5: 1 of 30 COPYRIGHT © AREMA 2012 Module 5:Tractive Effort.

5: 1 of 30COPYRIGHT © AREMA 2012

Module 5:Tractive EffortModule 5:Tractive Effort


Module Objectives

• Learn About Tractive Effort (the Amount of Force at the Wheels Available for Moving a Train)

• Understand the Effects of Combining Steep Grades and Horizontal Curvature


Energy UtilizationThe two primary aspects of transportation energy efficiency:

– Resistance – How much work is required to move something

– Energy Efficiency – How well energy is converted into useful work


Train Resistance

Resistance is typically measuredin “pounds per ton” (in U.S.)

Friction

• For our purposes, Resistance is the combination of forces that work against a train’s movement.

• Early measurement of railcar resistance simply involved piling on weight, w, and determining how much was needed to make the car move.

• If the weight, w, is great enough to overcome the static friction, the car will start to move.


Trains VS. Trucks• Trains require less energy to move than trucks because of smaller resistive forces:

• Lower friction factor (0.18)– Smaller contact area

– Steel wheels on steel rails

– Rubber tires on pavement

• Less wind resistance per pound of load

• Size of contact area?


Horsepower Tractive EffortHorsepower Tractive Effort• Tractive Effort

– The point of contact between the wheel and the rail is where the torque of the motor is converted to a force that is called tractive effort.

Power to auxiliaries(cooling fans,motor blowers,locomotive controls, airBrake compressor, etc)

Loss in generator (orAlternator/ rectifier)Converting crankshaftPower to electricity

Traction motor lossesGear friction

Power to move, lift,& accelerate weight oflocomotive itself(varies with speed, grade,Curvature, loco/ trainWeight ratio)

)(308

lb-fV

HPTE


Traction ForcesTraction Forces

W

TE

WTEmax x

=AdhesionW = Weight on Drivers


AdhesionAdhesion Adhesion

– Percentage of a locomotive’s weight on its driving wheels, converted into tractive effort.• DC locomotives can achieve a

maximum peak of 30 % adhesion on dry rail.

• Through advanced control, AC locomotives can achieve up to 40 % adhesion in many weather conditions.


Factors Affecting AdhesionFactors Affecting AdhesionWheel/Rail Contact Factors• Wheel-Rail materials• Hertzian (Rolling Wheel)

Stresses• Rail Metal Creep

(Longitudinal Movement)

Track factors• Rail surface condition• Rail profile irregularities• Curvature of track

Vehicle factors• Mechanical

– Loco weight and axle weight distribution

– Weight transfer– Speed– Wheel size variation

• Electrical– Torque control method– Traction motor

characteristics– Power circuit

configuration– Slip-slide control


Train ResistanceTrain Resistance

• Two Elements:– Rolling Resistance (On Level Tangent Track)

• Friction related• Journal, wheel, track quality, track modulus• Aerodynamics of equipment

– Grade & Curve Resistance• Track Profile & Alignment related• Change in potential energy head


Rolling ResistanceRolling ResistanceRolling ResistanceRolling Resistance• Rolling Resistance

– The resistance for train movement on straight and level track can be determined by W. J. Davis formula:

R=A+BV+CV²Where

R= Train rolling resistanceA= Rolling resistance component independent of train speedB= Train resistance dependant on speedC= Drag coefficient based on the shape of the front of the train and other features affecting air turbulanceV= Train speed

– The Train resistance on level tangent track is the sum of locomotive and train resistances.


Freight Train Speed V Resistance

At low speeds, journal resistance dominates, as speed increases air resistance is increasingly most important

Res

ista

nce

(lbs.

/ton)

Speed (mph)10 20 30 40 50 60 70 80 90 100

0

1

2

3

4

5

6

7

8

"Journal" Resistance (A)

"Flange" Resistance (BV)

Air Resistance (CV2)

CV2

BV

A


Davis Equation Modifications• The Davis Equation has been substantially updated to reflect

modern developments, but its basic form is the same.

• Ro = 1.5 + 18N/W + 0.03V + CaV2/10,000W (CN Equation 1990)

where:

Ro = resistance in lbs. per ton

N = Number of Axles

W = Total Weight in Tons of Locomotive or Cars

V = Velocity of Train (MPH)

a = Cross-sectional Area of Vehicle in ft2

C = Canadian National Streamlining Coefficient

– See AREMA Manual for Railway Engineering Chapter 16 - 2.1.3 for latest version of formula


Resistance Versus Speed

0

10,000

20,000

30,000

40,000

50,000

60,000

0 10 20 30 40 50 60 70 80

Re

sist

ance

(lb

s.)

Speed (mph)

10,000 Ton Train


Grade Resistance

1% Grade = Approximately 20 lbf / ton


Curve Resistance

10 = 0.8 lbf / ton


Compensated Grade

Gc = G + Dc * 0.04


Typical Freight Consist

Typical modern freight consist

6000 horsepower,212 tons

100 cars x 143 tons each = 14,300 tons

Typical modern locomotive


Speed/Tractive Effort Curve

0

20,000

40,000

60,000

80,000

100,000

120,000

140,000

160,000

180,000

0 10 20 30 40 50 60 70 80

Tra

ctiv

e E

ffort

(lb

s.)

Speed (mph)

At low speed, tractive effort is limited by adhesion, not power

Modern Locomotive - Level Grade


0

20,000

40,000

60,000

80,000

100,000

120,000

140,000

160,000

180,000

0 10 20 30 40 50 60 70 80

Tra

ctiv

e E

ffort

(lb

s.)

Speed (mph)

Tractive force = resistance @ 35,000 lbs.

Modern Locomotive - Level Grade

Maximum Possible Train Speed?

At low speed, tractive effort is limited by adhesion, not power

Train Resistance

About 58 mph. This is referred to as the “balancing speed, why?


0

20,000

40,000

60,000

80,000

100,000

120,000

140,000

160,000

180,000

0 10 20 30 40 50 60 70 80

Tra

ctiv

e E

ffort

(lb

s.)

Speed (mph)

• Available acceleration declines as speed increases• At balanced speed it is zero.• So, the rate of acceleration declines with speed.

Q: How much force is available for acceleration at 15 mph?

Q: How much force is available for acceleration at 35 mph?

A: 135,000 - 15,000 = 120,000 lbs.

A: 59,000 - 21,000 = 38,000 lbs.

Resistance V Acceleration


Capability of “multiple unit” control makes this possible

0

50,000

100,000

150,000

200,000

250,000

300,000

350,000

0 10 20 30 40 50 60 70 80

Tra

ctiv

e E

ffort

(lb

s.)

Speed (mph)

What If We Need More PowerT

ract

ive

Effo

rt (

lbs.

)


Freight Time/Speed Graph

This curve depicts a single locomotive.How will the curve change if a second locomotive is added?

0

10

20

30

40

50

60

70

0 500 1000 1500 2000 2500 3000

Spe

ed (

mph

)

Time (seconds)

About 900 seconds = 15 minutes

How long will it take for this train to reach 40 mph?


Time/Speed Graph

0

10

20

30

40

50

60

70

0 500 1000 1500 2000 2500 3000

Spe

ed (

mph

)

Time (seconds)

Now how long will it take to reach 40 mph?

About 300 seconds≈ 5 minutesS

pee

d (

MP

H)


Freight Distance/Speed Graph

0

10

20

30

40

50

60

70

0

50,0

00

100,

000

150,

000

200,

000

250,

000

300,

000

350,

000

400,

000

Sp

ee

d (

mp

h)

Distance (feet)

How many miles until this train reaches 40 mph?

Velocity Profile h (ft) = 0.03 V2

About 75,000 feet ≈ 14 miles

Sp

eed

(M

PH

)


2 Unit Distance/Speed Graph

0

10

20

30

40

50

60

70

0

50,0

00

100,

000

150,

000

200,

000

250,

000

300,

000

350,

000

400,

000

Sp

ee

d (

mp

h)

Distance (feet)

With 2 locomotives, only about 25,000 feet ≈ 5 miles

Sp

eed

(M

PH

)


Horsepower:Trailing Tonnage• Long-distance train with

few stops along the way.– Low horsepower:trailing ton

ratio. 12,000 hp: 14,300 tons = 0.83 hp:ton

– Typical of many freight trains

• High-speed train with frequent stops and starts.– High horsepower:trailing ton

ratio may be as high as2 to 4 hp:ton

– Typical of intermodal trainsand may be even higher for passenger trains


Stopping the Train

• Safety is the most important consideration!

• Adhesion Limits Braking Ability.

• Stopping Train Vs. Motor Vehicle.

6,000’


Stopping Distance V Speed

0

10

20

30

40

50

60

70

0 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000

Spe

ed (

mph

)

Distance (feet)

Stopping a train can often take a mile or more


QUESTIONS?Authors:

Joseph E. Riley, P.E.

Federal Railroad Administration

(202) 493-6357

[email protected]

Paul Li

UMA Engineering

(780) 486-7914

[email protected]

Revisions:

Robert Kimicata, P.E.

Kimicata Rail Consulting

(847) 394-4105

[email protected]

John G. Green, Ph.D., P.E.

CH2M Hill, inc.

(213) 348-5030

[email protected]

5: 1 of 30 COPYRIGHT © AREMA 2012 Module 5:Tractive Effort.

Documents

copyright arema

train resistance resistance

tractive effort slide

rolling resistance

wind resistance

locomotives weight

weight of locomotive

horizontal curvature