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175 comments on Rail Efficiencies

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Brother Kornhoer on December 26, 2008 - 9:54pm Permalink | Subthread | Parent | Comments top

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.

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barrett on December 27, 2008 - 1:19am Permalink | Subthread | Parent | Comments top

So, if you double the speed you quadruple the force of drag.

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).

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Brother Kornhoer on December 27, 2008 - 2:55pm Permalink | Subthread | Parent | Comments top

Right - thus the power output of the engine has to double again, as I stated originally.

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barrett on December 29, 2008 - 1:44pm Permalink | Subthread | Parent | Comments top

Indeed, I didn't read closely enough.

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dwcal on December 29, 2008 - 4:51am Permalink | Subthread | Parent | Comments top

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.

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175 comments on Rail Efficiencies

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