175 comments on Rail Efficiencies
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175 comments on Rail Efficiencies
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The link is to Transportation Data Book 27. I believe this is the 27th edition of this book. Some of the exhibits give a history over the years of Btu/passenger mile, and how they have changed.
There are a few freight comparisons.
Exhibit 2.15 compares railroad to intercity waterborne commerce for freight. According to the table, railroad comes out ahead of waterborne freight, on a Btu per ton/mile basis. Rail is shown a 337 and waterborne commerce at 514. I do not understand exactly what kind of waterborne freight this is. The relationship seems strange. If it were ocean going freight, it seems like it would be lower. It may be that the waterborne freight there are looking at is only going a short distance, so there are big loading and unloading costs.
Exhibit 2.16 gives a Btu per "Heavy-single unit combination truck" mile. How much one can ship in a truck would depend on how dense the cargo is, so it is hard to directly compare.
I haven't looked at Transportation Data Books for other years. They may provide additional data.
The only way I can see water born freight having higher energy cost than rail is if the ships are made to travel very quickly. I would like some physicists and engineers to check my factoids, but I believe the following is true: While air resistance rises as a cube function of velocity (third power), with movement through water it rises as a function of the sixth power.
Hence, if ocean going vessels have been "pedal to the medal" they may be less efficient than rail freight, but if they slow down they could be much more efficient.
I think the water case is more complicated. Fluid dissipation pretty much scales as the cube, but ships also have to contend with wave drag, whereby the ship creates a surface wave, that radiates energy away. The power in this wave, may vary with velocity, as the shape/wavelength of the wave interacts with the waterline of the ship. Those bulbous underwater blobs on the bows of ships can decrease wave drag, by displacing the bow wave ahead of the main body of the ship. I suspect all things being equal, that wave drag does increase pretty rapidly (I don't know if your sixth power is right). Nevertheless, the discussions of fuel saving for cargo ships that I've seen, seem to assume the cube law.
There's a thing called "Hull Speed" with displacement hulls. As the boat goes faster the surface wave emanates from farther back on the boat. When you've reached the speed where the wave is emanating from the back of the boat, you are at "Hull Speed" and it take substansive amount of power to go faster (then you would be planing). The "Hull Speed" for a displacement hull is a function of its length (1.34 * sqrt(waterline length)).
OK I have a BS in Physics and an MS in Engineering, but my fluid mechanics book is at work, and I'm studiously avoiding going near the office over the four-day holiday weekend. So, I had to resort to Wikipedia. The coefficient of drag equation is
Drag_force = (1/2) * rho * v^2 * Cd * A
where
rho = fluid density
v = velocity
Cd = coefficient of drag
A = reference area (for cars, frontal cross-sectional area; for ships, wetted area (air resistance of a ship is neglected as inconsequential))
So, if you double the speed you quadruple the force of drag. Since work = force * distance, by doubling the speed you have quadrupled the work necessary to move each mile, so your engine has to increase proportionally. Also, since you are covering each mile in half the time, the power output of the engine has to double again. As you can imagine, the horsepower requirements ramp up quickly. For example, the 2009 Chevrolet Corvette ZR-1 has 638 hp and a top speed of 205 mph. The fastest production car in the world, the Shelby Supercar Ultimate Aero, has over double the horsepower - 1,287 hp claimed - but a top speed only 52 mph faster - 257 mph.
There's something else to consider. The v^2 in the equation is an artefact of the kinetic energies involved in colliding with molecules impeding your movement. When you double your speed the collisions have quadrupled in force, but in a given time interval t you have also doubled the number of molecules you are colliding with because you are moving thru them twice as fast.
That makes the total drag at any given instant proportional to v^3, total energy expenditure going from point A to point B is still proportional to v^2 (trip time is reduced if speed is increased).
Right - thus the power output of the engine has to double again, as I stated originally.
Indeed, I didn't read closely enough.
It's been a long time since I've done fluid mechanics myself, but that equation assumes a constant Reynolds number, a valid assumption for air resistance of cars and trains, not so for ships in water.
The top speed of supercars is good for bragging rights and not much else. Once you get much over 200 mph, you're limited as much by aerodynamic stability and tire safety as by power and drag; the Mclaren F1 reached a top speed of 231 mph with 627 hp. The Wikipedia page says the SSC Aero has a theoretical top speed of 273 mph; I suppose that's based on power and drag.
I do not understand exactly what kind of waterborne freight this is. [...]
I see lots of coal, iron ore, and gravel on barges on the Ohio River. They move freight boxes too. Jeffboat in Jeffersonville IN builds most of the barges, their business picks up when fuel prices go up.