Rail vs Auto Energy Efficiency

by David S.Lawyer mailto:davylawyer1@gmail.com More articles by David Lawyer

v0.10, July 2004 (original January 2001)

1. Copyright

2. Introduction

3. Vehicle Resistance

4. Thermal Efficiency

5. Rolling Resistance

6. Passenger Trains Are Heavy

7. Other Factors

8. Improving Energy Efficiency

9. Conclusions

10. Notes and References




1. Copyright

Copyright 2002-4 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

For references see the section: Notes and References

The railroad was originally invented because rail used far less energy than animal hauled carts to move heavy freight on dirt roads. "Railroads" were first used to haul coal from mines and were pulled by animals. The rolling resistance of a train (per ton of vehicle weight) is only a small fraction of that of an automobile or truck. Thus one would expect railroads to be a few times more energy-efficient than autos or trucks. While this is often true for the comparison with trucks, it's seldom true when comparing a passenger train with the automobile.

It turns out that in spite of it's low rolling resistance, passenger trains in the US today (including rail transit) are not much more more energy efficient than the auto. See Rail Statistics, etc and Statistics It wasn't always like this. From the late 1930's thru the 1960's diesel passenger trains were significantly more energy efficient than the auto. During World War II they were 2 to 3 times as energy efficient. See Statistics. Then in the 1970's, federal mantdates greatly improved the energy efficiency of the auto. There were no federal mandates to improve rail energy-efficiency. To understand why rails are not as efficient as one might expect, it's necessary to first understand various technical concepts, especially rolling resistance.

3. Vehicle Resistance

When a vehicle moves forward, there is a force which resists moving the vehicle forward. This force is known as "resistance". The amount of force required depends on many things such as the vehicle's weight, speed, condition of the pavement or rail, and grade. It takes still additional force to accelerate the vehicle. The resistance force is normally positive since it resists the forward motion of the vehicle. But on a steep downgrade this force may be negative and tends to pull the vehicle forward.

The mechanical energy expended in moving a vehicle is just the resistance times the distance traveled. Thus if one wanted to compare the 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.

To find the total mechanical energy used, the forces of acceleration, deacceleration, braking, and grades would need to be added to resistance force.

4. Thermal Efficiency

In order to determine the fuel energy consumed, the mechanical energy used must be divided by thermal efficiency of the engine-transmission. For example if the transmission is 90% efficient and the engine converts 30% of the fuel energy into mechanical work, the efficiency is 0.9 x 0.3 = 0.27. 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 autos this efficiency is roughly 30% under the best conditions. This is also the case for electric trains. Thus if thermal efficiency is roughly the same, the comparison of vehicle resistance will give a good indication of the fuel consumption of different vehicles (under the best conditions).

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.

5. Rolling Resistance

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. In such units, the typical automobile tire has a rolling resistance of about 10 (when properly inflated). Truck tires inflate to much higher pressure (such as 100 pounds) and typically have a rolling resistance of about 7. 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.

Why is the rolling resistance so much less for a steel wheel than for a pneumatic tire? The reason is that the rubber tires flex a lot and thereby absorb much more energy than the steel wheel which flexes far less. If you look at the tires on parked autos you will notice a big flat spot at the bottom of the tires where the tire is deformed. As the tire rolls, this deformation is applied to the entire tread surface (and sidewalls too) of the tire. The result is much flexing of the rubber which causes the tire to absorb energy and become hot.

In addition to the tire energy loss, there are some other losses that contribute to rolling resistance for both rail and highway 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 pavement/rail. These losses have been included in the example values shown above. Such losses are relatively more 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. An inflated rubber tire is about 30 times higher. 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.

While auto tire rolling resistance increases only slightly with speed, rail rolling resistance increases faster with speed, especially if the track is in poor condition and has dips in it. As an auto tire wears out, its rolling resistance drops since there is less rubber to flex. Tire rolling resistance drops as temperature increases while driving, partly due to the increase in pressure due to the higher temperature. If may take a half-hour of driving before the tire reaches a stable temperature so rolling resistance tests are done only after "warmup". Most all these factors tend to make the auto tire more efficient than one might expect (but still not nearly as efficient as a rail wheel).

6. Passenger Trains Are Heavy

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 heavier than autos (on a per passenger basis). Previously, the units used were rolling resistance per unit weight. If one takes into account the weight of the train per passenger, and then examines the rolling resistance per passenger, the advantage of rail over the auto drastically drops. For a very heavy passenger train, it will even favor the auto.

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.

7. Other Factors

7.1 Heating

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

7.2 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.

8. Improving Energy Efficiency

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

9. Conclusions

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 automobile. 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.

10. Notes and References

Why so many Russian railroad references? It's because such material is not available in English. In the 1970s and 1980s, the USSR published about a thousand times as many technical books on railroads as did the US. Although the last college railroad engineering program came to an end in the US, the USSR continued to train many thousands of railroad engineers at its special railroad colleges. Even though the quality of their railroad hardware was often lacking, it was very well documented including its technical characteristics and theory. Developments outside of Russia were also well documented in Russian. They even compared the reliability of US vs USSR locomotives (using US locomotives left in Vietnam) and found the US ones to be about twice as reliable.

It was sometimes said that the USSR copied US locomotives. Not exactly, since we didn't make many electric locomotives and Russian diesel locomotives were different, such as having 16 controller positions for forward speed instead of 8 for the US. But their diesel locomotives were similar to ours in many respects. For this reason, using Russian data to estimate what happens in US railroad operations (since US data is not available and likely was not even collected) has some validity.


11.1 Electric Railroads

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

11.2 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).

11.3 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 are 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.

11.4 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

11.5 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.

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.

CRS Report: 96-22 - Amtrak and Energy Conservation in Intercity Passenger Transportation - NLE. Or alternate site if above link broken. 2. Fuel Efficiency of Travel in 20th Century: Amtrak. 3. USA Railroad Passenger-Miles per Gallon 1936-1963 by David S. Lawyer


1. ACEEE's Green Book, The Environmental Guide to Cars and Trucks, Model Year 2000 by DeCicco, John et. al., American Council for an Energy-Efficient Economy, Washington D.C. 2000. Tables on pp. 57-103 show fuel economy.

2. Model T Ford by McCalley, Bruce W., Krause Publications, Iola WI, 1994. Shipping Weights: p. 16: 1910 Touring 1200 lb (only about 19,000 made that year); pp. 305-11 1921-1925 Two Door Sedan 1875 lb., Touring 1620-1650 lb. Seated 4 (5 cramped). For 1910: 1200/4 = 300 lb./seat or 0.15 tons/seat. If all 5 seats were occupied with 167 lb. each then we have 0.203 tons/seat. For the 1920 sedans: 0.234 tons/seat.


1. 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 at Transportation Energy Data Book, Ch. 2.