Train vs Airplane Energy Efficiency

by David S.Lawyer mailto:dave@lafn.org More articles by David Lawyer

2008-2010
This is a work in progress. The historical part is mostly completed. But the technical part comparing vehicle resistance is still in a state of flux. Since I started with the rail vs. auto as a template and deleted most of the data about autos, you'll find a lot of techical details about rail but no comparison to airplanes.

1. Copyright

2. Introduction

3. Historical Overview

4. Technology Compared

5. Specific Vehicle Resistance/Drag

6. Thermal Efficiency of Engine and Transmission

7. Rolling Resistance (to-do compare w/air)

8. Passenger Trains Are Heavy (to-do compare w/air)

9. Other Factors (to-do compare w/air)

10. Improving Energy Efficiency to-do add air

11. Conclusions to-do more re air

12. Appendix: Train vs. Plane Statistics

13. Railroad Energy References

14. Airplane Energy References

15. Sources of Data For Historical Energy-Efficiency Table

16. Turbofan engines more efficient


1. Copyright

Copyright 2008 by David S. Lawyer. Feel free to make copies but commercial use of it is prohibited. For example, you can't (except to an insignificant degree) combine it with advertising on the Internet. Please let me know of any errors or suggestions for improvement.

2. Introduction

Which is more energy efficient in the U.S. (in terms of passenger-miles per gallon) a railroad passenger train or an airline passenger airplane? While most people expect the train to be more efficient, the reported statistics, after correcting, indicate that the airplane is perhaps 15% more energy efficient. See Train vs. Plane Statistics

Trains have the reputation of being energy-efficient due to their low rolling resistance. It turns out that in spite of it's low rolling resistance, passenger trains in the US today (including rail transit) are no more more energy efficient than the airplane (and also about the same efficiency as for the automobile --but the comparison to the automobile was the topic of another article by me: Train vs. Auto Energy. See it for the bibliography regarding train resistance

The table below Historical Energy-Efficiency shows some of the the history of the statistical energy efficiency of trains vs. planes in the U.S.

2.1 Historical Energy-Efficiency Table 1935-2005

PM/gal = Passenger-Miles per Gallon (auto gasoline)
BTU/PM = BTU per Passenger-Mile
% share = market share of total intercity passenger-miles by all modes

  Scheduled Domestic Air     |      Passenger Rail                 
 per Energy in Am. Economy:  |  David Lawyer |  Eric Hirst  |   David Lawyer
                         Mkt | diesel trains | all trains   | steam  | electric
        PM/gal  BTU/PM %share| PM/gal BTU/PM | BTU/PM %share| BTU/PM | BTU/PM 
1935:   12.8    9,770    0.1 |  51    2,440* | to-do    8.3 | 23,100*| 5,400*
1940:   17.5    7,150    0.4 |  41    3,080  | to-do    7.5 | 17,900 | to-do
1945:   28.6    4,370    1.2 |  85    1,480  | to-do   27.1 |  8,100 | to-do
1950:   21.8    5,720    1.8 |  42    2,950  | 7,400    6.5 | 15,400 | to-do
1955:   24.2    5,160    3.0 |  41    3,010  | 3,700    4.0 |        | to-do
    per Eric Hirst:             * => 1936                   |        |
1955:   26.0    4,800    3.0 |  41    3,010  | 3,700    4.0 |        | to-do
1960:   18.1    6,900    4.1 |  41    3,0l0  | 2,900    2.8 |        | to-do
1965:   15.3    8,200    5.9 |  40    3,160* | 2,700    1.9 |        | 2,900
1970:   14.9    8,400    9.3 |               | 2,900    0.5            (1963)
         per Transportation Energy Data Book:
 includes international      | Amtrak: diesel and electric trains.      
1970:   13.9    8,980    9.3 |  41    2,900 (per Eric Hirst)
1975:   19.2    6,510   10.1 |  34    3,677             0.5
1980:   26.8    4,660   13.9 |  39    3,176             0.4
1985:   28.5    4,390   17.0 |  45    2,800             0.3
1990:   30.4    4,110   18.7 |  48    2,609             0.3
1995:   35.6    3,510   19.3 |  48    2,590             0.3
2000:   37.9    3,300   24.5 |  38    3,253             0.3
2005:   45.6    2,740   24.7 |  45    2,784             0.3           

Sources: See Data Sources for the above table

Notes: Air: Correction for air freight: Hirst used 1 ton = 5 passengers. Lawyer applied 1 ton = 4 passengers to Transportation Energy Data Book (TEDB) data. Note the discrepancies for both 1955 Diesel locomotive trains and 1970 due to different authors. No correction was made by anyone for circuity. Pass-Mi/gal (or PM/gal) is shown for the automotive gasoline BTU equivalent and can be though of as per gallon of gasoline. If you want to get PM/gal-of-kerosene (jet fuel) increase PM/gal-of gasoline by 8%. Likewise, for diesel train fuel increase PM/gal by 10%.

2002 4,137 BTU/PM Reported by Amtrak but retracted 2003 4,830 " " " " " "

The high efficiency for 1945 was due to planes being full due to wartime conditions. Note the big drop in energy efficiency from 1960 to 1975 due to the introduction of "jet" (really turbofan) aircraft and the recovery starting in 1970 due to larger engine fans (high bypass ratio) and the fuel economies of scale for larger aircraft.

The 0 for the low-order digit of the BTU/PM is due to rounding so as to retain 3 significant figures. Eric Hirst has 00 and only retains 2 significant figures. Due to the uncertainties of allocating fuel to cargo transport, retaining only two or three significant figures is reasonable.

3. Historical Overview

While railroads got their start in the 1830's, airlines didn't appear until 100 years later in the 1930's when railroads had lost most of their passenger traffic to autos but still retained an 8% share of intercity travel (as compared to only a 0.3 % share today). Airlines were especially competitive with railroads due to the similarities of the service: has schedules, no driving required, need to obtain local transportation at destination such as auto rental or public transportation.

But while the railroad's share was low in the 1930's, the airlines share was roughly 100 times lower at only 0.1% (in 1934). See. Passenger-Mile Data. Flying was dangerous, expensive, and slow as compared to today. For example,in 1936 the fastest flights coast-to-coast across the U.S. took 14 hours with 3 intermediate stops for refueling. This was still a lot faster than going by train.

What about fuel economy? Before the introduction of the streamlined Douglas DC-3 airplane in 1936 (and other more efficient airplanes, airlines got only about 13 passenger-miles per gallon (in 1935). This was about as poor as driving alone in a luxury auto but still much better than the steam-powered railroad trains which burned coal or fuel oil and only got the equivalent of 5 passenger-miles per gallon.

While 90% of rail passengers rode on such trains, some went on electric trains which were about twice as efficient as airplanes, and a relatively few went on the new diesel trains which were about 4 times as energy efficient at airplanes. The fact that it then took about twice as much fuel to generate a kilowatt-hour of electricity as it does today mostly explains why diesel trains were about twice as efficient as electric trains at that time.

After the mid 1930's, airline fuel economy went on a roller coaster ride, rapidly improving until the late 1950's when the inefficient "jet" airplanes replaced the more efficient propeller airplanes. Improvements (before the "jets") included better streamlining, larger planes with less surface area per passenger to cause drag, and flying higher where the air is thinner resulting in less aerodynamic drag. Railroads improved energy efficiency at a faster pace than airlines by simply but slowly replacing the steam locomotives with diesels which were nearly 8 times more efficient. The pace of dieselization of rail passenger travel (which began in the mid 1930's) continued apace after 1949 (when it was half-way completed) becoming fully completed in the mid 1950's. See Car-mi by Diesel (from ICC data)

The result was that by the mid 1950's, passenger rail had surpassed the airlines in fuel efficiency. As airlines introduced inefficient "jets" in the late 1950's trains became more than twice as fuel efficient as flying. But unfortunately, rail traffic was declining and in 1957, airline travel surpassed that of rail so the increase in rail efficiency was becoming of less significance as passengers gave up on rail travel for airplanes. Enticement to the airplane was due in part to air travel being faster and cheaper but the neglect of passenger traffic by railroads as well as labor union rules played a significant role in rail passenger decline.

Then starting in the 1970's, airlines did something about the poor fuel economy of the "jets". Note that "jet" is quoted because they were really turbo-fan aircraft that are similar to turbo-props, except that a hidden fan replaces the propeller. By making these fans much larger and thus making the aircraft more like propeller aircraft, the airlines significantly improved their efficiency. See Turbofan engines more efficient. The result was that by about 2005, flying surpassed trains in energy-efficiency.

So now that planes are just as energy-efficient as trains, aren't we better off since planes travel faster and thus save time. Not necessarily. The slowness of train deterred people from making so many long trips. If there were no travel by airplane there would likely be a lot less long distance travel, thereby saving energy.

4. Technology Compared

4.1 Air and Rail Terminology are Different

Aeronautical Engineers seldom (if ever) talk with Railroad Engineers (not the train driver sort of engineer) about technical factors affecting energy efficiency. It they did, it would seem that they were speaking different languages since the terminology is almost completely different. What a railroad engineer would call train resistance, and aeronautical engineer would call drag. What a railroad engineer would call specific train resistance is the inverse of what an aeronautical engineer would call the lift-to-drag ratio. But there are many factors for air for which there is no close equivalent for rail and conversely and thus the use of different terminology for different concepts is inherently necessary in some cases.

4.2 Vehicle Resistance

When a train or plane moves forward, there is a resitance (for trains) or drag (for airplanes) force which resists moving the vehicle forward and which is directed along the path which the vehicle takes. For a train, this path is just the railroad tracks. But for a plane this drag force, caused by the headwind hitting the plane is, directed along the direction of such a headwind. For a plane, if the air is still, both on the ground and aloft (no natural wind), then this drag direction is just the flight path of the airplane with respect to the earth. If there is a natural wind, things are a bit more complex as will be explained later to-do.

The amount of force required depends on many things such as the vehicle's weight and speed. It takes still additional force to accelerate the vehicle or to ascend grades (trains) or climb (planes). For level travel, drag (planes) is equivalent to resistance (planes). But for grades (trains) or climbs (planes) and decents (planes) the forces due to the vehicle weight are similar but go by different name. For trains they are called grade resistance and serve to increase or decrease the total train resistance when going uphill or downhill respectively. But for airplanes, one doesn't normally call climb (grade resistance) "climb drag". Instead it's commonly know by the force needed to overcome such resistance: "excess thrust" for climb. A train descending a grade faces negative grade resistance which helps move the train down the grade. But a descending airplance wouldn't clasify this as negative drag although that's what it amounts to. Thus for both a train and plane, the concepts are about the same but the terminology is different. There are some major diffences in perfomance since, unlike a train which follows a fixed path set by the rails, a plane has options of alternate paths and can select a decent (glide path) that will result in no power (thrust) needed for the descent.

The mechanical energy expended in moving a vehicle is just the resistance force times the distance traveled. Thus if one wanted to compare the mechanical energy used to move two vehicles a fixed distance, and one vehicle had twice the resistance of the other, then it would take twice as much mechanical energy to move that vehicle. If the resistance varied over this fixed distance then one would use average resistance (averaged over distance and not time). Thus by comparing the total resistances of two vehicles on level ground one may compare the mechanical energy needed to move the vehicles a given distance.

One may think of vehicle resistance/drag as the energy required to move the vehicle a unit distance (such as a meter, foot, kilometer, or mile). For example, if the resistance of a train is 100 kilo-newtons then the energy required to move a kilometer is just 100 kilo-newton-kilometers or 100 mega-joules, since a joule is just a newton-meter.

To find the total mechanical energy used, the forces of acceleration, deacceleration, braking, and grades (climb/descent) would need to be added to level resistance force or drag. But obviously under cruising conditions where there is no acceleration, braking, or grades, there's nothing to be added.

5. Specific Vehicle Resistance/Drag

To converts vehicle resistance to what is equivalent to energy intensity, one may divide the resistance force by the vehicle weight to get a specific resistance (trains) or use the inverse: lift-to-drag ratio (airplanes) since lift is the planes weight and drage is the plane resistance. In olden days in the US, trains used units of pounds of force per ton. If it was say 20 pounds per ton (20 lb/ton) then it would take a pull of 20 pounds to keep a one ton of train moving forward at steady speed on a level path. Other units of specific resistance are kilogram-force per metric-ton (kgf/tonne) or newtons-force per metric ton. Since a metric ton is just 1000 kg, the unit of kgf/tonne is just parts per thousand (independent of what units are used. For example a resistance of 10 parts per thousand would be the same as 10 pounds force per 1000 pounds weight or 10 kgf/ton. For a plane using the above values, a lift of 1000 pounds would require a drag of 10 pounds resulting in a lift-to-drag ratio of 100 (which is unrealistically high since it's usually under 20).

6. Thermal Efficiency of Engine and Transmission

In order to determine the fuel energy consumed, the mechanical energy used must be divided by thermal efficiency of the engine-system. For a train diesel-electric locomotive, the "engine-system" consists of a diesel engine and an electric transmission. For a plane, it consists of just a turbofan engine that throws a high speed stream of air and exhaust out the back of it.

Thus a plane seemingly has no transmission losses, but acutally it has something like it, since it transmitts force to the atmosphere by pushing air backwards to the direction of flight while a train locomotive pushes back directly on the earth via the rails. The air the plane pushes back on is not confined and as a result it flows backwards behind the plane, leaving a backward flowing (with respect to the earth) wake of air behind the plane. This flowing air (with a little exhaust gas mixed in) represents energy wasted in generating engine thrust and represents something like transmission losses. The efficiency of this type of "transmission" is known as 'propulsion efficiency". Manufacturers of turbofan engines for "jet" aircraft don't nornally provide data on propulsion efficiency but include such losses in the data on engine efficiency, which for the Pratt & Whitney JT9D-7 turbofan engine used on the Boeing 747 was about 29% efficent

For a locomotive, if its transmission is 80% efficient and the engine converts 35% of the fuel energy into mechanical work, the efficiency is 0.8 x 0.35 = 0.28 (i.e. 28%). Since mechanical work is measured at the driving wheels, transmission energy losses must be included.

For electrically powered trains, one should not only consider the efficiency of the electric motors on the train, but the energy loss in transmitting the electric energy from the power plant to the train. Of course, the efficiency of the power plant in converting fossil fuel energy into electricity must be counted too.

So what are typical values for such efficiency? It turns out that for both trains and older planes this efficiency is roughly 30% under the best conditions. This is also the case for electric trains. For newer planes the efficiency is higher to-do.

But actual conditions are mostly far worse than the best. The actual thermal efficiency is often well below 30% and can even be zero. For example, if an auto is going down a hill with the engine running at cruising rpm, but it could have also coasted down the hill at the same speed (in neutral gear with the engine shut off), then all the power being put out by the engine is wasted. The car could have descended the hill at the same speed with no fuel used at all. Under this condition the engine is being operated at 0% efficiency. Even if the car is going down the hill under engine power at a speed only slightly higher than the coasting speed, the efficiency may only be a few percent.

Any motor that is operated at low torque (low power output for the speed it's turning at) will have low efficiency. This is even true for electric motors powering trains at extremely low torque. At very high current (and torque) the efficiency of electric motors drops also since ohmic losses are proportional to the square of the the current. Although the efficiency of the electric motor alone is much higher than that of an internal combustion engine (gasoline or diesel) an electric motor that drops to say 60% efficiency will result in an overall efficiency of about 20% due to the losses in the generation and transmission of electricity.

For passenger trains, a significant amount of energy is used to air condition the cars (including electric heating on diesel trains). This energy cost was neglected in the above discussion but it can't be neglected in the final results. Automobiles utilize waste engine heat to heat them which tends to make them more energy efficient.

7. Rolling Resistance (to-do compare w/air)

One component of vehicle resistance is rolling resistance. This is the force opposing the forward motion of a vehicle due to the rolling of its wheels. It doesn't include the wind forces. At low speed in still air on level ground, almost all the resistance is rolling resistance. If you've ever pushed an automobile by hand, you should know what rolling resistance is: it's the force you have to push the car with to keep it rolling at steady speed on level ground. Besides rolling resistance, there's another resistance known as aerodynamic drag. This is the wind force against the vehicle. You can feel this force by sticking your open hand out the window of a fast moving car. Aerodynamic drag increases proportional to the square of the velocity so it's not very significant at low speed. It also takes additional force to move a vehicle up a grade or to accelerate its speed but these are neither rolling resistance nor aerodynamic drag.

Rolling resistance may be given as a percentage of the vehicle weight. For example, if an automobile weighs 3000 lb. and has 1% rolling resistance, then it would take 30 lbs. (1% of 3000) to push it slowly on level ground. But rolling resistance is commonly expressed in units of "per thousand" which is ten times the percentage value. Railroad steel wheels on a steel rail have a low rolling resistance of between 1 to 2. The 1 value is for a fully loaded railroad freight car, while the 2 value is for an empty car. Rail passenger cars tend to be closer to 2 than 1.

For railroads, rolling resistance (in percentage terms) is lower when the vehicle is heavier. With a heavier load, the total rolling resistance goes up, but not as fast as the load increases. This "economy of scale" is due in part to the spreading out of the pressure caused by the heavier wheel load along a longer length of rail. It one doubles the wheel load, the pressure under the rail doesn't double, because the additional force is spread out over a longer length of rail. Of course, there's a trade-off since very heavy loads will cause more damage to the roadbed.

In addition to the wheel energy loss, there are some other losses that contribute to rolling resistance of rail vehicles. These are: friction losses in the wheel bearings, shaking and vibration of both the roadbed and the vehicle (including energy absorbed by the vehicle's shock absorbers), and slight sliding of the wheels on the rail. Such losses are quite significant for rail since pure rail rolling resistance is so low.

For rail, pure rolling resistance (under ideal conditions) is only about a third of the total rolling resistance with a value of about 0.33 for a fully loaded freight car. Significant amounts of rail energy are used in shaking/vibrating the earth (and the rail cars). The wheels not only roll but they also slide a little from side to side, thus using energy. A pair of rail wheels are rigidly mounted on the same axle so the wheels on each side of the rail car spin at the same angular velocity (rpm). This may result in slipping if the wheel diameters are slightly different or when going around curves. It's actually a lot more complicated than this since wheels are made with the tread slightly tilted so that by moving sideways a little the same wheel will in effect become slightly larger/smaller in diameter. While auto tires make contact with the road over their entire width of the tread, rail wheels only make contact over only small part of their tread width (about the size of a dime). Thus they can vary the part of the wheel that they ride on by shifting sideways. This happens automatically and the wheels tend to move such so that the slipping is reduced. But this reduced loss still contributes to the rolling resistance. Rail rolling resistance increases with speed, especially if the track is in poor condition and has dips in it.

8. Passenger Trains Are Heavy (to-do compare w/air)

The question still remains: Why aren't passenger trains more energy efficient if their rolling resistance is so low? There are a number of reasons, the major one being that trains are usually much quite heavy (on a per passenger basis). Previously, the units used were rolling resistance per unit weight. But the unit that counts is the rolling resistance per passenger and this become high due to the high weight of passenger trains.

Just how heavy are passenger trains? There are various types of trains, some pulled by heavy locomotives and some that are driven by electric motors under each car. The ones pulled by locomotives tend to be very heavy and estimates made from US government data for 1963 (the government ceased collecting such data after that date) indicate about 3.7 tons/passenger. Automobiles are roughly one ton/passenger with an average of 1.6 persons/auto in an auto weighing 3,200 pounds. Thus rail was (in 1963) about 3.5 times heavier per passenger.

If one compares a lightweight auto with a lightweight train car, the train car weighs about twice as much per seat. A lightweight auto will weigh about 2,000 pounds with 5 seats (0.2 tons/seat). The (mostly aluminum) BART car (for the San Francisco rail transit) weighed 30 tons with 72 seats (0.42 tons/seat). The percentage of seats occupied by passengers on trains, is often not much different than for automobiles.

The Acela electric trainsets introduced by Amtrak in the early 21st century, are 2.1 tons/seat. This is ten times higher than that of a lightweight auto.

The heavy weight of trains not only increases rolling resistance, it also increases the energy used for climbing up a grade or accelerating from a stop. If the weight triples, so does such energy use.

9. Other Factors (to-do compare w/air)

9.1 Heating

Passenger trains today usually use electric heating which is quite inefficient. Automobiles get heated free using waste heat from the engine (radiator water).

9.2 Aerodynamic Drag

As a vehicle goes faster, the wind force against the front of the vehicle increases. You may get a sense of this force by holding your open hand out the window of a speeding automobile.

This aerodynamic drag is proportional to the square of the velocity. It not only acts on the front of a vehicle but also on all other surfaces of the vehicle. It even creates a suction (partial vacuum) on the rear of the vehicle which opposes its forward motion. If there is a natural wind blowing over the land, the aerodynamic drag is likely to increase considerably (even if the wind is blowing from the side). For a train, such a wind constantly injects fresh air between the train cars and energy is consumed by accelerating this air to the speed of the train.

A train has less aerodynamic drag (per seat) than an auto (at the same speed) even though its frontal area is much larger than an auto. This is true even though the front ends of many trains are not well streamlined. However, since a train may go much faster than an auto, its aerodynamic drag may turn out to be quite high. If the train travels at twice the speed of an auto, it's aerodynamic drag is four times higher than what it would be if it only went at the same speed of the auto.

10. Improving Energy Efficiency to-do add air

Even with its high weight, in many cases the train still has significantly less rolling resistance per seat than the auto. But the energy per passenger used to accelerate and climb grades is a few times higher than the auto. This additional energy that the heavy train must use to accelerate and climb grades can be partially recovered in two ways.

The first method is by coasting. A train approaching a slower speed zone or a stopping point can coast instead of brake. Technically speaking, it is recovering some of the kinetic energy of the train. Then when the speed is low enough, it can apply the brakes. Such a coasting scheme slows down the average speed of the train and thus is apparently not used much even though it is worthwhile in most cases to at least do a little coasting.

The second method is by use of regenerative braking for the case of an electric railroad. This is where the electric motors on the train work as generators during braking. The electric energy so generated is returned to the overhead wire and used to power other trains (or even returned to the power grid). For low voltage systems, there usually needs to be another train nearby which is under power and can absorb this energy. Due to losses in electric generators, wires, and electric motors, only part of the kinetic energy of a braking train is recovered. Not all electric railroads and equipment can do regenerative braking.

One may show that even if one has regenerative braking available, it is still better in most cases to coast for a ways before applying it. The reason is that for coasting, all of the kinetic energy decrease of the train is recovered (with no losses). For regenerative braking, there is energy lost due to generator losses, ohmic losses of the current in the overhead wire, and losses in the electric motors of the train that eventually receives this regenerated energy. There is also losses in power electronic circuits used to transform voltages, etc. For example, only 60% of the kinetic energy loss of a braking train may find it's way into an increase in the kinetic energy of the train that gets the regenerated energy. The other 40% is wasted in heat.

Nevertheless, a combination of coasting and regenerative braking can recover a significant amount of energy and the coasting is almost free, since computers that can control it are quite cheap today. In the old Soviet Union, rail coasting policies were developed and monetary incentives given to locomotive drivers who saved energy. But it didn't work out too well due to congested rail lines and dispatchers giving the green light to friends so that they would get undeserved bonuses. The Soviet railroads reported a 20% savings of electricity due to regeneration on lines with steep grades and high traffic. See Electric Railroads

11. Conclusions to-do more re air

The very low rolling resistance of a steel wheel on a rail is partially canceled out by the high weight of passenger trains. The higher weight also means more energy used for accelerating and climbing grades although some of this could be recovered by coasting and regenerative braking. Aerodynamic drag is low for a train at moderate speed but increases rapidly (with the square of the speed). Thus one may say that passenger trains are potentially energy efficient, but in actual practice such trains turn out to be little more energy-efficient than the airplane. What institution changes are needed to realize the potential of rail's inherent energy-efficiency are not clear. Neither private ownership nor government monopoly has been very efficient in providing passenger service.

12. Appendix: Train vs. Plane Statistics

Per Transportation Energy Data Book for 2005 Amtrak used 2,709 BTU/pass-mi vs. 3,264 for Certified U.S. air carriers. However, a footnote warns: " These energy intensities may be inflated because all energy use is attributed to passengers --cargo energy use is not taken into account.

Correcting Amtrak for circuity results in 2,709 x 1.2 = 3251 TU/pass-mi. The airplane Cargo correction results in 3,264/1.19 = 2,743 BTU/pass-mi. These correction change the "reported" 20% advantage of the train to about a 18% disadvantage.

12.1 Airplane Cargo correction

A major problem is how to allocate aircraft fuel between freight and passengers since passenger flights often carry mail and freight (other than the baggage of passengers). [Hirst] p. 35, considered 400 lbs. of mail/freight equivalent to one passenger. This may be too low so I've used 500 lbs. (or 4 passengers = 1 ton cargo)

12.2 Circuities

Airplanes fly more or less directly to their destinations while passenger trains must follow the railroads which due to mountains and the serving to cities enroute, often don't go in a straight line between city-pairs.

See "Energy Intensity and Related parameters of Selected Transportation Models: Passenger Movements" by A. B. Rose. Oak Ridge National Laboratory, U.S. Dept. of Energy, Jan. 1979. Table B.3 "Mean passenger Rail Circuities by Distance Category" p. B-4 shows a mean circuity ratio of about 1.4. However, city pairs with poor circuities likely have less rail passenger traffic. It turns out that Amtrak had a circuity ratio of only 1.24, counting only riders who didn't switch trains. This report will use 1.2 which is on the low side but also partly reflect the fact that airplanes are assumed here to have 1.0 circuity but actually have slightly higher circuity.

This report (see p. B-2) assigned 1.0 circuity to aircraft which is not precisely correct since airplanes may need to circle airports before landing and often need to circle back in the opposite direction just after taking off or just before landing since runways usually only allow landings and takeoffs in one direction.

12.3 Passenger-Mile Data

For estimates from 1929 to 1965 see Bus Facts, 1966 (34th. edition) p.6: "Intercity Travel in the United States 1929-1965". Bus Facts was published by NAMBO = National Association of Motor Bus Operators.

From 1939 onwards see: "Transportation in America" (annual) by the Eno Transportation Foundation, Washington DC. (Formerly Transportation Facts and Trends, by the Transportation Association of America) Some of their "statistics" are now found in the "Statistical Abstract of the U.S."). The 18th edition of Trans. in America is available with a "Historical Compendium 1939-1999" which covers years that other editions omit. The table "Domestic Intercity Passenger-Miles by Mode" shows the modal split for intercity travel (but excludes international air travel).

To fairly compare rail and air passenger-miles one should include some international air travel on flights, since portions of these flights were sometimes over U.S. territory. But the figures used here are only for domestic transportation between points within the U.S. In the early days of air travel when there was railroad competition, international travelers from the U.S might first take a train to a seaport to board an ocean ship or to a border point to board a Mexican or Canadian train. This portion of the trip compares to part of a flight on an international air carrier where the flight begins somewhere deep within U.S territory. At the same time, air travel to Hawaii and Alaska shouldn't be counted as there were (and are) no railroads serving those locations. Thus these two errors tend to cancel out each other and no corrections have been made.

13. Railroad Energy References

13.1 Electric Railroads

1. Elektricheskie Zheleznye Dorogi by Plaksa, A. V. et. al. Moskva, Transport 1993. See p. 55 for regenerative braking.

13.2 Engine Efficiency

1. Ekonomiia Topliva i Teplo-Tekhnicheskaiia Modernizatsiia Teplovozov (Fuel Economy and the Thermodynamic Improvement of the Diesel Locomotive) by Komich, A. Z. et. al. Moskva, Transport, 1975. See p. 15, fig. 4 for how thermal efficiency depends on power output. Efficiency ranges from 13% at 13% power to 28% at 100% power. Note that the manufacturer claimed 30% maximum, etc. but actual tests showed lower values.

Since a diesel locomotive consumes about 10% of its fuel while idling (see p. 16) and operates at part loads where efficiency is lower than nominal, the average efficiency is only 21-22% (see pp. 6,18).

There exists a 1987 "revision" with a new title: Toplivaia Effektivost' i Vspomogatel'nye Rezhimy Teplovoznykh Diselei (Thermal Efficiency and Non-Standard Modes of Operation of Diesel Locomotive Motors).

2. Energetika Lokomotivov (Locomotive Energy) 2nd ed. by Kazan, MM. Moskva, Transport, 1977. See p. 94+ for a comparison of Diesel vs. Electric efficiency; Nominal values (at full load) diesel 32.6%, electric 31.2% (30.0% after transmission losses from the power plant to the railroad substation). See p. 52). This calculation assumes modern electric generation facilities with 43% efficiency and admits that the such efficiency in the USSR at that time (1977) averaged only 33% and not 43%. However, the efficiencies of various diesel locomotives ranged from 25.7% to 32.5% per Table 17, p. 92. Compare this with the 22% actual efficiency for diesel locomotives as found in reference 1. above. My conclusion: electric and diesel traction have thermal efficiencies of roughly 30% at nominal operating conditions (but significantly lower under actual operating conditions).

13.3 Railroad Resistance

1. Soprotivlenie Dvizheniiu Zheleznodorozhnogo Podvizhnogo Sostava (Resistance to Motion of Railroad Rolling Stock) by Astakhov, P. N. Moskva, Transport (publisher) (in Russian), 1966. Issue 311 of the series: Trudy vsesoiuznogo Nauchno-Issledovatel'skogo Instituta Zheleznodorozhogo Transporta. Chapter 4 (p. 73+) partitions resistance into 6 components with a section on each component: bearing, rolling, sliding, shaking the earth, aerodynamic, vehicle vibration and shock absorbers. The quadratic formulas for rolling resistance used in various countries areis compared and plotted (fig. 2.3, p. 35) and includes the "Davis" formula used in the United States.

2. Tiaga Poezdov (Train Traction) by Deev, V. V. Moskva, Transport (publisher) (in Russian), 1987. The components of resistance are discussed in section 5.2 (p. 78+). The diagram of forces and pressures acting on a wheel (fig. 5.3 on p. 80) is interesting.

3. Rolling Friction (in 4 parts) by Hersey, Mayo D. et. al. in "Journal of Lubrication Technology" April 1969 pp. 260-275 and Jan. 1970 pp. 83-88. Part II is for cast-iron rail car wheels. Contains no info on rubber tires. See p 267 for variation of resistance with diameter.

13.4 Train Weights

1. BART Prototype Care Development Program--Volume 1, Program Synopsis. Report No. UMTA-CA-006-0032-73-1 by Rohr Industries, Chula Vista, CA for the US Department of Transportation, Urban Mass Transportation Administration. March 1973. This is the rail transit system of the San Francisco Bay region in California.

p. 72 typical weights 58.5k lb. (B-cars); 60k lb. (A-cars). p. 73: 62k lbs. for tests to simulate zero passenger loads. P. 5: (Car and Train Configuration) 72 seats in either A or B cars. 60k/72 = 833 lbs./seat or 0.417 tons/seat. Crush load (most people standing) is 216. For this case the weight of the passengers is very significant and the vehicle weight becomes 98k lb. (AW-3 on p. 73 assumes 167/lbs per passenger). 98k/216 => 0.227 tons/person.

2. The Acela train-set weighs 1.9 tonnes/seat (equivalent to 2.1 tons/seat). See Acela Express

13.5 Railroad Aerodynamic Drag

1. Hoerner, Sighard F., "Fluid Dynamic Drag", published by the author, 1965. (See Ch. 12 for train data.)

2. Ober, Shatswell, "Air Resistance of the Burlington Zephyr", Diesel Railway Traction, June 14, 1935, pp. 1184-5.

3. Johansen, F. C., "The Air Resistance of Passenger Trains", The Institution of Mechanical Engineers (London), Proceedings, Vol. 134, 1936, pp.91-208. Covers increased drag due to yaw.

4. DeBell, George W., "Effect of Natural Winds on Air Drag", Railway Mechanical Engineer, April, 1936, pp.145-7.

5. Klemin, A. "Aerodynamics of the Railway Train", Railway Mechanical Engineer, Vol. 108 (1934): Aug. p. 282, Sept. p. 312, Oct. p. 357.

6. Lipetz, A. I. "Simplified Formulas for Calculating the Air Resistance of Trains", Railway mechanical Engineer, April 1935, pp. 129+.

7. Astakhow, P. N. "Soprotivlenie Dvizheniiu Zheleznodorozhnogo Podvizhnogo Sostava", Transport Press, Moscow, 1966 (in Russian). pp. 87-104 (LC call number: TF4M67, Vol. 311)

8. Deev, V. V. "Tiaga Poezdov", Transport Press, Moscow, 1987 (in Russian) pp. 81-2.

13.6 Rail Statistics, etc.

Amtrak CRS Report

CRS Report: 96-22 - Amtrak and Energy Conservation in Intercity Passenger Transportation - NLE

Amtrak (from Fuel Eff. of Travel in 20th Century)

Fuel Efficiency of Travel in 20th Century: Amtrak.

Car-mi by Diesel (from ICC data)

The ICC publication used for car-mi by fuel changed names between 1936 and 1963. In 1936 they were issued by the ICC's "Bureau of Statistics". In 1963 it was "Bureau of Transport Economics and Statistics". In all cases "Switching and Terminal Companies Not Included" appears after the title (in smaller print). Below find the starting name of the publication in 1936 and the ending name in 1963.

1936: "Passenger Train Performance of Class I Steam Railways in the United States" (Statement M-213)
1963: "Passenger Train Performance of Class I Railroads in the United States" (Statement Q-213)

A secondary source is Bituminous Coal Annual. The division of passenger train car-miles by fuel for the years 1936 thru 1950 may be found in the 1951 issue, p. 115 (table 49). Unfortunately, as the use of coal by railroads decreased, later annual issues reduced and then eliminated this data.

14. Airplane Energy References

14.1 Major Technical Books:

1.Mechanics of Flight by Warren F. Phillips, John Wiley & Sons, Hoboken NJ, 2004. For turbofan engines see Ch. 2 "Overview of Propulsion" section 2.1 "Introduction" and section 2.9 "Turbofan

15. Sources of Data For Historical Energy-Efficiency Table

15.1 Market Share of Rail and Air.

Except for 1935, the market share percentages (percent of intercity passenger-miles by all modes) is from "Transportation in America" (annual) by the Eno Transportation Foundation, Washington DC. (Formerly Transportation Facts and Trends, by the Transportation Association of America) Some of their "statistics" are now found in the "Statistical Abstract of the U.S."). The 18th edition of Trans. in America is available with a "Historical Compendium 1939-1999" which covers years that other editions ignore. The table "Domestic Intercity Passenger-Miles by Mode" shows the modal split for intercity travel, but only includes domestic air travel (excludes international).

For 1935, the data is from Bus Facts, 34th edition, 1966: Table: "Intercity Travel in the United States" p. 6 (published by NAMBO = National Association of Motor Bus Operators).

15.2 Airline Energy Statistics

Sources of airline energy statistics:
1935-1955: [Energy in Am. Economy] p. 550
1950-1970: EI 1950-1970 per Hirst pp. 9, 21, 34-5
1970-2005: Trans. Energy Data Book

For airplane fuel efficiency for 1935-1955 see the book: "Energy in the American Economy, 1850-1975" by Sam H. Schurr and Bruce C. Netschert. The Johns Hopkins Press, Baltimore MD, 1960. See p.550, Table XXVI: "Petroleum Products Consumed Compared to Work Performed by Aircraft, Selected Years 1935-1955".

In using this data, I assumed that one ton of cargo is fuel-equivalent to 4 passengers. All reported jet fuel use by this Table xxvi was disregarded, since per footnote c only an insignificant amount was used by "scheduled air carriers" (most of jet fuel was likely used by the military). International flights (not shown in the table: Historical Energy-Efficiency were significantly less energy-efficient than domestic prior to 1955, but by 1955 there was only a little over 10% difference. For a table which shows the efficiency of international flights prior to 1955 see the webpage Fuel-Efficiency of Travel in the 20th Century

Heat values used are: for automotive gasoline: 125 k BTU/gal, aviation gasoline: 120.2 k BTU/gal and for jet fuel (kerosene): 135 k BTU/gal. Actual reported gallons consumed was converted to both BTUs and to equivalent automotive gasoline, using these values which are from Transportation Energy Data Book edition 26, 2007, table B.4: "Heat Content for Various Fuels". Note that aviation gasoline was phased out during the period centering around 1960 and replaced by kerosene jet fuel which has a higher heat value.

Energy in the American Economy" has an erroneous Table D-51 (p. 667): "Miles per Gallon in Passenger Service of Domestic Scheduled Air Carriers". It wasn't used due to its failure to account for aircraft fuel used for cargo and mail transport by both cargo and passenger aircraft. The same error was made by TEDB. If one uses Transportation Energy Data Book edition 26, 2007, table 9.2: "Summary Statistics for U.S. Domestic and International Certified Route Air Carriers" and assumes that one ton-mi of cargo is equivalent to 4 pass-mi one obtains the equivalent of almost 38 pass-mi per gallon of automobile gasoline for the year 2000.

15.3 Rail Energy Data

For passenger trains in the US from 1936 to 1963 see: USA Railroad Passenger-Miles per Gallon 1936-1963 by David S. Lawyer.

15.4 Major Multimodal Statistical Books/Reports

Transportation Energy Data Book

Transportation Energy Data Book (annual) by Stacy Davis, Oak Ridge National Laboratory, U.S. Dept. of Energy. The most significant table is: "Energy Intensities of ... Passenger Modes" in Ch. 2. The latest edition is on the Internet. Ch. 2 is on the web at Transportation Energy Data Book, Ch. 2. Ch. 9 is on the web at Transportation Energy Data Book, Ch. 9 (for table 9.2 on airplane energy).

Transport EI 1950-70 by Hirst

Energy Intensiveness of Passenger and Freight Transport Modes 1950-1970 by Eric Hirst. Oak Ridge National Laboratory (then part of the U.S. Atomic Energy Commission, now part of the U.S Dept. of Energy), 1973 (ORNL-NSF-EP-44).

16. Turbofan engines more efficient

Note that per Historical Energy-Efficiency Table energy intensity increased after 1955 from about 5k BTU/PM to about 9k BTU/PM in 1970. This was mainly due to the introduction of inefficient "jet" aircraft. But after 1970 the energy intensity decreased to less than it was in 1955, due in large part to the introduction of turbofan engines with high bypass ratios. See Mechanics of Flight

The word "jet" regarding passenger aircraft is actually a misnomer. While some military aircraft use turbojet engines, most passenger commercial aircraft today use turbofan engines. Although people call them "jets", they are similar to propeller craft where the propellers are concealed from view and are called "fans". A gas turbine, powered by kerosene, drives a large fan which surrounds the turbine and throws air out the rear of it, pushing the plane forward much like a propeller. Some of the "air" thrown back is exhaust gas from the turbine, but most of it is just plain air. This air bypasses the turbine and is not used for combustion. It just flows backwards around the outside of turbine. The bypass ratio is the mass of the bypass air to the mass of the air used for combustion. So an engine with a high bypass ratio will have a high volume of air go thru the fan and will be more energy-efficient as will be explained later.

Originally, passenger "jet" aircraft were turbojet but by the early 1960s, turbofans with low bypass ratios were being introduced. For example, early Boeing 707's were turbojet but later 707's were turbofan. The introduction of low-bypass ratio turbofans and then increasing the amount of air bypassed (high-bypass ratio) resulted in later models "jet" aircraft being much more energy efficient than earlier models. Some additional improvement was obtained by by increasing compression ratios,

Why are high-bypass-ratio turbofan engines more efficient? We'll take a simplified example where an airplane is flying in level flight at constant speed thru still air (no natural winds). This airplane shoots out a mixture of exhaust gas and air from its turbofan engines, leaving a mixture of air and exhaust moving backwards, which we'll just call exhaust. Now the kinetic energy of this exhaust is just the mass of it times one-half of the square of the velocity (to an observer looking up from the ground). All this kinetic energy of the exhaust in the sky moving backwards was supplied by the kerosene fuel. Cut this velocity in half and you reduce this energy loss by a factor of 4 (due to the v-squared law where v is velocity).

Except there's one problem if this velocity is halved. The airplane always sees the velocity of the air entering the engine from the front as equal to the speed of the airplane. The thrust force generated by acceleration of air in the fan (and in the turbine too) is the air flow (in kg/sec) times its change in velocity (as viewed by an observer in the plane) and if you think about it, this change is just equal to the exhaust velocity as viewed by an observer on the ground. So if you halve the velocity of the exhaust you halve the change in velocity (between intake and exhaust) as viewed by an observer on the airplane and thus halve the thrust force. But thrust force must be maintained so as to maintain speed (or climb). Thus if one cuts in half the velocity change, one must at the same time double the exhaust flow to keep thrust constant. This doubling is done by increasing the bypass ratio.

The doubling of exhaust flow doubles the wasted energy in the moving exhaust air. But remember that halving the velocity has decreased the this energy by a factor of 4 so the overall result is cutting in half the wasted energy of the moving exhaust in the sky.

Note that the fuel consumption has by no means been cut in half. There is still a lot of air being directed downward by the wings so as to push up on the wings to keep the plane from falling out of the sky. And there is air being pushed forward as the front of the aircraft hits the still air. So why did high bypass ratios make such a big difference? It was because the ratios were greatly increased and the velocity was reduced much more than in the example just presented

The above example is overly simplistic as it has neglected the part of the exhaust that represents the kerosene fuel (the carbon and hydrogen components of the exhaust in the compounds of carbon dioxide and water). But carbon and hydrogen constitute only a few percent of the exhaust (for bypass ratios greater than one) and can be neglected in a rough example.

For an interesting history of the turbofan aircraft engine see: Jet Fans, Dec. 2003