US 3473370 A Abstract available in Claims available in Description (OCR text may contain errors) @ct. 21, 1969 E. J. MARCINIAK 3 7 CORRELATED SET OF GOLF CLUBS HAVING THE SAME MOMENT OF INERTIA Original Filed July 10, 196? 2 Sheets-Sheet 1 I'll, III. mo M IIOO . INVENTOR. 6 7 55 9 Emu JMa/"cinak 1 ATTORNEYS @ct. 2L 1969 E. J. MARCINIAK CORRELATED SET OF GOLF CLUBS HAVING THE SAME MOMENT OF INER'TIA Original Filed July 10, 1967 2 Shee'ts--Sheetv 2 HEAD Wefi's. 025. INVEIYTQR. EmzZ J Marcuuak GM-A k L flTTUfNEYfi United States Patent 3,473,370 CULATED SET OF GOLF CLUBS HAVING THE SAME MOMENT OF INERTIA lEmil J. lvlarciniak, Easthampton, Mass., assignor to A. G. Spaldmg & Bros., Inc., Chicopee, Mass, a corporation of Delaware Continuation of application Ser. No. 652,149, July 10, 1967. This application May 20, 1968, Ser. No. 731,687 Int. Cl. 601m 1/12; A63b 53/00 US. Cl. 73-65 3 Claims ABSTRACT OF THE DISCLOSURE A set of golf clubs and method for producing the same in which each club has a shaft provided with a grip at one and and a head at the other end and having substantially the same moment of inertia about a predetermined point with respect to the club to provide a uniform feel in the swinging of any club of the set resulting in better play with the set of clubs. This application is a continuation of application Ser. No. 652,149, filed July 10, 1967 and now abandoned. Heretofore it has been the practice to provide a balanced set of golf clubs by employing the swing weight theory as set forth in the Adams Patent 1,953,916. However, this theory, which is based on a system involving static measurements of the clubs and disregards the dynamic considerations, is not an accurate correlation of the clubs to provide the optimum uniform swinging and playing characteristics throughout the set. The present invention provides a new dynamic correlation of the clubs in a set of clubs, including both irons and woods and the method of obtaining such sets whereby the correlation is based on the moment of inertia of the club with all of the clubs in the set having the same moment of inertia. With this system for example, having a known club which has the desired swinging and playing action for the user, the remaining clubs in the set can be correlated or matched to the moment of inertia of the known club so that all of the clubs in the set will have the same feel and playing characteristics. This is accomplished by determining the moment of inertia of the known club about its center of gravity by means of a torsional pendulum; selecting another club in the set and adjusting the head weight by applying heads of different weights until the same moment of inertia is obtained by the torsional pendulum. The shaft length and head weight points of each are plotted on a log-log graph and connected by a straight line. This is a constant moment of inertia line and provides a means for reading off the required head weight for each of the varying shaft lengths of the set which are each progressively shorter by a predetermined amount as they proceed toward the #9 iron. This will produce a correlated set of clubs having substantially the same moment of inertia for all of the clubs. In such a set of clubs all of the shafts will have the same stiffness characteristics depending on the shaft design, such as disclosed in Patent No. 2,822,174, and will have the same shaft and grip weights with all of the heads being of the same design, i.e., having the same mass distribution in the head, all within allowed manufacturing tolerances. Another method of correlating the clubs in a set is to determine the moment of inertia of a plurality of clubs for each club in the set which will have the same shaft length and heads of different weights, plotting the moment of inertia against head weight and connecting these points for each club. Having determined the desired moment of inertia, the person can then check the graph for the proper head weight for each shaft length which would give him the same moment of inertia throughout the set. In measuring the moment of inertia this can be measured through the center of gravity of each club, or by the theory of parallel axis the moment of inertia can be translated at any point for the club, for example, the point of rotation for the club which is usually in the wrist and located about 2.25" above the end of the club. Other features and advantages of the invention will be apparent from the specification and claims when taken in connection with the accompanying drawings in which: FIGURE 1 shows a diagrammatic view of a torsional pendulum. FIG. 2 is the log-log graph on an expanded scale showing the moment of inertia line for the set. FIG. 3 shows the linear graph in Cartesian coordinates showing the various moments of inertia for each club in the set having different head weights. Golf is a dynamic game played with a plurality of clubs and there is usually at least one club in the set which has a desired feel in the swing and playability for the player. It has been determined that all of the clubs in the set, both woods and irons, can be given this same feel in the swing and playability if they are correlated to have the same moment of inertia about a predetermined point for the club. A set of clubs, therefore, according to the present invention can be produced which has the same feel and playability as the known or desired club. All of the clubs have a shaft with a grip at one end and a head at the other. The clubs all have shafts having a similar stiffness characteristic, said shafts and grips being of similar weight and all having similar head design, i.e., mass distribution. Their shafts diminish in length by a predetermined unit. For example, in the irons the difference is between each shaft as the shafts go toward the #9 shaft. The clubs have their head weights correlated to each shaft so as to produce a set of clubs having a predetermined similar moment of inertia about a similar point throughout the entire set of clubs. This is accomplished by determining the moment of inertia of the known club, for example the #2 iron, about its center of gravity. Because it is an irregularly shaped body this is done by the use of a torsional pendulum as shown in FIG. 1 wherein a carrier 10 is supported at the end of a stiff wire 11 of known length. The empty carrier is given a twist and the period of oscillation of the carrier measured. This period is r Thereafter a steel bar whose moment of inertia has been determined by calculation is placed in the carrier 10 with its center of gravity in a line with the wire 11 and the carrier given a twist and its period of oscillation measured. This period is r The steel bar is removed and the golf club to be measured is applied to the carrier 10 with its center of gravity in line with the wire 11 and the carrier twisted and its period of oscillation determined. This period will be r With this information the moment of inertia I of the club about its center of gravity is determined by the formula: I =Unkn0Wn moment of inertia of the golf club I =Known moment of inertia of the steel bar by calculation r =Period of golf club r =Period of steel bar r =Period of torsional pendulum. Should it be preferred to translate the moment of inertia of the club about another point for the club, for example the pivot point or point of rotation of the club in play which is located in the wrist usually about 2.25" above the grip end of the club, this can be accomplished by using the theory of parallel axis wherein: I =Moment of inertia through wrists I =Moment of inertia through center of gravity of club c.g.=Center of gravity as measured from the club end 2.25"=Location of point in wrists from end of club M=Total weight of club in lbs. divided by gravity of 32.2 ft./sec. or 386 in./sec. In the example the moment of inertia of the #2 club was found to be 1080 in. lbs. In order to derive the correlated set, another club in the set, say a #9 iron, had heads of various weights applied to the shaft therefor until the club has a moment of inertia, as determined as above, of 1080 in. lbs. or is equal to the moment of inertia of the #2 iron. The club length and head weight of each club are plotted on a log graph as shown in FIG. 2 and connected by a straight line X. This line will be the constant moment of inertia line for the Whole set of clubs and the required head weight for the various different shaft lengths in the set of clubs can be readily determined from the graph. This is indicated on the graph by the club number followed by the W or I suffix to indicate woods and irons. This method can be used for both irons and woods so that they all have the same moment of inertia. In the illustration in FIG. 2 the line X represents 1080 in. lbs. It has been found that lines parallel to but spaced from the line X a predetermined distance will represent a definite different moment of inertia. In the drawing line Y=l090 in. lbs. and line Z=l100 in. lbs. This will enable sets having different moment of inertia to be correlated accurately and quickly. Another method of correlating the clubs in a set is to determine the moment of inertia for several different head weights for each club. Since the shafts for each of these clubs are of the same length, the moment of inertia and head weight for each club are then plotted on linear Cartesian coordinates as shown in FIG. 3. A straight line is drawn through each of these plotted points. This will provide a series of lines, one for each club, wood and iron. These lines are indicated on the graph by the number of the club and the suflix W or I to designate wood or iron. Knowing the desired moment of inertia for the set of clubs, the required head weight for each club can be readily determined so as to produce a correlated set having a constant moment of inertia throughout. Variations and modifications may be made within the scope of the claims and portions of the improvements may be used without others. I claim: 1. A method of producing a dynamically matched set of golf clubs having substantially the same moment of inertia about a predetermined similar point for each'club in the set, the clubs in each set having a shaft provided with a grip at one end and a head at the other end and in which the shaft length and club head weight of each club in the set varies while the shafts in the set have the same stiffness and uniform weight characteristics, the grips have uniform weight and the heads are of a similar design, the steps of determining the moment of inertia, by means of a torsional pendulum, of a club in the set having the desired playing characteristics, applying to the shaft for another club in the set a proper head for said shaft and adjusting the head weight by applying heads of different weights until the club has a moment of inertia as determined by means of a torsional pendulum which is substantially equal to that of the first club, plotting the club length and head weight values of the two clubs on a loglog graph and connecting said points with a straight moment of inertia line, and assembling heads on the other shafts of the set, each having a proper head weight for the shaft length as determined by the graph so as to produce a matched set of clubs having a substantially uniform moment of inertia throughout. 2. A method of producing a dynamically matched set of golf clubs having substantially the same moment of inertia about a predetermined similarpoint foreach club in the set, the clubs in each set having a shaft provided with a grip at one end and a head at the other end and in which the shaft length and head weight of each club in the set varies while the shafts in the set'have the same stiffness characteristics, the grips have uniform weight and the'heads are of similar design, the steps of determining the moment of inertia, by means of a torsional pendulum, of a plurality of clubs each having the shaft of the same length and different head weights for the clubs, plotting on a linear graph the value of the moment of inertia and head weight for each length of club shaft. connecting the plotted points by a straight line which will produce a moment of inertia line for each shaft to indicate the proper head Weight for the different moments of inertia for each club of the same shaft length, selecting a club having a shaft length and head weight to provide the desired playing characteristics, and determining the moment of inertia of said club from said graph and supplying heads of the proper weight for each shaft of varying length as determined by the moment of inertia value on said graph to produce a correlated set of clubs having a substantially uniform moment of inertia throughout the set of clubs. 3. The method of producing a dynamically matched set of golf clubs having the same moment of inertia, the steps of measuring by means of a torsional pendulum the moment of inertia of a plurality of golf clubs, each having a shaft, grip and head, with the shafts being of different lengths and having the same stiffness characteristics and uniform weight characteristics, the grips being of the same weight, and the heads being of the same design and differing weights, plotting the moment of inertia lines for said clubs, and producing a set of correlated golf clubs having substantially the same moment of inertia throughout by assembling with the shafts the head having required head weights for given shaft lengths as determined by the moment of inertia curve. References Cited UNITED STATES PATENTS 1,594,801 8/1926 Stackpole 7365 2,349,736 5/1944 Knobel et a1. 73-65 2,822,174 2/1958 Brandon 273 3,106,091 10/1963 Korr 7365 FOREIGN PATENTS 1,045,614 10/1966 Great Britain. RICHARD C. QUEISSER, Primary Examiner ROBERT S. SALZMAN, Assistant Examiner US. Cl. X.R. 7 Patent Citations
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