Method of stabilizing flight of a flying body and flight-stabilized flying body

A method of stabilizing flight of a flying body having a circular cross-section by the use of a plurality of tripping wires, when the flying body flies in an air current at a high angle of attack with respect to the air current. And also a flight-stabilized flying body having a circular cross-section, comprising at least two tripping wires attached to the periphery of said flying body. The tripping wires are attached to the outer periphery of the flying body, by which an asymmetric side force acting on the flying body is reduced, thereby suppressing bad motion of the flying body, such as, rotation around the center of gravity of the flying body in a plane of an attack angle, i.e. the flat spin, yawing and the like motion. In a case of attaching two tripping wires to the flying body, an optimal angle of wire attachment for suppressing the undesirable motion resides in a region from 60.degree. to 45.degree. for the non-dimensional wire height of a region from 0.007 to 0.014. In a case of attaching more than two tripping wires to the flying body, an optimal distance of angle between adjacent two tripping wires resides in a region from 15.degree. to 45.degree. for non-dimensional wire height of a region from 0.007 to 0.014 and thus a number of the tripping wires required resides in a region from 24 to 8. In a case of the flying body comprising cylindrical and conical portions, the tripping wires are attached only to the cylindrical portion of the flying body for a Reynolds number region from 2.times.10.sup.5 to 4.4.times.10.sup.5.

BACKGROUND OF THE INVENTION 
Field of the Invention 
This invention relates to a method of stabilizing flight of a flying body 
by reducing asymmetric side force, which occurs when the flying body flies 
at a high angle of attack with respect to an air current, so as to 
suppress bad or undesirable motion of the flying body. An example is 
rotation around the center of gravity of the flying body in a plane of an 
attack angle, called as flat spin, yawing or the like, due to the 
asymmetric side force, by means of aerodynamic means. 
This invention further relates to a flying body which is stabilized in its 
flight by aerodynamic means. 
The nature of stream of air current flowing along a fuselage of a flying 
body such as rocket, aircraft, and so on is characterized by a 
non-dimensional parameter called as a Reynolds number R.sub.e. Now assume 
that, for example, a slender flying body is flying at a high angle of 
attack with respect to an air current. If the Reynolds number based on a 
diameter of the flying body resides in a subcritical Reynolds number 
region which is lower than a critical Reynolds number region of R.sub.e 
=3.4.times.10.sup.5 -3.6.times.10.sup.5 laminar separation may occur in 
the stream or flow on left and right sides of the fuselage. If the 
Reynolds number resides within a supercritical Reynolds number region 
which is higher than the critical one, turbulent separation may occur in 
the stream or flow. However, the flow patterns or conditions at the both 
sides of the fuselage are same, so that any asymmetric side force acting 
on the flying body does not occur on the fuselage. 
If the critical Reynolds number region, short bubbles occur only on the one 
side of the fuselage and its occurrence continues, and therefore an 
asymmetric pressure difference appears between the one side and the other 
side of the fuselage. This asymmetric pressure difference causes the 
asymmetric side force acting on the fuselage. This fact has been verified 
from wind tunnel experiments for a two dimensional cylindrical body and a 
three dimensional body designed in imitation of a head portion of a 
rocket. 
This type of asymmetric side force occurring when the slender flying body 
flies at high angle of attack, for example, 30.degree.-90.degree. with 
respect to the air current or stream causes aerodynamically unstable 
flight of the flying body, rotation thereof in a plane perpendicular to 
the air current called as flat spin and so on, and therefore such side 
force is unfavorable to the actual flight of the flying body. 
SUMMARY OF THE INVENTION 
The asymmetric side force is caused by the difference in flow patterns or 
conditions around the fuselage of the flying body at the critical Reynolds 
number region. Thus, in order to reduce the asymmetric side force, an 
aerodynamic means is required. 
This invention is based on the recognition that in order to eliminate the 
flow difference it is effective to attach at least two tripping wires to 
the cylindrical portion of a flying body at its outer periphery in 
parallel with an axis of the cylindrical portion, thereby urging early 
occurrence of the turbulent separation. 
An object of this invention is to provide a concrete method of stabilizing 
flight of a tubular, slender or elongated flying body having a circular 
cross-section by reducing an asymmetric side force acting on the flying 
body and suppressing rotation thereof caused by the side force. 
It is heretofore well known that early transition from laminar flow to 
turbulent flow is attained by the surface roughness, but the method in 
accordance with the invention is based on results obtained from systematic 
wind tunnel experiments with the use of tripping wires. 
Another object of the invention is to provide that flight-stabilized flying 
body having a circular cross-section which any bad motion of the flying 
body such as flat spin, yawing and the like can be suppressed during 
flight of the flying body. 
According to the invention, a method of stabilizing flight of a flying body 
having a circular cross-section, comprises a step of suppressing 
undesirable motion of the flying body such as flat spin, yawing and the 
like, for stable flight of the flying body, by reducing an asymmetric side 
force occurring when said flying body flies at a high angle of attack with 
respect to an air current by means of at least two tripping wires provided 
on the outer periphery of said flying body. 
According to the present invention, a flight-stabilized flying body having 
a circular cross-section, comprises at least two tripping wires provided 
on the outer periphery of said flying body, thereby reducing an asymmetric 
side force occurring when said flying body flies at a high angle of attack 
with respect to an air current so as to suppress bad motion of said flying 
body such as flat spin, yawing and the like caused by said asymmetric side 
force. 
According to a preferred embodiment of the invention in a case where a 
number of said tripping wires is two and an initial stagnation point of 
the air current lies on a midpoint between said tripping wires and on said 
outer periphery of said flying body, an optimal azimuthal angle for 
tripping wire position resides in a region from 60.degree. to 45.degree. 
for non-dimensional tripping wire height normalized by the diameter of 
said flying body residing in a region from 0.007 to 0.014. 
According to another preferred embodiment of the invention, in a case where 
said tripping wires are provided on said flying body over its whole outer 
periphery in a manner to be spaced apart from each other by an equal 
distance of angle, an optimal distance of angle between the adjacent two 
tripping wires resides in a region from 15.degree. to 45.degree. for 
non-dimensional tripping wire height normalized by the diameter of said 
flying body residing in a region from 0.007 to 0.014 and a number of said 
tripping wires resides in a region from 24 to 8. 
According to the further preferred embodiment of the invention, said flying 
body comprises a cylindrical portion and a conical portion and, for a 
Reynolds number region from 2.times.10.sup.5 to 4.4.times.10.sup.5, said 
tripping wires are only provided on said cylindrical portion.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
FIG. 1A is an elevational view of a flying body consisting of a cylindrical 
portion and conical portion, the cylindrical portion having two wires 
attached or mounted thereon, and FIG. 1B is a right side view of the 
flying body shown in FIG. 1A. In FIGS. 1A and 1B, reference numeral 1 
shows a flying body proper and 2 wires attached to an outer periphery on 
surface of the cylindrical portion of the flying body proper in parallel 
with an axis of the cylinder. The flying body may be of tubular, 
elongated, slender or other type. The tripping wire used here is straight 
one having a constant diameter, thickness, width or height and functions 
to disturb or trip a boundary layer flowing along the flying body. The 
tripping wire means not only a so-called wire but also a rod-like one and 
a pole-like one. Further the shape in cross-section of the tripping wire 
may be n-sided polygon (n.gtoreq.3). Further the tripping wires may be 
provided on the flying body by connecting means such as rivetting, 
welding, adhesion, etc. or may be integral with the flying body during 
manufacturing process. 
FIGS. 2A-2C are cross-sectional views of the flying body with a plurality 
of tripping wires, each having the shape in cross-section of n (n=5)-sided 
polygon, respectively, and also show the patterns of tripping wire 
attachment, respectively. In each of FIGS. 2A-2C, the direction of an air 
current or free stream is shown by an arrow and the velocity of the air 
current is shown by a letter U. In the case where the tripping wires are 
mounted on the periphery of circular cross-section of the flying body and 
spaced apart from each other by an equal distance of angle .phi., the 
patterns of tripping wire attachment are classified into following three 
types in view of the relationship between the direction of the air current 
and the tripping wire attaching position. 
Type A: One tripping wire 3 is positioned on the cylindrical portion at a 
stagnation point P of the air current and other tripping wires 4 and 5 are 
spaced apart from the wire 3 by an angle .phi., respectively (FIG. 2A). 
Type B: The tripping wires 6 and 7 are attached to the flying body at 
positions separated from the stagnation point P by an equiangular distance 
.psi. (.psi.=1/2.phi.), respectively (FIG. 2B). 
Type C: The tripping wires 8 and 9 are attached to the flying body at 
positions separated from the stagnation point P by angles .psi..sub.1 and 
.psi..sub.2 (.psi..sub.1 .noteq..psi..sub.2), respectively (FIG. 2C). 
FIGS. 3A-3C show, by way of example, patterns of tripping wire attachment 
and notations thereof, respectively. (A): The notation ".phi.30-A(12)" 
shows that the pattern of tripping wire attachment belongs to Type A and 
that the twelve tripping wires are attached to the flying body so as to be 
spaced apart from each other by an angle of 30.degree.. (B): The notation 
".psi.60-B(2)" representing the pattern of FIG. 3B shows that the pattern 
of the tripping wire attachment belongs to Type B, that two tripping wires 
are spaced apart from each other by an angle of 120.degree. and that the 
midpoint between adjacent two tripping wires is located to the stagnation 
point P. In this case azimuthal angle .psi. is 60.degree.. (C): The 
notation ".psi..sub.1 75-.psi..sub.2 15-C(2)" representing the pattern of 
FIG. 3C shows that the pattern of the tripping wire arrangement belongs to 
Type C and that two tripping wires are attached to the flying body in such 
a manner that one of the wires is separated from the stagnation point P by 
an angle of 75.degree. and the other by an angle of 15.degree.. The shape 
in cross-section of the tripping wire shown in FIGS. 3A-3C is an n-sided 
polygon, particularly a pentagon. 
Many experiments were carried out to verify the suppression or reduction of 
the occurrence of the asymmetric side force and the flat spin caused 
thereby with respect to various models of the flying body with a plurality 
of tripping wires each having a circular cross-section (n=.infin.). These 
models are disposed in the air current at the high angle of attack to the 
flow direction of the stream. More concretely, the experiments were made 
by using a Gottingen type wind tunnel. In that case, the flying body model 
was supported at its center of gravity by a supporting rod in the free 
stream of the wind tunnel. 
FIG. 4A shows an arrangement of the wind tunnel and the flying body model. 
In FIG. 4A, reference numeral 10 shows the wind tunnel apparatus by which 
flat spin caused by the asymmetric side force is simulated, 11 and 12 wind 
tunnels, 13 a supporting rod for the flying body 1 and 14 supporting 
members for measuring flat spin rate. Further, FIG. 4B is a diagrams 
showing dimensions of the various parts of the model used in the 
experiments, in which reference numeral 1A designates the cylindrical 
portion of the flying body, 1B the conical portion thereof and 15 a 
supporting point, that is, center of gravity of the flying body at which 
the flying body 1 is supported by the supporting rod 13. The dimensions of 
the model used are selected as follows: the entire length L of the flying 
body is 800 mm, the diameter D of the cylindrical portion 1A is 210 mm, 
the length l of the conical portion 1B is 305 mm and the distance X.sub.G 
is 550 mm. Furthermore, the tripping wires having their diameters d of 1.5 
mm, 2.0 mm and 3.0 mm, respectively, are used in the experiments so as to 
systematically change a height and position of the surface roughness. The 
experiments were carried out by using a 1.5 m.phi. Gottingen type wind 
tunnel and at a Reynolds number region of 2.0.times.10.sup.5 
-4.4.times.10.sup.5. 
The results of the wind tunnel experiments and the effects of the invention 
will be hereinafter be described. 
(1) Flying Body with Two Tripping Wires 
FIG. 5A is a diagram showing the results of the wind tunnel experiments for 
the model with two tripping wires, in which the ordinate shows side force 
coefficient C.sub.Y, the positive or negative value of which represents a 
measure of the magnitude of the side force and the abscissa R.sub.e shows 
the Reynolds number. FIG. 5B is a diagram for showing pattern of tripping 
wire attachment on a flying body model used in the experiments. As seen 
from a curve A in FIG. 5A, there occurs the asymmetric side force in the 
case of the flying body with no surface roughness, that is, having no 
tripping wires attached thereto. However, in the case of the model 
".psi.60-B(2)", the asymmetric side force is reduced as shown by a curve B 
in FIG. 5A. Further, it is seen from curves C-G in FIG. 5A that the 
asymmetric side force is not reduced in the case of other models 
".psi..sub.1 75-.psi..sub.2 45-C(2)", ".psi..sub.1 90-.psi..sub.2 
30-C(2)", ".psi..sub.1 105 -.psi..sub.2 15-C(2)", ".psi..sub.1 
120-.psi..sub.2 0-C(2)" and ".psi..sub.1 135-.psi..sub.2 (-15)-C(2)". 
Further, it is known from the FIG. 5A that, when the two tripping wires 
are arranged asymmetrically with respect to the stagnation point P of the 
stream, the possibility of occurrence of the assymetric side force 
increases correspondingly. 
FIG. 6A is a diagram showing one example of a flat spin rate, that is, 
number of rotation N of each of the models used in the respective 
experiments. In FIG. 6A, the ordinate shows the flat spin rate N (r.p.m.) 
and the abscissa shows the Reynolds number R.sub.e. FIG. 6B is a diagram 
showing the type of the model used in the experiment. The used models 
belong to the Type B and thus have two tripping wires, the azimuthal angle 
for attachment .psi. being changed from 30.degree. to 80.degree.. In FIG. 
6A, a curve A corresponds to the model having no surface roughness and 
curves B, C, D, E and F to those each having same surface roughness 
height: d=1.5 mm. Further, these models corresponding to the curves B, C, 
D, E and F are shown by the notations ".psi.30-B(2)", ".psi.35-B(2)", 
".psi.45-B(2)", ".psi.60-B(2)" and ".psi.80-B(2)", respectively. From this 
experimental results shown in FIG. 6A, it is seen that, at and around 
azimuthal angles of 30.degree. and 35.degree., the rotation of the models 
having surface roughness is rather encouraged. It may be estimated that 
this phenomenon is caused by the fact that, in the case of the small 
azimuthal angle for attachment .psi., the boundary layer once disturbed or 
tripped upstream flows downstream along the surface of the flying body and 
reattaches again to a downstream surface region, thereby causing 
asymmetric separation of the boundary layer. Due to this separation, the 
asymmetric side force occurs and therefore the flat spin begins. Then, the 
stagnation point of the stream having the resultant velocity of the free 
stream velocity and the circumferential velocity deviates from the 
original position. Due to the deviation, the flow pattern changes to the 
other flow pattern corresponding to the model of Type C (refer to FIG. 
2C). Accordingly, the arrangement of two tripping wires disposed at 
azimuthal angles .psi..sub.1 and .psi..sub.2, respectively, would 
encourage the rotation of the model. 
To the contrary, if the azimuthal angle .psi. is large, laminar separation 
occurs before the stream reaches the tripping wires, that is, before the 
boundary layer is tripped and, in this case, the flat spin begins. This 
phenomenon is similar to that in the case of the model with no surface 
roughness. For the comparison purpose, the experimental result for the 
model with no surface roughness is shown by a curve A in FIG. 6A. 
In the case of the model with no surface roughness, that is, having no 
tripping wires, the flat spin rate N of the flying body caused by the 
asymmetric side force reaches 400 r.p.m.-500 r.p.m. at and near the 
Reynolds number of 3.5.times.10.sup.5, as shown by the curve A in FIG. 6A. 
However, if the model is provided with at least two tripping wires, there 
is an optimal azimuthal angle for tripping wire attachment .psi..sub.opt 
which lowers the number of rotation, that is, flat spin rate down to 
approximately zero. Regarding this point, a description will hereinafter 
be given with reference to FIGS. 7A-7F. FIGS. 7A, 7C and 7E are diagrams, 
each showing the experimental result of the relationship between the flat 
spin rate, that is, number of rotation N of the model and the azimuthal 
angle .psi., in which the ordinate shows the flat spin rate N (r.p.m.) and 
the abscissa the azimuthal angle for attachment .psi.(deg). Further, FIGS. 
7A, 7C and 7E show the experimental results for the non-dimensional 
tripping wire height d of 0.007, 0.010 and 0.014, respectively. These wire 
heights d correspond to the wire diameters of 1.5 mm, 2.0 mm and 3.0 mm, 
respectively and are derived by normalizing the wire diameters by the 
model base diameter D, respectively. FIGS. 7B, 7D and 7F are diagrams, 
each showing a pattern of tripping wire attachment. As is seen from these 
figures, the models used in the experiments have two tripping wires which 
are attached to the cylindrical portion of the model in such a manner that 
the initial flow stagnation point lies on the midpoint between the two 
tripping wires. Accordingly, these models belong to the Type B shown in 
FIG. 2B. It is known from FIGS. 7A, 7C and 7E that the optimal azimuthal 
angles for attachment are approximately 60.degree., 50.degree. and 
45.degree. for the non-dimensional wire heights of 0.007, 0.010 and 0.014, 
respectively. For the high surface roughness, the flow condition at the 
upstream region affects that at the downstream region, and thus it seems 
to be valid to estimate that the optimal azimuthal angle .psi..sub.opt 
decreases according as the tripping wire diameter increases. It should be 
noted that the experimental results shown by the curves A, B and C in the 
respective FIGS. 7A, 7C and 7E correspond to the Reynolds numbers of 
2.6.times.10.sup.5 , 3.5.times.10.sup.5 and 4.0.times.10.sup.5, 
respectively. 
(2) More than Two Tripping Wires Attachment on the Cylindrical Portion 
With reference to FIGS. 8A and 8B, a description will hereinafter be given 
to experimental results in the case of the model which more than two 
tripping wires are attached to the cylindrical portion on its whole 
periphery and which the initial flow stagnation point may lie at any 
position on the periphery. FIGS. 8A and 8B are diagrams, each showing the 
experimental results of the relationship between the flat spin rate and 
the Reynolds number, in which the ordinate shows the flat spin rate, that 
is, number of the rotation N (r.p.m.) of the model and abscissa the 
Reynolds number R.sub.e. Further, FIGS. 8A and 8B show the experimental 
results for the non-dimensional tripping wire heights d of 0.007 and 
0.014, respectively. In FIG. 8A, a curve A shows a result for a model 
without surface roughness. Further, curves B, C, D, E, F, G, H and I show 
results for models designated by the notation ".phi.60-A-WP(6)", 
".phi.60-B-WP(6)", ".phi.45-A-WP(8)", ".phi.45-B-WP(8)", 
".phi.30-A-WP(12)", ".phi.30-B-WP(12)", ".phi.15-A-WP(24)" and 
".phi.15-B-WP(24)", respectively. In these notations, the "WP" is an 
abbreviation of the words "whole periphery" and, by way of example, the 
notation ".phi.60-A-WP(6)" means that the model used belongs to the Type A 
shown in FIG. 2A and that six tripping wires are attached to the 
cylindrical portion over the whole periphery in a manner to be spaced 
apart from each other by an equal distance of angle of 60.degree.. In FIG. 
8B, a curve A shows the result for a model without surface roughness and 
curves B and C for models designated by the notation ".phi.45-A-WP(8)" and 
".phi.45-B-WP(8)", respectively. 
It is known from the experimental results of FIGS. 8A and 8B that optimal 
angles for tripping wire attachment are 15.degree. and 45.degree. in the 
case of the non-dimensional wire heights d of 0.007 and 0.014, 
respectively, and that in that case the numbers of the tripping wires to 
be required are 24 and 8 correspondingly. It is known from the 
above-mentioned facts that, when the surface roughness height becomes 
higher, the distance of the angle between the adjacent tripping wires 
becomes larger correspondingly and accordingly the effect of the increase 
of the surface roughness height becomes more larger. Further, the change 
of the surface roughness height is accompanied with the change of the 
optimal angle for tripping wire attachment. This fact can be explained 
that the degree of the disturbance of the flow due to the tripping wires 
depends upon the surface roughness height. 
(3) Tripping Wire Attachment only on the Conical Portion and Both on the 
Cylindrical and Conical Portions 
It may be estimated that, in the case of a model having the cylindrical and 
conical portions being combined with each other, the existence of the 
conical portion is significant and that, in the case of the model without 
surface roughness, the asymmetric side force occurs, thereby causing the 
flat spin even at the supercritical region for the cylindrical portion. In 
the experiments for the model of the tripping wire attachment only on the 
cylindrical portion, it is observed that, at the critical Reynolds number 
region, there is no occurrence of the asymmetric side force acting on the 
cylindrical portion and hence of the flat spin due to the side force but, 
at the supercritical Reynolds number region, there are some flat spin 
phenomena which are seemed to be caused by the existence of the conical 
portion having no tripping wires. One example of such flat spin phenomenon 
for the model of ".psi.45-B(2)" is shown by a curve D in FIG. 6A. 
FIG. 9A is a diagram showing the experimental results for the models with 
and without surface roughness on the conical portion. The models used in 
this experiment have a plurality of tripping wires arranged on the 
cylindrical portion and/or conical portion in a pattern of the notation 
".phi.30-A(12)", as shown in FIG. 9B. In FIG. 9A, the ordinate shows the 
flat spin rate N (r.p.m.) and the abscissa the Reynolds number R.sub.e. 
Further, a curve A shows the result for the model without surface 
roughness, that is, without any spin alleviating or suppressing device, a 
curve B the result for the model with the tripping wires only on the 
cylindrical portion, a curve C the result for the model with the tripping 
wires only on the conical portion, and a curve D the result for the model 
with the tripping wires both on the cylindrical and conical portions. It 
is known from the experimental results shown in FIG. 9A that the surface 
roughness on the conical portion makes the critical Reynolds number lower 
and causes the considerably large flat spin rate at the lower Reynolds 
number region. However, it may be estimated that the effect of the surface 
roughness on the conical portion is not larger at the high Reynolds number 
region. 
Accordingly, it is concluded at the Reynolds number region of 
2.0.times.10.sup.5 -4.4.times.10.sup.5 that the asymmetric side force 
reducing effects and hence flat spin suppressing effects of the tripping 
wires attached only to the conical portion and both to the cylindrical and 
conical portions are inferior to those of the tripping wires attached only 
to the cylindrical portion. 
(4) Relationship between the Number of Rotation and Moment of Rotation 
Now, consider the relationship between the flat spin rate and the flat spin 
moment. When the model initially set in the stream so as to be of the Type 
B as shown in FIG. 2B begins to rotate for any reason, the current 
direction of the stream striking a surface area of the model between the 
adjacent two tripping wires changes from its original current direction 
with respect to the same surface area and therefore the model changes from 
Type B to Type C. It is impossible to perfectly simulate such condition as 
described above and to estimate flat spin moment from its result. 
Accordingly, the qualitative measurement of the flat spin moment was tried 
under such condition that .psi..sub.1 +.psi..sub.2 was held constant and 
that the current direction of the stream was changed variously. FIG. 10 
shows the results of this measurement for the models in which d=1.5 mm and 
.psi..sub.1 +.psi..sub.2 =60.degree.. In FIG. 10, the ordinate shows the 
flat spin moment C.sub.n and the abscissa the Reynolds number R.sub.e and 
curves A, B, C, D and E correspond to the models of ".psi.30-B(2)", 
".psi..sub.1 45-.psi..sub.2 15-C(2)", ".psi..sub.1 60-.psi..sub.2 0-C(2)", 
".psi..sub.1 75-.psi..sub.2 (-15)-C(2)" and ".phi.15-B(25)" , 
respectively. The flat spin moment C.sub.n around the supporting point of 
the model is small when .psi..sub.1 and .psi..sub.2 have equal values, but 
this moment increases when .psi..sub.1 and .psi..sub.2 become different 
from each other for any reason. This facts explain good the increase of 
the flat spin rate for the model ".psi.30-B(2)" as shown by the curve B in 
FIG. 6A. 
According to the above described results of the measurement, it is known 
that the flat spin moment at the high Reynolds number region is not so 
large and that the flat spin moment C.sub.n of the model having the 
tripping wires arranged over the whole periphery every angular distance of 
15.degree. is small and accordingly does not cause the flat spin. 
As mentioned above, in accordance with a method and an apparatus of this 
invention, the suitable positions and numbers of the tripping wires to be 
attached to the outer periphery of the tubular, slender or elongated 
flying body are defined beforehand, so that it is possible to reduce the 
asymmetric side force acting on the flying body and to suppress the 
undesirable motion, for example, rotation thereof caused by the side force 
as well as, for example, the flat spin of a rocket being recovered at a 
relatively low velocity. Further, in accordance with the invention, it is 
also possible to prevent a tubular, slender or elongated body, which is 
moving in a wind blowing in the forward direction, from yawing due to the 
wind. 
While the embodiments of the invention, as herein disclosed and described, 
constitute a preferred form, it is to be understood that other forms might 
be adopted.