referring now to fig1 an impact indicating athletic training apparatus in the form of a heavy bag apparatus is generally indicated by reference number 10 . the apparatus includes a hitting bag 12 for receiving impacts from the hands , feet or body of an athlete . bag 12 is suspended from its upper end by chains , ropes or cables 14 which are attached to the bag . chains 14 extend to a stationary support 16 overhead . a spring 17 can be interposed between chains 14 and support 16 to dampen secondary force waves resulting from impacts on the bag . in one preferred form , bag 12 has a compressible foam filling and a dense core . as shown in fig2 the filling can comprise a hollow foam cylinder 17 having a sand - filled core 19 . the foam should have high tear strength , and it should be compressible and resilient . particularly suitable forms are white ether foams having density values of sl23 and sl65 from stephenson and lawyer grand rapids , michigan . various polyurethane foams would also be suitable . the bag should have a resilient , durable covering 21 which serves as a container for the filling . it can be an impermeable bag made of nylon impregnated vinyl . in an alternate form of the embodiment of fig1 bag 12 is comprised of a resilient outer membrane layer 21 and is fully filled with water or other incompressible fluid . bag 12 then includes an inlet valve which can be selectively opened and closed to admit or discharge the fluid . the valve may be attached to a hose to fill the bag . in the preferred forms of the embodiment of fig1 the bag is cylindrical in shape with a height of 36 - 45 inches , an outer diameter of 14 - 16 inches , and a circumference of 36 - 45 inches . the bag may be of the type commercially available from powair corporation . flexible transducer means 22 is mounted on bag 12 . in the preferred form of the embodiment of fig1 transducer means 22 is a strip of piezoelectric material which runs about the circumference of the bag below its upper end . as later explained , the piezoelectric strip is oriented to measure dimensional changes in the bag caused by impacts imparted by the athlete . the piezoelectric film used in the preferred forms of the invention is of the type sold by pennwalt corporation , piezo film group . applicant has found that it is desirable to laminate the film on both sides with a covering of 4 - 5 mil mylar material . this protects the film from dirt and prevents damage from the impacts , especially from inadvertent direct blows to the transducer strip which may occur from time - to - time . the film is bonded to the surface of bag 12 using an adhesive material such as type 94 / 84 vinyl resistant tape produced by the 3m company . the ends of the strip of piezoelectric film are adjacent each other and are connected to a two - conductor cable 24 . cable 24 is connected to an indicating apparatus 26 which in fig1 can be a digital readout device or an analog readout device such as an oscilloscope . the apparatus provides on its screen 28 either a digital or an analog readout of the change in the electrical voltage potential of the piezoelectric strip . further details of the indicating device are provided below . in operation , an athlete strikes bag 12 at a location away from the sensing means . the impact deforms resilient outer covering 21 of the bag and displaces the bag &# 39 ; s contents inside adjacent the place of contact . the displacement of the water causes a rapid dimensional expansion of the circumference of the bag away from the place of impact . the dimensional change in the circumference of the bag results in a corresponding elongation of the piezoelectric strip . the strip changes its electrical potential in response to the dimensional change . this change in the electrical potential is transmitted as an electrical signal through cable 24 to indicating apparatus 26 where it produces digital readout or a wave form on screen 28 , depending on the nature of apparatus 26 . another embodiment of the invention is shown in fig3 . a body shield 30 is depicted for receiving blows from the feet , hands or body of a martial arts practitioner . body shield 30 has a generally parallelepiped configuration , and includes a cover or container 32 of this configuration for holding an appropriate filler . a pair of handles 34 are secured on opposite sides of cover 32 , which , as shown in fig4 can be comprised of gripper tubes 36 disposed within webbing wraps 38 . wraps 38 can be attached at their ends to cover 32 by means of leather reinforcing tabs 40 stitched around corners on opposite sides of cover 32 . cover 32 preferably contains a foam insert 42 of the type shown in fig5 . insert 42 preferably is slightly larger than the inner dimensions of cover 32 , so that the insert overstuffs cover 32 and is under continuous compression when in the cover . for example , cover 32 preferably has a height of 24 inches , a width of 14 inches and a depth of 5 inches ; and insert 42 has a height of 24 inches , a width of 15 inches and a thickness of 6 inches . this assures a constant stress on the transducer or sensor as discussed below . the foam is preferably an open cell , light , resilient foam material such as an appropriate white ether foam or a polyurethene foam as described earlier . cover 32 preferably is made of a durable , flexible material such as nylon impregnated vinyl , and has had orifices 43 defined by grommets 44 and / or perforations 46 for discharging air when the shield is struck by a blow . a flexible transducer 22 &# 39 ; of the type identified by reference number 22 in fig1 is disposed near an end of the body shield where it is unlikely to be struck by a blow . an appropriate distance for a shield having the dimensions referred to above would be 6 inches from the top of the shield . transducer 22 &# 39 ; is preferably a mylar laminated piezoelectric strip secured to cover 32 by means of an appropriate adhesive as discussed above with reference to transducer means 22 . its ends are spaced slightly from each other and connected to a two - conductor cable 24 , which is in turn connected to an electronic indicator 26 having a screen 28 . in use , while one person holds body shield 30 against the body by means of handles 34 , the user strikes the face of the shield somewhere below transducer 22 &# 39 ;. the blow compresses the filling of cover 32 by an amount corresponding to the strength of the blow , and the filling expands elsewhere including in the space within transducer 22 &# 39 ;. this expansion deforms the transducer and causes the latter to generate a voltage signal corresponding to the amount of its deformation , and this signal causes a display reflective of the value of the signal on screen 28 &# 39 ;. air driven away from the compressed part of shield 30 causes a discharge of air through orifices 43 and / or perforations 46 . when the compressed material returns to its uncompressed state , air is drawn back into the contents . a smaller version of this embodiment can be attached to a wall or other support , such as by means of a velcro strip attached to the back of the shield for releasable engagement with a corresponding velcro strip attached to the support . referring next to fig6 - 8 , a punch mitt 50 is shown . mitt 50 has an outer cover 52 of generally parallelepiped configuration , and is preferably made from nylon impregnated vinyl to give it the desired flexibility and suppleness . it can be made from flat panels which are stitched at the seams . a transducer strip 22 &# 34 ;, much like strips 22 and 22 &# 39 ; described previously and composed of mylar laminated piezoelectric film , is wrapped around mitt cover 52 near the base portion thereof so as to be out of the normal hitting area of the mitt as discussed below . for a mitt of a preferred height of 11 inches , a width of 8 inches and a thickness of 6 inches , the strip should be disposed about 1 inch from the base . as in the preceding embodiments , strip 22 &# 34 ; should have ends which are close to each other and connected by electrical leads to provide a closed circuit . leads 24 run from strip 22 &# 34 ; to electronic indicator 26 for effecting an output on screen 28 . although liners such as flexible and resilient foams or incompressible fluids could be used as a filler for mitt 50 , an inflatable liner or bladder 54 which has an elastomeric composition is preferred for its ease of installation , ease of inflation ( with a common air pump ) and comfort to one striking the mitt . liner 54 should be inflated to over fill cover 52 as shown most clearly in fig8 . a preferred pressure range is 0 . 8 to 1 . 5 psi , since higher pressures can cause the mitt to be so hard as to cause pain to the user and lower pressures preclude an adequate rebound of a blow . liner 54 should have a conventional air inlet / discharge valve and cover 52 can have a zipper or the like to permit insertion of the liner . a glove 56 is attached to the rear part of cover 52 as shown by dotted lines in fig6 . glove 56 is generally constructed like the back portion of a baseball catcher &# 39 ; s mitt , and includes a flexible outer panel having appropriate internal dividers to define a thumb stall 58 and finger stalls 60 . glove 56 and the finger stalls ( dividers ) is preferably made of the same material as cover 52 , e . g ., nylon impregnated vinyl , and the various components are held in place by stitching . the glove is located above transducer means 22 &# 34 ; to avoid any hindrance to the operation of the mitt . in use , one person puts his or her hand in mitt 56 and holds his arm outstretched to present a target to the user . the user strikes mitt 50 above transducer means 22 &# 34 ; on the face of the mitt , and the values associated with the blow are displayed on screen 28 . as discussed below , these values could include the force of the blow , the total energy transferred to the mitt over periods of time , the frequency at which blows are landed , etc . as in the other embodiments , as each blow is landed on mitt 50 , the liner is compressed at the place of impact , and a corresonding expansion of the liner occurs elsewhere -- including the space within transducer strip 22 &# 34 ;. the stress and distortion imparted to the transducer cause the generation of a voltage signal corresponding to the value of the impact . this signal is transmitted to indicator 26 where it is processed and its value is displayed on screen 28 . the piezoelectric material referred to with respect to the various embodiments described herein is preferably a polyvinylidene fluoride ( pvdf ) film , sandwiched between thin metallized layers of electrically conductive metal . this is the same material described in co - pending u . s . patent application ser . nos . 785 , 969 filed oct . 10 , 1985 and 904 , 356 filed sept . 8 , 1986 , and incorporated herein by reference . this multi - layered material is marketed under the trademark kynar by pennwalt corporation , 900 first avenue , king of prussia , pennsylvania . as used in the embodiments described herein , the piezoelectric film is approximately 28 microns in thickness , and the opposed metallized layers are silver of about 0 . 1 microns in thickness . a wave form produced by typical impact is shown in fig9 which illustrates an oscilloscope screen , which could constitute screen 28 on electronic indicators 26 . the wave form starts at an initial point 70 which corresponds with the athlete &# 39 ; s blow making contact with an impact measuring apparatus according to the invention . the wave form than rises upward with time to a peak 72 which corresponds to the maximum displacement of the surface of the apparatus by the impact . thereafter , the wave form falls with time in correspondence with the retraction of the athlete &# 39 ; s hand or foot from the surface of the apparatus falling back to its original electrical potential at 74 . thereafter , the residual waves in the bag caused by the impact create some anomalous signals or &# 34 ; noise &# 34 ; in the wave form 76 . the noise rapidly dampens out . thus , the device is able to provide accurate indication of impacts delivered in rapid succession . applicant has found that sensing the impact on the surface of the bag in the circumferential direction particularly reduces the amount of &# 34 ; noise &# 34 ; and allows the apparatus to measure numerous impacts per second . a digital version of readout or indicator 26 is shown in fig1 , where it is generally indicated by reference number 80 . the digital systems can employ any of various digital circuit designs . such digital circuits can have means for converting analog signals generated by the piezoelectric strip into digital signals , with the ultimate displays being light emitting diodes or the like . indicator 80 includes a first or force indicating screen 82 for indicating the value of the force of an impact applied to the impact receiving portion of the embodiment of the invention to which the piezoelectric device of indicator 80 is connected . a counter 84 can be provided for indicating the number of impacts rendered to the impact receiving portion . circuitry can be provided for only indicating the umber of impacts which exceed a specified threshold value , such as pounds of force , to avoid counting weak blows , glancing blows and noise . an electronic filter can be used to preclude the transmission of signals having magnitudes below a certain threshold value , and means can be employed for changing that threshold to accommodate the strength and skill of the person using the apparatus . means can be incorporated in indicator 80 for resetting force indicating screen 82 and / or counter 84 after the occurrence of some event , such as the passing of a pre - determined amount of time after a blow without the detection of a subsequent blow , or after the passing of a pre - determined period of time after the detection of a first blow . a clock 86 can be provided for indicating the amount of time during which the system has been in use in any session , or the amount of time which has transpired during a sequence of blows . the latter time value can be used to determine the rate at which blows having force magnitudes above a pre - determined level have been rendered . again , means can be provided for resetting counter 86 , and the resetting means can be manual or automatic . various other useful information can be displayed on the readouts of device 80 . for instance , the magnitudes of force signals rendered over a period of time can be integrated to indicate the energy transmitted to the impact receiving apparatus . values of velocity and power can be provided as well , as long as the system is provided with the necessary known values . integrating this area can be accomplished by using conventional apparatus and may be provided as feedback to the athlete as a digital readout . in other types of training , the velocity of the impact may be of most interest . velocity may be determined by differentiating a portion of the wave form between points 70 and 72 in fig9 . other impact characteristics can also be calculated depending on the parameter of interest . the indicating means may in some applications be combined or used in conjunction with a recording device . thus , the athlete can review a series of impacts or blows after a workout session . the recording devices used in conjunction with the apparatus of the present invention may be coordinated with a video recorder so that the athlete may review not only the impact of each blow , but also the technique that was used in delivering it . this provides the athlete with a further tool to analyze and develop technique . it can be noted that while the preferred form of the invention uses a piezoelectric film strip for sensing the elongation of the bag , other types of flexible transducing devices may also be used successfully . for example , strain gauges such as large area strain gauges manufactured by omega engineering , inc . of stamford , connecticut could be employed in place of the piezoelectric device described above . it has been found that strain gauges of sufficient length to extend around the container of the impact receiving device are not readily available , and it may be necessary to connect a number of such strain gauges together to extend around the container . three embodiments of the invention have been described above . as noted earlier , the invention is particularly suited for obtaining information about blows rendered by athletes . in addition to the bag , body shield and hitting mitt noted above , the invention can be employed in boxing gloves , football blocking and tackling dummies , targets at which balls and other projectiles are thrown , and the like . furthermore the invention could be used for scoring purposes to indicate , for example , both the landing of a blow and the force or other characteristics of the blow . the use of a piezoelectric film as the flexible transducer makes possible a very durable product since there are few if any mechanical connections ( such as linkages , screws , nuts and bolts , etc .). furthermore , since piezoelectric films are very sensitive and yield a linear response over a broad range of force inputs , accurate results are obtainable for impacts varying from those of only a few pounds to impacts of hundreds of pounds and more , without the need for costly detecting devices . the flexible piezoelectric film strip preferred herein can be assembled on new products , and in addition can be retrofitted on existing sports equipment such as body shields , punching bags , etc . to enable the measure of various values associated with the impacts with the impacts . the invention has been described in detail , with particular emphasis on the preferred embodiments , but it should be understood that variations and modifications within the spirit and scope of the invention may occur to those skilled in the art to which the invention pertains .