STATEMENT OF GOVERNMENT RIGHTS  
       [0001] The United States Government has certain rights in the following invention under contract NAS8-97238 with Thiokol, Inc., now Alliant Techsystems, Inc. 
     
    
     
       BACKGROUND OF THE INVENTION  
         [0002]    1. Field of the Invention  
           [0003]    The present invention relates generally to laminar composite structures such as, for example, ablative coatings and ablative structures and, more specifically, to such structures which incorporate a variable angle tape wrap relative to a defined axis so as to maintain the angle of a given tape or ply at a specified angle relative to an associated tangent of the resulting surface geometry of the structure being formed.  
           [0004]    2. State of the Art  
           [0005]    Composite materials are often used to form ablative coatings or structures, referred to generally herein as ablative structures. Such ablative structures are conventionally used to dissipate thermal energy away therefrom so as to protect the vehicle or structure in which they are incorporated from exceeding a specified temperature and thereby preventing temperature-induced failure of the vehicle or structure. An exemplary use of ablative materials includes the forming of structures, or the coating of specified surfaces for various components, associated with aerospace vehicles including both internal and external components of such vehicles.  
           [0006]    The ablation of such a coatings or structures is a known phenomenon by which energy incident upon an ablating material is dissipated through vaporization of the material rather than conversion of the energy into heat. Thus, during exposure to the heat energy, the material of the ablative coating or structure is eroded away through vaporization, thereby dissipating the incident heat energy by converting the solid material into vaporous matter.  
           [0007]    For example, ablative coatings are conventionally utilized as heat shields for exposed surfaces of aerospace equipment such as rockets, missiles, space shuttles and similar vehicles. The ablative material serves to protect the structure from high thermal energy experienced due to high velocity conditions such as, for example, during launch or during re-entry into the earth&#39;s atmosphere.  
           [0008]    Ablative materials are also used to line the nozzles of rockets such as solid rocket motors. When employed in such a manner, the ablative material serves to protect the nozzle during the exhaust of high temperature gases therethrough.  
           [0009]    One conventional manner of forming ablative nozzle liners includes wrapping a plurality of plies of a carbon cloth phenolic (CCP), or other prepreg material about a mandrel to form a layered structure. After removal from the mandrel, the layered structure is cured and consolidated. The consolidated structure may be machined or otherwise prepared so as to fit within, and be bonded to, the interior surface of the nozzle.  
           [0010]    However, liners constructed in the above-described manner may experience “pocketing” or “ply lifting” during exposure of the liner to the flame and exhaust gases during ignition of a rocket and combustion of the rocket fuel. Such phenomena result in accelerated erosion and unpredictable char of the ablative material thus hampering the overall performance of the rocket motor.  
           [0011]    It has been recognized that the application angle of the individual plies of the ablative material used in forming the liner has a substantial effect on the phenomena of ply lifting and pocketing. For example, it has been determined that ply lifting and pocketing are substantially decreased when the ablative material is applied with the individual plies being oriented constantly at an optimum angle with respect to the heated surface of the liner itself. However, the ablative material is conventionally applied by wrapping the material, conventionally in tape form, circumferentially about a mandrel at a fixed angle relative to a defined axis such as the centerline of the liner. The conventional wrapping of plies at a fixed angle relative to a defined axis, coupled with the fact that most nozzles, and thus their associated liners, include convex and/or concave surfaces, results in a plurality of plies within the structure which fail to maintain the optimum angle with respect to the resulting heated surface of the liner.  
           [0012]    For example, referring to FIG. 1, a portion of an ablative liner  10  for a rocket nozzle is shown. The ablative liner  10  is formed of a plurality of plies  12  of a CCP or other appropriate ablative material. It is noted that, for purposes of clarity, cross-hatching is not used in depicting the cross-sectional area of the plurality of plies  12 .  
           [0013]    The ablative liner  10  includes an exterior surface which is intended to be the heated surface  14  during the ignition of an associated rocket motor and combustion of its associated fuels. The heated surface  14  includes a convex geometry such as, for example, one might see in the throat region of a rocket nozzle as will be appreciated by those of ordinary skill in the art.  
           [0014]    At a first end  16  of the heated surface, the plies  12  are oriented at a first angle, for example, approximately 45° to the heated surface  14 . More specifically, a ply  12 A at the first end  16  is oriented at an angle of approximately 45° to an associated tangent  18 A of the heated surface  14  at the first end  16 . However, because of the geometry of the heated surface  14 , and because the plies  12  have been applied at a fixed angle relative to a centerline  20  of the liner  10  (which is also the centerline of a mandrel on which the liner is formed), the angle of the plies  12  at a second end  22  of the heated surface  14  are oriented at an angle which substantially deviates from the desired 45° orientation.  
           [0015]    In other words, a ply  12 B spaced further towards the second end  22  of the heated surface  14  is oriented at an angle substantially greater than 45° to a tangent  18 B of the heated surface  14  at the second end  22 . Indeed, depending on the geometry of the ablative liner  10 , the angle of a given ply may approach 90° relative to an associated tangent, at which angle pocketing becomes more pronounced. A similar result may occur with other geometries, including, for example, a convex geometry. Furthermore, in some geometries, the plies  12  may change angles, relative to a tangent of the heated surface  14 , from, for example, 45° towards 0°, at which angle ply lifting becomes more pronounced.  
           [0016]    Thus, a nozzle liner having a heated surface geometry which features any curves or changes in angle relative to its centerline, and which is formed through continuous wrapping at a fixed ply angle, is likely to experience some degree of ply lifting and pocketing during ignition of the rocket motor.  
           [0017]    Some efforts have been made to tailor the angle of the plies depending on their respective location within a nozzle. For example, U.S. Pat. No. 6,330,792, issued Dec. 18, 2001, and U.S. Pat. No. 6,195,984, issued Mar. 6, 2001, both to Cornelius et al., describe a process of forming an ablative liner for a rocket nozzle. The Cornelius patents disclose the formation of a first segment of the nozzle liner, extending approximately from the exhaust end of the nozzle to near the throat prior to substantial constriction thereof, with the plies being wrapped about a mandrel at a specified angle relative to the axis of the mandrel. The first section is then cured and the terminating end of the section is machined to a specified angle, different than that of the ply angle exhibited within the first formed section.  
           [0018]    A second section of the liner is then formed by wrapping additional plies from the machined end of the first section to approximately the constricted portion of the throat. The ply angle for the second section is determined by the angle of the first section&#39;s machined end. The second section is cured and its terminating end is machined at a new angle, different from that of the ply angle exhibited within the second formed section.  
           [0019]    The process thus continues with the forming the liner section by section with each new section being cured and machined to effect a change of angle in the plies for any new section to follow. However, the process described by Cornelius requires a relatively complex fabricating process which includes laying up the plies of tape, individually curing each section and machining the terminating end of each cured section. Additionally, there may be issues of integrity due to the individual curing of each segment or section of the liner and subsequent bonding together of such segments due to the discontinuity of the material. In other words, individual segments are bonded together solely by the matrix material due to the discontinuity of fibers therebetween.  
           [0020]    Furthermore, while the Cornelius patents allow for a limited number of changes in the ply angle, each section of the liner is actually being formed with the plies being wrapped or laid-up at a fixed angle relative to the centerline of the mandrel. In other words, while ply angles change from section to section, the ply angles remain fixed within each given section. Thus, with a curved geometry, the liner will, as a practical matter, continue to have a number of plies which vary from an optimally specified angle.  
           [0021]    In view of the shortcomings in the art, it would be advantageous to provide an ablative coating or structure, and a method of forming such a coating or structure, which allows for continuous variability in the ply angles of the coating or structure relative to a specified axis. Additionally, it would be advantageous to provide such a structure and method which enables substantially all of the plies to be positioned and oriented at a specified angle relative to the intended heated surface or, more specifically, to an associated tangent of the intended heated surface.  
         BRIEF SUMMARY OF THE INVENTION  
         [0022]    In accordance with one aspect of the present invention, a method is provided for forming a laminar structure. The method includes providing a substantially continuous length of composite tape, wherein the composite tape exhibits a specified nominal width. The substantially continuous length of composite tape is wrapped about a mandrel to form a structure having a plurality of laminar plies. The initial ply of the wrap about the mandrel is oriented at a first specified angle relative to a centerline of the mandrel. As the tape is wrapped about the mandrel, a change in the cross-sectional angle of the composite tape, relative to the centerline, may be induced from one ply to another ply other than by reference to the shape of the mandrel.  
           [0023]    The change in angle between plies may be effected by building or introducing a ramp structure within the laminar structure amongst individual plies. For example, a ramp structure may be introduced by varying the width of the composite tape as it is wound around the mandrel such that one or more plies having a width different than the nominal width are disposed between two plies of nominal width. In another example, a ramp structure may be introduced which includes a plurality of sections of composite tape which each exhibit a substantially serpentine profile along an edge thereof. The serpentine profile may define a set of fingers extending transversely relative to the respective length of a given section. The plurality of sections may then be disposed adjacent each other in an overlaying fashion with the set of fingers of one section being laterally offset, in a direction along the length of the respective section, relative to the set of fingers on an adjacent section of composite tape.  
           [0024]    In accordance with another aspect of the invention, a method of forming an ablative structure is provided. The method includes laying up a continuous length of composite tape material in a laminar manner to define an intended heat receiving surface of the ablative structure wherein at least a portion of the intended heat receiving surface exhibits a nonlinear cross-sectional geometry as taken parallel to a defined centerline of the ablative structure. The plurality of plies are oriented such that each ply is substantially at a predefined cross-sectional angle relative to an associated tangent of the intended heat receiving surface. The method may further include introducing or building ramps within the structure in a manner such as is described herein.  
           [0025]    In accordance with another aspect of the present invention, an ablative structure is provided. The ablative structure includes a plurality of plies of a composite tape material which are continuously laid-up in a laminar manner to define an intended heat receiving surface. The intended heat receiving surface exhibits a nonlinear surface geometry relative to a defined centerline of the ablative structure. Each of the plurality of plies are substantially oriented at a predefined cross-sectional angle relative to an associated tangent with the intended heat receiving surface.  
           [0026]    The ablative structure may further include ramps which are formed within the structure to assist in maintaining the angle of individual plies substantially at a predefined angle. The structure may further be configured as a nozzle liner wherein the intended heat receiving surface includes a relatively constricted throat section 
       
    
    
     BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS  
       [0027]    The foregoing and other advantages of the invention will become apparent upon reading the following detailed description and upon reference to the drawings in which:  
         [0028]    [0028]FIG. 1 is a cross-sectional view of a portion of a prior art ablative liner for a rocket nozzle;  
         [0029]    [0029]FIG. 2 is a cross-sectional view of a rocket motor including a nozzle having an ablative liner according to one embodiment of the present invention;  
         [0030]    [0030]FIG. 3A is a partial cross-section view of an ablative liner being formed on a mandrel according to an embodiment of the present invention;  
         [0031]    [0031]FIG. 3B is a detailed view of a portion of the ablative liner of FIG. 3A in accordance with an embodiment of the present invention;  
         [0032]    [0032]FIG. 3B is a detailed view of a portion of the ablative liner of FIG. 3A in accordance with another embodiment of the present invention;  
         [0033]    [0033]FIG. 4A and 4B show elevational views of ramped sections of plies which may be used according to an embodiment of the present invention;  
         [0034]    [0034]FIGS. 5A and 5B are elevational front and side views, respectively, of tape plies used in forming an ablative structure according to an embodiment of the present invention; and  
         [0035]    [0035]FIGS. 6A and 6B are elevational front and side views, respectively, of tape plies used in forming an ablative structure according to an embodiment of the present invention. 
     
    
     DETAILED DESCRIPTION OF THE INVENTION  
       [0036]    Referring to FIG. 2, an exemplary rocket motor  100  is shown including generally a nose cone  102 , a body portion or fuselage  104 , and a nozzle  106 . The rocket motor  100  includes a source of fuel such as, for example, a solid fuel source  108 , although the present invention may be practiced with other types of rockets and rocket motors.  
         [0037]    The nozzle  106  includes an outer shell structure  110  and an ablative liner  112  disposed therein adjacent an interior surface of the shell structure  110 . The nozzle  106  includes a combustion end  114  coupled with the aft end  116  of the rocket motor&#39;s body portion  104 , an exhaust end  118  and a throat section  120  between the combustion end  114  and the exhaust end  118  which is of a relatively constricted diameter as compared to the combustion and exhaust ends  114  and  118 .  
         [0038]    Referring to FIG. 3A, the ablative liner  112  may be formed of a prepreg material such as, for example, a carbon cloth phenolic (CCP) material, by wrapping a continuous length  119  of the CCP or other ablative material, in tape form, circumferentially about a mandrel  121  such that individual wraps or plies  122  of the material are built up in a laminar manner. It is noted that FIG. 3A and the subsequently described FIGS.  3 B- 6 B do not include cross hatching in the cross-sectional views of the various plies (e.g. plies  122 ) for purposes of clarity. It is also noted that, while the present invention is discussed in exemplary embodiments of ablative structures such as an ablative liner  112 , other composite and laminar-type structures may be formed in accordance with the present invention.  
         [0039]    Referring to FIG. 3B, a detailed view of a portion of the ablative liner  112 , as indicated in FIG. 3A, is shown including a portion which is located in the throat section of the liner  112 . The heated surface, or more aptly, the intended heat receiving surface  124  of the ablative liner  112  exhibits a generally non-linear cross-sectional geometry relative to the longitudinal centerline  126  of the ablative liner  112  (see also FIG. 3A). As discussed above herein, conventional techniques of forming an ablative liner would require that the plies be oriented at a fixed cross-sectional angle relative to the centerline  126  resulting in non-optimal angles of the plies relative to intended heat receiving surface. However, the present invention allows for continuously variable ply angles throughout a given geometry.  
         [0040]    Still referring to FIG. 3B, the individual plies  122  of the ablative liner  112  have been wrapped about a mandrel  121  (FIG. 3A) to form a laminar structure. However, at various locations, plies of strategically varied width (see plies  128 ) have been laid up among the individual plies  122  of nominal or conventional width. The interspersement of plies  128  having varied widths allows for an effective “ramp structure” to be built into the laminar structure which forms the ablative liner  112 , thereby causing a desired shift in the cross-sectional angle of the plies  122 , relative to the centerline  126 , as one traverses longitudinally along the intended heat receiving surface  124  of the ablative liner  112 .  
         [0041]    For example, plies  122 A and  122 B are of a specified nominal width while one or more, in this example two, varied width plies  128 A and  128 B are disposed therebetween. It is additionally noted that the two varied width plies  128 A and  128 B are also of different widths as compared to each other. Such a combination of the two variable width plies  128 A and  128 B produce a ramp structure which effects a desired change in angle from the first adjacent nominal width ply  122 A to the next adjacent nominal width ply  122 B. Such a process allows for a controlled change, which may be as gradual as desired, in the cross-sectional ply angle relative to the centerline  126 .  
         [0042]    Stated otherwise, the ablative liner  112 , or other structure formed according to the present invention, results in a laminar structure wherein the individual plies  122  are substantially maintained at a specified cross-sectional angle with respect to a tangent associated with each ply at the intended heat receiving surface  124  of the ablative liner  112 . Thus, for example, ply  122 A is oriented substantially at a specified or predetermined cross-sectional angle with respect to a tangent  129 A associated with the ply  122 A at the intended heat receiving surface. Additionally, ply  122 C, while oriented at a different cross-sectional angle than ply  122 A relative to the centerline  126 , is oriented at substantially the same cross-sectional angle with respect to its associated tangent  129 B at the intended heat receiving surface  124  of the ablative liner  112 .  
         [0043]    In one example, varied width plies  128  are utilized to maintain each of the nominal width plies  122  at an cross-sectional angle of substantially 45° relative to an associated tangent of the intended heat receiving surface  124 . Utilizing varied width plies  128  to vary the cross-sectional angle (relative to the centerline  126 ) throughout the ablative liner, the nominal width plies  122  may be kept at the specified cross-sectional angle within a specified tolerance of, for example, ±5° relative to an associated tangent of the intended heat receiving surface  124 .  
         [0044]    It is noted that ramp structures of various sizes and configurations may be incorporated to effect angle changes of varied magnitudes among the plies  122  as needed or desired. Thus, while the above example discusses the formation of a ramp structure utilizing two varied width plies  128 A and  128 B, numerous plies of varied width may be used in any desired sequence to build a relatively larger ramp structure effecting a larger substantially instantaneous change of angle within the structure. Also, a single varied width ply may be employed to effect a smaller change in ply angle. Furthermore, it is noted that the actual width(s) of the varied width plies  128  may be strategically designed to help influence the magnitude of change in the ply angle.  
         [0045]    Referring briefly to FIG. 3C, another exemplary embodiment is shown wherein varied width plies  128  are generally of random frequency and width relative to the nominal width plies  122 . Thus, an angle change need not be effected by a series of adjacent varied width plies  128  which sequentially and continually decrease in width—or increase in width, as the case may be. Rather, the varied width plies  128  may be place periodically among the nominal width plies  122  and at random widths in order to effect a desired rate of turn and/or in order to obtain a desired level of uniformity. Such randomness in the width and frequency of placement of the varied width plies  128  may help to avoid resin rich edges, provide greater uniformity and improve the overall quality of the final structure.  
         [0046]    Referring now to FIG. 4A, an exemplary ramped structure  130  is formed from a plurality of varied width plies  128 . The varied width plies  128  exhibit a differential in width D 1  between adjacent plies. By varying this differential D 1  the angle θ may be altered. Thus, if the differential D 1  is increased, the ramp structure will exhibit a relatively smaller angle θ and vice versa.  
         [0047]    Referring briefly to FIG. 4B, it is also noted that a ramped structure  130 ′ may be formed wherein the differential in width between adjacent varied width plies  128  need not be constant at each step. Thus, there may be a first differential D 1  of a first magnitude between two adjacent plies  128  in one portion  132  of the ramp structure  130 ′ and a second differential D 2  of a another magnitude between two adjacent plies  128  in another portion  134  the ramp structure  130 ′. Additionally, as noted above, a ramp structure may also include a single varied width ply  128  disposed between to nominal width plies  122 .  
         [0048]    As noted above, an ablative structure such as the liner  112  shown and described in FIGS.  3 A- 3 C may be formed by continuously wrapping the tape or individual plies  122  and  128  about a mandrel  121  in a laminar fashion. The change in ply angle, through the introduction of varied width plies  128 , may be effected by slitting, cutting, or trimming the width of the tape “on the fly” just prior to the tape&#39;s application to the mandrel  121 . Thus, an ablative structure may be formed having a continually varied or adjusted cross-sectional ply angle, relative to the defined centerline  126 , by cutting tape to a desired width during application thereof to form ramp structures, as needed, during the wrapping process. Such a process is advantageous as it does not require the wrapping process to stop and start numerous times in order to perform associated curing and/or machining processes and the effective width of a ply may be reduced from the nominal width to a varied width in a continuous manner, linearly or nonlinearly, rather than in an abrupt stepped manner. Accordingly, integrity of the resulting laminate structure may be enhanced through a reduction of potential void space.  
         [0049]    Further, as noted above, the continual and gradual nature of the process allows for more comprehensive control of the ply angle. Thus, rather than changing the cross-sectional ply angle three or four times, such as by forming individual sections or segments with each section having a newly defined but constant cross-sectional ply angle, the cross-sectional ply angle is continuously varied according to the present invention to ensure that each ply is substantially at an optimal cross-sectional angle relative to a tangent of the intended heat receiving surface. Furthermore, the process according to the present invention is advantageous in that the ablative liner  112 , or other laminar structure, may be cured and consolidated as unitary member rather than the separate curing and/or consolidating of individual sections which are subsequently assembled together and which lack fiber continuity therebetween.  
         [0050]    Referring now to FIGS. 5A and 5B, a ramp structure  130 ″ is shown for use in altering the ply angle of an ablative structure according to another embodiment of the present invention. The ramp structure  130 ″ includes a plurality of serpentine plies  140  which exhibit an undulating profile with respect to their respective widths. Thus, for example, referring to the top serpentine ply  140 A of FIG. 5A, the width of the ply  140  alternately varies between a minimum width W 1  and a maximum width W 2  such that a repeating pattern of transversely extending fingers  142  are effectively defined along length of the ply  140 .  
         [0051]    In forming the ramp structure  130 ″, the top serpentine ply  140 A overlays the second serpentine ply  140 B in an offset manner such that the fingers  142  of the top serpentine ply  140 A intermesh, or are effectively interdigitized, with the fingers  142  of the second serpentine ply  140 B. In other words, if the undulating profile of the serpentine plies  140 A and  140 B were described as being substantially sinusoidal (although, it is noted that such a description is only exemplary), the sinusoidal patterns of the two plies  140 A and  140 B might be described as being 180° out of phase with one another.  
         [0052]    The overlaying and interdigitized relationship of the of the two serpentine plies  140 A and  140 B result in a cross-sectional profile of a ramp structure  130 ″ such as is shown in FIG. 5B. The fingers  142  of the two plies  140 A and  140 B intermesh to form a first section  144  which is effectively one ply thick, while a second section  146  is two plies thick wherein portions of each ply  140 A and  140 B are stacked upon each other in a laminar manner.  
         [0053]    It is noted that, while FIG. 5B shows a “step”  148  between the first section  144  and the second section  146 , it is somewhat exaggerated for purposes of illustration. Rather, the transition between the two sections  144  and  146  is actually more continuous and gradual than that which is illustrated. The use of such a ramp structure  130 ″ having a more continuous and gradual transition between ply thicknesses may be helpful in smoothing out ply distortions in the resulting structure and provides smoother transitions when used to change the cross-sectional ply angles in a laminar structure.  
         [0054]    Referring now to FIGS. 6A and 6B, another ramp structure  130 ′″ is shown which is formed with serpentine-type plies  140 A- 140 D. The ramp structure  130 ′″ is generally similar to that which is shown and described with respect to FIGS. 5A and 5B except that more plies  140 A- 140 D are being used and they are positioned differently with respect to each other. For example, rather than the fingers  142  of the top ply  140 A being intermeshed or interdigitized with the fingers  142  of the next underlying ply  140 B, the fingers  142  of adjacent plies (e.g., plies  140 A and  140 B, plies  140 B and  140 C, etc.) are offset from one another a specified lateral distance X.  
         [0055]    Thus, in the exemplary embodiment of FIGS. 6A and 6B, which includes four overlaying plies  140 A- 140 D, the offset distance X may be, for example, one fourth (¼) of the distance Y between two adjacent fingers  142 A and  142 B of a given ply (e.g., ply  140 A) and, thus, using the prior phase angle analogy, each ply is 90° out of phase with the next adjacent ply. It is noted, however, the offset distance X need not be inversely related to the number of plies being used and that the offset distance may varied to specify the angle of a given ramp structure.  
         [0056]    Referring to FIG. 6B, the resulting ramp structure  130 ′″ includes a first section  150  having the equivalent thickness of a single ply, a second section  152  having the equivalent thickness of two plies, a third section  154  having the equivalent thickness of three plies and a fourth section  156  having a thickness of four plies. Again, it is noted that while the transitions between adjacent sections  150 ,  152 ,  154  and  156  are shown as steps for purposes of illustration, the transitions are actually more continuous and gradual.  
         [0057]    It is noted that the width of the individual fingers  142 , as well as spacing therebetween, may be a function of one or more variables including, for example, the desired rate of change in the cross-sectional angle, the desired thickness of the final structure, and/or the diameter of the mandrel or structure to which the tape is being applied. Furthermore, the width of the fingers  142  and the spacing therebetween need not be dependent on each other. In other words, one embodiment might include relatively wide fingers  142  with relatively narrow spacing therebetween, while another embodiment might include relative narrow fingers  142  with relative wide spacing therebetween.  
         [0058]    The application of the varied width plies  128 , or the serpentine plies  142 , may be effected by utilizing one or more rolls of such plies and introducing them into the structure (i.e., between nominal width plies) as required to effect a desired cross-sectional angle change. Indeed, multiple rolls of varied width plies  128  may be used wherein ply width is varied from one roll to another. In one embodiment, the varied width plies  128  (or serpentine plies  142 ) may be fed through a cut, clamp and restart mechanism. In another embodiment, the varied width plies  128  (or serpentine plies  142 ) may hand fed into the into the structure as it is being formed.  
         [0059]    As noted previously above, the application of varied width plies  128  may also be effected by using a trim feature wherein the nominal width ply is trimmed prior to placement on the structure, thereby forming a varied width ply, from the nominal width ply, on demand. Such a trimming apparatus might include, for example, a platen, over which a nominal width ply is passed, and a knife member which is selectively actuated to trim the ply to a desired width. The trimming apparatus might further include a scraper or other mechanism to assist in removing the trimmed or unwanted section away from the newly formed varied width ply.  
         [0060]    Regardless of the manner of application, it may also be desirable to control the angle of any apparatus used to apply the plies (e.g., a roller or platen used to press the plies into place) such that constant application pressure is applied across the cross sectional width of each ply of the structure being formed. Thus, as the cross-sectional angle of the plies is varied, it may be desirable to monitor (or predict) such change in angle and likewise cause the angle of an applying roller or platen to vary in a congruous manner.  
         [0061]    While the invention may be susceptible to various modifications and alternative forms, specific embodiments have been shown by way of example in the drawings and have been described in detail herein. However, it should be understood that the invention is not intended to be limited to the particular forms disclosed. Rather, the invention includes all modifications, equivalents, and alternatives falling within the spirit and scope of the invention as defined by the following appended claims.
Composite laminar structures which exhibit nonlinear surfaces and which exhibit a variable ply angle relative to a defined axis, and methods of forming the same. A change in ply angle may be induced by the formation of a ramp structure, such as by the introduction of one or more adjacent or periodically place plies of varied width. Varied width plies may be introduced by cutting or trimming the width of a nominal width ply during lay-up of the composite material. In another embodiment, the ramp structures may be formed by introducing multiple sections of composite material, each of which exhibits a substantially serpentine profile along an edge thereof so as to define a plurality of fingers extending transversely relative to the respective length of each section. The plurality of sections may then be layered adjacent one another, or periodically dispersed, with each respective set of fingers being offset relative to the set of fingers of a next closest layer.