Heavy duty radial tire carcass profile

A heavy duty radial tire includes at least one radial carcass extending from one bead portion to the other bead portion and using inextensible cords and a belt arranged outwardly of the radial carcass for reinforcing a tread of the tire. The tire comprises, during expanding of the tire from 5% to 100% of a normal inner pressure, a first profile portion expanding radially outwardly in a tread zone, a second profile portion depressing axially inwardly of the tire in a radially outer zone of a sidewall from one end of said tread to a tire maximum width position when filled with the normal inner pressure, and a third profile portion expanding axially outwardly of the tire in a radially inner zone of the sidewall from the tire maximum width position when filled with the normal inner pressure to a parting point of the sidewall from the rim, thereby properly distributing strains occurring in the tire in filling with the normal inner pressure.

BACKGROUND OF THE INVENTION 
This invention relates to a pneumatic radial tire and more particularly to 
a heavy duty radial tire for trucks or buses, whose durability is improved 
by preventing separations occurring at ends of a belt for reinforcing a 
tread and at ends of carcass plies for principally reinforcing the tire. 
In order to improve the durability of bead portions of pneumatic radial 
tires, techniques of turn up of carcass plies and materials and 
constructions of chafers or stiffeners as reinforcements have been 
generally investigated. However, with all proposed solutions, applications 
are limited to tires of same particular sizes although they are relatively 
effective for tires of some limited sizes. Moreover, proposed solutions 
sometimes tend to increase costs of tires. Therefore, a fundamental 
solution has not been provided yet. 
In order to obtain required performances of tires, in general, carcass 
configurations have been determined so as to expand uniformly when filled 
with inner pressure. The equilibrium configuration curve of a carcass line 
of a tire has been used in this industrial field, which is based on the 
so-called "natural equilibrium theory" assuming that carcass cords are not 
extensible and deformations of the tire are not affected by inner 
pressures. A carcass of such a tire is uniformly subjected to tensile 
forces and therefore its various performances are good. However, such a 
tire is a theoretical one which could not exist in fact. It is considered 
that an actual tire which approximates to such a theoretical tire as much 
as possible can be obtained by making the actual tire which uniformly 
inflates or is similar in figure before and after the inflation. An actual 
tire obtained in this manner has a "natural equilibrium shape" of a 
carcass. In the following publications disclosed hitherto measures for 
controlling the change in shape of tires when they are filled with inner 
pressure have been employed. 
In U.S. Pat. No. 4,155,392, when a tire is being filled with inner 
pressure, maximum width portions of the tire are displaced radially 
inwardly to reduce tensile strains occurring in sidewalls, thereby 
improving the durability of the life of the tire referring to FIG. 3 of 
the U.S. Pat. No. 4,155,392. In this case, however, parts of a tread and 
shoulders are also moved axially and radially inwardly to reduce initial 
tensions acting upon a belt of the tire so that moving performances of the 
tire and durability at ends of the belt are detrimentally affected. 
U.S. Pat. No. 4,481,994 discloses a technique similar to the measure 
disclosed in the above United States Patent specification. In this case, 
portions extending from ends of a belt to shoulders are also moved axially 
and radially inwardly of a tire when filling normal pressure. As a result, 
initial tensions of the belt become small which detrimentally affect 
various performances of the tire. 
Moreover, U.S. Pat. No. 4,513,802 discloses a feature of changing a tire 
configuration to reduce the rolling resistance of a tire. In this case, 
however, as radially outward portions of sidewalls outwardly expand when 
filling normal inner pressure, expanding deformations are insufficient in 
bead portions and tread portion. Therefore, strain distributions in the 
tire resulting from the expanding deformations are improper and therefore 
sufficient durability for heavy duty tires is not obtained. 
SUMMARY OF THE INVENTION 
It is a principal object of the invention to provide a heavy duty pneumatic 
tire whose durability at bead and belt portions is effectively improved 
without detrimentally affecting other portions of the tire. 
In order to accomplish this object, in a heavy duty radial tire including 
at least one radial carcass extending from one bead portion to the other 
bead portion and using inextensible cords and a belt arranged outwardly of 
the radial carcass for reinforcing a tread of the tire according to the 
invention, the improvement comprises an outer profile of the tire in 
radial cross-sections mounted on an approved rim whose width is not wider 
than that of a design rim and under no load condition during filling inner 
pressure from 5% to 100% of a normal inner pressure, said outer profile of 
the tire comprising a first profile portion expanding radially outwardly 
in a tread zone from one end of said tread through a crown center to the 
other end of said tread, a second profile portion depressing axially 
inwardly of the tire at least in a part of a radially outer zone of a 
sidewall from said one end of said tread to a tire maximum width position 
when filled with the normal inner pressure, and a third profile portion 
expanding axially outwardly of the tire in a radially inner zone of said 
sidewall from said tire maximum width position when filled with the normal 
inner pressure to a parting point of the sidewall from said rim, thereby 
properly distributing strains occurring in the tire in filling with the 
normal inner pressure. 
The invention by which a useful improvement of the heavy duty radial tire 
is accomplished resides in the discovery that strain distributions in the 
tire suitable for improving the durability of the tire can be obtained by 
a novel and excellent measure for controlling the change in configuration 
of the tire when it is filled with inner pressure. 
In order that the invention may be more clearly understood, preferred 
embodiments will be described, by way of example, with reference to the 
accompanying drawings.

DESCRIPTION OF THE PREFERRED EMBODIMENTS 
FIGS. 1 and 2 illustrate heavy duty radial tires of different sizes 
according to the invention. In each drawing, solid lines illustrate 
carcass path lines 1 and a tire profile 2 determined thereby in a radial 
cross-section under a standard status when the tire mounted on a rim is 
filled with an inner pressure 5% of a normal inner pressure. A belt on a 
carcass for reinforcing a tread is arranged in lamination embedded in a 
tread of the tire substantially over an overall width of the tread in 
substantially the same manner as in tires of the prior art although the 
belt is not shown in order to avoid a complication caused by deformations 
of the tire. 
The standard status of a tire is defined herein by the change in 
configuration or the condition when filled with the slight pressure for 
reason that it is necessary for the present invention to keep 
configurations of the tire and carcass in any radial cross-sections when 
the tire formed and vulcanized in a mold is mounted on a design rim among 
approved rims with a narrowed distance between beads of the tire or a rim 
having a width not wider than that of the design rim. 
In case that a tire is difficult to fit on a rim or a tire is considerably 
deformed due to piled or stored conditions, after the tire is filled with 
normal inner pressure and kept for more than twenty four hours, the inner 
pressure is exhausted to 5% of the normal inner pressure. When carcass 
deformations of tires are extreme due to stored conditions, the inner 
pressure is exhausted to 5% of the normal inner pressure after removing 
particularly deformed shapes by running of several tens km. In this 
manner, a precise standard shape of the tire is obtained. The status of 
the tire at this moment, which keeps configurations of the tire and the 
carcass can be used a standard status. 
In FIGS. 1 and 2, solid lines illustrate carcass path lines 1 and 2 when 5% 
of normal inner pressure is filled and broken lines illustrate carcass 
path lines 1' and tire profiles 2' when normal inner pressure is filled. 
The distinctive feature of the deformed tire configuration according to 
the invention is clearly evident from these solid lines 1 and 2 and broken 
lines 1' and 2'. It is clearer in comparison with FIG. 3 illustrating a 
deformed status of a comparison tire formed in so-called "natural 
equilibrium configuration" according to the prior art. 
According to the invention, a substantially uniform expansion g occurs 
radially outwardly of the tire on a tread 5 from one end 4 of a ground 
contact surface through a tread center 3 to the other end (not shown) of 
the ground contact surface, while a depression d occurs axially inwardly 
of the tire over at least part of a radially outer zone 7 of a sidewall 
from the end 4 of the ground contact surface to a tire maximum width 
position 6 after filled wiht the normal inner pressure. Moreover, an 
expansion f occurs axially outwardly of the tire over a radially inner 
zone of the sidewall from the tire maximum width position 6 to a point 8 
where the sidewall leaves a rim flange or a parting point of the sidewall 
from the rim flange. 
As can be seen from the drawings, we now consider one half of a tire. For 
example, therefore, we mentioned the sidewall as single although one tire 
includes two sidewalls. 
There are the outward expansions at the tread portion 5 and the radially 
inner zone of the sidewall and the inward depression at the radially outer 
zone 7 in this manner when the tire is filled with the normal inner 
pressure according to the invention. The particular change in 
configuration according to the invention is accomplished by utilizing the 
following general properties: 
(1) The tire tends to expand as a whole, 
(2) The carcass configuration tends to approach a natural equilibrium 
configuration, 
(3) If substantially inextensible cords are used for carcass cord, the 
carcass does not extend very well, and 
(4) The deformations of the carcass by the filling of the inner pressure 
are caused as a chain reaction. A deformation does not occur in only one 
part. 
In this manner, the carcass line of the tire mounted on a rim and filled 
with the inner pressure 5% of the normal inner pressure is located in the 
tread portion 5 inside the carcass line or the equilibrium configuration 
curve of the tire filled with the normal inner pressure. The carcass line 
in the radially outer zone 7 of the sidewall has a larger curvature than 
that of the carcass line of the equilibrium configuration curve and 
located outside the carcass line of the naturally equilibrium 
configuration of the tire when filled with the normal inner pressure. 
Moreover, the carcass line from the radially inward zone 9 of the sidewall 
to the bead portion is located considerably inside the carcass line of the 
equilibrium configuration curve of the tire when filled with the normal 
inner pressure. Further, substantially inextensible cords such as steel 
cords and aromatic polyamide cords are used for the carcass plies so that 
when filled with the normal inner pressure, the carcass line is inwardly 
depressed in the radially outer zone of the sidewall and in connection 
therewith is greatly expanded outwardly in the crown portion and the 
radially inner zone. 
For example, in case that the radially outer zone of the sidewall is 
similar to the naturally equilibrium configuration, the carcass in this 
zone is expanded or substantially not deformed so that the expansion 
required in the crown zone and the great expansion in the radially inner 
zone of the sidewall could not be accomplished. Therefore, the strain 
distribution required for the improvement of the durability could not be 
realized. 
In practice, the particular change in configuration can be easily obtained 
by ensuring the configuration of the carcass when the tire mounted on a 
rim is filled with 5% of the normal inner pressure on the basis of 
limitations of the present invention as explained hereinafter. 
The carcass configurations when tires are filled with inner pressure 5% of 
the normal inner pressure are defined separately on the tires of a tube 
type to be mounted on 5.degree. flat base rims whose bead seats engaging 
bead portions of the tires make approximately 5.degree. with rotating axes 
of the tires and tires of tubeless type to be mounted on 15.degree. drop 
center rims whose bead seat make approximately 15.degree. with rotating 
axes of the tires, respectively, because lengths of flanges of the rims of 
the two kinds are different in radial directions so that distances from 
the rotating axes of the tires to respective reference points of the tires 
are different. 
With a heavy duty radial tire mounted on a rim having a bead seat inclined 
at a degree of 5.degree. relative to a rotating axis of the tire, 
according to the invention, a carcass profile in the radial cross-sections 
of the tire mounted on the approved rim and filled with an inner pressure 
5% of the normal inner pressure and under no load condition is a composite 
curve smoothly passing through points B, A and D, where the point A is an 
intersection of a carcass line C of the carcass profile with a tangent mm' 
in a radial direction to the carcass line at a carcass line maximum width 
position and the points B and D are intersections of the carcass line C 
and a perpendicular pp' to a bead base line RL, the perpendicular pp' 
spaced apart axially outwardly from an equatorial plane M of the tire by a 
distance of 0.45 times a rim width W corresponding to a distance between 
flanges of the rim, and the carcass profile fulfills three relations, a 
first relation 5&lt;240/H.times.u&lt;35, where u is a distance from the point A 
to a point E, where the point E is a point of contact where said tangent 
mm' contacts an equilibrium configuration curve N passing through the 
points B and D, and H is a maximum height of the carcass line C from the 
bead base line RL, a second relation 5.0&lt;240/H.times.S&lt; 13.0, where S is a 
maximum distance of the carcass line C spaced inwardly from the 
equilibrium configuration curve N in the radial inner zone of the 
sidewall, and a third relation 2.0&lt;240/H.times.t&lt;10.0, where t is a 
maximum distance of the carcass line C spaced outwardly from the 
equilibrium configuration curve N in the radial outer zone of the 
sidewall. 
As illustrated in FIG. 1 a carcass configuration in a radially inner zone 
of the sidewall between a bottom end N on the carcass inflated line of a 
perpendicular to that line to the tire maximum width position 6 and a 
bottom end N is either a straight line or a curved line having a center of 
curvature when the tire is filled to 5% of normal inflation pressure. 
With a heavy duty radial tire tire mounted on a rim having a bead seat 
inclined at a degree of 15.degree. relative to a rotating axis of the 
tire, according to the invention, a carcass profile in the radial 
cross-sections of the tire mounted on the approved rim and filled with an 
inner pressure 5% of the normal inner pressure and under no load condition 
is a composite curve smoothly passing through points B, A and D. The point 
A is a point of contact of a carcass line C of the carcass profile with a 
tangent mm' in a radial direction to the carcass line at a carcass line 
maximum width position. The points B and D are intersections of the 
carcass line C and a perpendicular pp' to a bead base line RL, said 
perpendicular pp' spaced apart axially outwardly from an equatorial plane 
M of the tire by a distance of 0.45 times a rim width W corresponding to a 
distance between flanges of the rim. The carcass profile fulfills three 
relations first 5&lt;210/H.times.u&lt;25, where u is a distance from the point A 
to a point E, where the point E is a point of contact where said tangent 
mm' contacts an equilibrium configuration curve N passing through the 
points B and D, and H is a maximum height of the carcass line C from the 
bead base line RL, second 3.0&lt;210/H.times.S&lt;9.0, where S is a maximum 
distance of the carcass line C spaced inwardly from the equilibrium 
configuration curve N in the radial inner zone of the sidewall, and third 
1.0&lt;210/H.times.t&lt;5.0, where t is a maximum distance of the carcass line C 
spaced outwardly from the equilibrium configuration curve N in the radial 
outer zone of the sidewall. 
The equilibrium configuration curve N is indicated by the following 
equation following to the so-called "equilibrium configuration theory". 
##EQU1## 
where .PSI. is an angle made by a tangent on a profile line of a carcass 
and a line parallel to the rotating axis of the tire and located at a 
distance R from the rotating axis, 
R.sub.E is a distance from the rotating axis to a point E where the profile 
line of the carcass has the maximum width in a direction of the rotating 
axis, and 
R.sub.S is a distance from the rotating axis to a point S where a tangent 
to an extension of the equilibrium profile line becomes parallel to the 
rotating axis of the tire. 
An equilibrium profile line of the carcass passing through the carcass 
maximum width point E, points B and D and the tangent mm' (determined by 
the standard or the like) is shown in broken lines in FIGS. 5 and 6 as a 
reference line. In this case, the point B is located at a distance of 0.15 
H to 0.30 H from the rotating axis and the point D is at a distance of 
0.82 H to 0.98 H. The distance HE, illustrated in FIG. 1 from the turn-up 
end of the carcass ply is 10-35% of a maximum tire height SH measured from 
a bead base line when the tire is filled to its normal inflation pressure. 
FIGS. 7 and 8 illustrates carcass profiles in solid lines in radial 
cross-sections and equilibrium configuration curves of carcass in broken 
lines which pass through points B and D and contacts tangents of the 
carcass lines, when tires of the naturally equilibrium configurations of 
the prior art mounted on rims are filed with the inner pressure 5% of the 
normal inner pressure, which are tube and tubeless tires, respectively. 
The solid and broken lines are substantially coincident with each other 
and therefore it is clear that the tires of the prior art are designed on 
the basis of the equilibrium configuration curves. 
Referring to FIG. 5, according to the invention with a tire using a 
5.degree. flat base rim, a carcass line passes outside the line N of the 
equilibrium configuration in a radially outer zone of sidewalll within a 
range of 2.0&lt;240/H.times.t&lt;10.0, where t is the maximum deviation from the 
line N of the equilibrium configuration. In the radially outer zone of the 
sidewall, moreover, in order to obtain a larger curvature, a carcass 
profile maximum width point A, where a width of the carcass profile in the 
direction of the rotating axis of the tire is maximum, is located radially 
outwardly of a carcass profile maximum width point E of the equilibrium 
configuration by a distance u between the points A and E within a range of 
5.0&lt;240/H.times.u&lt;35. With this arrangement, it is possible to realize the 
sufficient outward expansion in the crown portion and the radially inner 
zones of the sidewalls and the sufficient inward depression in the 
radially outer zones of the sidewalls according to the invention when the 
tire is filled with the normal inner pressure. In the radially inner zone 
of the sidewall, furthermore, the maximum deviation s of the carcass 
profile from the line N of the equilibrium configuration is within a range 
of 5.0&lt;240/H.times.S&lt;13.0 according to the invention. This feature brings 
about a configuration tending to approach the equilibrium configuration 
when filled with the normal inner pressure in conjuction with the feature 
of the carcass line passing inside the equilibrium configuration, thereby 
improving the durability of the tire. 
Referring to FIG. 6 with a tire using a 15.degree. drop center rim, 
according to the invention, a carcass line passes outside the line N of 
the equilibrium configuration in a radially outer zone of a sidewall 
within a range of 1.0&lt;210/H.times.t&lt;5.0 where t is the maximum deviation 
from the line N of the equilibrium configuration. In the radial outer zone 
of the sidewall, moreover, in order to obtain a larger curvature, a 
carcass profile maximum width point A is located radially outwardly of a 
carcass profile maximum width point E of the equilibrium configuration by 
a distance u between the points A and E within a range of 
5.0&lt;210/H.times.u&lt;25. In this manner, it is possible to realize the 
sufficient outward expansion in the crown portion and the radially inner 
zone of the sidewall when filled with the normal inner pressure. In the 
radially inner zone of the sidewall, moreover, the maximum deviation s of 
the carcass profile from the line N of the equilibrium configuration is 
within a range of 3.0&lt;210/H.times.S&lt;9.0 according to the invention. This 
feature brings about a configuration tending to approach the equilibrium 
configuration when filled with the normal inner pressure in conjuction 
with the feature or the carcass line passing inside the equilibrium 
configuration, thereby improving the durability of the tire. 
With values of the t, s and u smaller than their minimum values, the 
sufficient change in configuration could not be obtained when filled with 
the normal inner pressure, so that the durability could not be improved. 
On the other hand, with values of the t, s and u larger than their maximum 
values, a deformation when filled with the normal inner pressure becomes 
excessive to increase shearing strains at ends of plies so that the 
durability of the tire lowers. 
With a heavy duty radial tire mounted on a rim having a bead base engaging 
said bead portions, said bed seat inclined at a degree of 5.degree. 
relative to a rotating axis of the tire, according to the invention, a 
carcass profile in the radial cross-sections of the tire mounted on the 
approved rim and filled with an inner pressure 5% of the normal inner 
pressure and under no load condition is a composite curve smoothly passing 
through points F, A and G, where the point A is a point of contact of a 
carcass line C of the carcass profile with a tangent mm' in a radial 
direction to the carcass line at a carcass line maximum width position and 
the points F and G are intersections of the carcass line C and a 
perpendicular ll' to a bead base line RL, the perpendicular ll' spaced 
apart axially outwardly from an equatorial plane M of the tire by a 
distance of 0.5 times a rim width corresponding to a distance between 
flanges of the rim, and the carcass profile fulfills three relations, a 
first relation 0&lt;240 /H.times.v&lt;3.5, where v is a maximum distance of the 
carcass line C spaced outwardly of a segment of line FI connecting the 
points F and I, where the point I is an intersection of the tangent mm' 
and a straight line jj' which is in parallel with a rotating axis of the 
tire and spaced from the bead base line RL by a distance LH of 0.55 times 
H, where H is a maximum height of the carcass line C from the bead base 
line RL, a second relation 4.0&lt;240/H.times.w&lt;9.5, where w is a maximum 
distance of the carcass line C spaced outwardly of an arc GI passing 
through the point G and contacting the tangent mm' at the point I, and a 
third relation 15&lt;240/H.times.x&lt;35, where x is a distance between the 
points A and I. 
With a heavy duty radial tire mounted on a rim having a bead seat inclined 
at a degree of 15.degree. relative to a rotating axis of the tire, 
according to the invention, a carcass profile in the radial cross-sections 
of the tire mounted on the approved rim whose and filled with an inner 
pressure 5% of the normal inner pressure and under no load condition is a 
composite curve smoothly passing through points F, A and G, where the 
point A is a point of contact of a carcass line C of the carcass profile 
and a tangent mm' in a radial direction to the carcass line at a carcass 
line maximum width position and the points F and G are intersections of 
the carcass line C and a perpendicular ll' to a bead base line RL, the 
perpendicular ll' spaced apart axially outwardly from an equatorial plane 
M of the tire by a distance of 0.5 times a rim width corresponding to a 
distance between flanges of the rim, and the carcass profile fulfills 
three relations, first 0&lt;210/H.times.v&lt;5.0, where v is a maximum distance 
of the carcass line C spaced outwardly of a segment of line FI connecting 
the points F and I, where the point I is an intersection of the tangent 
mm' and a straight line jj' which is in parallel with a rotating axis of 
the tire and spaced from the bead base line RL by a distance LH of 0.55 
times H, where H is a maximum height of the carcass line C from the bead 
base line RL, second 2.0&lt;210/H.times.t&lt;8.0, where t is a maximum distance 
of the carcass line C spaced outwardly of an arc GI passing through the 
point G and contacting the tangent mm' at the point I, and third 
6.0&lt;210/H.times.x&lt;30.0, where x is a distance between the points A and I. 
FIGS. 9 and 10 illustrate carcass lines of tires of preferable embodiments 
of the invention in section using 5.degree. flat base rim and 15.degree. 
drop center rim, respectively. On the other hand, FIGS. 11 and 12 
illustrate tires of the equilibrium configuration of the prior art the 
same in size as those shown in FIGS. 9 and 10. In FIGS. 11 and 12, a 
difference between the carcass line of the tire of the prior art and an 
arc GI is small so that the arc GI substantially indicates the carcass 
profile of the tire of the prior art. On the other hand, the carcass 
profile is greatly deviated from a straight line FI in the zone from the 
radially inner area of the sidewall to a bead portion as shown in FIGS. 11 
and 12 illustrating tires of the prior art. 
In contrast herewith, according to the embodiment of the invention a 
carcass line of a tire using a 5.degree. flat base rim is deviated in the 
radially outer zone of the sidewall outwardly from a reference line (arc 
.solthalfcircle.GI) indicating the carcass line of the tire of the prior 
art by a distance within a range of 4.0&lt;240/H.times.w&lt;9.5 as shown in FIG. 
9. A carcass line of a tire using a 15.degree. drop center rim is deviated 
outwardly from the arc GI by a distance within a range of 
2.0&lt;210/H.times.w&lt;8.0 as shown in FIG. 10. 
In order to deform the carcass in the radially inner zone of the sidewall 
selectively and greatly outwardly when filled with the normal inner 
pressure, it is necessary to arrange the carcass line in this zone inside 
the line of the naturally equilibrium configuration. According to the 
invention, therefore, the carcass line of a tire using a 5.degree. flat 
base rim in the radially inner zone of the sidewall is preferably located 
inwardly of the straight line FI by a distance v within a range of 
0&lt;240/H.times.v&lt;3.5. The carcass line of a tire using a 15.degree. drop 
center rim is preferably located inwardly of the straight line FI by a 
distance v within a range of 0&lt;210/H.times.v&lt;5.0. Moreover, with the tire 
using the 5.degree. flat base rim, a carcass maximum width point A is 
preferably located radially outwardly from the standard intersection point 
I by a distance x within a range of 15&lt;240/H.times.x&lt;30. With the tire 
using the 15.degree. drop center rim, a carcass maximum width point A is 
preferably located radially outwardly from the point i by a distance x 
within a range of 6.0&lt;210/H.times.x&lt;30.0. The purpose of this feature is 
to obtain a curvature of the carcass line in the radially outer zone 
larger than that in the tire of the prior art. 
With values of the w and x smaller than their minimum values and values of 
the v larger than its maximum value, the sufficient change in 
configuration could not be obtained as described later when filled with 
the normal inner pressure. On the other hand, with values of the w and x 
larger than their maximum values, a deformation when filled with the 
normal inner pressure becomes excessive to increase shearing strains so 
that the durability of the tire rather lowers. 
With a heavy duty radial tire mounted on a rim having a bead seat inclined 
at a degree of 5.degree. relative to a rotation axis of the tire, 
according to the invention, a carcass profile in the radial cross-sections 
of the tire mounted on the approved rim and filled with an inner pressure 
5% of the normal inner pressure and under no load condition is a composite 
curve smoothly passing through points R, A and G. The point A is a point 
of contact of a carcass line C of the carcass profile with a tangent mm' 
in a radial direction to the carcass line at a carcass line maximum width 
position. The point R is an intersection of the carcass line C and a 
straight line kk' in parallel with and spaced from a bead base line RL by 
a distance MH of 0.3 times a maximum height H of the carcass line C from 
the bead base line RL. The point G is an inter-section of the carcass line 
C and a perpendicular ll' to a bead base line RL, the perpendicular ll' 
spaced apart axially outwardly from an equatorial plane M of the tire by a 
distance of 0.5 times a rim width corresponding to a distance between 
flanges of the rim. The profile fulfills three relations. A first relation 
is 6.0&lt;210/H.times.y&lt;11.5, where y is a maximum distance of the carcass 
line C from an arc IR which passes through the point R and contacts the 
said tangent mm' at a point I, where the point I is an intersection of the 
tangent mm' and a straight line jj' which is in parallel with a rotating 
axis of the tire and spaced radially outwardly from the bead base line RL 
by a distance LH 0.55 times the maximum height H of the carcass line C. A 
second relation is 4.0&lt;210/H.times.w&lt;9.5, where w is a maximum distance of 
the carcass line C from an arc .solthalfcircle.GI which passes through the 
point G and contacts the tangent mm' at the point I. A third relation 
15&lt;210/H.times.x&lt;35, where x is a radially outward distance between the 
points A and I. 
With a heavy duty radial tire mounted on a rim having a bead seat inclined 
at a degree of 15.degree. relative to a rotating axis of the tire, 
according to a carcass profile in the radial cross-sections of the tire 
mounted on the approved rim and filled with an inner pressure 5% of the 
normal inner pressure and under no load condition is a composite curve 
smoothly passing through points R, A and G. The point A is a point of 
contact of a carcass line C of the carcass profile and a tangent mm' in a 
radial direction to the carcass line at a carcass line maximum width 
position. The point R is an intersection of the carcass line C and a 
straight line kk' in parallel with and spaced from a bead base line RL by 
a distance LH of 0.3 times a maximum height H of the carcass line C from 
the bead base line RL. The point G is an intersection of the carcass line 
C and a perpendicular ll' to a bead base line RL, the perpendicular ll' 
spaced apart axially outwardly from an equatorial plane M of the tire by a 
distance of 0.5 times a rim width corresponding to a distance between 
flanges of the rim. The carcass profile fulfills three relations, a first 
relation 3.0&lt;210/H.times.y&lt;8.0, where y is a maximum distance of the 
carcass line C from an arc .solthalfcircle.IR which passes through the 
point R and contacts the tangent mm' at a point I, where the point I is an 
intersection of the tangent mm' and a straight line jj' which is in 
parallel with a rotating axis of the tire and spaced radially outwardly 
from the bead base line RL by a distance LH b 0.55 times the maximum 
height H of the carcass line C. A second relation is 
2.0&lt;210/H.times.w&lt;8.0, where w is a maximum distance of the carcass line C 
from an arc .solthalfcircle.GI which passes through the point G and 
contacts the tangent mm' at the point I. A third relation is 
6.0&lt;210/H.times.x&lt;30.0, where x is a radially outward distance between the 
points A and I. 
FIFS. 13 and 14 illustrates carcass lines of tires of further preferable 
embodiments of the invention in section using 5.degree. flat base rim and 
15.degree. drop center rim, respectively. FIGS. 15 and 16 illustrate tires 
of the equilbrium configuration of the prior art of the same in size as 
those shown in FIGS. 13 and 14. In FIGS. 15 and 16 , a difference between 
the carcass line of the tire of the prior art and an arc GI is small so 
that the arc GI substantially indicates the carcass profile of the tire of 
the prior art. Moreover, the carcass profile is greatly deviated from a 
straight line IR in comparison with those shown in FIGS. 1 and 4. 
In order to deform the carcass in the radially inner zone of the sidewall 
selexctively and greatly outwardly when filled with the normal inner 
pressure, it is necessary to arrange the carcass line in this zone inside 
an arc .solthalfcircle.IR. According to the invention, there-fore, the 
carcass line of a tire using a 5.degree. flat base rim in the radially 
inner zone of the sidewall is preferably located inwardly of the arc IR by 
a distance y within a range of 6.0&lt;210/H.times.y&lt;11.5. The carcass line of 
a tire using a 15.degree. drop center rim is preferably located inwardly 
of the arc .solthalfcircle.IR by a distance y within a range of 
3.0&lt;210/H.times.8.0. 
In general, most failures of a tire occur at ends of a carcass or bead 
portions. 
In order to elimainate the failures at the ends of the carcass ply, 
appropriate compression stresses are applied to the ends of the carcass 
ply to prevent the failures at the ends of the carcass ply so as to 
improve the durability of the bead portions. 
In more detail, when the expansion f in the radially inner zone of the 
sidewall is caused axially outwardly by filling with the normal inner 
pressure, the proximity of the end e of the carcass ply within a zone of 
.+-.10-20 mm is extended radially inwardly as well as axially outwardly as 
shown in broken lines in FIG. 17, so that the application of the 
compression force to the end of the carcass ply is realized. 
In order to apply an appropriate compression force, moreover, it is 
preferable that a center of radius of curvature of the carcass line in the 
radially inner zone of the sidewall is inside of the tire or the carcass 
line is similar to a straight line. 
The tensile force in the belt is increased by expanding the crown zone or 
more particularly the part from an equatorial line to the ends of the 
maximum ground contact width when filling with the inner pressure. 
The increase of the tension of the belt greatly contributes to the 
improvement of the durability at the ends of the belt, because strains 
occuring between belt layers when a load is applied are mitigated to 
prevent separations at the ends of the belt. 
In other words, referring to FIG. 18 illustrating a deformation of a belt 
caused by a load applied to the tire, when an initial tension applied to 
the belt is large, a center O of the circle in a solid line is positioned 
higher from a center O' of the circle in a dot-and-dash line when an 
initial tension applied to the belt is small. Therefore, the deformation 
of the belt in a deformation zone R on the ground contact side is small, 
so that the shearing strains between belt layers whose cords extend in 
intersecting directions are mitigated, thereby improving the durability at 
ends of the belt. 
The strain distribution above described is obtained by particularly linked 
deformations caused when fille with the normal inner pressure to achieve 
the improvement of the durability at the crown portion and the bead 
portions. 
Examples of tires according to the invention and comparative examples of 
tires of the prior art will be explained hereinafter. 
EXAMPLE 1 OF THE INVENTION 
______________________________________ 
Tire size 10.00 R 20 
Rim size 7.50 V 20 
(5.degree. flat base rim) 
Normal inner pressure 
7.25 kg/cm.sup.2 
Carcass outermost height H 
240 mm 
______________________________________ 
Referring to FIG. 5, the height H is a distance from the outermost position 
of the carcass to a bead base line or rim diameter line (RL) which is 
parallel to a rotating axis of the tire and passes through a point on a 
normal outer distance of the rim. In this case, the point on the normal 
outer diameter of the rim corresponds to a point of intersection between a 
surface of the rim engaging a bead of the tire and a flange surface of the 
rim perpendicular to the rotating axis of the tire. 
Referring to FIG. 5, tires of the Example 1 of the invention for trucks and 
buses were produced by way of trial, which had values S=10.0 mm, t=7.8 mm 
and u=23.9 mm with respect to its carcass line C determined by the points 
B and D located at distances from the line RL:53.2 mm (0.22.H) and 226 mm 
(0.94.H), respectively. 
Moreover, these steel radial tires had values, d=1.3 mm, f=6.7 mm, g=1.9 
mm, h=26.5 mm, c=75 mm and HE=67.2 mm referring to FIG. 1. In this case, 
s, t and u are within the following ranges. 
##EQU2## 
COMATIVE EXAMPLE 1 
______________________________________ 
Tire size 10.00 R 20 
Rim size 7.50 V 20 
(5.degree. flat base rim) 
Normal inner pressure 
7.25 kg/cm.sup.2 
Carcass outermost height H 
240 mm 
______________________________________ 
Referring to FIG. 7, tires of the Comparative Example 1 for trucks and 
buses were produced for a comparison. These tires had values s=1.6 mm, 
t=0.3 mm and u=0.2 mm with respect to its carcass line C' determined by 
the points B and D located at distances from the line RL:49.0 mm (0.20.H) 
and 224.2 mm (0.91.H), respectively. These steel radial tires had the 
naturally equilibrium configuration exhibiting the uniformly expanded 
deformations of the prior art when filled with the normal inner pressure 
as shown in FIG. 3. As can be seen from the following values, the carcass 
lines are considerably deviated from the carcass line C according to the 
invention. 
##EQU3## 
EXAMPLE 2 OF THE INVENTION 
______________________________________ 
Tire size 7.50 R 16 
Rim size 600 GS 16 
(5.degree. flat base rim) 
Normal inner pressure 
7.0 kg/cm.sup.2 
Carcass outermost height H 
178 mm 
______________________________________ 
Referring to FIG. 5, tires of the Example 2 for trucks and buses were 
produced by way of trial, which had values s=4.6 mm, t=2.8 mm and u=8.5 mm 
with respect to its carcass line C determined by the points B and D 
located at distances from the line RL:41.5 mm (0.23.H) and 166 mm 
(0.93.H), respectively. Moreover, these steel radial tires had values, 
d=0.8 mm, f=5.0 mm, and c=1.0 mm referring to FIG. 1. 
COMATIVE EXAMPLE 2 
______________________________________ 
Tire size 7.50 R 16 
Rim size 600 GS 16 
(5.degree. flat base rim) 
Normal inner pressure 
7.0 kg/cm.sup.2 
Carcass outermost height H 
178 mm 
______________________________________ 
Referring to FIG. 7, tires of the Comparative Example 2 for trucks and 
buses had values s=1.2 mm, t=0 mm and u=0.5 mm with respect to its carcass 
line C' determined by the points B and D located at distances from the 
line RL:40.2 mm (0.23.H) and 161.5 mm (0.91.H), respectively. These tires 
were steel radial tires of the naturally equilibrium configuration of the 
prior art when filled with the normal inner pressure as shown in FIG. 3. 
EXAMPLE 3 OF THE INVENTION 
______________________________________ 
Tire size 10.00 R 20 
Rim size 7.50 V 20 
(5.degree. flat base rim) 
Normal inner pressure 
7.25 kg/cm.sup.2 
Carcass outermost height H 
241 mm 
______________________________________ 
Steel radial tires for trucks and buses of the Example 3 of invention were 
produced for trial, which had values s=7.0 mm, t=5.9 mm and u=16.7 mm with 
respect to its carcass line C determined by the points B and D located at 
distances from the line RL:50 mm (0.21.H) and 229.7 mm (0.95.H), 
respectively, by referring to FIG. 5 and had values, d=1.5 mm, f=5.0 mm, 
and e=1.8 mm referring to FIG. 1. 
COMATIVE EXAMPLE 3 
______________________________________ 
Tire size 10.00 R 20 
Rim size 7.50 V 20 
(5.degree. flat base rim) 
Normal inner pressure 
7.25 kg/cm.sup.2 
Carcass outermost height H 
240 mm 
______________________________________ 
Tires of the Comparative Example 3 were produced for comparison, which were 
steel radial tires for trucks and buses having the naturally equilibrium 
configuration when filled with the normal inner pressure as shown in FIG. 
3, and having values, s=3.0 mm, t=9 mm and u=qb 2.5 mm with respect to its 
carcass line C' determined by the points B and D located at distances from 
the line RL: 48.7 mm (0.20.H) and 226.0 mm (0.94.H), respectively, by 
referring to FIG. 7. 
Distributions of tensions in belts in radial cross-sections of the tires of 
the Example 1 to the invention and the Comparison Example 1 of the prior 
art were obtained by the finite-element method, results of which are shown 
in FIG. 9. The respective tires have four belt layers in the order of 
first, second, third and fourth layers from the radially inner to radially 
outer side. The distributions of the tension of the second and third 
layers are shown in FIG. 19. In this case, the distributions of the 
tension were analyzed under no load when the normal inner pressure was 
filled. 
As can be seen from FIG. 19, the circumferential tension in the tire 
according to the invention is larger than that in the tire of the 
Comparative Examples. This holds true in the relations between the 
Examples 2 and 3 of the invention and the Comparative Examples 2 and 3. 
Comparative tests were carried out to determine the effect of the increase 
in tension of the belts on the durability ofg ends of the belts by a slip 
angled drum test wherein a tire arranged with a slip angle relative to a 
drum in contact with a tread of the tire was driven by the drum. The tires 
were driven at a speed of 60 km/hr with a slip angle 3.degree. with the 
normal inner pressure umnder twice the normal load. 
As results of the test, when tires of the Examples 1, 2 and 3 of the 
invention had run ran 895 km, 802 km and 840 km, slight separations 
occured at ends of belts. On the other hand, separations occured at ends 
of belts when the tires of the Comparative Examples 1, 2 and 3 had run 630 
km, 625 km and 592 km, respectively. 
Moreover, these tires were tested with a drum testing machine for examining 
the durability at bead portions. 
These tires were driven at 60 km/hr with the normal inner pressure under 
twice the normal load. 
As results of the test, after the tires of the Example 1 of the invention 
had run 20,000 km, any failures did not occur, but slight separations 
occurred at ends of plies when the tires of the Examples 2 and 3 had run 
19,800 km and 19,500 km, respectively. 
Separations occured when the tires of the Comparative Examples 1, 2 and 3 
had run 14,500 km, 14,550 km and 15,000 km. 
EXAMPLE 4 OF THE INVENTION 
______________________________________ 
Tire size 11/70 R 22.5 
Rim size 8.25 .times. 22.5 
(15.degree. drop center rim) 
Normal inner pressure 
8.0 kg/cm.sup.2 
Carcass outermost height H 
166 mm 
______________________________________ 
Steel radial tires for trucks and buses of the Example 4 of invention were 
produced for trial, which had values s=5.8 mm, t=1.7 mm and u=9.0 mm with 
respect to its carcass line C determined by the points B and D located at 
distances from the line RL:30.5 mm (0.18.H) and 157.2 mm (0.94.H), 
respectively, by referring to FIG. 6 and had values, d=1.1 mm, f=4.2 mm, 
g=1.7 mm, h=13.2 mm c=41 mm and HE=19 mm referring to FIG. 2. In this 
case, s, t and u are within the following ranges. 
##EQU4## 
COMATIVE EXAMPLE 4 
______________________________________ 
Tire size 11/70 R 22.5 
Rim size 8.25 .times. 22.5 
(15.degree. drop center rim) 
Normal inner pressure 
8.0 kg/cm.sup.2 
Carcass outermost height H 
166 mm 
______________________________________ 
Tires of the Comparative Example 4 were produced for comparison, which were 
steel radial tires for trucks and buses having the naturally equilibrium 
configuration when filled with the normal inner pressure as shown in FIG. 
4, and having values, s=1.2 mm, t=0.5 mm and u=1.0 mm with respect to its 
carcass line C' determined by the points B and D located at distances from 
the line RL:30.5 mm (0.18.H) and 157.2 mm (0.94.H), respectively, by 
referring to FIG. 8. 
In this case, the carcass lines are considerably deviated from the carcass 
line C according to the invention. 
##EQU5## 
EXAMPLE 5 OF THE INVENTION 
______________________________________ 
Tire size 285/75 R 24.5 
Rim size 8.25 .times. 24.5 
Normal inner pressure 
7.7 kg/cm.sup.2 
Carcass outermost height H 
183 mm 
______________________________________ 
Steel radial tires for trucks anmd buses of the Example 5 of the invention 
were produced for trial, which had values s=5.0 mm, t=2.5 mm and u=9.0 mm 
with respect to its carcass line C determined by the points B and D 
located at distances from the line RL:38.8 mm (0.21.H) and 172.5 mm 
(0.95.H), respectively, by referring to FIG. 6 and had values, d=2.5 mm, 
f=7.3 mm, and g=1.8 mm referring to FIG. 2. 
COMATIVE EXAMPLE5 
______________________________________ 
Tire size 285/75 R 24.5 
Rim size 8.25 .times. 24.5 (15.degree. drop 
center rim) 
Normal inner pressure 
7.7 kg/cm.sup.2 
Carcass outermost height H 
183 mm 
______________________________________ 
Tires of the Comparative Example 5 were produced for comparison, which were 
steel radial tires for trucks and buses having the naturally equilibrium 
configuration when filled with the normal inner pressure as shown in FIGS. 
3 and 4, and having values, s=1.5 mm, t=0 mm with respect to its carcass 
line C' determined by the points B and D located at distances from the 
line RL: 39.0 mm (0.21.H) and 172.2 mm (0.94.H), respectively, by 
referring to FIG. 4. 
EXAMPLE 6 OF THE INVENTION 
______________________________________ 
Tire size 11 R 22.5 
Rim size 8.25 .times. 22.5 (15.degree. drop 
center rim) 
Normal inner pressure 
7.0 kg/cm.sup.2 
Carcass outermost height H 
210 mm 
______________________________________ 
Steel radial tires for trucks and buses of the Example 6 of the invention 
were produced for trial, which had values s=7.0 mm, t=3.5 mm and u=12.5 mm 
with respect to its carcass line C determined by the points B and D 
located at distances from the line RL:40.5 mm (0.19.H) and 190 mm 
(0.90.H), respectively, by referring to FIG. 6 and had values, d=1.2 mm, 
f=7.5 mm, and g=1.8 mm by referring to FIG. 2. 
COMATIVE EXAMPLE 6 
______________________________________ 
Tire size 11 R 22.5 
Rim size 8.25 .times. 22.5 
(15.degree. drop center rim) 
Normal inner pressure 
7.0 kg/cm.sup.2 
Carcass outermost height H 
210 mm 
______________________________________ 
Tires of the Comparatrive Example 6 were produced for comparison, which 
were steel radial tires for trucks and buses having the naturally 
equilibruim configuration when filled with the normal inner pressure as 
shown in FIG. and having values, s=0.8 mm, t=0.5 mm and u=1.8 mm with 
respect to its carcass line C' determined by the points B and located at 
distances from the line RL:40.5 mm (0.19.H) and 190.0.H), respectively, by 
referring to FIG. 8. 
Comparative tests were effected to examine the effect of the increase in 
tension of the belts on the durability of ends of the belts by the slip 
angled drum test as above described. 
The tires were driven at a speed of 60 km/hr with a slip angle 3.degree. 
with a normal inner pressure under twice the normal load, 
As results of the test, when the tires of the Examples 4, 5 and 6 of the 
invention had run 806 km, 818 km and 828 km, slight separations occured at 
ends of plies. On the other hand, separations occured at ends of belts 
when the tires of the Comparative Examples 4, 5 and 6 had run 605 km, 640 
km and 603 km, respectively. 
Moreover, these tires were tested with the drum testing machine for 
examining the durability at bead portions. 
These tires were driven at 60 km/hr with the normal inner pressure under 
twice the normal load. 
As results of the test, slight separations occurered at ends of plies when 
the tires of the Examples 4, 5 and 6 had run 19,050 km, 19,300 km and 
19,750 km, respectively. 
Separations occurred when the tires of the Comparative Examples 4, 5 and 6 
had run 14,500 km, 15,700 km and 16,400 km. 
EXAMPLE 7 OF THE INVENTIONM 
______________________________________ 
Tire size 10.00 R 20 
Rim size 7.50 V 20 
(5.degree. flat base rim) 
Normal inner pressure 
7.25 kg/cm.sup.2 
Carcass outermost height H 
240 mm 
______________________________________ 
Steel radial tires for trucks and buses of the Example 7 of the invention 
were produced for trial, which had values v=0 mm, w=7.8 mm, and x=23.9 mm 
with respect to its carcass line C determined by the points I, F and G 
located at distances from the line RL:132 mm (0.55.H) and 68.5 mm (0.29.H) 
and 221 mm (0.92.H), respectively, by referring to FIG. 9 and had values, 
v=0 mm, w=7.8 mm, and x=23.9 mm referring to FIG. 1. In this case, v, w 
and x are within the following ranges. 
##EQU6## 
COMATIVE EXAMPLE 7 
______________________________________ 
Tire size 10.00 R 20 
Rim size 7.50 V 20 
(5.degree. flat base rim) 
Normal inner pressure 7.25 kg/cm.sup.2 
Carcass outermost height H 
240 mm 
______________________________________ 
Steel radial tires for trucks and buses of the Comparative Example 7 were 
produced for comparison, which were steel radial tires having the 
naturally equilibruim configuration when filled with normal inner pressure 
as shown in FIG. 3, and having values, v=4.3 mm, w=3.0 mm and x=9.3 mm 
with respect to its carcass line C' determined by the points I, F and G 
located at distances from the line RL:132 mm (0.55.H), 65.5 mm (0.27.H) 
and 217.5 mm (0.90.H), respectively, by referring to FIG. 11. 
In this case, as can be seen from the following values, the carcass lines 
are considerably deviated from the carcass line C according to the 
invention. 
##EQU7## 
EXAMPLE 8 OF THE INVENTION 
______________________________________ 
Tire size 7.50 R 16 
Rim size 6.00 GS 16 
(5.degree. flat base rim) 
Normal inner pressure 7.0 kg/cm.sup.2 
Carcass outermost height H 
178 mm 
______________________________________ 
Steel radial tires for trucks and buses of the Example 8 of invention were 
produced for trial, which had values v=0 mm, w=3.4 mm and x=16.8 mm with 
respect to its carcass line C determined by the points I, F and G located 
at distances from the line RL:97.9 mm (0.55.H), 55.0 mm (0.31.H) and 161.0 
mm (0.9.H), respectively, by referring to FIG. 9 and had values, v=0 mm, 
w=3.4 mm and x=16.8 mm by referring to FIG. 1. 
COMATIVE EXAMPLE 8 
______________________________________ 
Tire size 7.50 R 16 
Rim size 6.00 GS 16 
(5.degree. flat base rim) 
Normal inner pressure 7.0 kg/cm.sup.2 
Carcass outermost height H 
178 mm 
______________________________________ 
Tires of the Comparative Example 8 were produced for comparison, which were 
steel radial tires for trucks and buses having the naturally equilibrium 
configuration when filled with the mormal inner pressure as shown in FIG. 
3, and having values, v=4.8 mm, w=0.9 mm and x=4.8 mm with respectr to its 
carcass line C' determined by the poibnts I, F and G located at doistances 
from the line RL:97.9 mm (0.55.H), 49.0 mm (0.28.H) and 150.0 mm (0.85.H), 
respectively, by referring to FIg. 11. 
EXAMPLE 9 OF THE INVENTION 
______________________________________ 
Tire size 10.00 R 20 
Rim size 7.50 V 20 
(5.degree. flat base rim) 
Normal inner pressure 7.25 kg/cm.sup.2 
Carcass outermost height H 
241.5 mm 
______________________________________ 
Steel radial tires for trucks and buses of the Example 9 of invention were 
produced for trial, which had values v=0 mm, w=7.5 mm and x=28.5 mm with 
respect to its carcass line C determined by the points I, F and G located 
at distances from the line RL:132/9 mm (0.55.H), 57.5 mm (0.24.H) and 224 
mm (0.93.H), respectively, by referring to FIG. 9 and had values, d=1.5 
mm, f=6.5 mm and g=1.8 mm by referring to FIG. 1. 
COMATIVE EXAMPLE 9 
______________________________________ 
Tire size 10.00 R 20 
Rim size 7.50 V 20 
(5.degree. flat base rim) 
Normal inner pressure 7.25 kg/cm.sup.2 
Carcass outermost height H 
241.5 mm 
______________________________________ 
Tires of the Comparative Example 9 were produced for comparison, which were 
steel radial tires for trucks and buses having the naturally equilibruim 
configuration when filled with the normal inner pressure as shown in FIG. 
3, and having values, v=4.5 mm, w=3.8 mm and x=3.8 mm with respect to its 
carcass line C' determined by the points I,F and G located at distances 
from the line RL:132.8 mm (0.55.H), 57.5 mm (0.24.H ) and 224 mm (0.93.H), 
respectively, by referring to FIG. 11. 
Comparative tests were effected to examine the effect of the increase in 
tension of the belts on the durability of ends of the belts by the slip 
angled drum test as above described. 
The tires were driven at a speed of 60 km/hr with a slip angle 3 .degree. 
with the normal inner pressure under twice the normal load. 
As results of the test, slight separations occured when the tires of the 
Examples 7, 8 and 9 of the invention had run 865 km. On the other hand, 
separations occured at ends of belts when the tires of the Comparative 
Examples 7, 8 and 9 had run 630 km, 673 km and 600 km, respectively. 
Moreover, these tires were tested with a drum testing machine for 
exampining the durability at bead portions. 
These tires were driven at 60 km/hr with the normal inner pressure under 
twice the normal load. 
As results of the test, slight separations occured at ends of plies when 
the tires of the Examples 7 and 8 had run 19,450 km and 19,000 km, 
respectively, while the tires of the Example 9 had run 20,000 km without 
causing any failure. 
As results of the test, slight separations occurred at ends of plies when 
the tires of the Examples 4, 5 and 6 had run 19,050 km, 19,300 km and 
19,750 km, respectively. 
Separations occurred when the tires of the Comparative Examples 7, 8 and 9 
had run 14,000 km, 15,700 km and 15,000 km. 
EXAMPLE 10 OF THE INVENTION 
______________________________________ 
Tire size 11/70 R 22.5 
Rim size 8.25 .times. 22.5 
(15.degree. drop center rim) 
Normal inner pressure 
8.0 kg/cm.sup.2 
Carcass outermost height H 
167.5 mm 
______________________________________ 
Steel radial tires for trucks and buses of the Example 10 of invention were 
produced for trial, which had values v=2.5 mm, w=3.0 mm and x=15.4 mm with 
respect to its carcass line C determined by the points I, F and G located 
at distances from the line RL:92.1 mm (0.55.H), 44.3 mm (0.26.H) and 146 
mm (0.87.H), respectively, by referring to FIG. 10 and had values, d=1.1 
mm, f=4.2 mm, g=1.7 mm, h=13.2 mm and HE=19 mm by referring to FIG. 2. 
In this case, v, w and x are within the following ranges. 
##EQU8## 
COMATIVE EXAMPLE 10 
______________________________________ 
Tire size 11/70 R 22.5 
Rim size 8.25 .times. 22.5 (15.degree. drop 
center rim) 
Normal inner pressure 
8.0 kg/cm.sup.2 
Carcass outermost height H 
166.0 mm 
______________________________________ 
Tires of the Comparative Example 10 were produced for comparison, which 
were steel radial tires for trucks and buses having the naturally 
equilibrium configuration when filled with the normal inner pressure as 
shown in FIG. 4, having values, v=6.3 mm, w=1.2 mm and x=2.5 mm with 
respect to its carcass line C' determined by the points I, F and G located 
at distances from the line RL:91.3 mm (0.55.H), 44.0 mm (0.27.H) and 146.4 
mm (0.88.H), respectively, by referring to FIG. 12. 
In this case, the carcass lines are considerably deviated from the carcass 
line C according to the invention 
##EQU9## 
EXAMPLE 11 OF THE INVENTION 
______________________________________ 
Tire size 285/75 R 24.5 
Rim size 8.25 .times. 24.5 
(15.degree. drop center rim) 
Normal inner pressure 
7.7 kg/cm.sup.2 
Carcass outermost height H 
183 mm 
______________________________________ 
Steel radial tires for trucks and buses of the Example 11 of the invention 
were produced for trial, which had values v=2.0 mm, w=3.7 mm and x=18.0 mm 
with respect to its carcass line C determined by the points I, F and G 
located at distances from the line RL:100.7 mm (0.55.H), 49.41 mm (0.27.H) 
and 66.5 mm (0.91.H), respectively, by referring to FIG. 10 and had 
values, d=2.5 mm, f=8.0 mm, and g=1.8 mm by referring to FIG. 2. 
COMATIVE EXAMPLE 11 
______________________________________ 
Tire size 285/75 R 24.5 
Rim size 8.25 .times. 24.5 
(15.degree. drop center rim) 
Normal inner pressure 
7.7 kg/cm.sup.2 
Carcass outermost height H 
183 mm 
______________________________________ 
Tires of the Comparative Example 11 were produced for comparison, which 
were steel radial tires for trucks and buses having the naturally 
equilibrium configuration when filled with the normal inner pressure as 
shown in FIG. 4, and having values, v=5.0 mm, w=0.8 mm and x=4.0 mm with 
respect to its carcass line C' determined by the points I, F and G located 
at distances from the line RL:100.7 mm (0.55.H), 49.0 mm (0.27.H) and 
166.8 mm (0.91.H), respectively, by referring to FIG. 12. 
EXAMPLE 12 OF THE INVENTION 
______________________________________ 
Tire size 11 R 22.5 
Rim size 8.25 .times. 22.5 
(15.degree. drop center rim) 
Normal inner pressure 
7.0 kg/cm.sup.2 
Carcass outermost distance H 
210 mm 
______________________________________ 
Steel radial tires for trucks and buses of the Example 12 of the invention 
were produced for trial, which had values v=2.9 mm, w=3.8 mm and x=16.7 mm 
with respect to its carcass line C determined by the points I, F and G 
located at distances from the line RL:115.5 mm (0.55.H), 54.5 mm (0.26.H) 
and 181.0 mm (0.86.H), respectively, by referring to FIG. 10 and had 
values, d=1.2 mm, f=6.3 mm, and g=1.7 mm by referring to FIG. 2. 
COMATIVE EXAMPLE 12 
______________________________________ 
Tire Size 11 R 22.5 
Rim size 8.25 .times. 22.5 
(15.degree. drop center rim) 
Normal inner pressure 
7.0 kg/cm.sup.2 
Carcass outermost height H 
210 mm 
______________________________________ 
Tires of the Comparative Example 12 were produced for comparison, which 
were steel radial tires for trucks and buses having the naturally 
equilibrium configuration when filled with the normal inner pressure as 
shown in FIG. 4, and having values, v=5.8 mm, w=1.2 mm and x=5.0 mm with 
respect to its carcass line C' determined by the points I, F and G located 
at distances from the line RL:115.5 mm (0.55.H), 154.5 mm (0.26.H) and 
180.7 mm (0.86.H), respectively, by referring to FIG. 12. 
Comparative tests were effected to examine the effect of the increase in 
tension of the belts on the durability of ends of the belts by the slip 
angled drum test as above described. 
The tires were driven at a speed of 60 km/hr with a slip angle 3.degree. 
with the normal inner pressure under twice the normal load. 
As results of the test, slight separations occurred at the ends of the 
belts when the tires of the Example 10, 11 and 12 had run 803 km, 815 km 
and 833 km, respectively. On the other hand, separations occurred at the 
ends of belts when the tires of the Comparative Examples 10, 11 and 12 had 
run 605 km, 645 km and 592 km, respectively. 
Moreover, these tires were tested with the drum testing machine for 
examining the durability at bead portions. 
These tires were driven at 60 km/hr with the normal inner pressure under 
twice the normal load. 
As results of the test, slight separations occurred at ends of plies when 
the tires of the Examples 10, 11 and 12 had run 18,500 km, 19,200 km and 
20,000 km, respectively. 
Separations occurred when the tires of the Comparative Examples 10, 11 and 
12 had run 13,200 km, 16,500 km and 15,900 km. 
EXAMPLE 13 OF THE INVENTION 
______________________________________ 
Tire size 10.00 R 20 
Rim size 7.50 V 20 
(5.degree. flat base rim) 
Normal inner pressure 7.25 kg/cm.sup.2 
Carcass outermost height H 
242 mm 
______________________________________ 
Steel radial tires for trucks and buses of the Example 13 of invention were 
produced for trial, which had values y=10.0 mm, w=7.8 mm and x=23.9 mm 
with respect to its carcass line C determined by the points I, R and G 
located at distances from the line RL:133.1 mm (0.55.H) and 72.6 mm 
(0.30.H) and 220 mm (0.91.H), respectively, by referring to FIG. 13 and 
had values, d=1.3 mm, f=6.7 mm, g=2.0 mm, h=27.0 mm, c=75.0 mm and HE=67.1 
mm by referring to FIG. 1 
In this case, y, w and x are within the following ranges. 
##EQU10## 
COMATIVE EXAMPLE 13 
______________________________________ 
Tire size 10.00 R 20 
Rim size 7.50 V 20 
(5.degree. flat base rim) 
Normal inner pressure 7.25 kg/cm.sup.2 
Carcass outermost height H 
242 mm 
______________________________________ 
Tires of the Comparative Example 13 were produced for comparison, which 
were steel radial tires for trucks and buses having the naturally 
equilibrium configuration when filled with the normal inner pressure as 
shown in FIG. 3, and having values, y=4.4 mm, w=3.0 mm and x=9.3 mm with 
respect to its carcass line C' determined by the points I, R and G located 
at distances from the line RL:133.1 mm (0.55.H), 72.4 mm (0.03.H) and 219 
mm (0.09.H), respectively, by referring to FIG. 15. 
As can be seen from the following values, the carcass lines are 
considerably deviated from the carcass line C according to the invention. 
##EQU11## 
EXAMPLE 14 OF THE INVENTION 
______________________________________ 
Tire size 7.50 R 16 
Rim size 600 GS 16 
(5.degree. flat base rim) 
Normal inner pressure 
7.0 kg/cm.sup.2 
Carcass outermost height H 
178 mm 
______________________________________ 
Steel radial tires for trucks and buses of the Example 14 of the invention 
were produced for trial, which had values y=5.5 mm, w=3.4 mm and x=16.8 mm 
with respect to its carcass line C determined by the points I, R and G 
located at distances from the line RL:97.9 mm (0.55.H), 53.4 mm (0.30.H) 
and 162.5 mm (0.91.H), respectively, by referring to FIG. 13 and had 
values, d=2.8 mm, f=5.1 mm, and g=1.0 mm referring to FIG. 1. 
COMATIVE EXAMPLE 14 
______________________________________ 
Tire size 7.50 R 16 
Rim size 600 GS 16 
(5.degree. flat base rim) 
Normal inner pressure 
7.0 kg/cm.sup.2 
Carcass outermost height H 
178 mm 
______________________________________ 
Tires of the Comparative Example 14 were produced for comparison, which 
were steel radial tires for trucks and buses having the naturally 
equilibrium configuration when filled with the normal inner pressure as 
shown in FIG. 3, and having values, s=3.0 mm, t=0.9 mm and u=2.5 mm with 
respect to its carcass line C' determined by the points I, R and G located 
at distances from the line RL:97.9 mm (0.55.H), 53.4 mm (0.30.H) and 162.5 
mm (0.91.H), respectively, by referring to FIG. 15. 
EXAMPLE 15 OF THE INVENTION 
______________________________________ 
Tire size 10.00 R 20 
Rim size 7.50 V 20 
(5.degree. flat base rim) 
Normal inner pressure 
7.25 kg/cm.sup.2 
Carcass outermost height H 
241 mm 
______________________________________ 
Steel radial tires for trucks and buses of the Example 15 of the invention 
were produced for trial, which had values y=9.8 mm, w=6.5 mm and x=23.5 mm 
with respect to its carcass line C determined by the points I, R and G 
located at distances from the line RL:132.6 mm (0.55.H), 72.3 mm (0.30.H) 
and 226 mm (0.94.H), respectively, by referring to FIG. 13 and had values, 
d=1.5 mm, f=5.0 mm, and g=1.8 mm by referring to FIG. 1. 
COMATIVE EXAMPLE 15 
______________________________________ 
Tire size 10.00 R 20 
Rim size 7.50 V 20 
(5.degree. flat base rim) 
Normal inner pressure 
7.25 kg/cm.sup.2 
Carcass outermost height H 
241 mm 
______________________________________ 
Tires of the Comparative Example 15 were produced for comparison, which 
were steel radial tires for trucks and buses having the naturally 
equilibrium configuration when filled with the normal inner pressure as 
shown in FIG. 3, and having values, y=3.6 mm, w=3.8 mm and x=3.8 mm with 
respect to its carcass line C' determined by the points I, R and G located 
at distances from the line RL:132.6 mm (0.55.H), 72.0 mm (0.3.H) and 226.5 
mm (0.94.H), respectively, by referring to FIG. 15. 
Comparative tests were effected to examine the effect of the increase in 
tension of the belts on the durability of ends of the belts by the slip 
angled drum test as above described. 
The tires were driven at a speed of 60 km/hr with a slip angle 3.degree. 
with the normal inner pressure under twice the normal load. 
As results of the test, slight separations occurred at ends of the belts 
when the tires of the Examples 13, 14 and 15 had run 890 km, 820 km and 
851 km. On the other hand, separations occurred at ends of belts when the 
tires of the Comparative Examples 13, 14 and 15 had run 585 km, 640 km and 
612 km, respectively. 
Moreover, these tires were tested with the drum testing machine for 
examining the durability at bead portions. 
These tires were driven at 60 km/hr with the normal inner pressure under 
twice the normal load. 
As results of the test, slight separations occurred at ends of plies when 
the tires of the Examples 13 and 15 had run 18,500 km and 19,000 km, 
respectively, while the tires of the Example 14 ran 20,000 km without 
causing any separation. 
Separations occurred when the tires of the Comparative Examples 13, 14 and 
15 had run 14,900 km, 16,000 km and 15,550 km. 
EXAMPLE 16 OF THE INVENTION 
______________________________________ 
Tire size 11/70 R 22.5 
Rim size 8.25 .times. 22.5 (15.degree. drop 
center rim) 
Normal inner pressure 
8.0 kg/cm.sup.2 
Carcass outermost height H 
168.2 mm 
______________________________________ 
Steel radial tires for trucks and buses of the Example 16 of invention were 
produced for trial, which had values y=4.8 mm, w=3.0 mm and x=15.4 mm with 
respect to its carcass line C determined by the points I, R and G located 
at distances from the line RL:92.5 mm (0.55.H), 50.5 mm (0.30.H) and 148 
mm (0.88.H), respectively, by referring to FIG. 14 and had values, d=1.1 
mm, f=4.2 mm, g=1.7 mm, h=13.2 mm, c=41 mm and HE=19 mm by referring to 
FIG. 2. 
In this case, y, w and x are within the following ranges. 
##EQU12## 
COMATIVE EXAMPLE 16 
______________________________________ 
Tire size 11/70 R 22.5 
Rim size 8.25 .times. 22.5 
(15.degree. drop center rim) 
Normal inner pressure 
8.0 kg/cm.sup.2 
Carcass outermost height H 
167.5 mm 
______________________________________ 
Tires of the Comparative Example 16 were produced for comparison, which 
were steel radial tires for trucks and buses having the naturally 
equilibrium configuration when filled with the normal inner pressure as 
shown in FIG. 4, and having values, y=2.0 mm, w=1.2 mm and x=2.8 mm with 
respect to its carcass line C' determined by the points I, R and G located 
at distances from the line RL:92.1 mm (0.55.H), 50.3 mm (0.3.H) and 152 mm 
(0.91.H), respectively, by referring to FIG. 16. 
As can be seen from the following values, the carcass lines are 
considerably deviated from the carcass line C according to the invention. 
##EQU13## 
EXAMPLE 17 OF THE INVENTION 
______________________________________ 
Tire size 285/75 R 24.5 
Rim size 8.25 .times. 24.5 (15.degree. drop 
center rim) 
Normal inner pressure 
7.7 kg/cm.sup.2 
Carcass outermost height H 
183 mm 
______________________________________ 
Steel radial tires for trucks and buses of the Example 17 of the invention 
were produced for trial, which had values y=5.1 mm, w=3.7 mm and x=18.3 mm 
with respect to its carcass line C determined by the points I, R and G 
located at distances from the line RL:100.7 mm (0.55.H), 54.9 mm (0.30.H) 
and 165.5 mm (0.90.H), respectively, by referring to FIG. 14 and had 
values, d=2.5 mm, f=7.3 mm, and g=1.8 mm referring to FIG. 2. 
COMATIVE EXAMPLE 17 
______________________________________ 
Tire size 285/75 R 24.5 
Rim size 8.25 .times. 24.5 (15.degree. drop 
center rim) 
Normal inner pressure 
7.7 kg/cm.sup.2 
Carcass outermost height H 
183 mm 
______________________________________ 
Tires of the Comparative Example 17 were produced for comparison, which 
were steel radial tires for trucks and buses having the naturally 
equilibrium configuration when filled with the normal inner pressure as 
shown in FIG. 4, and having values, y=1.9 mm, w=0.8 mm and x=4.0 mm with 
respect to its carcass line C' determined by the points I, G and R located 
at distances from the line RL:100.7 mm (0.55.H), 54.9 mm (0.30.H) and 
165.1 mm (0.90.H), respectively, by referring to FIG. 16. 
EXAMPLE 18 OF THE INVENTION 
______________________________________ 
Tire size 11 R 22.5 
Rim size 8.25 .times. 22.5 
(15.degree. drop center rim) 
Normal inner pressure 
7.0 kg/cm.sup.2 
Carcass outermost height H 
210 mm 
______________________________________ 
Steel radial tires for trucks and buses of the Example 18 of the invention 
were produced for trial, which had values u=4.9 mm, w=3.8 mm and x=16.7 mm 
with respect to its carcass line C determined by the points I, R and G 
located at distances from the line RL:115.5 mm (0.55.H), 54.5 mm (0.30.H) 
and 181.4 mm (0.86.H), respectively, by referring to FIG. 5 and had 
values, d=1.2 mm, f=7.5 mm, and g=1.7 mm by referring to FIG. 2. 
COMATIVE EXAMPLE 18 
______________________________________ 
Tire size 11 R 22.5 
Rim size 8.25 .times. 22.5 (15.degree. drop 
center rim) 
Normal inner pressure 
7.0 kg/cm.sup.2 
Carcass outermost height H 
210 mm 
______________________________________ 
Tires of the Comparative Example 18 were produced for a comparison, which 
were steel radial tires for trucks and buses having the naturally 
equilibrium configuration when filled with the normal inner pressure as 
shown in FIG. 4, and having values, y=1.8 mm, w=1.2 mm and x=4.4 mm with 
respect to its carcass line C' determined by the points I, R and G located 
at distances from the line RL:115.5 mm (0.55.H), 54.5 mm (0.30.H) and 
181.4 mm (0.86.H), respectively, by referring to FIG. 16. 
Comparative tests were effected to examine the effect of the increase in 
tension of the belts on the durability of ends of the belts by the slip 
angled drum test as above described. 
The tires were driven at a speed of 60 km/hr with a slip angle 3.degree. 
with the normal inner pressure under twice the normal load. 
As results of the test, slight separations occurred at the ends of the 
belts when the tires of the Examples 16, 17 and 18 had run 865 km, 802 km 
and 845 km. On the other hand, separations occurred at ends of belts when 
the tires of the Comparative Examples 16, 17 and 18 had run 620 km, 629 km 
and 598 km, respectively. 
Moreover, these tires were tested with the drum testing machine for 
examining the durability at bead portions. 
These tires were driven at 60 km/hr with the normal inner pressure under 
twice the normal load. 
As results of the test, slight separations occurred at ends of plies when 
the tires of the Examples 16 and 17 had run 18,800 km and 18,550 km, 
respectively, while the tires of the Example 18 ran 20,000 km without 
causing any failure. 
Separations occurred when the tires of the Comparative Examples 16, 17 and 
18 had run 14,200 km, 15,750 km and 16,050 km. 
As can be seen from the above explanation, the heavy duty radial tire 
according to the invention is considerably improved in durability at bead 
portions and ends of the belt. 
It is further understood by those skilled in the art that the foregoing 
description is that of preferred embodiments of the disclosed tires and 
that various changes and modifications may be made in the invention 
without departing from the spirit and scope thereof.