Tire tread to compensate residual aligning torque

The tread of a rib type tire is modified to provide draft angles in lateral grooves of selected ribs to compensate the tire's residual aligning torque (RAT). This allows the vehicle to have straight ahead motion with no steering pull. The draft angles are achieved by inclining the radial centerline of the lateral grooves to be sloped forward on one side of the midcircumferential plane and sloped backward on the other side of the midcircumferential plane. The centerline draft angle results in tread blocks sloped forward and backward during forward motion of the vehicle. The sloping tread blocks produces an effective rolling radius change on selected ribs of the tread pattern. Effective rolling radius of selected ribs is a concept introduced to explain the physical relationships that exist in the contact patch of the tire with the ground surface. The resulting contact change introduces longitudinal tangential stress changes that induce a torque to compensate for the inherent residual aligning torque due to the unmodified tire's construction and tread pattern.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
This invention relates to a pneumatic tire and more specifically to the 
modified tread of the tire. 
2. Description of the Art 
Vehicles have generally become smaller and tighter, or sharper, in steering 
response and sensitivity. The distribution of forces and moments on the 
tires from the ground surface at the contact patch interface are becoming 
more critical for obtaining good vehicle steering stability and handling. 
For example, steering pull is manifested as a tendency for a vehicle to 
drift left or right when the steering wheel is released. This pull is 
caused by a twisting moment on the tire about a Z-axis normal to the 
contact patch, and a lateral force perpendicular to the forward velocity 
of the vehicle along a Y-axis at the contact patch. This Z-axis moment is 
called the aligning torque and the Y-axis force is called the lateral 
force on the contact patch. 
When a midcircumferential plane of the tire has an orientation at a small 
slip angle (say 0.25 degrees) with respect to its forward velocity vector, 
the lateral forces on the contact patch can be reduced to zero. This small 
slip angle is called the neutral slip angle. However, there remains a 
Z-axis moment at the contact patch called the residual aligning torque 
(RAT). Also, there is another small slip angle (say 0.35 degrees) of the 
tire plane with respect to the forward velocity vector where the Z-axis 
moment is zero. At this small slip angle a Y-axis force exists called the 
residual cornering force (RCF). Generally speaking, it is not possible to 
achieve a zero aligning torque at the same slip angle that yields a zero 
cornering force. In fact, most vehicle/tire combinations operate at a 
small steady state slip angle to yield a zero lateral force, and the 
steering system is used to provide a torque to compensate for the residual 
aligning torque. When the steering wheel is released, the vehicle will 
drift right or left depending on the magnitude and direction of the 
residual aligning torque. Vehicle manufacturers have established limits on 
the amount of drift allowed. For example, one vehicle manufacture limits 
the drift from tire sources to 3 meters in a forward distance of 100 
meters, or a drift angle of 1.72 degrees. The theory of tire induced 
steering pull is documented in the Society of Automotive Engineers (SAE) 
Publication No. 750406. Aligning torque and lateral force are defined as 
they relate to the commonly used terms of plysteer and conicity in SAE 
Publication No. 870423. 
It is known in the art that the tire belt structure and its cross-ply 
laminate of reinforcing members can cause a residual aligning torque or a 
residual cornering force. This is due to the bending-shear coupling of the 
belt package and especially due to the bending-twisting coupling within 
the belt package when the tire contacts the ground surface. The 
bending-twisting deformations in the contact patch have a greater 
significance than the bending-shear deformations. Small shear deformations 
have less impact than small twisting deformations because the twisting 
more directly affects the local contact stresses in the contact patch. SAE 
Publication No. 870423 discloses the influences on residual aligning 
torque due to both reinforcing member spacing and reinforcing member angle 
from a midcircumferential plane for a belt package having two belt plies. 
The publication also discloses the effect of having different bottom belt 
ply reinforcing member angles compared with top belt ply reinforcing 
member angles on the residual aligning torque. No procedure to eliminate 
residual aligning torque by belt reinforcing member changes was disclosed 
in this publication. 
It is also known in the art that major modifications in the belt package 
construction can reduce an average lateral force at a zero slip angle 
(plysteer) to a small value. The average lateral force at zero slip angle 
is determined by rolling the tire about its axis of rotation and measuring 
a first lateral force magnitude then reversing the rotation of the tire 
and measuring a second lateral force magnitude. The average of these two 
lateral force magnitudes is called "plysteer" in the literature. In U.S. 
Pat. No. 3,945,422 plysteer is substantially reduced by constructing the 
belt package with multiple plies (3) which are symmetrically disposed. 
Other multiple belt package configurations are disclosed in SAE 
Publication No. 760731. However, reducing the plysteer to zero does not 
eliminate the residual aligning torque at the zero neutral slip angle. 
Furthermore, these references do not teach how to make modifications in 
the construction of a tire to reduce residual aligning torque. 
It is also known in the art that the tread pattern and tread structure also 
have an effect on the residual aligning torque which is independent from 
the construction of the tire. Tread pattern and tread structure effects 
can have the same relative impact on residual aligning torque as changes 
in the belt package construction have. 
The design of the tread effects both the residual aligning torque and the 
residual cornering force. When the tread pattern changes, the stiffness of 
the tread blocks are modified. For example, changes in the circumferential 
grooves in the tread pattern will change lateral stiffness and effect the 
residual aligning torque and the residual cornering force. Changes in 
lateral grooves can also modify the stiffness of the tread of the tire and 
cause bending-twisting deformation changes within the tread. Changes in 
the lateral groove angles can result in less differential contact patch 
tangential forces between the various tread elements. Hence, the tread 
becomes more compliant as the tire rolls. U.S. Pat. No. 4,819,704 
discloses how modifications in the size and shape of tread blocks produced 
by circumferential and lateral groove changes reduce plysteer. The angle 
of the direction of the maximum shear rigidity of the tread blocks is 
specified between 40 and 75 degrees from a midcircumferential plane, and 
is opposite to the angle of reinforcing members in the outermost belt 
layers. The total surface area of the tread blocks is also disclosed as a 
factor in reducing plysteer. However, the reference does not disclose a 
procedure to change the residual aligning torque, and the reference does 
not teach how to change lateral groove angles without influencing tread 
induced tire noise and traction. The importance of tire lateral groove 
angles on noise is disclosed in U.S. Pat. No. 5,125,444. 
It is also known in the art that tread rigidity along with asymmetrical 
treads can effect plysteer. For example, U.S. Pat. No. 5,016,695 discloses 
a directional tire having an asymmetrical tread pattern wherein the rib 
having the highest rigidity (no lateral grooves) is positioned to one side 
of the midcircumferential plane. This tread pattern alters the shape of 
the contact patch to give excellent driving stability at slip angles as 
small as 1 degree, and improves ride comfort during straight ahead 
traveling. However, there is no discussion in this patent of the effect of 
this tread pattern on residual aligning torque is given, and the disclosed 
driving stability is at angles larger than nominal neutral slip angles 
where the lateral force is zero. 
The tread surface profile also influences the aligning torque and lateral 
forces on a free rolling tire. A difference in the tread radius and 
differences in rates of ground contact area were disclosed to promote the 
maneuverability of a car in Japanese Patent No. 57-147901 (JP). In this 
reference, the tread radius on the outside of the midcircumferential plane 
is made larger than the tread radius on the inside. This difference in 
tread radius and difference in shape of the ground contact area (contact 
patch) causes a conicity force. This basic construction of the tire 
results in one shoulder having a 1-2 millimeter larger radius than the 
other shoulder. This difference does not change with the rotation of the 
tire, therefore, the conicity force is in the same direction with 
clockwise or counterclockwise rotation. Opposed conicity forces exist when 
such a tire is mounted on the left compared with the right side of the 
vehicle and with the same side of the tire mounted to the exterior. 
In addition to the influence of tread pattern and tread surface profile 
changes on the tire's contact patch forces, tangential stresses at this 
interface can be changed by the inclination of the tread blocks. The angle 
between the tread surface and the approximately radial faces of the 
lateral grooves has an important effect on the traction and uneven wear 
performance of the tread. This angle is also important in the driving and 
braking forces achieved by a tread block, especially on snow, ice and 
rough ground surfaces. The influence on overall driving and braking pull 
of a tread pattern having sloping tread block elements is disclosed in 
Japanese Patent Nos. 63-97,405 (JP) 2-293,206 (JP), and 2-293,205 (JP). 
The performance of the tire on ice, snow and rough roads are enhanced by 
the tilting of tread blocks forward or backward. 
In JP 2-293206 the tire is actually reversed from early days of wear to 
last days of wear to take advantage of the changing stiffness of the tread 
blocks with wear. The disclosure of JP 63-97,405 optionally combines tread 
blocks to give a tread pattern that functions effectively on respective 
road surfaces. However, these patents do not teach how inclined tread 
blocks can be positioned and sloped to have an influence on the residual 
aligning torque. The aligning torque on the tires disclosed would be 
random as optionally combined, and may in fact increase the magnitude of 
the residual aligning torque. Japanese Patent No. 2-293,205 discloses 
similar sloping tread blocks resulting from the inclination of 
approximately radial faces of the lateral grooves to improve drive and 
brake performance. No specific tread pattern is illustrated in this 
patent. 
Other similar patents which disclose sloping tread blocks which result from 
the inclination of lateral grooves in circumferential ribs are U.S. Pat. 
Nos.: 3,104,693; 4,284,115; 4,298,046 and 5,044,414. Durability of the 
tire at high speed is the problem addressed in U.S. Pat. No. 5,044,414 and 
improved by lateral groove shape and groove bottom curvature. The same 
problem and a similar solution is disclosed in U.S. Pat. No. 4,284,115. 
Tires having improved gripping and longitudinal adherence with treads 
biting into the rough road surfaces as well as ice and snow surfaces are 
disclosed in U.S. Pat. No. 3,104,693 and U.S. Pat. No. 4,298,046. Once 
again, driving and braking performance of the tire as a whole is 
disclosed. Random residual aligning torque values are anticipated when 
using the treads of these patents. 
A tread pattern having modified ribs based on the direction of plysteer due 
to tire construction and the ground contact reaction force is disclosed in 
U.S. Pat. No. 4,305,445. This patent describes how the wear is influenced 
by the direction of "internal camber thrust" acting on the tire. The 
ground contact pressure is modified by providing small holes near the 
leading edge of lateral groove surfaces on one side and small holes near 
the trailing edges of lateral groove surfaces on the other side of the 
midcircumferential plane. This modifies the rigidity of tread blocks as 
they enter the contact patch on one side and exit the contact patch on the 
opposite side. No indication is given as to influence of these small holes 
on the plysteer or residual aligning torque, and random influences can be 
anticipated. 
The sloping tread blocks disclosed in U.S. Pat. application Ser. No. 
07/652,412 are provided to control uneven wear on a directional tire 
having an asymmetrical tread pattern. The two lateral ribs, each having 
tread blocks sloped in the same direction, have reduced braking forces 
from tread block radial deformations. The central ribs each having tread 
blocks sloped in a reverse direction, have reduced driving forces from 
tread block radial deformations. The driving axle tires are reverse 
rotated from the steer axle tires. No changes in the residual aligning 
torque is anticipated from the tire treads of this invention. 
Even though there are different known ways to reduce plysteer, there 
remains a need to be able to control and reduce the residual aligning 
torque on the tire from the ground surface. This residual aligning torque 
remains even after the tread pattern and tire construction have been 
modified to reduce plysteer or conicity. This moment or torque exists even 
at a small slip angle (neutral slip angle) or at zero slip angle when 
plysteer is zero. These corrections are made difficult by a desire to 
avoid changes in the tread pattern that influence other tire performance 
characteristics. The optimum solution is to reduce the residual aligning 
torque to approximately zero with little or no change in the tire's 
construction and basic tread pattern in contact with the ground surface 
(contact patch). Such a solution would maintain the noise, traction and 
wear performance of the tire. There is no need to address improvements in 
driving or braking traction to eliminate steering pull when the steering 
wheel is released. Hence, in accordance with this invention, the tire 
should be first optimized for noise, traction and wear by changes in the 
tire's construction and tread pattern, then certain modifications can be 
made in the tread to reduce the residual aligning torque without 
influencing the initial optimization. 
SUMMARY OF THE INVENTION 
The object of this invention is to obtain a tire having an improved tread 
for straight ahead driving of a vehicle during free rolling (no steering) 
operation. In particular, an improved tread is desired that will result in 
the tire having essentially no residual aligning torque at a neutral slip 
angle. The improved tread of the tire is achieved by making a modification 
to the tread blocks, which can be determined by a method disclosed herein. 
This can be accomplished with little or no change in the tread pattern 
within the contact patch or in the tire's construction. 
One embodiment of this invention is an improved tread for a tire having a 
plurality of ribs. A modified first rib is determined which includes a 
plurality of lateral grooves. Each of the first rib lateral grooves 
separates a pair of circumferentially adjacent first tread blocks. The 
first rib lateral grooves are defined by a first centerline draft angle. 
The first draft angle extends at an acute angle relative to a plane 
extending radially from the axis of rotation. A modified second rib is 
determined which is axially spaced from the first rib to the opposite 
axial side of a midcircumferential plane. The second rib also includes a 
plurality of lateral grooves each separating a pair of circumferentially 
adjacent second tread blocks. The second rib lateral grooves are defined 
by a second centerline draft angle. The second draft angle extends at an 
acute angle relative to a plane extending radially from the axis of 
rotation. The first draft angle extends in a direction relative to a 
radial plane opposite the direction that the second draft angle extends 
relative to another radial plane. 
During a first rotation of the tire about an axis of rotation, with the 
tire in contact with a ground surface, the modified first rib has an 
effective rolling radius greater than a respective rolling radius of an 
unmodified first rib. The modified second rib has an effective rolling 
radius smaller than a respective rolling radius of an unmodified second 
rib with this first rotation. During a second rotation of the tire, 
opposite to the first rotation about the axis of rotation and with the 
tire also in like contact with the ground surface, the modified second rib 
has an effective rolling radius greater than the respective rolling radius 
of the unmodified second rib. For this second rotation the modified first 
rib has an effective rolling radius smaller than the respective rolling 
radius of the unmodified first rib. The resulting residual aligning torque 
on the tire from the ground surface is substantially eliminated during 
both the first and second rotations of the tire. 
In a preferred embodiment of this invention, the first and second ribs are 
symmetrically positioned from the midcircumferential plane of the tire. In 
a most preferred embodiment, the first draft angle is selected equal to 
the second draft angle and the tread is a non-directional tread. 
In another embodiment of the present invention, the tread further comprises 
at least one modified third rib and at least one modified fourth rib, each 
of which include a plurality of lateral grooves. Each third rib lateral 
groove separates a pair of circumferentially adjacent third tread blocks. 
The third rib lateral grooves are defined by a third centerline draft 
angle. The third rib is located on the same axial side of the 
midcircumferential plane of the tire as the position of the first rib. The 
third rib lateral groove draft angle extends in the same direction 
relative to a respective radial plane as the first rib lateral groove 
draft angle extends. Each of the fourth rib lateral grooves separates a 
pair of circumferentially adjacent fourth tread blocks. The fourth rib 
lateral grooves are defined by a fourth centerline draft angle. The fourth 
rib is located on the same axial side of the midcircumferential plane of 
the tire as the position of the second rib. The fourth rib lateral groove 
draft angles extend in the same direction relative to a respective radial 
plane as the second rib lateral groove draft angles extend. 
A method for modifying the tread of tires to essentially eliminate a 
residual aligning torque for the tires is also presented and comprises the 
following steps. (1) A unmodified test tire is made having a predetermined 
rib type tread pattern with zero centerline draft angles for all lateral 
grooves separating circumferentially adjacent tread blocks. (2) The 
unmodified test tire is tested to determine a first residual aligning 
torque. (3) A modified test tire is made having the rib type tread pattern 
as in (1) but having centerline draft angles on both first and second 
ribs. The modified second rib is axially spaced apart from the modified 
first rib to the axially opposite side of a midcircumferential plane. The 
centerline draft angle of the first rib has an orientation with respect to 
a radial plane extending radially from the axis of rotation opposite to an 
orientation of the centerline draft angle of the second rib which extends 
from a respective radial plane. (4) The modified test tire is tested to 
determine a second residual aligning torque. (5) A system constant is 
calculated which is the second residual aligning torque minus the first 
residual aligning torque all divided by the centerline draft angle. (6) A 
final centerline draft angle is calculated for the tire as the first 
residual aligning torque as determined in (2) divided by the system 
constant. (7) Finally, a plurality of tires having the rib type tread 
pattern with the final draft angle in each lateral groove of both the 
modified first and second ribs are made and tested to verify that the tire 
has a modified residual aligning torque which is essentially zero. If not, 
the steps can be repeated to obtain a residual aligning torque near zero. 
This method can also be modified for use with tires having more than two 
modified ribs with centerline draft angles.

DESCRIPTION OF THE PREFERRED EMBODIMENTS 
The deviation of a vehicle equipped with typical tires from straight ahead 
travel is illustrated in FIG. 1. When the steering wheel is released at a 
forward travel position, X=0, the residual aligning torque on the typical 
tires will cause the vehicle to follow a free control path with a lateral 
displacement Y. At some distance X1 the lateral displacement Y1 is 
measured and a deviation angle P can be computed. Vehicle manufacturers 
provide specifications that limit the lateral displacements Y1 or 
deviation angle P at a travel distance X1 as a result of the residual 
aligning torque (RAT) of the tire. 
The Tire and Rim Association (T&RA) of Copley, Ohio specifies the 
construction and loading parameters for a standard radial pneumatic tire 
for passenger cars, light trucks and the like. The standard or typical 
tire has a construction such that a lateral force and an aligning torque 
or moment is exerted on the tire by the ground surface when the tire is 
rolling straight ahead (no slip angle). These forces and moments are 
illustrated in FIG. 2. Initially at rest the tire is rotated clockwise as 
viewed from the white sidewall (WS) side at a constant speed V1 for a time 
t1. During time t1, the lateral force YR in the positive Y-direction 
exists on the tire along with an aligning torque T0 as shown in FIGS. 2(A) 
and 2(C). Torque T0 is nominally counterclockwise as viewed from the top 
of the tire, as in FIG. 2(A), when a two ply standard belt package has a 
right/left orientation. For example, a right orientation of the 
reinforcing members of the first or interior ply of the belt package 
extends upward and to the right. The tire is then stopped and the rotation 
as viewed from the WS side is reversed to counterclockwise at a constant 
speed V2 for a time t2. A negative lateral force YL exists on the tire 
during time t2 along with an aligning torque of approximately the same 
magnitude T0 counterclockwise. Other belt packages having orientations and 
number of plies other than two plies right/left are also within the scope 
of this patent. 
The positive lateral force YR for clockwise rotation and the negative 
lateral force YL for counterclockwise rotation of the typical tire 10 can 
be considered as a combination of two component forces C and PS as shown 
in FIG. 2(C). These are commonly known as the conicity force C and the 
plysteer force PS discussed in the literature. Conicity force C does not 
change with the direction of rotation. Plysteer force PS (CW) is 
associated with clockwise rotation and plysteer force PS (CCW) is 
associated with counterclockwise rotation, as viewed from the WS side. 
Lateral forces YR and YL will also make the vehicle have a lateral 
displacement during straight ahead steering (FIG. 1). However, the lateral 
forces YR, YL can be reduced to near zero by steering the tire/wheel 
system 12 relative to the velocity vector V1 to a steer angle AR as shown 
in FIG. 2(B). Angle AR is the neutral steer angle for clockwise rotation 
of the tire when viewed from the WS side. The problem of straight ahead 
travel of the vehicle now depends only on the residual torque TR at a slip 
angle AR. The disclosure of this invention teaches one skilled in the art 
how to essentially eliminate this residual aligning torque without 
internal tire construction changes or tread pattern changes in the contact 
patch. 
The tire can be used on either the left or right side of the vehicle. With 
the white sidewall (WS) side of the tire exterior to vehicle on the right 
the tire is rotating clockwise when the vehicle moves forward and when 
viewed from this WS side. In reverse, the tire is rotating 
counterclockwise on the left side of the vehicle when it is mounted with 
the WS side to the exterior of the vehicle, when viewed from WS side and 
the vehicle moving forward. The result expressed in an X-Y coordinate 
system, is that lateral forces are in the same direction for left and 
right tires on a single axle. However, at some slip angle AL on the left 
side and at another slip angle AR on the right side, the lateral forces 
are near zero. 
Lateral force and aligning torque as a function of slip angle are 
illustrated in FIG. 3. If the tire is mounted on the right side of the 
vehicle and rotates clockwise (CW), a slip angle AR is shown to yield a 
zero lateral force and a negative aligning torque TR. The lateral force at 
a zero slip angle is force YR as previously illustrated in FIG. 2. If the 
tire instead is mounted on the left side of the vehicle and rotates 
counterclockwise (CCW), a slip angle AL is shown to yield a zero lateral 
force and a negative aligning torque TL. The lateral force at a zero slip 
angle is force YL as previously illustrated in FIG. 2. Other force and 
torque values, C, PS and TO which were shown in FIG. 2 are also 
illustrated in FIG. 3. At an average slip angle AA the average aligning 
torque is called the residual aligning torque (RAT). This invention 
discloses how to reduce the residual aligning torque RAT to essentially 
zero. The difference between the aligning torque TR for clockwise rotation 
or the aligning torque TL for counterclockwise rotation and the residual 
aligning torque RAT is small (FIG. 3). Actually, a tire according to the 
invention would be slightly overcompensated in one rotation and slightly 
undercompensated in the opposite rotation. Hence, in theory, if the same 
tire could be used on both sides of the vehicle, the resultant torque 
would be essentially zero. However, two different tires must be used. 
The effect of having two tires A and B on one axle is illustrated in FIG. 
4. The force and torque values illustrated are actual tests results for 
two production P215/65 R15 tires of the same manufacturer and tire line. 
Small variations are noted between tire A and tire B with the total 
residual aligning torque (TRAT) being again an average of the residual 
aligning torques RATs for each tire. This graph illustrates that 
uniformity of the tire is not a problem provided the same tire type 
(manufacturer and tire line) is used on both sides of the vehicle. Hence, 
correcting a tire line for RAT in accordance with this invention will 
produce the desired straight ahead steering behavior for a vehicle having 
all tires of the same line. 
The embodiments of this invention are preferably used with a rib type tire. 
For example, the contact patch of a simplified rib type tire 20 is 
illustrated in FIG. 5 showing 5 circumferential ribs 1-5 separated by 4 
circumferential grooves 22. The tire illustrated is a non-directional tire 
having a symmetrical tread pattern with respect to a midcircumferential 
plane M. The circumferential grooves 22 can be linear, curvilinear or 
zig-zag, and all such grooves are within the scope of this invention. The 
ribs 1-5 are each divided by a plurality of circumferentially spaced 
lateral grooves 24. Each lateral groove 24 separates a pair of 
circumferentially adjacent tread blocks 26. The lateral grooves 24 may 
also be linear, curvilinear or zig-zag, as well as discontinuous, and all 
such grooves are within the scope of this invention. Discontinuous lateral 
grooves extend only partially from one circumferential groove 22 to the 
adjacent circumferential grove 22. Small cuts or sipes 28 may also 
subdivide the tread blocks 26 to modify their relative X-axis to Y-axis 
stiffness properties. 
It was found that the lateral groove angles in the contact patch G1-G5 have 
a direct influence on the residual aligning torque RAT. For example, the 
graph of FIG. 6 illustrates how the change in groove angles DG from a 
groove angle of 90 degrees changes the RAT. For a tire two belt package 
construction with right/left belt ply reinforcing member orientations or 
directions for the interior ply and exterior ply respectively, the 
interior ribs 2,3 & 4 produce a change in RAT opposite to the lateral ribs 
1 and 5. The residual aligning torque RAT has a value TZ when all lateral 
groove angles G1-G5 are 90.degree.. 
Changes within the tread pattern lateral groove angles in the contact patch 
are within the scope of this disclosure. However, groove angles have only 
limited impact when compared with the total magnitude of the residual 
aligning torque to be compensated for in a tire. Clearly these tread 
pattern changes can be used with this invention to essentially eliminate 
the influence of residual aligning torque on the straight ahead steering 
of the vehicle. However, changes made in the form of lateral groove angles 
in the contact patch for the purpose of reducing residual aligning torque 
(RAT) can also introduce noise, traction and wear changes that are not 
acceptable. A unique feature of this invention is that it can be used to 
substantially eliminate residual aligning torque after the tread pattern 
of the tire has been optimized for noise, traction and wear performance. 
The invention resides in selectively changing the ribs in the tread of the 
tire to effectively modify the rolling radius of the selected ribs. Before 
these inventive modifications are described in detail it is helpful to 
describe observations and measurements made on a typical rolling tire 30 
as illustrated in FIG. 7. The tire 30 has a forward velocity V as viewed 
from the top side of the tire, and is rolling under load on a level 
surface. Having access to the necessary instruments, machines and 
vehicles, it is a relatively simple task to define the tire's "rolling 
circumference", which is the distance run by the tire 30 while rotating by 
exactly one turn. Measurements can be done on a free rolling tire to 
obtain the rolling circumference CX of the whole tire. This is illustrated 
by the graph of FIG. 8 where the tire started at X=O and rolls forward for 
one revolution a distance CX. 
In addition to this global measurement of the whole tire, it is possible to 
define the rolling circumference of each circumferential row of blocks, or 
ribs 11, 12, 13, 14, 15 of the tread pattern widthwise across the 
curvilinear surface 32 of the tire 30. This analysis has shown, for 
example, that the individual rolling circumferences CL, CC, CR of ribs 11, 
13, 15 can differ significantly from the rolling circumference CX of the 
whole tire. This takes into consideration several tire design factors such 
as the load carried by each rib, the widthwise curvature of the surface 
32, circumferential flexibility of the tread and the length of each rib in 
the contact patch. 
In general, the rolling circumference CC of the center rib 13 situated near 
the center 36 of the tire tread is greater than the rolling circumference 
CX of the whole tire. Conversely, the rolling circumferences CL and CR of 
ribs 11 and 15, situated near the lateral edges 34 of the tread, are 
smaller than rolling circumference CX of the whole tire, as shown in FIG. 
8. This is in part due to the widthwise crown surface of the tread 32 
(FIG. 7) having a larger radius RC in the center 36 than a radius RL on 
both lateral edges 34. The ribs which have the greatest rolling 
circumference will tend to pull the tire forward, while those which have 
the smallest rolling circumference will tend to pull it backward. This 
"Tug of War" results in longitudinal tangential forces FX11 and FX15 on 
lateral ribs 11 and 15 respectively and force FX13 on center rib 13. These 
forces are constantly exerted by the ground surface on the tread elements. 
A driving or braking torque applied to the tire will not significantly 
change the inequality in rolling circumferences between the rows of 
blocks, or ribs. The applied torque will only tend to lengthen or shorten 
all the rolling circumferences, without significantly changing their 
relative differences. 
The widthwise average of the actual stress distribution on each individual 
rib 11, 12, 13, 14 and 15 is important in understanding the improvements 
made by the invention. Typical tangential stresses in a lateral Y-axis 
direction are illustrated in FIG. 9 for a typical radial pneumatic tire 
having five ribs. Similarly, typical tangential stresses in a longitudinal 
X-axis direction are illustrated in FIG. 10. Stresses on the various ribs 
of a rolling and loaded tire are discussed in SAE Publication No. 740072. 
Stresses are those exerted on the tire by the ground surface in the 
contact patch resulting from the contact of the tire with the ground 
surface. The nonsymmetrical lateral stress distribution in the Y-direction 
shown in FIG. 9 results in unbalanced forces FY that produce a torque or 
moment TY about a Z-axis normal to the contact patch. The nonsymmetrial 
longitudinal stresses of FIG. 10 also result in unbalanced forces FX that 
produce a torque or moment TX about the Z-axis. The combined torque TY+TX 
at a zero slip angle is equal to the aligning torque TO illustrated in 
FIGS. 2 and 3. 
Of particular interest is the shape of the longitudinal stresses of FIG. 
10. A distribution of longitudinal stresses is noted which is typical of 
most rib type tread patterns. During initial contact, the stresses are 
driving (+X direction) and during final contact the stresses are braking 
(-X direction). A modification of this stress distribution will be 
discussed in more detail below. 
We have found that the inequality in rolling circumference between ribs, as 
illustrated in FIG. 8, can be used to introduce additional tangential 
force differences between respective ribs. These differences can be used 
to introduce an aligning torque T to a free rolling tire that essentially 
compensates for the tire's own residual aligning torque RAT. As seen in 
FIGS. 7 and 8, the rolling circumference is directly proportional to a 
rolling radius RC or RL of the respective rib. The inventors have 
discovered that an "effective rolling radius" of any circumferential row 
of blocks (ribs), can be changed by the inclination of the lateral grooves 
separating the adjacent blocks in a rib, as illustrated in FIG. 11. 
Therefore, in this invention, not all the tread blocks are disposed 
exactly radially, as shown in section A of FIG. 11, but some are angled 
forward or backward, as shown in section B of FIG. 11 and section C of 
FIG. 11 respectively, to provide a modified effective rolling radius 
(rolling circumference) for selected ribs. 
The modifications of the rolling circumference of a circumferential row of 
tread blocks, or rib, by the use of inclined lateral grooves, and thereby 
inclined tread blocks, takes advantage of a tendency for lifting or 
lowering of the ground contacting surface of the individual tread, as 
illustrated in FIGS. 12 and 13. Under the effect of longitudinal 
tangential stresses SX exerted by the ground at the entrance of the 
contact patch, the effective rolling circumference of a modified rib 50, 
60 of this invention is different from that of an unmodified rib 40. The 
lifting or lowering changes the rolling radius RR to an effective rolling 
radius R1, R2 for the circumferentially adjacent tread blocks 52, 62. 
The concept of using the tangential stress SX on inclined stress blocks to 
introduce a virtual or effective rolling radius is introduced in this 
invention. The actual rolling radius RR is the distance from the axis of 
rotation to the ground surface and the rolling circumference of the whole 
tire is equal to 2 .pi.RR. The effective rolling radius of various ribs in 
introduced to help understand the nature of the tangential stresses or 
forces on the contact patch of the tire from the ground surface supporting 
the tire. 
To investigate the potential from effective rolling radius changes, a tire 
can be modified to have all its tread blocks inclined in one direction 
(say 5 degrees). Rolling this tire in one direction the revolutions per 
mile are measured and a first actual rolling radius computed. Reversing 
the rotation of the tire, the revolutions per mile are again measured and 
a second actual rolling radius computed. The actual rolling radius with 
tread blocks sloped forward as viewed from the top of the tire are 
anticipated to be approximately 3 percent greater than the actual rolling 
radius with tread blocks sloped backward. 
The validity of this discovery was also confirmed by actual measurements of 
the longitudinal tangential stresses between tire and ground on each rib 
of the tread pattern. By selecting the appropriate centerline draft angles 
for the lateral grooves between adjacent pairs of blocks in preselected 
circumferential rows of blocks, or ribs, of the tread pattern, it was 
found possible to introduce a compensating aligning torque that 
essentially eliminates all the residual aligning torque between the tire 
and the ground surface for a freely rolling tire. A centerline draft angle 
is defined herein as the inclination of the lateral groove centerline E 
from a plane R extending radially from the axis of rotation A. Draft 
angles are measured in a plane parallel to the midcircumferential plane M 
of the tire. 
The selection of the centerline draft angles of the lateral grooves can be 
made by the use of computer modeling or by actually measuring changes in 
the longitudinal tangential stress SX exerted by the ground on each 
circumferential rib (FIG. 16 for example). Analyzing the results, it is 
simple to decide in which direction the centerline draft angle of each 
lateral groove in a rib of the tread pattern should be inclined to obtain 
a desired rolling radius change. 
The illustrations of FIG. 11 show the three possible conditions that can 
exist on an individual rib. Each condition represents a different 
inclination for lateral groove centerlines E, E1, E2 from the radial plane 
R, R1, R2 in a plane parallel to the midcircumferential plane M of the 
tire. The condition illustrated in section A of FIG. 11 shows a rib 40 
having a zero centerline draft angle for the lateral groove 44, and the 
tread block 42 is not inclined. This condition is typical, within 
manufacturing tolerances, of the standard T&RA tire. The condition 
illustrated in section B of FIG. 11 shows a rib 50 having a centerline 
draft angle D1 for the lateral groove 54, and the tread block 52 is 
inclined forward with an angular rotation W of the tire. The condition 
illustrated in Section C of FIG. 11 shows a rib 60 having a centerline 
draft angle D2 for the lateral groove 64, and the tread block 62 is 
inclined backward during angular rotation W. 
Generally speaking, the tread blocks 62 of the rib 60 are inclined backward 
from the direction of rotation to decrease the effective rolling radius 
from RR to R2 as illustrated in FIG. 13. Conversely, blocks 52 of the rib 
50 are inclined forward from the direction of rotation to increase the 
effective rolling radius from RR to R1 as illustrated in FIG. 12. This 
effective rolling radius increase on rib 11 of the tire of FIG. 7, for 
example, will increase its rolling circumference from a value of CL to a 
larger value C1 (FIG. 8). This increase will reduce the braking force FX11 
of rib 11. An effective rolling radius decrease on rib 15 of FIG. 7, for 
example, will decrease the rolling circumference from a value of CR to a 
smaller value C2. This decrease will increase the braking force FX15 of 
rib 15. 
As previously disclosed, forward and backward inclined tread blocks are 
formed by inclining a centerline axis E of the lateral grooves with 
respect to a plane R extending radially from the axis of rotation of the 
tire as shown in FIG. 11. Forward and backward inclined tread blocks are 
also related to the direction of rotation W of the tire about its axis of 
rotation A. Forward inclined tread blocks 52 have an acute angle D1 to the 
centerline axis E1 of the lateral groove 54 from the radial plane R of the 
tire in the same (clockwise or counterclockwise) direction as the rotation 
of the tire W about its axis of rotation A. Conversely, backward inclined 
tread blocks 62 have an acute angle D2 to the centerline axis E2 of the 
lateral groove 64 from the radial plane R of the tire in an opposite 
direction to the rotation W of the tire about its axis of rotation A. 
The preferred values of the centerline draft angles D1 or D2 of the lateral 
grooves 54, 64 are influenced by many variables, such as the transverse 
crown radius of the tire, the construction of the belt package plies, the 
modulus of the tread rubber, the contact surface ratio of the tread 
pattern and of course the shape, size and siping of individual tread 
blocks. However, an experimental procedure has been developed to determine 
the preferred centerline draft angles for each type of tire. A detailed 
experimental procedure or method is disclosed later in this discussion. 
Such a method is very convenient, and takes only a few hours. Using this 
method, the definition and magnitude of centerline draft angles can be 
determined in a relatively short period of time. 
To achieve the effect of centerline draft angles it is necessary that the 
width of the lateral grooves be such that each individual tread block 52 
or 62 has the flexibility to be pushed backward or forward, and thus 
effectively change height, while its ground contacting surface remains 
sensibly in the plane of the ground surface at the contact patch. The 
sidewall and bottom configuration of lateral grooves is not critical to 
achieve the improvements disclosed in this invention. The configuration of 
two typical lateral grooves 56 and 66 in a plane parallel to the 
midcircumferential plane M are illustrated in FIGS. 14 and 15. The 
sidewalls 57 or 67 may be converging or parallel respectively, with either 
a bottom contour 58 having a single radius or a bottom contour 68 having 
multiple radii. A line which bisects two respective sidewalls is the 
centerline E of the lateral groove. The total centerline draft angle D of 
the lateral groove centerline E from the radial plane R is the structural 
feature that is varied to change the effective rolling radius of a rib. In 
addition, the angle between sidewalls 57 or 67 and their respective 
surfaces 59 and 69 have only limited influence on the residual aligning 
torque and correction procedure disclosed in this invention. 
Siping in the tread blocks 52, 62 are usually not wide enough to allow 
effective rolling radius changes before the adjacent blocks come into 
contact. Also, friction between sipe defined contacting blocks frequently 
locks them together, cancelling the effect to be achieved. If inclined 
sipes are placed in a tread block which is delimited by radial grooves, 
the effect of the inclined sipes on the rolling circumference of the rib 
is usually negligible and not predictable. 
A further explanation of the influence of centerline draft angles is 
illustrated in FIG. 16. This illustration shows the longitudinal 
tangential stresses SX on the two unmodified lateral ribs 1 and 5 (solid 
line) previously shown in FIG. 10, and the new stresses SX as a result of 
centerline draft angles on the same lateral ribs after being modified 
(dashed line). The lateral rib 1 of this example has centerline draft 
angles to provide an effective increase in the rolling radius by sloping 
the tread blocks forward. The initial longitudinal force FX1 resulting 
from the stresses shown by the solid line has been modified by the stress 
changes to new stresses shown by the dashed line. The result is a change 
FX1 in longitudinal force FX1 (FIG. 16(a)). The other lateral rib 5 of 
this example has centerline draft angles to provide an effective decrease 
in the rolling radius by sloping the tread blocks backward. The initial 
longitudinal force FX5 resulting from the stresses shown by the solid line 
has been modified by the stress changes to new stresses shown by the 
dashed line. The result is a change FX5 in longitudinal force FX5 (FIG. 
16(b)). If centerline draft angles are selected equal on the two sides of 
a symmetrical tread pattern, force changes FX1 and FX5 will be 
approximately equal and opposite in direction. No changes in driving or 
braking forces are expected using equal centerline draft angles which are 
symmetrically positioned. The resulting force changes introduce an 
aligning torque T that compensates for the original RAT of the unmodified 
tire. 
The result of having one rib 50 on one side of the midcircumferential plane 
M with forward inclined tread blocks (FIG. 12) and the other rib 60 on the 
other side of the midcircumferential plane M with backward inclined tread 
blocks (FIG. 13) will produce an effective rolling radius R1 on the former 
side larger than another effective rolling radius R2 on the latter side of 
the tire, as previously disclosed. This configuration of the tire 
effectively introduces a condition where the rolling circumference C1 on 
one rib of the tire is larger than the rolling circumference C2 on another 
rib of the tire, as shown in FIG. 8. This is similar to providing an 
effective conicity. However, a conicity force C is always extended in the 
same lateral direction for clockwise and counterclockwise rotation of the 
tire as illustrated in FIG. 2(C). This is not the condition with the tire 
of this invention. For example, a modified rib having forward inclined 
tread blocks being a first rib increases its rolling circumference, and 
another modified rib having backward inclined tread blocks of a second rib 
decreases its rolling circumference. A change in the direction of rotation 
of the tire would cause the first rib to have its tread blocks inclined 
backward (thus decreasing its rolling circumference) while the second rib 
would have its tread blocks inclined forward (thus increasing its rolling 
circumference). However, this change in direction of rotation would not 
reverse the direction of the induced torque T. Hence, this torque T could 
again help compensate the residual aligning torque RAT, as previously 
disclosed. 
The ribs having a greater influence on the aligning torque as a result of 
changing their effective rolling radius (rolling circumference) are the 
lateral ribs of the tread pattern. This is due to the larger axial 
distances "d" to the ribs from the midcircumferential plane M. For 
example, the contact patch of a tread 70 is shown in FIG. 17. The change 
in longitudinal tangential force FX of a lateral rib 50 or 60 times a 
moment arm d gives a torque FX.times.d about the Z-axis. This induced 
torque T can compensate for the residual aligning torque RAT inherent in 
the construction and tread pattern of the tire. Using both lateral ribs 50 
and 60 with tread blocks 52 of one rib 50 inclined forward and tread 
blocks 62 of the other rib 60 inclined backward, the induced torque T 
about the Z-axis is even greater, being the combined sum of the individual 
lateral rib force changes or T=FX.times.2d. The other ribs 72, 73 and 74 
shown in FIG. 17 have tread blocks 42 with zero centerline draft angles in 
the lateral grooves 44. 
It is within the scope of this invention to modify the tread to have 
centerline draft angles D in lateral grooves of ribs other than the two 
lateral ribs. Whereas, the modification to have centerline draft angles on 
lateral ribs is preferred, there may be other performance parameters, such 
as tread wear, that make intermediate rib modifications more suitable. For 
example, the contact patch of a tread 80 having two intermediate ribs 82, 
84 with lateral grooves 54, 64 having centerline draft angles D1, D2 is 
illustrated in FIG. 18. Rib 82 has draft angle D1 (FIG. 12) in the lateral 
grooves 54 to give tread blocks 52 which are inclined forward during 
forward motion V of the vehicle. Rib 84 has draft angle D2 (FIG. 13) in 
the lateral grooves 64 to give tread blocks 62 which are inclined backward 
during forward motion V of the vehicle. The resulting change in 
longitudinal forces FX times the moment arm 2e gives an induced torque 
T=FX.times.2e to help compensate for the residual aligning torque RAT of 
the tire. The other ribs 81, 83 and 85 shown in FIG. 18 have radial tread 
blocks 42 with zero centerline draft angles in the lateral grooves 44. 
Sections A, B and C in FIGS. 17 and 18 refer to the partial rib sections 
of FIGS. 11(A) and 11(B) and 11(C) respectively. The induced torque T 
using intermediate ribs with centerline draft angles has been found to be 
about one fourth as effective as using centerline draft angles within 
lateral ribs. 
Relatively small changes in the residual aligning torque RAT can be 
realized by incorporating draft angles in the center rib of tread patterns 
having a center rib. However, the moment arm (d and e in the previous 
examples) is essentially zero in such cases and changes in the rolling 
circumference of center rib 3 alone (FIG. 8) does not induce a torque T. 
A combination of modifications in the centerline draft angles of the 
lateral grooves of both the lateral and intermediate ribs is within the 
scope of this invention. If the residual aligning torque RAT is large, it 
may be desirable to modify the draft angles in all the lateral grooves to 
provide a first plurality of tread ribs formed on a first side of the 
midcircumferential plane and a second plurality of tread ribs formed on a 
second side of said midcircumferential plane. Using this invention, a 
person skilled in the art may select lateral ribs, intermediate ribs or 
both to essentially eliminate the residual aligning torque RAT by 
modifying the tread to have centerline draft angles within the lateral 
grooves. 
A relationship can be established and used to determine the preferred 
centerline draft angles to essentially eliminate the residual aligning 
torque RAT. For example, a 4 or 5 rib symmetrical tread pattern (for 5 
ribs see FIG. 5) of a non-directional tire can be characterized by the 
following relationships: 
G1=G5 (lateral groove angle for ribs 1 and 5 in the contact patch); 
G2=G4 (lateral groove angle for ribs 2 and 4 in the contact patch); and 
D1=D2 (equal and opposite centerline draft angles symmetrically 
positioned). 
As previously mentioned, the center rib 3 with its lateral groove angle G3 
(FIG. 5) has little influence on the residual aligning torque RAT. In a 
preferred embodiment of this invention, lateral grooves of a center rib 3 
are not modified. 
The modified residual aligning torque RAT on the tire of this invention at 
a neutral slip angle AA, can be formulated as 
##EQU1## 
where TC is the aligning torque in Newton meters due to the overall tire 
construction, D1 is the centerline draft angle in degrees. The two terms 
K.sub.1 .times.G1 and K.sub.2 .times.G2 are aligning torques in newton 
meters due to the tread pattern lateral groove angles G1=G5 and G2=G4 and 
K.sub.3 is an experimentally determined system constant (Nm/deg) for the 
tire and tread. The first three terms on the right are the unmodified 
tread's residual aligning torque RAT as previously disclosed and 
illustrated in FIG. 3. That is, 
EQU RAT=TC+K.sub.1 .times.G1+K.sub.2 .times.G2=(TR+TL)/2 
Therefore, the modified residual aligning torque RAT becomes 
##EQU2## 
The system constant K.sub.3 is determined experimentally using the 
following steps: 
a) a test tire is made having a predetermined tread pattern wherein all 
centerline draft angles have D1=0; 
b) the value of RAT.sub.1 is determined experimentally at a neutral slip 
angle AA as previously defined, see FIG. 3, where RAT.sub.1 =RAT as D1=0. 
c) another test tire is made having the same tread pattern as in (a) but 
having a relatively large centerline draft angle D1 (for example 10 
degrees); 
d) a new value of RAT.sub.2 at a neutral slip angle AA is experimentally 
determined as in (b) above; and 
e) the system constant K.sub.3 is calculated from the relationship 
##EQU3## 
We know that the desired value for the modified residual aligning torque 
RAT is zero. That is, 
EQU RAT=0=RAT+K.sub.3 .times.D1. 
This equation can be solved for the final centerline draft angle D1 (where 
D1 is equal and opposite to D2). Draft angle D1 is the draft angle which 
essentially eliminates the residual aligning torque at a neutral slip 
angle AA. 
The desired draft angle is then calculated as 
##EQU4## 
Tires are then manufactured with these draft angles and evaluated to prove 
the validity of the modifications. 
The steps outlined above are as illustrated in FIG. 19. At centerline draft 
angles equal to zero the residual aligning torque RAT is equal to the 
value RAT.sub.1. At a second value of the centerline draft angle D1, D2 
the residual aligning torque has a value RAT.sub.2. These two values are 
used to calculate the slope of the residual aligning torque RAT vs. draft 
angle D1, D2 curve. The constant slope is referred to as the system 
constant K.sub.3. Numerous experimental tests have been conducted which 
verify the linear relationship between the modified residual aligning 
torque and centerline draft angles. This fact allows the single linear 
term K.sub.3 .times.D1 to be used in the formulation above for the 
symmetrical tread with two modified ribs. 
This analytical/experimental method can be expanded, for example, to 
determine modifications for two symmetrical pairs of two ribs each having 
lateral grooves with centerline draft angles. In this example, the ribs 
are preferably symmetrical with respect to a midcircumferential plane of 
the tire. This is illustrated by combining the features of one centerline 
draft angle for the lateral grooves of two symmetrically positioned two 
lateral ribs (FIG. 17) and another centerline draft angle for the lateral 
grooves of two symmetrically positioned intermediate ribs (FIG. 18). To 
introduce this into the modified residual aligning torque RAT equation, 
the term +K.sub.4 .times.D3 is added to the right side of the initial 
equation. For example, in FIG. 17 the centerline draft angle D3 is the 
draft angle for the lateral grooves of rib 72, which is equal and opposite 
to the centerline draft angle D4 for the lateral grooves of rib 74. 
Centerline draft angle D3 has the same orientation to the radial plane R 
as the centerline draft angle D1, and centerline draft angle D4 has an 
opposite orientation to the radial plane R. The system constant K.sub.4 
(Nm/deg) is also determined experimentally. 
To determine system constant K.sub.4 requires additional steps in the 
procedure outlined above. First, a second smaller centerline draft angle 
(for example D1=D3=5 degrees) is carved into a modified but identically 
constructed tire having the same tread pattern. Then, the above step (c) 
should be performed with D1 and D3 both having a first relatively large 
centerline draft angle (for example 10 degrees) before RAT.sub.2 is 
determined. Next, a third value of the modified residual aligning torque 
RAT.sub.3 is experimentally determined with this second centerline draft 
angle. Finally, the system constants K.sub.3 and K.sub.4 are determined by 
solving the equations 
EQU RAT.sub.1 =RAT, D1=D2=D3=D4=0 
EQU RAT.sub.2 =RAT+K.sub.3 .times.D1+K.sub.4 .times.D3 
EQU RAT.sub.3 =RAT+K.sub.3 .times.D1+K.sub.4 .times.D3 
The system constants K.sub.3, K.sub.4, are used in the original equation, 
wherein the modified residual aligning torque is made essentially zero. 
That is, 
EQU RAT=0=RAT+K.sub.3 .times.D1+K.sub.4 .times.D3. 
In this case, either the value of D1 or D3 can be selected and the 
remaining value determined to provide the desired RAT=0. Selection of one 
or the other centerline draft angles, D1 or D3, may be based on the 
performance requirements of the tread, such as uniform wear or a need to 
maintain water evacuation through the lateral grooves. 
This same analytical and experimental approach can be used for a 
directional tire having an asymmetrical tread pattern. However, the 
residual aligning torque and associated vehicle drift problems with 
directional tires having asymmetrical tread patterns are generally not as 
amplified as with symmetrical tread patterns. Furthermore, asymmetrical 
tread patterns can be selected to more effectively reduce the RAT. This is 
due to the type of asymmetrical tread patterns used and the mounting 
limitations placed on tires with directional requirements. The method of 
this invention would require more experimental testing and evaluation for 
some asymmetrical tread patterns. In addition, it may be more difficult to 
define two symmetrically positioned ribs from a midcircumferential plane 
which can have draft angles D1 and D2 respectively. However, it is within 
the scope of this invention to apply the teachings herein to asymmetrical 
tread patterns and directional tires. 
Centerline draft angles have been determined for a variety of tire sizes 
and tire lines using the method of this invention. For example, centerline 
draft angles were used on the two lateral ribs of a 195/60 R15 Michelin 
MX4 tire. The tread pattern and construction had an initial residual 
aligning torque RAT of 1.4 Newton meters at a neutral slip angle AA of 
0.26 degrees (See FIG. 3). A centerline draft angle for each lateral 
groove on one lateral rib was determined to give forward inclined tread 
blocks 52 (FIG. 11(B)). A centerline draft angle for the lateral grooves 
on another lateral rib was determined to give backward inclined tread 
blocks 62 (FIG. 11(C)). It was found that centerline draft angles of 4 
degrees substantially compensated for the residual aligning torque RAT of 
the unmodified tire to the extent that the modified residual aligning 
torque RAT was equal to only 0.1 Newton meters. 
Considerable experimental evidence has been collected to verify the utility 
of this invention. Tires of various size and shape have been modeled and 
tested with nonzero centerline draft angles in lateral grooves of various 
circumferential ribs. The residual aligning torques of these tires have 
been compensated by the induced torque T using this invention. Centerline 
draft angles in a range of about 3 to 15 degrees have compensated for RAT 
when two symmetrical positioned lateral ribs alone were used. When four or 
more symmetrical ribs have nonzero centerline draft angles in their 
lateral grooves, the range of centerline draft angles was from about 2 to 
12 degrees to compensate for the RAT. Without symmetry of two modified 
ribs from the midcircumferential plane M, centerline draft angles of from 
about 2 to 20 degrees can be effectively used. 
The magnitude of the centerline draft angles D required to produce an 
induced torque T to compensate for the residual aligning torque RAT 
depends somewhat on the effectiveness of the tread pattern in reducing RAT 
without modifying the tread to have nonzero draft angles. For example, the 
lateral grooves G1-G5 of the tread pattern illustrated in FIG. 5 have an 
independent influence. This was modeled in the analysis above as K.sub.1 
.times.G1+K.sub.2 .times.G2. Studies have shown that the centerline draft 
angles can be expressed as a percentage of the angle between the lateral 
groove axial centerline at the tread surface separating adjacent tread 
blocks in a rib and the midcircumferential plane (lateral groove angle). 
The practical limit on this angle for most tires is 60 to 150 degrees as 
illustrated in FIG. 5, for example. Centerline draft angles in a range of 
about 2 to 30 percent of the lateral groove angle have been verified by 
analysis. 
From the above description of the invention, those skilled in the art will 
perceive improvements, changes and modifications. Such improvements, 
changes and modifications within the skill of the art are intended to be 
covered by the appended claims.