Are trucks more efficient than cars?

[Somes J]

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 - 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.

 

[xxChrisxx]

These types of questions are broad to the point of the questions losing meaning.

Trucks are obviously more efficient at hauling tons of cargo around a country. Cars are more efficient at ferrying around a couple of people. It's a case of the right tool for the right job.

In this case you've picked an application that diesels are really good at, large, slow revving and cruising at 55-60mph, and something that batteries would be terrible at. Turn it around, the truck and the car are driving through town in a traffic jam.

 

[russ_watters]

Transportation costs and efficiencies are often rated per pound (or ton) - mile. Trucks beat cars at that score when fully loaded.

 

[Somes J]

Let me try rephrasing the OP a bit.

In my calculation 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 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 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 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? Any holes here?

 

[DaveC426913]

Does this sound reasonable to you guys? Any holes here?

Certainly. It is elemental that transport efficiency increases with scale.

That's why vehicles get bigger and bigger. If efficiency increased as the inverse of increasing scale, well ... we'd see billions of toy trucks on the roads, each carrying one matchstick - and billions of toy ships in the seas, each carrying one thimble of oil.

 

[Somes J]

I decided to try a different approach here. There are commercial cars that run on diesel, that should allow a more reliable car/truck comparison, as now I'm comparing the same type of engine, not converting between different engine types.

The http://www.hybridcars.com/diesel-efficient-cars". That works out to 6-8 times the mileage per gallon of a big truck (5-6 mpg). If I use the fully loaded weight of the truck (36 tons) it has 1/24 the weight, if I use 20 tons it has 1/13 times the weight.

I did another calculation with the Audi A3 TDI, which is also http://www.mpgomatic.com/2010/02/13/2010-audi-a3-tdi-review/" and gets 35 MPG, that works out to a big truck with 13-24 times its weight having ~1/7-1/6 its gas mileage.

So it looks like, on a pound per pound basis, big trucks use ~1.5-4 times less diesel than cars. Which fits relatively well with my original calculation, where I got a truck being ~1.75-2.6 times more energy efficient on a pound for pound basis.

Another data point, according to this an empty 18 wheeler tractor http://www.chacha.com/question/what-kind-of-fuel-mileage-does-a-fully-loaded-18-wheeler-truck-get.-and-what-does-one-get-pulling-an-empty-trailer", which comes out to a ~1.5X greater pound for pound efficiency for the big truck.

Certainly. It is elemental that transport efficiency increases with scale.

That's why vehicles get bigger and bigger. If efficiency increased as the inverse of increasing scale, well ... we'd see billions of toy trucks on the roads, each carrying one matchstick - and billions of toy ships in the seas, each carrying one thimble of oil.

Yeah, but I figured with trucks it had more to do with duplication of effort than energy efficiency (a smaller fleet of big trucks would need less components and less manpower).