wider question that you have coming out of this?
Also, would you consider that the definition of efficiency always has, for the real world, to be taken in the context of the 'value' of what you are achieving, ie. moving plastic-mouldings on a road out of rural China will have (by some measure) a lower value than flying the head of a Multinational to broker a deal on the other side of the Atlantic.
Having a 5-seater car to drive yourself to work in obviously falls somewhere in between...
[using the same principle as a lorry I can move lots of people around a city with an omnibus (I hear they're catching on!) [:D] ]
-
Is there a wider question that you have coming out of this?
Yes. I got a result that a truck used less energy than a car pound for pound for a given mileage even assuming the engine efficiency was the same. This seemed puzzling to me because if anything I'd expect it to be the opposite (truck is less aerodynamic). I was wondering whether this has any basis in the physical world or if it was just an artifact of calculation imprecision. One possibility that occurred to me is air resistance is a major factor at highway speeds and I figured a big factor in air resistance is going to be frontal area, which will scale up more slowly than a vehicle's mass and volume (a big truck looks long in comparison to its width and height compared to a car, and all else being equal volume and hence freight capacity scales by the cube while area scales by the square).
I think I found a site that might help me with this (http://physics.ucsd.edu/do-the-math/2011/07/100-mpg-on-gasoline/), it gives a formula for air resistance:
1/2CdpAD(v^2)
Cd = drag coefficient
p = 1.3 kg/m^3 (density of air at sea level)
A = cross sectional area of the vehicle
D = distance travelled
v = velocity
They say Cd for a Prius is .25, for a sedan is .3, and for a SUV or pickup truck .5-.6. I'm not sure what the proper units are for the rest but I'll use meters. I'll approximate the car's frontal area as 1.5X2=3m and the truck's as 3X3=9m, so the truck has 3X the frontal area of the car, and give the car a Cd of .25 and the truck a Cd of .6. The rest of the variables I'll keep constant (65 mph, 65 miles travelled, converted to meters and m/s).
Car = 1/2(.25)(1.3)(3)(104,000)(29^2) = 32,799,000
Truck = 1/2(.6)(1.3)(9)(104,000)(29^2) = 306,998,640
I get 9.36 times the air resistance for the truck as for the car.
I'm not sure I'm doing this right (especially as I think this (http://mb-soft.com/public2/car.html) suggests I should drop the 1/2 from the equation - and I get more consistent results without it), but generally playing around with the formula I get in the ballpark of 4-10 times the air resistance for increasing frontal area by a couple of times and increasing Cd by a factor of 2 or so (which I think would probably model the comparison between a car and a large truck fairly well).
Now according to this (http://www.consumerreports.org/cro/cars/tires-auto-parts/car-maintenance/fuel-economy-save-money-on-gas/overview/index.htm) at highway speeds air drag can account for half or more of energy consumption. And the truck I was using in my calculation was 36 tons while the car was 1.5 tons. So this fits with the at first puzzling result I got, that a truck used less energy pound for pound for the same mileage; it's 24 times heavier but only gets maybe 5-10 times the air resistance because of its less aerodynamic frontal profile and bigger frontal area. So it looks like there's an economy of scale here with big vehicles: air resistance scales with frontal area, which scales up slower than volume and mass assuming a relatively long vehicle (like a truck with a trailer).
Does this sound reasonable to you guys?
-
As Peppercorn pointed out, when you talk about "efficiency", you have to decide what resource you are being efficient with. For example, you might only be concerned about time, in which case an aeroplane is probably your best bet.
-
As Peppercorn pointed out, when you talk about "efficiency", you have to decide what resource you are being efficient with.
My question concerns energy consumption of the engine to move a given mass a given mileage.
-
If your pickup gets 15MPG carrying a ton.
And a truck gets 5MPG carrying 35 tons.
The truck is using 3x as much fuel to carry 35x as much product.
-
As Peppercorn pointed out, when you talk about "efficiency", you have to decide what resource you are being efficient with.
My question concerns energy consumption of the engine to move a given mass a given mileage.
Clifford gives a good example. As long as the truck is carrying a decent size payload, it's going to be much more fuel efficient.
-
yes your absolutely right, the more bigger the engine is the more power it generates and less the fuel consumption. the smaller the engine the less the energy generation and more the fuel consumption. Lets take the example of electric generators, the more bigger the generator is the more kWa it produces and the less the fuel it consumes as compared to one small generator or various smaller ones making an equivalent to that big one.
-
qazibasit - Thanks for adding nothing new to the discussion!
[ -Shrinkage- will follow in a few days, I expect! - A. Mod]
-
Just for interest's sake:-
I remember that in the 1970's, a good Diesel engine (Gardner LX or LW) was quoted as having a thermal efficiency of 38%. These days I would guess that over 40% (perhaps 45% is possible).
The trouble is that (as I.C. engine fans tend to forget) the efficiencies quoted are those obtained on a dynamometer, are the best for the engine under test, and occur over a relatively small part of the speed range. The efficiency in normal operation is well below the peak figure appearing in the engine's specification. By contrast the effiency of a modern electric motor can be 90%, occurring over almost the entire speed range. Hence a series hybrid vehicle that uses it's engine at it's fixed, most efficient speed, to charge the battery for the electric motor, using the far superior efficiency of the latter for moving the vehicle , is a much better solution.
As regards the difference between large and smaller engines:-
I was taught that in general terms, a larger engine is less efficient because of "friction and pumping" losses. These are present because an engine has to use some of the energy it produces to pump air in and out of it's cylinders, compress the gases, pump oil and water around it's lubrication system and cooling system. These and the larger areas of moving frictional surfaces, lead to greater losses in larger engines. I guess these must be offset to an extent by the fact that larger engines (especially Diesels) have a lower speed range, so the constraints mentioned above re. efficiencey and speed range will have a smaller effect. I guess this must mean that a slower revving engine must be better.
-
I guess this must mean that a slower revving engine must be better.
There are so many variables involved that it's really hard to make a general statement that will always be true. F1 racing engines are very efficient from many perspectives, but unfortunately, they don't go for very long. Big diesels may be less efficient, but they go for a very long time.