## Introduction

I was listening to an advertisement where CSX made the claim that they move 1 ton of freight 423 miles for 1 gallon of fuel. This is an interesting measure of efficiency. Let's see if we can confirm this using a couple of different analysis approaches.

## Top-Down Approach

CSX issues quarterly reports, which contains data that we can use to estimate the miles per gallon-ton of freight. This forum article has some interesting data from the 4Q2007 CSX financial statement.

- CSX moved 253 billion revenue ton-miles of goods in the 12 months ending 12/31/07.
- During this period, CSX consumed 569 million gallons of diesel #2 fuel.

This makes computing the efficiency *eff* of a train (mile-ton per gallon) easy, which is shown in Equation 1.

Eq. 1 |

This number is close to what CSX is using its advertisement. So their number is credible based on their business statment.

## Bottom-Up Approach

It is a bit more difficult to look at the problem from the standpoint of friction and energy, but let's take a wack at it.

First, let's gather some data.

- Energy per gallon of #2 diesel fuel is 138,700 BTU/US gal (Source)
- Efficiency of a diesel engine is ~46% (Source and Source)
- Diesel to rail conversion efficiency of 80% (Source)

There is some loss of power due to transmission inefficiency in the diesel-electrical-rail transfer of power. I am using the value of 80% for the transmission efficiency based on a reference from the 1950s that was comparing steam to diesel-electric locomotives. This number is probably out of date, but is a reasonable start for a rough estimate. - Train expends 20 lb of pulling force per ton of load (Source)

This number is subject to variation due to track condition, weather, grade, and curvature of the track. I am assuming an average value that is in the ballpark, but could easily be off by ±20% or more. Remember, we are just trying to determine if the CSX efficiency number is reasonable.

I would propose that one simple model would be to equate the energy dissipated against the rolling resistance of the train to the energy available from a gallon of diesel fuel.

Eq. 2 |

Where *d* is the distance traveled, *F _{FrictionPerTon}* is the resistance of a ton of load (= 20 lb per ton),

*E*is the energy per gallon of #2 diesel fuel (=138,700 BTU/US gal),

_{FuelOilPerGal}*e*is the efficiency of a modern diesel engine (=46%), and

_{Diesel}*e*is the diesel-to-rail conversion efficiency (=80%).

_{c}We can solve Equation 2 for

*d*and substitute our assumed values.

Eq. 3 |

This value is close enough that feel I have verified the CSX number from the bottom up.

## Conclusion

Moving one ton of freight 423 miles on one gallon of fuel seems like a reasonable value. This exercise really shows the efficiency of moving material in bulk.

Great! Thanks for doing this calc. I had a similar desire, but didn't find the friction value.

I have just one teensy nitnoid. Your units on the last equation show miles*ton/gal, but it really should be mile*ton/gal; plural units do not belong in equations. I'm surprised that that Mathcad accepted that.

Thanks for the correction. I have updated the post. That part of the post was done in Mathtype, which does not do unit checking.

Could you be high because there is some loss in converting from the diesel motor to electricity?

Probably. I have found several sources that said that locomotive diesels operate about 46%. The Wikipedia reports that the most efficient diesel engine operates at 54%. So I think I know the range of diesel efficiency.

However, I found little information on the conversion efficiency of diesel power to rail power. One source commented that the conversion from diesel to rail cost about 20% (I had to back that out). That would mean the overall efficiency was about 46%·80%=37%. This would drop my efficiency estimate down to 370 mile·ton/gal. I will update the post to reflect this updated estimate.

Good catch.

Pingback: Fuel Efficiency Math | Math Encounters Blog