Describe the Four Main Types of Resistance Forces
Describe the Four Main Types of Resistance Forces
Rolling resistance, sometimes chosen
rolling friction
or
rolling elevate, is the force resisting the motion when a body (such as a ball, tire, or bike) rolls on a surface. It is mainly caused by nonelastic effects; that is, not all the energy needed for deformation (or movement) of the wheel, roadbed, etc., is recovered when the pressure is removed. Two forms of this are hysteresis losses (see beneath), and permanent (plastic) deformation of the object or the surface (eastward.g. soil). Note that the slippage between the wheel and the surface also results in free energy dissipation. Although some researchers have included this term in rolling resistance, some suggest that this dissipation term should be treated separately from rolling resistance because information technology is due to the applied torque to the wheel and the resultant slip between the wheel and ground, which is called
skid loss
or
sideslip resistance.
^{[1]}
In addition, only the socalled slip resistance involves friction, therefore the proper name “rolling friction” is to an extent a misnomer.
Analogous with sliding friction, rolling resistance is often expressed as a coefficient times the normal force. This coefficient of rolling resistance is generally much smaller than the coefficient of sliding friction.^{[2]}
Any coasting wheeled vehicle will gradually slow down due to rolling resistance including that of the bearings, simply a railroad train car with steel wheels running on steel rails will curlicue farther than a bus of the same mass with condom tires running on tarmac/cobblestone. Factors that contribute to rolling resistance are the (amount of) deformation of the wheels, the deformation of the roadbed surface, and motion below the surface. Additional contributing factors include bicycle diameter,^{[iii]}
load on wheel, surface adhesion, sliding, and relative microsliding betwixt the surfaces of contact. The losses due to hysteresis besides depend strongly on the textile properties of the wheel or tire and the surface. For case, a safe tire volition have higher rolling resistance on a paved route than a steel railroad wheel on a steel runway. Also, sand on the ground will requite more rolling resistance than concrete. Sole rolling resistance factor is not dependent on speed.
Primary crusade
[edit]
The primary cause of pneumatic tire rolling resistance is hysteresis:^{[5]}
A characteristic of a deformable cloth such that the free energy of deformation is greater than the free energy of recovery. The condom compound in a tire exhibits hysteresis. Every bit the tire rotates under the weight of the vehicle, it experiences repeated cycles of deformation and recovery, and it dissipates the hysteresis energy loss as heat. Hysteresis is the principal crusade of energy loss associated with rolling resistance and is attributed to the viscoelastic characteristics of the rubber.
 — National Academy of Sciences^{[6]}
This principal principle is illustrated in the effigy of the rolling cylinders. If two equal cylinders are pressed together then the contact surface is flat. In the absenteeism of surface friction, contact stresses are normal (i.e. perpendicular) to the contact surface. Consider a particle that enters the contact surface area at the right side, travels through the contact patch and leaves at the left side. Initially its vertical deformation is increasing, which is resisted by the hysteresis upshot. Therefore, an additional pressure is generated to avoid interpenetration of the 2 surfaces. Later its vertical deformation is decreasing. This is once more resisted by the hysteresis consequence. In this case this decreases the pressure that is needed to go on the two bodies separate.
The resulting force per unit area distribution is asymmetrical and is shifted to the right. The line of activity of the (aggregate) vertical force no longer passes through the centers of the cylinders. This means that a moment occurs that tends to retard the rolling motion.
Materials that have a large hysteresis effect, such as rubber, which bounciness back slowly, showroom more rolling resistance than materials with a smallscale hysteresis consequence that bounce back more quickly and more completely, such as steel or silica. Low rolling resistance tires typically contain silica in identify of carbon blackness in their tread compounds to reduce lowfrequency hysteresis without compromising traction.^{[7]}
Notation that railroads likewise have hysteresis in the roadbed structure.^{[8]}
Definitions
[edit]
In the broad sense, specific “rolling resistance” (for vehicles) is the force per unit vehicle weight required to motility the vehicle on level ground at a constant hohum speed where aerodynamic drag (air resistance) is insignificant and also where there are no traction (motor) forces or brakes applied. In other words, the vehicle would be coasting if information technology were not for the force to maintain constant speed.^{[9]}
This broad sense includes bicycle bearing resistance, the energy dissipated by vibration and oscillation of both the roadbed and the vehicle, and sliding of the wheel on the roadbed surface (pavement or a track).
But there is an fiftyfifty broader sense that would include energy wasted by wheel slippage due to the torque applied from the engine. This includes the increased power required due to the increased velocity of the wheels where the tangential velocity of the driving wheel(s) becomes greater than the vehicle speed due to slippage. Since power is equal to force times velocity and the wheel velocity has increased, the ability required has increased appropriately.
The pure “rolling resistance” for a train is that which happens due to deformation and possible pocketsized sliding at the wheelroad contact.^{[10]}
For a safe tire, an analogous energy loss happens over the entire tire, only it is however called “rolling resistance”. In the broad sense, “rolling resistance” includes wheel bearing resistance, free energy loss by shaking both the roadbed (and the earth underneath) and the vehicle itself, and by sliding of the wheel, road/rail contact. Railroad textbooks seem to cover all these resistance forces but practise non call their sum “rolling resistance” (broad sense) as is done in this article. They just sum up all the resistance forces (including aerodynamic elevate) and call the sum bones railroad train resistance (or the like).^{[11]}
Since railroad rolling resistance in the broad sense may exist a few times larger than merely the pure rolling resistance^{[12]}
reported values may exist in serious conflict since they may exist based on unlike definitions of “rolling resistance”. The train’s engines must, of class, provide the free energy to overcome this broadsense rolling resistance.
For tires, rolling resistance is divers every bit the energy consumed by a tire per unit distance covered.^{[13]}
It is also called rolling friction or rolling drag. It is one of the forces that act to oppose the motion of a driver. The main reason for this is that when the tires are in motion and affect the surface, the surface changes shape and causes deformation of the tire.^{[14]}
For highway motor vehicles, there is obviously some energy prodigal in shaking the roadway (and the earth beneath information technology), the shaking of the vehicle itself, and the sliding of the tires. But, other than the additional power required due to torque and wheel begetting friction, nonpure rolling resistance doesn’t seem to have been investigated, perchance because the “pure” rolling resistance of a rubber tire is several times higher than the neglected resistances.^{[15]}
Rolling resistance coefficient
[edit]
The “rolling resistance coefficient” is defined past the following equation:^{[6]}

$$
F
=
C
r
r
N
{\displaystyle \ F=C_{rr}N}
 where

$$
F
{\displaystyle F}
is the rolling resistance forcefulness (shown as
R
{\displaystyle R}
in figure ane), 
$$
C
r
r
{\displaystyle C_{rr}}
is the dimensionless
rolling resistance coefficient
or
coefficient of rolling friction
(CRF), and 
$$
N
{\displaystyle N}
is the normal forcefulness, the force perpendicular to the surface on which the wheel is rolling.

is the forcefulness needed to button (or tow) a wheeled vehicle forward (at constant speed on a level surface, or zero form, with zero air resistance) per unit force of weight. It is causeless that all wheels are the same and bear identical weight. Thus:
means that it would only take 0.01 pounds to tow a vehicle weighing one pound. For a 1000pound vehicle, information technology would take thou times more tow forcefulness, i.e. 10 pounds. One could say that
is in lb(towstrength)/lb(vehicle weight). Since this lb/lb is force divided by force,
is dimensionless. Multiply it past 100 and yous get the percent (%) of the weight of the vehicle required to maintain dull steady speed.
is frequently multiplied by g to get the parts per g, which is the same equally kilograms (kg force) per metric ton (tonne = 1000 kg ),^{[16]}
which is the same as pounds of resistance per grand pounds of load or Newtons/kiloNewton, etc. For the US railroads, lb/ton has been traditionally used; this is just
. Thus, they are all just measures of resistance per unit vehicle weight. While they are all “specific resistances”, sometimes they are just called “resistance” although they are really a coefficient (ratio)or a multiple thereof. If using pounds or kilograms every bit force units, mass is equal to weight (in earth’s gravity a kilogram a mass weighs a kilogram and exerts a kilogram of force) then i could merits that
is as well the strength per unit of measurement mass in such units. The SI system would apply Northward/tonne (N/T, N/t), which is
and is force per unit mass, where
g
is the dispatch of gravity in SI units (meters per second square).^{[17]}
The above shows resistance proportional to
but does non explicitly show any variation with speed, loads, torque, surface roughness, diameter, tire inflation/wear, etc., because
itself varies with those factors. Information technology might seem from the above definition of
that the rolling resistance is direct proportional to vehicle weight but it is not.
Measurement
[edit]
There are at least two popular models for calculating rolling resistance.
 “Rolling resistance coefficient (RRC). The value of the rolling resistance force divided by the wheel load. The Society of Automotive Engineers (SAE) has adult examination practices to measure the RRC of tires. These tests (SAE J1269 and SAE J2452) are usually performed^{[
citation needed
]}
on new tires. When measured past using these standard test practices, virtually new passenger tires have reported RRCs ranging from 0.007 to 0.014.”^{[6]}
In the case of cycle tires, values of 0.0025 to 0.005 are achieved.^{[18]}
These coefficients are measured on rollers, with ability meters on road surfaces, or with declensiondownwardly tests. In the latter two cases, the effect of air resistance must be subtracted or the tests performed at very depression speeds.  The coefficient of rolling resistance
b, which has the dimension of length, is approximately (due to the pocketsizedangle approximation of
$$
cos
(
θ
)
=
1
{\displaystyle \cos(\theta )=1}
) equal to the value of the rolling resistance force times the radius of the wheel divided by the bike load.^{[3]}  ISO 18164:2005 is used to test rolling resistance in Europe.
The results of these tests can be hard for the general public to obtain as manufacturers prefer to publicize “comfort” and “operation”.
Physical formulae
[edit]
The coefficient of rolling resistance for a slow rigid bike on a perfectly elastic surface, non adjusted for velocity, can be calculated by
^{[xix]}
^{[
citation needed
]}

$$
C
r
r
=
z
/
d
{\displaystyle \ C_{rr}={\sqrt {z/d}}}
 where

$$
z
{\displaystyle z}
is the sinkage depth 
$$
d
{\displaystyle d}
is the diameter of the rigid wheel

The empirical formula for
for bandage iron mine car wheels on steel rails is:^{[twenty]}

$$
C
r
r
=
0.0048
(
18
/
D
)
1
2
(
100
/
West
)
ane
iv
=
0.0643988
Due west
D
2
4
{\displaystyle \ C_{rr}=0.0048(18/D)^{\frac {i}{2}}(100/W)^{\frac {1}{4}}={\frac {0.0643988}{\sqrt[{4}]{WD^{2}}}}}
 where

$$
D
{\displaystyle D}
is the bicycle diameter in inches 
$$
West
{\displaystyle W}
is the load on the wheel in poundsforce

As an alternative to using
one tin utilise
, which is a different
rolling resistance coefficient
or
coefficient of rolling friction
with dimension of length. Information technology is divers by the following formula:^{[three]}

$$
F
=
North
b
r
{\displaystyle \ F={\frac {Nb}{r}}}
 where

$$
F
{\displaystyle F}
is the rolling resistance force (shown in figure 1), 
$$
r
{\displaystyle r}
is the wheel radius, 
$$
b
{\displaystyle b}
is the
rolling resistance coefficient
or
coefficient of rolling friction
with dimension of length, and 
$$
Due north
{\displaystyle N}
is the normal force (equal to
W, not
R, as shown in effigy one).

The above equation, where resistance is inversely proportional to radius
seems to exist based on the discredited “Coulomb’s law” (Neither Coulomb’s changed square law nor Coulomb’s law of friction)^{[
citation needed
]}. See dependence on bore. Equating this equation with the force per the rolling resistance coefficient, and solving for
, gives
=
. Therefore, if a source gives rolling resistance coefficient (
) equally a dimensionless coefficient, it can be converted to
, having units of length, past multiplying
past bike radius
.
Rolling resistance coefficient examples
[edit]
Table of rolling resistance coefficient examples: [iv]
C _{ rr } 
b 
Description 
0.0003 to 0.0004^{[21]} 
“Pure rolling resistance” Railroad steel cycle on steel rail  
0.0010 to 0.0015^{[22]} 
0.1 mm^{[three]}  Hardened steel ball bearings on steel 
0.0010 to 0.0024^{[23]} ^{[24]} 
0.five mm^{[3]}  Railroad steel bike on steel rail. Passenger runway automobile about 0.0020^{[25]} 
0.0019 to 0.0065^{[26]} 
Mine auto cast iron wheels on steel track  
0.0022 to 0.0050^{[27]} 
Production bicycle tires at 120 psi (8.iii bar) and 50 km/h (31 mph), measured on rollers  
0.0025^{[28]}  Special Michelin solar machine/ecomarathon tires  
0.0050  Dirty tram rails (standard) with straights and curves^{[ citation needed ]}  
0.0045 to 0.0080^{[29]} 
Large truck (Semi) tires  
0.0055^{[28]}  Typical BMX bike tires used for solar cars  
0.0062 to 0.0150^{[30]} 
Machine tire measurements  
0.0100 to 0.0150^{[31]} 
Ordinary machine tires on concrete  
0.0385 to 0.0730^{[32]} 
Stage coach (19th century) on dirt road. Soft snow on road for worst case.  
0.3000^{[31]}  Ordinary motorcar tires on sand 
For example, in earth gravity, a car of thou kg on cobblestone volition demand a force of effectually 100 newtons for rolling (1000 kg × 9.81 chiliad/s^{2}
× 0.01 = 98.1 Due north).
Dependence on diameter
[edit]
Stagecoaches and railroads
[edit]
Coordinate to Dupuit (1837), rolling resistance (of wheeled carriages with wooden wheels with iron tires) is approximately inversely proportional to the square root of wheel diameter.^{[33]}
This rule has been experimentally verified for bandage iron wheels (eight” – 24″ diameter) on steel rail^{[34]}
and for 19th century carriage wheels.^{[32]}
Only there are other tests on wagon wheels that practise not agree.^{[32]}
Theory of a cylinder rolling on an rubberband roadway as well gives this same rule^{[35]}
These contradict earlier (1785) tests by Coulomb of rolling wooden cylinders where Coulomb reported that rolling resistance was inversely proportional to the diameter of the wheel (known as “Coulomb’southward law”).^{[36]}
This disputed (or wrongly applied) “Coulomb’s constabulary” is even so found in handbooks, withal.
Pneumatic tires
[edit]
For pneumatic tires on difficult pavement, it is reported that the effect of diameter on rolling resistance is negligible (within a practical range of diameters).^{[37]}
^{[38]}
Dependence on practical torque
[edit]
The driving torque
to overcome rolling resistance
and maintain steady speed on level footing (with no air resistance) can be calculated by:

$$
T
=
Five
s
Ω
R
r
{\displaystyle T={\frac {V_{s}}{\Omega }}R_{r}}
 where

$$
V
s
{\displaystyle V_{southward}}
is the linear speed of the body (at the axle), and 
$$
Ω
{\displaystyle \Omega }
its rotational speed.

It is noteworthy that
is ordinarily not equal to the radius of the rolling body as a result of wheel slip.^{[39]}
^{[40]}
^{[41]}
The slip between cycle and ground inevitably occurs whenever a driving or braking torque is applied to the bicycle.^{[42]}
^{[43]}
Consequently, the linear speed of the vehicle differs from the cycle`southward circumferential speed. It is notable that slip does non occur in driven wheels, which are not subjected to driving torque, nether different conditions except braking. Therefore, rolling resistance, namely hysteresis loss, is the primary source of free energy dissipation in driven wheels or axles, whereas in the bulldoze wheels and axles slip resistance, namely loss due to bike slip, plays the role also every bit rolling resistance.^{[44]}
Significance of rolling or slip resistance is largely dependent on the tractive force, coefficient of friction, normal load, etc.^{[45]}
All wheels
[edit]
“Applied torque” may either exist driving torque applied past a motor (often through a manual) or a braking torque applied past brakes (including regenerative braking). Such torques results in energy dissipation (above that due to the basic rolling resistance of a freely rolling, i.e. except sideslip resistance). This boosted loss is in part due to the fact that in that location is some slipping of the wheel, and for pneumatic tires, there is more flexing of the sidewalls due to the torque. Sideslip is divers such that a 2% slip means that the circumferential speed of the driving bicycle exceeds the speed of the vehicle past 2%.
A pocketsized percent slip tin result in a slip resistance which is much larger than the basic rolling resistance. For instance, for pneumatic tires, a 5% skid tin translate into a 200% increase in rolling resistance.^{[46]}
This is partly because the tractive forcefulness applied during this slip is many times greater than the rolling resistance force and thus much more ability per unit velocity is being applied (recollect power = force ten velocity so that ability per unit of measurement of velocity is just force). And then just a small percentage increase in circumferential velocity due to skid can translate into a loss of traction power which may even exceed the power loss due to basic (ordinary) rolling resistance. For railroads, this effect may be even more than pronounced due to the low rolling resistance of steel wheels.
Information technology is shown that for a passenger car, when the tractive forcefulness is virtually twoscore% of the maximum traction, the slip resistance is almost equal to the basic rolling resistance (hysteresis loss). Only in case of a tractive strength equal to lxx% of the maximum traction, slip resistance becomes ten times larger than the bones rolling resistance.^{[47]}
Railroad steel wheels
[edit]
In guild to apply any traction to the wheels, some slippage of the wheel is required.^{[48]}
For trains climbing up a grade, this sideslip is normally 1.5% to two.5%.
Slip (likewise known as pitterpatter) is ordinarily roughly directly proportional to tractive attempt. An exception is if the tractive effort is and so loftier that the wheel is close to substantial slipping (more than just a few per centum as discussed above), and so slip rapidly increases with tractive effort and is no longer linear. With a lilliputian higher applied tractive effort the wheel spins out of control and the adhesion drops resulting in the bicycle spinning even faster. This is the type of slipping that is observable by middle—the slip of say 2% for traction is only observed past instruments. Such rapid sideslip may consequence in excessive wear or damage.
Pneumatic tires
[edit]
Rolling resistance greatly increases with applied torque. At high torques, which apply a tangential strength to the road of about half the weight of the vehicle, the rolling resistance may triple (a 200% increase).^{[46]}
This is in office due to a slip of most 5%. The rolling resistance increase with applied torque is not linear, simply increases at a faster rate as the torque becomes college.
Dependence on wheel load
[edit]
Railroad steel wheels
[edit]
The rolling resistance coefficient, Crr, significantly decreases as the weight of the rail machine per cycle increases.^{[49]}
For example, an empty freight machine had nigh twice the Crr equally a loaded car (Crr=0.002 vs. Crr=0.001). This aforementioned “economy of scale” shows upward in testing of mine rail cars.^{[50]}
The theoretical Crr for a rigid wheel rolling on an elastic roadbed shows Crr inversely proportional to the square root of the load.^{[35]}
If Crr is itself dependent on bicycle load per an inverse squareroot rule, then for an increase in load of two% simply a 1% increase in rolling resistance occurs.^{[51]}
Pneumatic tires
[edit]
For pneumatic tires, the direction of change in Crr (rolling resistance coefficient) depends on whether or not tire aggrandizement is increased with increasing load.^{[52]}
It is reported that, if aggrandizement pressure is increased with load according to an (undefined) “schedule”, and so a 20% increase in load decreases Crr past iii%. But, if the aggrandizement pressure is non changed, then a 20% increase in load results in a 4% increment in Crr. Of form, this will increment the rolling resistance by 20% due to the increase in load plus ane.2 x 4% due to the increment in Crr resulting in a 24.8% increase in rolling resistance.^{[53]}
Dependence on curvature of roadway
[edit]
General
[edit]
When a vehicle (motor vehicle or railroad train) goes around a bend, rolling resistance commonly increases. If the curve is not banked then as to exactly counter the centrifugal force with an equal and opposing centripetal force due to the banking, and then there volition be a net unbalanced sideways force on the vehicle. This will result in increased rolling resistance. Banking is as well known as “superelevation” or “cant” (not to be dislocated with track cant of a rails). For railroads, this is called curve resistance but for roads it has (at least in one case) been called rolling resistance due to cornering.
Sound
[edit]
Rolling friction generates sound (vibrational) free energy, as mechanical energy is converted to this form of energy due to the friction. One of the most mutual examples of rolling friction is the motion of motor vehicle tires on a roadway, a process which generates audio equally a byproduct.^{[54]}
The sound generated by machine and truck tires every bit they curlicue (especially noticeable at highway speeds) is mostly due to the percussion of the tire treads, and compression (and subsequent decompression) of air temporarily captured inside the treads.^{[55]}
Factors that contribute in tires
[edit]
Several factors bear on the magnitude of rolling resistance a tire generates:
 As mentioned in the introduction: bike radius, forward speed, surface adhesion, and relative microsliding.
 Material – different fillers and polymers in tire limerick can meliorate traction while reducing hysteresis. The replacement of some carbon black with higherpriced silica–silane is one common mode of reducing rolling resistance.^{[6]}
The utilise of exotic materials including nanoclay has been shown to reduce rolling resistance in loftier operation prophylactic tires.^{[56]}
Solvents may also be used to dandy solid tires, decreasing the rolling resistance.^{[57]}  Dimensions – rolling resistance in tires is related to the flex of sidewalls and the contact area of the tire^{[58]}
For case, at the aforementioned pressure, wider wheel tires flex less in the sidewalls as they whorl and thus have lower rolling resistance (although higher air resistance).^{[58]}  Extent of inflation – Lower pressure in tires results in more flexing of the sidewalls and higher rolling resistance.^{[58]}
This energy conversion in the sidewalls increases resistance and can also atomic number 82 to overheating and may have played a part in the infamous Ford Explorer rollover accidents.  Over inflating tires (such a cycle tires) may not lower the overall rolling resistance as the tire may skip and hop over the route surface. Traction is sacrificed, and overall rolling friction may not be reduced every bit the wheel rotational speed changes and slippage increases.^{[ citation needed ]}
 Sidewall deflection is not a direct measurement of rolling friction. A high quality tire with a high quality (and supple) casing will allow for more flex per energy loss than a inexpensive tire with a stiff sidewall.^{[
commendation needed
]}
Once again, on a bike, a quality tire with a supple casing will all the same roll easier than a inexpensive tire with a stiff casing. Similarly, as noted by Goodyear truck tires, a tire with a “fuel saving” casing will benefit the fuel economy through many tread lives (i.e. retreading), while a tire with a “fuel saving” tread design will only benefit until the tread wears down.  In tires, tread thickness and shape has much to do with rolling resistance. The thicker and more contoured the tread, the higher the rolling resistance^{[58]}
Thus, the “fastest” bicycle tires have very little tread and heavy duty trucks become the best fuel economic system as the tire tread wears out.  Diameter effects seem to be negligible, provided the pavement is hard and the range of diameters is express. Come across dependence on diameter.
 Virtually all world speed records have been set on relatively narrow wheels,^{[
citation needed
]}
probably because of their aerodynamic advantage at high speed, which is much less of import at normal speeds.  Temperature: with both solid and pneumatic tires, rolling resistance has been found to decrease as temperature increases (within a range of temperatures: i.e. there is an upper limit to this effect)^{[59]}
^{[60]}
For a rise in temperature from 30 °C to 70 °C the rolling resistance decreased by 2025%.^{[61]}
Racers heat their tires before racing, but this is primarily used to increase tire friction rather than to decrease rolling resistance.
Railroads: Components of rolling resistance
[edit]
In a broad sense rolling resistance can exist divers as the sum of components^{[62]}):
 Bike begetting torque losses.
 Pure rolling resistance.
 Sliding of the wheel on the rail.
 Loss of energy to the roadbed (and earth).
 Loss of energy to oscillation of railway rolling stock.
Bicycle bearing torque losses can exist measured as a rolling resistance at the wheel rim, Crr. Railroads unremarkably use roller bearings which are either cylindrical (Russian federation)^{[63]}
or tapered (U.s.a.).^{[64]}
The specific rolling resistance in bearings varies with both bike loading and speed.^{[65]}
Bike bearing rolling resistance is lowest with loftier axle loads and intermediate speeds of lx–fourscore km/h with a Crr of 0.00013 (axle load of 21 tonnes). For empty freight cars with axle loads of 5.five tonnes, Crr goes up to 0.00020 at lx km/h just at a low speed of 20 km/h it increases to 0.00024 and at a loftier speed (for freight trains) of 120 km/h information technology is 0.00028. The Crr obtained in a higher place is added to the Crr of the other components to obtain the total Crr for the wheels.
Comparing rolling resistance of highway vehicles and trains
[edit]
The rolling resistance of steel wheels on steel runway of a train is far less than that of the rubber tires wheels of an automobile or truck. The weight of trains varies profoundly; in some cases they may be much heavier per passenger or per internet ton of freight than an automobile or truck, but in other cases they may be much lighter.
As an example of a very heavy passenger train, in 1975, Amtrak passenger trains weighed a little over seven tonnes per rider,^{[66]}
which is much heavier than an average of a trivial over one ton per passenger for an machine. This means that for an Amtrak passenger train in 1975, much of the free energy savings of the lower rolling resistance was lost to its greater weight.
An instance of a very light highspeed rider railroad train is the N700 Series Shinkansen, which weighs 715 tonnes and carries 1323 passengers, resulting in a perpassenger weight of virtually onehalf a tonne. This lighter weight per passenger, combined with the lower rolling resistance of steel wheels on steel track ways that an N700 Shinkansen is much more energy efficient than a typical automobile.
In the case of freight, CSX ran an advertisement campaign in 2013 claiming that their freight trains move “a ton of freight 436 miles on a gallon of fuel”, whereas some sources claim trucks motion a ton of freight about 130 miles per gallon of fuel, indicating trains are more efficient overall.
See likewise
[edit]
 Coefficient of friction
 Lowrolling resistance tires
 Maglev (Magnetic Levitation, the elimination of rolling and thus rolling resistance)
 Rolling chemical element bearing
References
[edit]

^
“SAE MOBILUS”.
saemobilus.sae.org. doi:x.4271/0611020014. Retrieved
202104nineteen
.

^
Peck, William Guy (1859).
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20071009
.
rolling friction less than sliding friction.

^
^{ a }
^{ b }
^{ c }
^{ d }
^{ e }
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^
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(PDF)
. Retrieved
20170711
.

^
A handbook for the rolling resistance of pneumatic tires Clark, Samuel Kelly; Dodge, Richard N. 1979 
^
^{ a }
^{ b }
^{ c }
^{ d }
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(PDF)
. Retrieved
20070811
.

^
TyresOnline: The Benefits of Silica in Tyre Design Archived 20130204 at the Wayback Machine 
^
Астахов, p.85 
^
An case of such usage for railroads is hither. 
^
Деев, p. 79. Hay, p. 68 
^
Астахов, Chapt. Four, p. 73+; Деев, Sect. five.ii p. 78+; Hay, Chapt. 6 “Train Resistance” p. 67+ 
^
Астахов, Fig. four.14, p. 107 
^
Andersen Lasse K.; Larsen Jesper G.; Fraser Elsje Southward.; Schmidt Bjarne; Dyre Jeppe C. (2015). “Rolling Resistance Measurement and Model Development”.
Journal of Transportation Technology.
141
(2): 04014075. doi:10.1061/(ASCE)TE.19435436.0000673.

^
“Rolling Resistance and Fuel Saving”
(PDF). Archived from the original
(PDF)
on 20160408.

^
If 1 were to assume that the resistance coefficients (Crr) for motor vehicles were the same equally for trains, then for trains the neglected resistances taken together have a Crr of nigh 0.0004 (see Астахов, Fig. 4.14, p.107 at 20km/hr and assume a total Crr =0.0010 based on Fig. iii.8, p.50 (patently bearings) and adjust for roller bearings based on a delta Crr of 0.00035 as read from Figs. iv.2 and 4.4 on pp. 74, 76). Compare this Crr of 0.0004 to motor vehicle tire Crr’southward of at least 10 times higher per “Rolling resistance coefficient examples” in this article 
^
kgf/tonne is used by Астахов throughout his book 
^
Деев uses N/T notation. Encounter pp. 7884. 
^
Willett, Kraig. “Roller Data”.
world wide web.biketechreview.com
. Retrieved
20170805
.

^
Guiggiani, Massimo (five May 2018).
The Science of Vehicle Dynamics. Springer Cham. p. 22. ISBN978three319732206.

^
Hersey, equation (two), p. 83 
^
Астахов, p. 81. 
^
“Coefficients of Friction in Bearing”.
Coefficients of Friction
. Retrieved
seven February
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^
Hay, Fig. six2 p.72(worst case shown of 0.0036 not used since it is probable erroneous) 
^
Астахов, Figs. 3.8, 3.ix, iii.11, pp. 5055; Figs. ii.iii, 2.iv pp. 3536. (Worst case is 0.0024 for an axle load of five.95 tonnes with obsolete obviously (friction –not roller) bearings 
^
Астахов, Fig. ii.1, p.22 
^
Hersey, Table half dozen, p.267 
^
“Roller Data”
(PDF).

^
^{ a }
^{ b }
Roche, Schinkel, Storey, Humphris & Guelden, “Speed of Light.” ISBN 073341527X 
^
Crr for large truck tires per Michelin 
^
Darkgreen Seal 2003 Report 
^
^{ a }
^{ b }
Gillespie ISBN one560911999 p117 
^
^{ a }
^{ b }
^{ c }
Baker, Ira O., “Treatise on roads and pavements”. New York, John Wiley, 1914. Stagecoach: Tabular array 7, p. 28. Diameter: pp. 2223. This volume reports a few hundred values of rolling resistance for various animalpowered vehicles nether various condition, mostly from 19th century data. 
^
Hersey, subsection: “Cease of dark ages”, p.261 
^
Hersey, subsection: “Static rolling friction”, p.266. 
^
^{ a }
^{ b }
Williams, 1994, Ch. “Rolling contacts”, eq. 11.1, p. 409. 
^
Hersey, subsection: “Coulomb on wooden cylinders”, p. 260 
^
U.S. National Bureau of Standards, Fig. ane.13 
^
Some^{[ who? ]}
think that smaller tire wheels, all else being equal, tend to have higher rolling resistance than larger wheels. In some laboratory tests, however, such as Greenspeed exam results (accessdate = 20071027), smaller wheels appeared to have like or lower losses than large wheels, but these tests were done rolling the wheels confronting a smallbore drum, which would theoretically remove the advantage of largediameter wheels, thus making the tests irrelevant for resolving this outcome. Another counter case to the claim of smaller wheels having higher rolling resistance tin can be establish in the area of ultimate speed lather box derby racing. In this race, the speeds take increased equally cycle diameters accept decreased by up to fifty%. This might suggest that rolling resistance may not be increasing significantly with smaller diameter inside a practical range, if whatever other of the many variables involved have been controlled for. See talk page. 
^
Zéhil, GérardPhilippe; Gavin, Henri P. (2013). “Threedimensional boundary element conception of an incompressible viscoelastic layer of finite thickness practical to the rolling resistance of a rigid sphere”.
International Periodical of Solids and Structures.
50
(vi): 833–842. doi:10.1016/j.ijsolstr.2012.11.020.

^
Zéhil, GérardPhilippe; Gavin, Henri P. (2013). “Simple algorithms for solving steadycountry frictional rolling contact problems in two and 3 dimensions”.
International Journal of Solids and Structures.
l
(half dozen): 843–852. doi:ten.1016/j.ijsolstr.2012.11.021.

^
Zéhil, GérardPhilippe; Gavin, Henri P. (2013). “Simplified approaches to viscoelastic rolling resistance”.
International Journal of Solids and Structures.
fifty
(6): 853–862. doi:10.1016/j.ijsolstr.2012.09.025.

^
“SAE MOBILUS”.
saemobilus.sae.org. doi:10.4271/06xi020014. Retrieved
202104xix
.

^
Sina, Naser; Hairi Yazdi, Mohammad Reza; Esfahanian, Vahid (20200301). “A novel method to improve vehicle free energy efficiency: Minimization of tire power loss”.
Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Auto Engineering science.
234
(4): 1153–1166. doi:ten.1177/0954407019861241. ISSN 09544070. S2CID 199099736.

^
Sina, Naser; Nasiri, Sayyad; Karkhaneh, Vahid (2015eleven01). “Furnishings of resistive loads and tire inflation pressure on tire power losses and CO2 emissions in existentworld atmospheric condition”.
Practical Free energy.
157: 974–983. doi:10.1016/j.apenergy.2015.04.010. ISSN 03062619.

^
“SAE MOBILUS”.
saemobilus.sae.org. doi:10.4271/0611020014. Retrieved
202104nineteen
.

^
^{ a }
^{ b }
Roberts, Fig. 17: “Effect of torque transmission on rolling resistance”, p. 71 
^
“SAE MOBILUS”.
saemobilus.sae.org. doi:x.4271/06xi020014. Retrieved
20210419
.

^
Деев, p.30 including eq. (2.seven) and Fig. ii.3 
^
Астахов, Figs. 3.viii, iii.9, 3.11, pp. l55. Hay, Fig. sixtyii, p. 72 shows the same phenomena but has higher values for Crr and not reported here since the railroads in 2011 [i]. were claiming about the aforementioned value equally Астахов 
^
Hersey, Table 6., p. 267 
^
Per this supposition,
$$
F
=
k
Due north
0.five
{\displaystyle F=kN^{0.5}}
where
F
{\displaystyle F}
is the rolling resistance force and
N
{\displaystyle N}
is the normal load forcefulness on the bike due to vehicle weight, and
k
{\displaystyle yard}
is a constant. It tin be readily shown by differentiation of
F
{\displaystyle F}
with respect to
North
{\displaystyle N}
using this rule that
d
Northward
Due north
=
two
d
F
F
{\displaystyle {\operatorname {d} Due north \over N}=2{\operatorname {d} F \over F}}

^
Roberts, pp. 6061. 
^
[2] A Relationship between Tyre Pressure and Rolling Resistance Force under Different Vehicle Speed  Apiwat Suyabodha Section of Automotive Engineering, Rangsit Academy, Lakhok, Pathumthani, Thailand  2017 
^
[3] C. Michael Hogan,
Analysis of Highway Dissonance, Periodical of Soil, Air and H2o Pollution, Springer Verlag Publishers, Netherlands, Volume 2, Number iii / September, 1973 
^
Gwidon W. Stachowiak, Andrew William Batchelor,
Engineering Tribology, Elsevier Publisher, 750 pages (2000) ISBN 0750673044 
^
http://144.206.159.178/ft/200/607426/12614863.pdf^{ [ permanent dead link ] }

^
http://www.rubberchemtechnol.org/resources/ane/rctea4/v3/i1/p19_s1?isAuthorized=no^{ [ permanent dead link ] }

^
^{ a }
^{ b }
^{ c }
^{ d }
“Schwalbe Tires: Rolling Resistance”.

^
The Recumbent Cycle and Homo Powered Vehicle Information Eye 
^
U.S National Bureau of Standards p.? and Williams p.? 
^
Roberts, “Effect of temperature”, p.59 
^
Астахов, p. 74, Although Астахов list these components, he doesn’t give the sum a name. 
^
Шадур. Л. А. (editor). Вагоны
(in Russian)(Railway cars). Москва, Транспорт, 1980. pp. 122 and figs. 6.1 p. 123 Vi.two p. 125 
^
Clan of American Railroads, Mechanical Division “Car and Locomotive Encyclopedia”, New York, SimmonsBoardman, 1974. Section 14: “Axle journals and bearings”. Nigh all of the ads in this section are for the tapered type of bearing. 
^
Астахов, Fig 4.2, p. 76 
^
Statistics of railroads of form I in the United states, Years 1965 to 1975: Statistical summary. Washington DC, Association of American Railroads, Economics and Finance Dept. Encounter table for Amtrak, p.16. To get the tons per passenger divide tonmiles (including locomotives) by passengermiles. To get tonsgross/tonsnet, divide gross tonmi (including locomotives) (in the “operating statistics” table by the revenue tonmiles (from the “Freight traffic” table)
 Астахов П.Н.
(in Russian)
“Сопротивление движению железнодорожного подвижного состава” (Resistance to movement of railway rolling stock) Труды ЦНИИ МПС (ISSN 03723305). Выпуск 311 (Vol. 311). – Москва: Транспорт, 1966. – 178 pp. perm. record at UC Berkeley (In 2012, full text was on the Internet but the U.S. was blocked)  Деев В.В., Ильин Г.А., Афонин Г.С.
(in Russian)
“Тяга поездов” (Traction of trains) Учебное пособие. – М.: Транспорт, 1987. – 264 pp.  Hay, William Due west. “Railroad Engineering” New York, Wiley 1953
 Hersey, Mayo D., “Rolling Friction”
Transactions of the ASME, Apr 1969 pp. 260–275 and
Journal of Lubrication Technology, January 1970, pp. 83–88 (one article split betwixt two journals) Except for the “Historical Introduction” and a survey of the literature, it is mainly about laboratory testing of mine railroad bandage fe wheels of diameters eight″ to 24 done in the 1920s (about a half century delay between experiment and publication).  Hoerner, Sighard F., “Fluid dynamic elevate”, published past the writer, 1965. (Chapt. 12 is “LandBorne Vehicles” and includes rolling resistance (trains, autos, trucks).)
 Roberts, Thousand. B., “Ability wastage in tires”, International Rubber Conference, Washington, D.C. 1959.
 U.Southward National Bureau of Standards, “Mechanics of Pneumatic Tires”, Monograph #132, 1969–1970.
 Williams, J. A.
Engineering tribology’. Oxford University Press, 1994.
External links
[edit]
 Rolling Resistance and Fuel Saving
 temperature vs rolling resistance
 Simple rolldownwardly test to measure Crr in cars and bikes
 Rolling Resistance Thresholds
Describe the Four Main Types of Resistance Forces
Source: https://en.wikipedia.org/wiki/Rolling_resistance