Patent Publication Number: US-7585235-B2

Title: Baseball or softball bat

Description:
This nonprovisional application is based on Japanese Patent Applications Nos. 2006-295920 and 2007-264003 filed with the Japan Patent Office on Oct. 31, 2006 and Oct. 10, 2007, respectively, the entire contents of which are hereby incorporated by reference. 
   BACKGROUND OF THE INVENTION 
   1. Field of the Invention 
   The present invention relates to a baseball or softball bat and, more specifically, to a baseball or softball bat having superior restitution characteristic. 
   2. Description of the Background Art 
   Baseball or softball bats formed of various materials including wood, metal such as titanium, titanium alloy and aluminum alloy, and fiber-reinforced plastic prepared by impregnating carbon fiber, glass fiber or the like with matrix resin and curing, have been available in the market. 
   Conventionally, in order to improve restitution characteristic of a bat, Japanese Patent Laying-Open No. 2002-052108 (Patent Document 1) discloses a bat having a tubular insert arranged on the inner circumferential side of a hitting portion and an elastomer filled between an inner wall and an outer circumferential surface of the tubular insert at the hitting portion. For further improvement of restitution characteristic, Japanese Patent Laying-Open No. 2001-190724 (Patent Document 2), for example, discloses a bat having fiber-reinforced plastic laminated on an outer circumference of a metal pipe, in which weak boundary layer is provided between the metal pipe and the fiber-reinforced plastic layer. Further, International Patent Publication No. 00/23151 (Patent Document 3) discloses a bat having a metal tubular member embedded in a tubular base forming the hitting portion of the bat, with a weak boundary layer formed on the surface of the metal tubular member. Here, the weak boundary layer is formed of a release agent such as wax or a release film such as polyethylene film, so as to prevent adhesion of members facing with each other with the weak boundary layer interposed. 
   The conventionally proposed bats described above, however, have the following problems. Specifically, in the bat disclosed in Patent Document 1, though different materials are laminated at the hitting portion of the bat, these layers are adhered and integrated to each other, and therefore, restitution characteristic is not much improved at the hitting portion of the bat at the time of hitting the ball. Further, dependent on the adhesion strength between the tubular insert and the inner wall of the hitting portion, the tubular insert may possibly be separated from the inner wall at the hitting portion, due to repeated hitting during use. 
   The bat disclosed in Patent Document 2 is said to improve restitution characteristic at the hitting portion of the bat, as the fiber-reinforced plastic layer and the metal pipe can deform independently when hitting the ball. In order to fix the position of fiber-reinforced plastic with respect to the metal pipe, however, the laminated body and the metal pipe are adhered without forming the weak boundary layer, at end portions (opposite ends in the axial direction of the bat) of the laminated body of fiber-reinforced plastic. Therefore, the laminated body does not move along the axial direction of the bat. Further, in the bat disclosed in Patent Document 3 also, the metal tubular member is embedded in the tubular base and, therefore, the metal tubular member does not move along the axial direction of the bat. 
   Therefore, in the bats disclosed in Patent Documents 2 and 3 above, vibration and shock of the bat at the time of hitting the ball would be alleviated, possibly at a high percentage, by energy loss due to the radial motion of the laminated body and the metal pipe or of the metal tubular member and the tubular base. As a result, such vibration and shock can be alleviated only moderately, and hence, feeling of hitting with the bat could be unsatisfactory. 
   SUMMARY OF THE INVENTION 
   The present invention was made to solve the above-described problem and its object is to provide a baseball or softball bat having improved restitution characteristic and capable of preventing degraded feel of hitting caused by vibration or shock at the time of hitting. 
   The present invention provides a baseball or softball bat including a ball hitting portion, a tapered portion and a grip portion, provided with an outer circumferential member, an inner circumferential member and a non-adhesive portion. The outer circumferential portion is a cylindrical member constituting at least the hitting portion. The inner circumferential member is arranged on the inner circumferential side of the outer circumferential member. The inner circumferential member has a taper side end, i.e., an end portion on the side of the tapered portion, and a tip side end positioned opposite to the taper side end, fixed on the outer circumferential member. The non-adhesive portion is arranged at least partially on a region where the outer circumferential member and an unfixed portion of the inner circumferential member are opposite to each other, in order to prevent adhesion of the outer circumferential member and the unfixed portion of the inner circumferential member, that is, a portion other than the tip side end and including the taper side end. 
   In such a structure, the hitting portion is formed by the outer circumferential member and the inner circumferential member, and the outer circumferential member and the inner circumferential member are arranged with the non-adhesive portion interposed. Therefore, at the time of hitting the ball, the inner circumferential member and the outer circumferential member can deform independent from each other. Specifically, the inner circumferential member and the outer circumferential member can elastically deform more easily when hitting the ball, as compared with the outer circumferential member and the inner circumferential member adhered to each other over the entire surfaces. Because of the restoring force of the outer circumferential member and the inner circumferential member from the elastic deformation, flying distance of the hit ball can be increased. In other words, a bat having superior restitution characteristic can be realized. 
   In the bat, the non-adhesive portion may extend to the taper side end of the inner circumferential member. 
   In that case, as the non-adhesive portion extends to the end of the inner circumferential member on the side of the tapered portion, the inner circumferential member is not adhered to the outer circumferential member at the taper side end. Specifically, the inner circumferential member is fixed to the outer circumferential member at the end (tip end side of the bat) opposite to the taper side end, and the taper side end of the inner circumferential member is not bound by the outer circumferential member. Therefore, when vibration or shock occurs as the bat hits the ball, the vibration and shock can be alleviated (damped) not only by displacement of the inner and outer circumferential members in the radial direction but also by displacement of the taper side end of the inner circumferential member in the axial direction of the bat. Therefore, the vibration and shock at the time of hitting can quickly be alleviated, and hence, bad feeling caused by such vibration can be avoided. 
   The non-adhesive portion may have any structure, provided that it can prevent adhesion between the inner and outer circumferential members. By way of example, the non-adhesive portion (also referred to as a weak boundary layer) may be a layer formed of a material having releasing effect. Specifically, the non-adhesive portion may be a releasing film formed of polypropylene, polyethylene, silicone or the like, or a sheet of releasing paper coated with such resin. Besides, the non-adhesive portion may be formed by applying or spraying wax-type releasing agent, silicone-based releasing agent or fluorine-based releasing agent, to the outer circumferential surface of the inner circumferential member and/or inner circumferential surface of the outer circumferential member. Further, as the non-adhesive portion, a structure in which the surface of inner circumferential member and the surface of the outer circumferential member are not adhered to each other but in slidable and/or separable contact, may be adopted. 
   In the bat described above, the inner circumferential member may consist of a plurality of layers laminated with other non-adhesive portions interposed, in the radial direction of the outer circumferential member. Tip side ends of the plurality of layers may be fixed to each other. At least one of the other non-adhesive portions may extend to the taper side end of the inner circumferential member. Further, in the bat described above, all of the other non-adhesive portions may extend to the taper side end of the inner circumferential member. 
   In such a case, as the inner circumferential member is formed of a plurality of layers, the number of layers that elastically deform independently at the time of hitting the ball can be increased. Consequently, the number of layers that generate restoring force from elastic deformation increases, and as a result, the flying distance of the ball can more reliably be increased. Further, assume that the inner circumferential member is formed by a plurality of layers while the total thickness of the inner circumferential member is not changed from when the inner circumferential member is formed of a single layer. In that case, the strength of the inner circumferential member as a whole can be made approximately equal to that when the inner circumferential member is formed of a single layer, while thickness of each of the plurality of layers is smaller than the single layer. Therefore, amount of elastic deformation of the inner circumferential member at the time of hitting becomes larger. Thus, the restoring force from elastic deformation can be increased, and the flying distance of the ball can more reliably be increased. 
   The bat may include a cap member covering an end of the outer circumferential member opposite to the taper side end. 
   In this case, as the end portion opposite to the taper side end of the outer circumferential member (that is, the tip side end of the bat) is covered by the cap member, the outer circumferential member can be prevented from directly bumping against the ground, when the batter lets go of the bat after hitting. Thus, possible damage to the outer circumferential member at the tip side end of the bat caused by bumping against the ground can be decreased. 
   In the bat, the cap member and the inner circumferential member may be formed integrally. As the inner circumferential member and the cap member can be formed at one time, the number of process steps in manufacturing the bat can be reduced. This lowers the manufacturing cost of the bat. 
   In the bat described above, the outer circumferential member may include a portion that will be a part of an end sidewall, forming an end surface of the bat, at the end opposite to the taper side end. At the portion that will be a part of the end sidewall of outer circumferential member, an opening may be formed. The inner circumferential member may include a portion that fills the opening and is adhered to the inner wall of the opening. 
   In that case, it becomes unnecessary to separately prepare a cap member that covers the end surface of the bat (that is, the tip end surface of the bat). Therefore, the number of components and the number of manufacturing steps of the bat can be reduced. Thus, the manufacturing cost of the bat can be reduced. 
   In the bat described above, the non-adhesive portion may be formed of at least one of a releasing film and a releasing agent. 
   In that case, by a simple method of placing the releasing film and/or releasing agent on the outer circumferential surface of the inner circumferential member in advance, the bat in accordance with the present invention can be formed. Here, the releasing film means a film body having releasing function such as a resin film formed of polypropylene, polyethylene or silicone as mentioned above, or a film having a releasing agent placed on or applied to its surface. 
   In the bat described above, the inner circumferential member may extend from the hitting portion to the tapered portion. In that case, as the inner circumferential member extends from the hitting portion to the tapered portion, the portion having improved restitution characteristic can be widened to the tapered portion of the bat. Therefore, even when the ball is hit at a boundary between the hitting portion and the tapered portion as is often experienced by amateur players or even at the tapered portion, the flying distance of the ball can be increased as compared with the conventional example. 
   By the present invention, a bat having improved restitution characteristic and not much degrading hit feeling can be realized. 
   The foregoing and other objects, features, aspects and advantages of the present invention will become more apparent from the following detailed description of the present invention when taken in conjunction with the accompanying drawings. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  is a schematic cross-section showing a structure of Embodiment 1 of the baseball or softball bat in accordance with the present invention. 
       FIG. 2  is a partial, enlarged schematic cross-section of the bat shown in  FIG. 1 . 
       FIG. 3  is a schematic cross-section along line III-III of  FIG. 2 . 
       FIG. 4  is a flowchart representing a method of manufacturing the bat shown in  FIGS. 1 to 3 . 
       FIG. 5  is a partial schematic cross-section showing a modification of Embodiment 1 of the bat in accordance with the present invention. 
       FIG. 6  is a partial schematic cross-section showing Embodiment 2 of the bat in accordance with the present invention. 
       FIG. 7  is a schematic cross-section along line VII-VII of  FIG. 6 . 
       FIG. 8  is a partial schematic cross-section showing a modification of Embodiment 2 of the bat in accordance with the present invention. 
       FIG. 9  is a partial schematic cross-section showing Embodiment 3 of the bat in accordance with the present invention. 
       FIG. 10  is a partial schematic cross-section showing Embodiment 4 of the bat in accordance with the present invention. 
       FIG. 11  is a partial schematic cross-section showing Embodiment 5 of the bat in accordance with the present invention. 
       FIG. 12  is a partial schematic cross-section illustrating a sample of Comparative Example 1 prepared for the embodiment of the present invention. 
       FIG. 13  is a partial schematic cross-section illustrating a sample of Comparative Example 2 prepared for the embodiment of the present invention. 
       FIG. 14  is a schematic illustration showing a structure of a measuring apparatus used for measuring restitution coefficient. 
       FIG. 15  is a graph showing result of measurement of restitution coefficients, measured for samples of Embodiment 1 and Embodiment 2 of the present invention and Comparative Example 1 and Comparative Example 2. 
       FIG. 16  is a schematic illustration showing a structure of a measuring apparatus used for measuring logarithmic decrement. 
       FIG. 17  is a graph showing result of measurement of logarithmic decrement of Embodiment 1, Embodiment 2, Comparative Example 1 and Comparative Example 2. 
       FIG. 18  is a schematic illustration showing a structure of a measuring apparatus used for measuring eigenfrequency of hitting portion of the bat. 
   

   DESCRIPTION OF THE PREFERRED EMBODIMENTS 
   In the following, embodiments of the present invention will be described with reference to the figures. Throughout the figures, the same or corresponding portions are denoted by the same reference characters, and description thereof will not be repeated. 
   Embodiment 1 
   Referring to  FIGS. 1 to 3 , Embodiment 1 of the bat in accordance with the present invention will be described. 
   Referring to  FIGS. 1 to 3 , a bat  1  in accordance with the present invention includes, from the tip end side, a tip end  10 , a hitting portion  11 , a tapered portion  12  and a grip portion  13 . Bat  1  includes an outer circumferential member  3  extending from tip end  10  to grip portion  13  and defining the shape of the bat as a whole; an inner circumferential member  5  adhered to outer circumferential member  3  on the side of tip end  10  of outer circumferential member  3 ; a grip end  15  connected and fixed to outer circumferential member  3  at the end of grip portion  13  (rear end of bat  1 ); and a non-adhesive portion  7  as a weak boundary layer (WBL) arranged between outer circumferential member  3  and inner circumferential member  5  positioned on the side of inner circumferential surface at hitting portion  1  of outer circumferential member  3 . At hitting portion  11 , as shown in  FIG. 3 , bat  1  has a three-layered structure including, from the outer circumferential side, outer circumferential member  3 , non-adhesive portion  7  and inner circumferential member  5 . 
   Inner circumferential member  5  is arranged to extend from the tip end  10  of the bat through hitting portion  11  to tapered portion  12 . A tip end portion  23  of inner circumferential member has an inner circumferential member extension  22  positioned to turn over the outer circumferential side of tip end  20  of the outer circumferential member. The extension  22  of inner circumferential member and tip end  20  of outer circumferential member are adhered to each other. Tip end  20  of outer circumferential member has an inclined side surface such that its diameter becomes gradually smaller toward the tip end of bat  1 , as compared with the diameter of outer circumferential member  3  at the hitting portion  11 . 
   Inner circumferential member  5  has a cylindrical shape conforming to the inner circumferential surface of outer circumferential member  3 . Further, between inner circumferential member  5  and outer circumferential member  3 , non-adhesive portion  7  is arranged as described above. Non-adhesive portion  7  is formed of a film of releasing resin such as polypropylene (PP). Non-adhesive portion  7  formed of such a film is arranged to cover outer circumferential surface of inner circumferential member  5  opposite to the inner circumferential surface of outer circumferential member  3 . Further, non-adhesive portion  7  is arranged to extend from the tapered side end  12  of inner circumferential member  5  to the tip end of tip side end  20  of outer circumferential member. As a result, inner circumferential member  5  is adhered to outer circumferential member  3  at tip end portion  10  of bat  1 , while the end portion of inner circumferential member  5  on the side of tapered portion  12  of bat  1  is not adhered to the inner circumferential surface of outer circumferential member  3 , as non-adhesive portion  7  is posed therebetween. As a result, the end portion of inner circumferential member  5  on the side of tapered portion  12  is not fixed to outer circumferential member  3  and is freely movable. 
   At grip portion  13 , a grip end  15  is fixed to outer circumferential member  3  at the rear end of bat  1 . Grip end  15  and outer circumferential member  3  may be fixed by an arbitrary method. By way of example, opposite wall surfaces of grip end  15  and outer circumferential member  3  may be threaded, and the end portion of grip end  15  may be screw-fixed to the rear end of outer circumferential member  3 . 
   Characteristic structure of bat  1  above will be summarized. Bat  1  in accordance with the present invention is a baseball or softball bat including hitting portion  11 , tapered portion  12  and grip portion  13 , provided with outer circumferential member  3 , inner circumferential member  5  and non-adhesive portion  7 . Outer circumferential member  3  is a cylindrical member constituting at least the hitting portion  11 . Inner circumferential member  5  is arranged on the inner circumferential side of outer circumferential member  3 . Inner circumferential member  5  has a taper side end, i.e., an end portion on the side of the tapered portion  12 , and a tip side end (tip end  23  of inner circumferential member) positioned opposite to the taper side end, fixed on outer circumferential member  3 . Non-adhesive portion  7  is arranged at least partially on a region where outer circumferential member  3  and an unfixed portion of inner circumferential member  5  are opposite to each other, in order to prevent adhesion of outer circumferential member  3  and the unfixed portion (where non-adhesive portion  7  is arranged in  FIGS. 1 and 2 ) of inner circumferential member  5 , that is, a portion other than the tip side end (tip end  23  of inner circumferential member) and including the end on the side of tapered portion  12 . Further, in bat  1  described above, non-adhesive portion  7  extends to the taper side end of inner circumferential member  5 . 
   In such a structure, hitting portion  11  is formed by outer circumferential member  3  and inner circumferential member  5 , and outer circumferential member  3  and inner circumferential member  5  are arranged with non-adhesive portion  7  interposed. Therefore, outer circumferential member  3  and the inner circumferential member  5  can elastically deform more easily when hitting the ball, as compared with outer circumferential member  3  and the inner circumferential member  5  adhered to each other over the entire surfaces. Because of the restoring force of outer circumferential member  3  and inner circumferential member  5  from the elastic deformation, flying distance of the hit ball can be increased. In other words, a bat having superior restitution characteristic can be realized. 
   Further, as non-adhesive portion  7  extends to the end of the inner circumferential member  5  on the side of the tapered portion  12 , inner circumferential member  5  is not adhered to outer circumferential member  3  at the end on the side of tapered portion  12 . Specifically, inner circumferential member  5  is fixed to outer circumferential member  3  at the end (tip end  23  of inner circumferential member) opposite to the taper side end, and the taper side end of inner circumferential member  5  is not bound by outer circumferential member  3 . Therefore, when vibration or shock occurs as bat  1  hits the ball, the vibration and shock can be alleviated/damped not only by displacement of the inner and outer circumferential members  5  and  3  in the radial direction but also by displacement of the taper side end of inner circumferential member  5  in the axial direction of bat  1 . Therefore, the vibration and shock at the time of hitting can quickly be alleviated, and hence, bad feeling caused by such vibration can be avoided. 
   In bat  1  described above, tip end  23  of inner circumferential member including extension  22  of inner circumferential member may be regarded as a cap member of the bat. In that case, bat  1  shown in  FIGS. 1 to 3  may be considered to have the cap member and inner circumferential member  5  formed integrally. 
   In that case, the number of process steps for manufacturing the bat can be reduced than when the cap member is prepared as a member separate from inner circumferential member  5  and attached separately to the tip end portion of bat  1 . Therefore, manufacturing cost of bat  1  can be reduced. 
   In bat  1  described above, non-adhesive portion  7  is formed of a PP film, as a releasing film. Thus, by a simple method of placing the PP film on the outer circumferential surface of inner circumferential member  5  in advance, bat  1  in accordance with the present invention can be formed. 
   In bat  1  described above, inner circumferential member  5  extends from hitting portion  11  to tapered portion  12 . As inner circumferential member  5  extends from hitting portion  11  to tapered portion  12 , the portion having improved restitution characteristic (sweet area) of bat  1  can be widened to tapered portion  12 . Therefore, even when the ball is hit at a boundary between hitting portion  11  and tapered portion  12  as is often experienced by amateur players or even at tapered portion  12 , the flying distance of the ball can be increased as compared with the conventional example. 
   Next, referring to  FIG. 4 , a method of manufacturing the bat shown in  FIGS. 1 to 3  will be described. 
   Referring to  FIG. 4 , first, the step (S 10 ) of preparing a base body to be inner circumferential member  5  and non-adhesive member  7  is executed. At this step (S 10 ), specifically, a glass sleeve, glass prepreg, carbon prepreg and the like are wound in a prescribed order on, for example, a mandrel (core metal). The glass prepreg, carbon prepreg and the like form the inner circumferential member  5  (see  FIG. 2 ). After prescribed numbers of glass prepreg and carbon prepreg are wound on the mandrel, a resin film (such as a PP film) to be non-adhesive portion  7  as the WBL is wound on the outermost side. 
   Next, the mandrel removing step (S 20 ) is executed. At this step (S 20 ), the mandrel is removed from the inner circumferential side of the base body formed by glass sleeve, glass prepreg, carbon prepreg and PP film as described above. 
   Next, the tube inserting step (S 30 ) is executed. At this step (S 30 ), an air injecting tube is inserted and arranged on the inner circumference of the base body, so that pressure can be applied from the inner circumferential side of the base body in a pressing step, which will be described later. 
   Next, the step of inserting the base body to the inside of a tapered metal tube to be the outer circumferential member  3  is executed (S 40 ). Here, the base body described above is arranged inside the tapered metal tube, which will be outer circumferential member  3 . Specifically, the tapered metal tube is opened at the tip end side of the bat, and the base body is inserted through the opening. At this time, part of the base body is kept protruded from the above-described opening of the tapered metal tube. 
   Next, the bat tip end processing step (S 50 ) is executed. Specifically, the part of base body protruding from the opening of tapered metal tube described above is bent to the outer side of tapered metal tube, so that the part of base body covers the outer circumferential portion of tapered metal tube. Thereafter, prepreg is further positioned on the part of base body bent outward from the opening of tapered metal tube, for reinforcement of the portion. Then, unnecessary portions of the prepreg is cut such that the prepreg comes to have approximately linear end surface at the end portion of prepreg positioned on the outer circumferential side of tapered metal tube (end portion on the side from tip end  10  to grip portion  13 ). 
   Next, the step of placing in a metal mold (S 60 ) is executed. At this step (S 60 ), the tapered metal tube having the above-described base body arranged therein is set in a metal mold. The metal mold has a recessed portion corresponding to the shape of the bat, and the tapered metal tube described above is set inside the recess. Further, a hose communicated with the tube in the base body is drawn out from the end portion of the bat to be the grip portion (rear end of the bat) to the outside of the metal mold. Here, as the metal mold, one that is divided into two parts in the up/down directions and having, in each part, a recess corresponding to the shape of the bat, may be used. 
   Next, the heating and pressing step (S 70 ) is executed. Specifically, at this step (S 70 ), the metal mold is pressed by a press machine and simultaneously, heated by a heater or the like. At this time, through the hose (air inlet pipe to the tube) drawn out of the metal mold from the portion to be the grip of the bat, high pressure air is supplied to the inside of the tube. As the high pressure air, air of at least 13 atm to at most 15 atm may be used. The heating temperature of the metal mold may be set to at least 100° C. and at most 170° C. and, preferably, at 150° C. The time of heating and pressing may be set to at least 20 minutes and at most 1 hour and, preferably to 30 minutes. In this manner, the tapered metal tube is press-processed along the shape of recess formed in the metal mold while high pressure air is supplied to the tube, so that the base body is pressed from the inside to the tapered metal tube, heated and cured, whereby the inner circumferential member is formed. 
   Next, the cooling and post processing step (S 80 ) is executed. At this step (S 80 ), the tapered metal tube molded to the shape of the bat is taken out from the mold, and the tapered metal tube is immersed in a coolant and cooled. As the coolant, water may be used. After the cooling step, the tube for air injection is taken out from the hole on the grip side (hole at the rear end of the bat), from the inside of tapered metal tube molded to the shape of the bat. 
   Next, the after-curing step (S 90 ) is executed. At this step (S 90 ), the tapered metal tube molded to the shape of the bat as described above is put in a drying chamber and heated for a prescribed time period. Thus, after-curing (that is, the step of fully curing prepreg forming the base body) is done. The drying temperature here may be set to at least 100° C. and at most 150° C. and, preferably, to 130° C. Further, the drying time may be set to at least 4 hours and at most 8 hours, and preferably, to 6 hours. 
   Thereafter, the final processing step (S 100 ) is executed. At this step (S 100 ), by way of example, the surface of tapered metal tube molded to the bat shape is polished, painted and dried. Further, a logo, mark and the like are printed on the surface of the tapered metal tube, and clear coating is provided. The coating is dried, and a grip end  15  (see  FIG. 1 ) is fixed to the hole at the end of the grip portion (rear end of the bat). As the method of fixing, arbitrary method such as screw fixing, adhesion using an adhesive, or welding may be used. Then, grip tape is wound around grip portion  13 . In this manner, the bat in accordance with the present invention shown in  FIGS. 1 to 3  is provided. 
   Next, a modification of Embodiment 1 of the bat in accordance with the present invention will be described with reference to  FIG. 5 .  FIG. 5  corresponds to  FIG. 2 . 
   Bat  1  shown in  FIG. 5  basically has the same structure as the bat shown in  FIGS. 1 to 3 , with the shape of non-adhesive portion  8  made different from the shape of non-adhesive portion  7  of the bat shown in  FIGS. 1 to 3 . Specifically, in bat  1  shown in  FIG. 5 , non-adhesive portions  8  are arranged in a discrete manner with gaps  9  interposed, to be arranged at least partially in the region where unfixed portion of inner circumferential member  5  and outer circumferential member  3  are opposite to each other, between inner circumferential member  5  and outer circumferential member  3 . In bat  1  shown in  FIG. 5 , non-adhesive portions  8  are each formed in a ring-shape, surrounding inner circumferential member  5 . The shape of non-adhesive portion  8  is not limited to the ring, and island-shaped non-adhesive portions  8  may be arranged discretely and spaced from each other between inner circumferential member  5  and outer circumferential member  3 . Two-dimensional shape of island-shaped non-adhesive portion  8  may be circular, polygonal or any other arbitrary shape. In the region between inner circumferential member  5  and outer circumferential member  3 , the ratio of the area covered with non-adhesive portion  8  may be at least 50%, preferably at least 60%, and more preferably, at least 70%. 
   Bat  1  having such a structure can also attain the same effect as attained by the bat shown in  FIGS. 1 to 3 . 
   Embodiment 2 
   Referring to  FIGS. 6 and 7 , Embodiment 2 of the bat in accordance with the present invention will be described.  FIGS. 6 and 7  correspond to  FIGS. 2 and 3 , respectively. 
   Bat  1  shown in  FIGS. 6 and 7  basically has the same structure as the bat shown in  FIGS. 1 to 3 , with the structure of inner circumferential member  5  made different. Specifically, in bat  1  shown in  FIGS. 6 and 7 , inner circumferential member  5  consists of concentric inner circumferential member parts  5   a ,  5   b  and a non-adhesive portion  7   b . Non-adhesive member  7   b  is positioned between inner circumferential member parts  5   a  and  5   b . Non-adhesive portion  7   b  is arranged to extend from the taper side end portion  5  of inner circumferential member part  5   b  to the tip end  23  of the inner circumferential member. As a result, inner circumferential member parts  5   a  and  5   b  are movable independent from each other at the side of tapered portion  12 , while they are connected on the side of tip end  23  of the inner circumferential member. Between inner circumferential member  5  and outer circumferential member  3  (that is, between the outer circumferential surface of inner circumferential member part  5   a  and the inner circumferential member  3 ), non-adhesive portion  7   a  is arranged. 
   Such a structure can also attain the same effect as attained by the bat shown in  FIGS. 1 to 3 . 
   Characteristic structure of bat  1  described above will be summarized. In bat  1  described above, inner circumferential member  5  consists of inner circumferential member parts  5   a  and  5   b  as a plurality of layers laminated with other non-adhesive portion or portions  7   b  interposed, in the radial direction of outer circumferential member  3 . Tip side end portions (end portions on the side of tip end  23  of inner circumferential member) of inner circumferential member parts  5   a  and  5   b  as the plurality of layers are fixed to each other. At least one of the other non-adhesive portions (non-adhesive portion  7   b ) extends to the taper side end of the inner circumferential member. Further, in bat  1  described above, if there are a plurality of other non-adhesive portions, all of the non-adhesive portions may extend to the taper side end of inner circumferential member  5 . Though two inner circumferential member parts  5   a  and  5   b  are shown in  FIG. 6 , the number of layers may be an arbitrary number not smaller than 3. 
   Here, as the inner circumferential member  5  is formed by inner circumferential member parts  5   a  and  5   b  as a plurality of layers, the number of layers that elastically deform independently when hitting the ball can be increased. This means that the number of layers that generate restoring force from elastic deformation increases. As a result, flying distance of the ball can surely be increased. Even when inner circumferential member parts  5   a  and  5   b  are made thin, total thickness of inner circumferential member  5  can be increased to some extent as there are a plurality of inner circumferential member parts, and hence, sufficient strength of the inner circumferential member can be ensured. 
   Next, a modification of Embodiment 2 of the bat in accordance with the present invention shown in  FIGS. 6 and 7  will be described with reference to  FIG. 8 .  FIG. 8  corresponds to  FIG. 6 . 
   Bat  1  shown in  FIG. 8  basically has the same structure as the bat shown in  FIGS. 6 and 7 , with the shape of non-adhesive portion  8  made different from the shape of non-adhesive portion  7   b  of bat  1  shown in  FIGS. 6 and 7 . Specifically, in bat  1  shown in  FIG. 8 , non-adhesive portions  8  are arranged in a discrete manner with gaps  9  interposed, between inner circumferential member parts  5   a  and  5   b . In bat  1  shown in  FIG. 8 , non-adhesive portions  8  are each formed in a ring-shape, surrounding inner circumferential member part  5   b . Similar to the non-adhesive portion  8  of bat  1  shown in  FIG. 5 , the shape of non-adhesive portion  8  is not limited to the ring, and island-shaped non-adhesive portions  8  may be arranged discretely and spaced from each other between inner circumferential member parts  5   a  and  5   b . Two-dimensional shape of island-shaped non-adhesive portion  8  may be circular, polygonal or any other arbitrary shape. In the region between inner circumferential member parts  5   a  and  5   b , the ratio of the area covered with non-adhesive portion  8  may be at least 50%, preferably at least 60%, and more preferably, at least 70%. 
   Bat  1  having such a structure can also attain the same effect as attained by the bat shown in  FIGS. 1 to 3 . 
   In bat  1  shown in  FIG. 8 , non-adhesive portion  7   a  may be non-adhesive portions  8  arranged discretely as shown in  FIG. 5 . In that case, non-adhesive portions arranged between inner circumferential member parts  5   a  and  5   b  may be positioned not to be overlapped (or partially overlapped but not fully overlapped) with the non-adhesive portions  8  arranged between inner circumferential member part  5   a  and outer circumferential member  3 , when viewed two-dimensionally. 
   Embodiment 3 
   Embodiment 3 of the bat in accordance with the present invention will be described with reference to  FIG. 9 .  FIG. 9  corresponds to  FIG. 2 . 
   Referring to  FIG. 9 , bat  1  of the present invention basically has the same structure as the bat shown in  FIGS. 1 to 3 , with the structure of tip end portion of the bat made different. Specifically, in the bat shown in  FIG. 9 , as a member forming the tip end portion of bat  1 , a cap member  27  is arranged to cover the end portion of outer circumferential member  3 , separate from inner circumferential member  5 . Cap member  27  is adhered to the outer surface of outer circumferential member  3  at tip end portion  10  (see  FIG. 1 ) of the bat. Further, tip end  23  of inner circumferential member is arranged to fill the opening at the tip end  20  of outer circumferential member. The surface of tip end  20  of outer circumferential member as the inner circumferential surface of the opening and the outer circumferential surface of tip end  23  of inner circumferential member are adhered to each other. As a result, outer circumferential member  3  and inner circumferential member  5  are fixed at the tip end side of bat  1 . 
   Such a structure can also attain the same effect as attained by the bat shown in  FIGS. 1 to 3 . 
   Characteristic structure of bat  1  described above will be summarized. Bat  1  described above includes cap member  27  that covers the end portion (tip end  20  of outer circumferential member) opposite to the taper side end of outer circumferential member  3 . Here, as tip end  20  of outer circumferential member  3 , that is, the tip end of the bat of outer circumferential member  3  is covered by cap member  27 , the outer circumferential member  3  at the tip end of bat  1  can be prevented from directly bumping against the ground, when the batter lets go of the bat  1  after hitting. Thus, possible damage to outer circumferential member  3  at the tip side end of the bat (tip end  20  of outer circumferential member) caused by bumping against the ground can be decreased. 
   Embodiment 4 
   Embodiment 4 of the bat in accordance with the present invention will be described with reference to  FIG. 10 .  FIG. 10  corresponds to  FIG. 2 . 
   Bat  1  shown in  FIG. 10  basically has the same structure as the bat shown in  FIGS. 1 to 3 , with the structure of tip end portion made different. Specifically, in bat  1  shown in  FIG. 10 , at the tip end portion of the bat, outer circumferential member  3  forms a part of the end surface of bat  1 . On the end surface of tip end side of bat  1 , an opening  29  is formed in outer circumferential member  3 . Tip end  23  of inner circumferential member is arranged to fill the opening  29 . A side wall of opening  29  (surface of tip end  20  of outer circumferential member) is adhered to the outer circumferential surface of tip end  23  of inner circumferential member, and hence, outer circumferential member  3  and inner circumferential member  5  come to be connected and fixed, at the tip end side of bat  1 . Further, non-adhesive portion  7  extends from the taper end side of inner circumferential member  5  to a portion adjacent to the inner circumferential sidewall at opening  29  of outer circumferential member  3 . 
   Bat  1  having such a structure can also attain the same effect as attained by the bat shown in  FIGS. 1 to 3 . 
   Characteristic structure of the bat described above will be summarized. In bat  1  described above, outer circumferential member  3  includes, at a tip end opposite to the taper side end (tip end of the bat), a portion to be an end sidewall (tip end  20  of outer circumferential member) forming a part of an end surface of bat  1 . Opening  29  is formed at the portion (tip end  20  of outer circumferential member) that will be the part of end sidewall of outer circumferential member  3 . Inner circumferential member  5  includes tip end  23  of inner circumferential member, which is a portion to fill the opening  29  and to be adhered to the inner wall of opening  29 . 
   Here, it is unnecessary to separately prepare a cap member that covers the end surface of bat  1  (end surface on the tip end side of the bat). Therefore, the number of components and the number of manufacturing steps of bat  1  can be reduced. Thus, the manufacturing cost of bat  1  can be reduced. 
   Embodiment 5 
   Embodiment 5 of the bat in accordance with the present invention will be described with reference to  FIG. 11 .  FIG. 11  corresponds to  FIG. 2 . 
   Referring to  FIG. 11 , bat  1  of the present invention basically has the same structure as the bat shown in  FIGS. 1 to 3 , with the structure of tip end portion of the bat made different. Specifically, in the bat shown in  FIG. 11 , outer circumferential member  3  has a cylindrical shape of substantially the same outer diameter, from the hitting portion to the tip end portion of bat  1 . At the tip end portion of bat  1  (tip end  20  of outer circumferential member), outer diameter of outer circumferential member  3  is made gradually smaller, while the inner diameter of outer circumferential member is kept approximately constant. Specifically, tip end  20  of outer circumferential member has a tapered cross section, which becomes thinner to the tip end side. 
   Further, outer circumferential member  3  has a recess  50  formed on the inner circumference at the tip end side. Recess  50  is an annular trench formed around the inner circumference of outer circumferential member  3 . At recess  50 , sidewall on the side of grip portion of bat  1  is inclined to the inner circumference of outer circumferential member  3 . 
   Inner circumferential member  5  is arranged to fill the tip end side opening of outer circumferential member  3  and to extend along the inner circumference of outer circumferential member  3 . Between the inner circumferential member  5  and the inner circumferential surface of outer circumferential member  3 , non-adhesive portion  7  is arranged. Non-adhesive portion  7  extends to the taper side end of inner circumferential member  5 . Non-adhesive portion  7  and inner circumferential member  5  include bent portions conforming to the shape of recess  50 , to fill the inside of recess  50  formed at the inner circumferential surface of outer circumferential member  3 . 
   Inner circumferential member  5  includes an extension  22  of inner circumferential member, continuous to tip end  23  of inner circumferential member and extending over the outer circumferential surface of tip end  20  of outer circumferential member. Extension  22  of inner circumferential member and outer circumferential member  3  are connected and fixed at tip end tapered portion  51 . Such a structure can also attain the same effect as attained by the bat shown in  FIGS. 1 to 3 . 
   The depth of recess  50  may be at most 50% of the thickness of outer circumferential member  3 . Further, the length of recess  50  in the direction of extension of bat  1  may be about 10 mm. Further, recess  50  may not be an annular trench but independent recesses formed at a plurality of positions in the circumferential direction, on the inner circumference of outer circumferential member  3 . Here, the plurality of recesses may be arranged at equal distance. Further, in the direction of extension of bat  1 , recesses  50  may be arranged at a plurality of portions (for example, at two or more portions). 
   In Embodiments 1 to 5 of the bat in accordance with the present invention described above, arbitrary material may be used as materials of outer circumferential member  3  and inner circumferential member  5 . By way of example, metal such as aluminum alloy may be used as outer circumferential member  3 , and fiber-reinforced plastic (FRP) or other material may be used for inner circumferential member  5 . Outer circumferential member  3  and inner circumferential member  5  may be formed of different materials as described above, or the members may be formed of the same material. 
   Thickness of outer circumferential member  3  and inner circumferential member  5  at the hitting portion may be arbitrarily determined. For instance, when aluminum alloy is used for outer circumferential member  3  of an “adult-size baseball bat”, thickness of outer circumferential member  3  may be set to at least 0.5 mm and at most 3.0 mm and, more preferably, at least 1.0 mm and at most 2.5 mm. When FRP is used for inner circumferential member  5 , the thickness may be set to at least 0.5 mm and at most 7.0 mm, and more preferably, at least 2.0 mm and at most 5.0 mm. 
   Further, as non-adhesive portion  7 , any material may be arranged in place of the PP film described above, provided that the material prevents adhesion between outer circumferential member  3  and inner circumferential member  5 . By way of example, as non-adhesive portion  7 , a releasing film of polyethylene, silicone or the like may be used. Alternatively, a layer formed by spraying an arbitrary releasing agent to the outer circumferential surface of inner circumferential member  5  and/or to the inner circumferential surface of outer circumferential member  3  may be used as non-adhesive portion  7 . Further, a structure in which surfaces of outer circumferential member  3  and of inner circumferential member  5  are not adhered to each other but in slidable and/or separable contact, without any particular layer such as the PP film, may be used, as non-adhesive portion  7 . In Embodiments 3 to 5 of the bat in accordance with the present invention, the structures of the non-adhesive portion and inner circumferential member such as shown in  FIGS. 5 to 8  may be applied. 
   (Test 1) 
   In order to confirm the effects of the bat in accordance with the present invention, bats in accordance with the embodiments of the invention and comparative examples are manufactured, and restitution coefficient of each bat was measured. 
   (Samples) 
   Specifically, samples of four different types, that is, bats in accordance with Embodiments 1 and 2 and Comparative Examples 1 and 2 were prepared. The bat in accordance with Embodiment 1 basically has the structure shown in  FIGS. 1 to 3 . The bat in accordance with Embodiment 2 basically has the structure shown in  FIGS. 6 and 7 . Specifically, as outer circumferential member  3 , aluminum alloy (JIS: A7050) was used. As inner circumferential member  5 , FRP was used. As non-adhesive portion  7 , a PP film was used. Bats in accordance with Comparative Examples 1 and 2 had the structures shown in  FIGS. 12 and 13 . 
   The bat in accordance with Comparative Example 1 basically has a structure similar to that shown in  FIGS. 1 to 3 , except that non-adhesive portion  7  extends only from the tip end side to a middle of hitting portion of bat  1 . As a result, in the bat shown in  FIG. 12 , inner circumferential member  5  adheres to outer circumferential  5  member  3  at opposite ends, that is, the tip end side and tapered portion of bat  1 . 
   The bat in accordance with Comparative Example 2 basically has a structure similar to that shown in  FIGS. 1 to 3 , except that non-adhesive portion  7  is not at all provided. As a result, the outer circumferential surface of inner circumferential member  5  is entirely connected and fixed to the inner circumferential surface of outer circumferential member  3 . Length and mass, positions of center of mass, moment of inertia, positions of center of hitting, outer diameter of hitting portion, thickness of outer circumferential member at the hitting portion and thickness of inner circumferential member at the hitting portion of the bats in accordance with Embodiments 1 and 2 and Comparative Examples 1 and 2 are as shown in Table 1. 
   
     
       
         
             
             
             
             
             
             
             
             
             
             
           
             
               TABLE 1 
             
             
                 
             
             
                 
                 
                 
               COM 
                 
                 
                 
                 
                 
                 
             
             
                 
                 
                 
               (Center 
               MOI 
               COP 
               Hitting 
               Outer member 
               Inner member 
                 
             
             
                 
                 
                 
               of 
               (Moment of 
               (Center of 
               portion 
               thickness at 
               thickness at 
             
             
                 
               Length 
               Weight 
               mass) 
               Inertia) 
               Percussion) 
               diameter 
               hitting portion 
               hitting portion 
             
             
               Material type 
               (mm/inch) 
               (g/oz) 
               (mm) 
               (kg · cm · sec 2 ) 
               (mm) 
               (mm) 
               (mm) 
               (mm) 
               Remarks 
             
             
                 
             
           
          
             
               Embodiment 
               837/33.0 
               892/31.5 
               524 
               2.18 
               689 
               66.5 
               1.5 
               3.5 
               Adhesion preventing 
             
             
               1 
                 
                 
                 
                 
                 
                 
                 
                 
               layer (WBL) formed 
             
             
                 
                 
                 
                 
                 
                 
                 
                 
                 
               of 2 films extends 32 cm 
             
             
                 
                 
                 
                 
                 
                 
                 
                 
                 
               from tip end 
             
             
               Embodiment 
               837/33.0 
               890/31.4 
               524 
               2.18 
               690 
               66.5 
               1.5 
               3.5 
               2 adhesion preventing 
             
             
               2 
                 
                 
                 
                 
                 
                 
                 
                 
               layers (WBL) formed 
             
             
                 
                 
                 
                 
                 
                 
                 
                 
                 
               of 2 films are 
             
             
                 
                 
                 
                 
                 
                 
                 
                 
                 
               provided 
             
             
               Comparative 
               837/33.0 
               885/31.2 
               525 
               2.17 
               689 
               66.5 
               1.5 
               3.5 
               Adhesion preventing 
             
             
               Example 1 
                 
                 
                 
                 
                 
                 
                 
                 
               layer (WBL) formed 
             
             
                 
                 
                 
                 
                 
                 
                 
                 
                 
               of 2 films extends 22 cm 
             
             
                 
                 
                 
                 
                 
                 
                 
                 
                 
               from tip end 
             
             
               Comparative 
               837/33.0 
               885/31.2 
               525 
               2.18 
               692 
               66.5 
               1.5 
               3.5 
               Adhesion preventing 
             
             
               Example 2 
                 
                 
                 
                 
                 
                 
                 
                 
               layer not provided 
             
             
                 
             
             
               * Film thickness: 0.02 mm 
             
          
         
       
     
   
   (Measurement) 
   The restitution coefficient was measured by the following method, using the apparatus arrangement shown in  FIG. 14 . The method of measuring the restitution coefficient will be described with reference to  FIG. 14 . 
   As shown in  FIG. 14 , for measuring the restitution coefficient, bat  1  as an object of measurement was placed on a bat base  36 , and using a pitching machine  35 , a ball  34  was got hit by bat  1 . The manner how ball  34  impacts against bat  1  was picked-up by a high-speed video camera  33 . High-speed video camera  33  is arranged immediately above bat  1  and picks up the image of ball  34  impacting against bat  1  from above. From the video images picked-up by high-speed video camera  33 , velocity (barycentric velocity) of ball  34  before impacting against bat  1 , velocity (barycentric velocity) of ball  34  after impacting against bat  1  and velocity of movement (barycentric velocity) of bat  1  are measured. 
   Using these measurement data, restitution coefficient “e” is calculated in accordance with the equation below.
 
 e=−{V   —   BL (OUT)−( V   —   BT (PAL)+ a·V   —   BT (ROT))}/ V   —   BL (IN)
 
e: restitution coefficient
 
V_BL(IN): Barycentric velocity of ball before impact (m/s)
 
V_BL(OUT): Barycentric velocity of ball after impact (m/s)
 
V_BT(PAL): Translational velocity of the center of mass of bat after impact (m/s)
 
V_BT(ROT): Angular velocity of bat around the center of mass after impact (rad/s)
 
a: Distance from the center of mass of bat to position of ball impact (grip side being positive).
 
   Resulting data are as shown in Table 2 and  FIG. 15 . 
   
     
       
         
             
             
             
           
             
                 
               TABLE 2 
             
           
          
             
                 
                 
             
             
                 
               Position from tip end (cm) 
                 
             
          
         
         
             
             
             
             
             
             
          
             
                 
               Material type 
               10 
               15 
               25 
               30 
             
             
                 
                 
             
             
                 
               Embodiment 1 
               0.576 
               0.602 
               0.520 
               0.425 
             
             
                 
               Embodiment 2 
               0.602 
               0.621 
               0.534 
               0.424 
             
             
                 
               Comparative Example 1 
               0.597 
               0.599 
               0.504 
               0.422 
             
             
                 
               Comparative Example 2 
               0.554 
               0.586 
               0.492 
               0.417 
             
             
                 
                 
             
          
         
       
     
   
   Referring to  FIG. 15 , the abscissa represents the position from the tip end of the bat, and the ordinate represents the restitution coefficient. As can be seen from  FIG. 15 , regarding the area having the restitution coefficient of 0.5 or higher as the sweet area, the sweet area is wider to the taper side of the bat in samples in accordance with Embodiments 1 and 2 of the invention than in the samples in accordance with Comparative Examples 1 and 2. For example, let us consider the position 25 cm from the tip end, having the highest restitution coefficient as the sweet spot. The width of the sweet area is evaluated by the position at the end of the sweet area. Here, when the position of the end is represented by the distance from the sweet spot, it is 12 cm in Embodiment 1 and 13 cm in Embodiment 2 of the present invention. The distance is 9 cm in Comparative Example 2. Specifically, when the width of sweet area is considered in terms of the distance from the sweet spot, it is 33% wider in Embodiment 1 and 44% wider in Embodiment 2, than Comparative Example 2. Further, restitution coefficient at the sweet spot is increased due to the formation of non-adhesive portion in the bats of Embodiments 1 and 2, as compared with Comparative Example 2. 
   As described above, it can be understood that restitution coefficient can be increased and wider sweet area can be provided by the bats in accordance with the embodiments of the present invention. 
   (Test 2) 
   Logarithmic decrement was measured, using the bat samples of Embodiments 1 and 2 and Comparative Examples 1 and 2 described above. 
   (Measurement) 
   Here, logarithmic decrement was measured by the following method, using the apparatus arrangement shown in  FIG. 16 . The method of measuring the logarithmic decrement will be described with reference to  FIG. 16 . 
   As shown in  FIG. 16 , the apparatus used for measuring logarithmic decrement (vibration damping measuring apparatus) includes a bat hanging base  44 , a chemical fiber string  45 , an impulse hammer  43 , an acceleration meter  46 , a signal conditioner  42 , an FFT (Fast Fourier Transformation) analyzer  41 , and a computer  40  as a controller. 
   Using such an apparatus arrangement, first, bat  1  is hung from bat hanging base  44 , using string  45 . String  45  is connected to the grip side of bat  1 . Acceleration meter  46  was set at the position 21 cm from the grip side end of the bat. Acceleration meter  46  is connected to signal conditioner  42 . Further, impulse hammer for hitting bat  1  is also connected to signal conditioner  42 . Signal conditioner  42  is connected to computer  40  through FFT analyzer  41 . 
   With this apparatus arrangement, measurement was done in the following manner. 
   First, bat  1  is hit by impulse hammer  43 . The hitting position was 30 cm from the head side (tip side) end of bat  1 . Hitting by impulse hammer  43  is done such that the point of measurement (position of acceleration meter) faces the same direction as the hitting point. Vibration of bat  1  caused by the hitting is measured as time-sequential data, by acceleration meter  46 . 
   Here, eigenfrequency of primary bending vibration of the bat is about 200 Hz, and therefore, the range of frequency to be measured was set to 0 to 250 Hz. The time of measurement was 3 seconds. By analyzing the result of measurement by FFT analyzer  41 , vibration damping was measured. The result of measurement is displayed/recorded by computer  40 . 
   As impulse hammer  43 , acceleration meter  46 , signal conditioner  42  and FFT analyzer  41 , apparatuses of type 208A04 of PCB PIEZOTRONICS INC, type 352A21 of PCB PIEZOTRONICS. INC, type 483A of PCB PIEZOTRONICS INC. and type DS-9110 of ONO SOKKI Kabushiki Kaisha, respectively, were used. 
   The results of measurement are as shown in  FIG. 17 . As shown in  FIG. 17 , it can be seen that the logarithmic decrement of the embodiments is approximately twice as high as Comparative Example 1 and approximately three times as high as Comparative Example 3. High logarithmic decrement means that vibration at the time of hitting the ball attenuates faster. Specifically, in bats in accordance with Embodiments 1 and 2 of the present invention, vibration of the bat at the time of hitting attenuates faster than Comparative Examples 1 and 2, and hence, the problem such as player&#39;s hand going numb because of bat vibration can be curbed. 
   (Test 3) 
   Eigenfrequency at the hitting portion of the four samples described above was measured. The measurement was done in accordance with the following method. 
   Referring to  FIG. 18 , the apparatus used for measuring the eigenfrequency at the hitting portion (vibration damping measuring apparatus) includes, similar to the vibration damping measuring apparatus used in Test 2, bat hanging base  44 , chemical fiber string  45 , impulse hammer  43 , acceleration meter  46 , signal conditioner  42 , FFT (Fast Fourier Transformation) analyzer  41 , and computer  40  as a controller. 
   Using such an apparatus arrangement, first, bat  1  is hung from bat hanging base  44 , using string  45 . String  45  is connected to the grip side of bat  1 . Acceleration meter  46  was set at the position  10  cm from the head (tip) side end of the bat. Acceleration meter  46  is connected to signal conditioner  42 . Further, impulse hammer for hitting bat  1  is also connected to signal conditioner  42 . Signal conditioner  42  is connected to computer  40  through FFT analyzer  41 . 
   With this apparatus arrangement, measurement was done in the following manner. 
   First, bat  1  is hit by impulse hammer  43 . The hitting position was 10 cm from the head side (tip side) end of bat  1 . As to the hitting portion, a plurality of hitting points (for example, 16 points) are set at approximately equal interval in the circumferential direction of the bat, as represented by hitting points  48   a  to  48   c  of  FIG. 18 . One of the 16 hitting points is determined to be the measurement point for setting acceleration meter  46 , and only the point where the hitting point and measuring point overlap, the hitting position is displaced by 10 mm to the grip side. 
   Then, the bat is hit by impulse hammer  43  and vibration of bat  1  caused by the hitting is measured as time-sequential data by acceleration meter  46 . By analyzing the result of measurement by FFT analyzer  41 , vibration damping was measured. The result of measurement is displayed/recorded by computer  40 . 
   Impulse hammer  43 , acceleration meter  46 , signal conditioner  42  and FFT analyzer  41  are the same apparatuses as those used in Test 2. 
   As a result, eigenfrequency of the bat in accordance with Embodiment 1 of the present invention was 2700 Hz, eigenfrequency of the bat in accordance with Embodiment 2 was 2200 Hz, eigenfrequency of the bat in accordance with Comparative Example 1 was 2875 Hz, and eigenfrequency of the bat in accordance with Comparative Example 2 was 3600 Hz. The smaller eigenfrequency represents better restitution of the bat. Specifically, also from the results of measurement described above, it can be seen that the bats in accordance with the present invention exhibited smaller eigenfrequencies than the bats in accordance with Comparative Examples 1 and 2. That the eigenfrequency is small means the bat has superior restitution characteristic. 
   Although the present invention has been described and illustrated in detail, it is clearly understood that the same is by way of illustration and example only and is not to be taken by way of limitation, the scope of the present invention being interpreted by the terms of the appended claims.