Putter heads

Abstract

A putter-head (1) giving positive ball-topspin (S) for impact-heights (h.sub.i) above 5 mm from its sole (6), has its center of mass (9) located p mm behind its impact face (8) at height h.sub.c mm above the sole (6), a mass M kgm and a radius of gyration K mm about the heel-toe axis (4-5) through the center of mass (9). The loft (.alpha.) of the impact face (8) increases monotonically with height from 5 to 15 mm above the sole (6), where (K.sup.2/p) is greater than 5 mm and S=S.sub.G+S.sub.L where S.sub.G and S.sub.L are percentage spin rates based on: S.sub.G=(250.times.h)/[(3.2+70.times.M).times.(K.sup.2/p)+p] S.sub.L=(-0.76.times..alpha..sub.i)/[1+0.04.times.(p/K).sup.2] for which: h=h.sub.i-h.sub.c-p.times.sin(a.sub.i) and .alpha..sub.i degrees is impact-face loft at height h.sub.i. From the sole (6) upwards, the impact face curves (16) from negative- to positive-loft and merges into an upper flat-portion (15) of positive loft. Alternatively, it has upper and lower flat-portions (21, 22) of positive- and negative-loft respectively. A hosel (30, 31) gives high compliance at impact for head-rotation relative to the shaft (33) about the heel-toe axis (4-5), and allows choice of lie in shaft-attachment.

Description

[0001] This invention relates to putter-heads and is concerned especially with putter-heads for imparting topspin to a golf ball at impact.

[0002] In putting a golf ball, it is desirable to impart forward rolling spin or topspin to the ball during the putting stroke. Topspin reduces ball skid on the putting surface and helps to initiate pure rolling motion. Imparted topspin is defined as the component of ball spin about a horizontal axis parallel to the putter impact-face imparted at impact by a putter such that the ball peripheral speed on the top surface of the ball exceeds its linear or translational speed.

[0003] It is known that putters with negative face-loft normally hit above the horizontal equator of a golf ball and thus tend to impart topspin. However, this type of impact disadvantageously forces the ball downwards and into the putting surface, causing erratic loss of launch energy, especially on soft putting greens.

[0004] Thus, it is preferable that the impact point on the ball is below its equator, which generally ensures that the ball lifts off the putting surface at impact. Impacts just above the horizontal equator of the ball are also acceptable, especially if combined with an upward putter-head trajectory as this ensures that the downward component of impact force is a small fraction of the total and so has negligible deleterious-effect on the putt.

[0005] It is one of the objects of the present invention to provide an improved putter-head for imparting topspin to a golf ball at impact.

[0006] According to the present invention there is provided a putter-head for imparting a positive rate (S) of topspin on a golf ball for impacts with the ball throughout a range of impact height (h.sub.i) extending above 5 millimetre from the bottom of the putter-head, wherein the head has a centre of mass located at a distance p millimetre behind its impact face and a height h.sub.c millimetre above the bottom of the head, a mass M kilogram and a radius of gyration K millimetre about the heel-toe axis through the centre of mass, and the loft (a) of the impact face increases monotonically with height from 5 to 15 millimetre above the bottom of the putter-head, and wherein: K.sup.2/p>5 (a) and S=S.sub.G+S.sub.L (b)

[0007] where the spin rates S.sub.G and S.sub.L expressed as percentages, are as follows: S.sub.G=(250.times.h)/[(3.2+70.times.M).times.(K.sup.2/p)+p] S.sub.L=(-0.76.times..alpha..sub.i)/[1+0.04.times.(p/K).sup.2] for which: h=h.sub.i-h.sub.c-p.times.sin(.alpha..sub.i)

[0008] and

[0009] .alpha..sub.i degrees is the impact-face loft at height h.sub.i millimetre.

[0010] The loft (.alpha..sub.15) at 15 millimetre above the bottom of the head may be at least 3 degrees larger than the loft (.alpha..sub.5) at 5 millimetre above the bottom of the head, but is preferably at least 5 degrees or more especially, 7 degrees, larger.

[0011] The minimum value of rate S of topspin may be at least +2.5% or, more preferably, +5.0% for values of h.sub.i above 5 millimetre from the bottom of the putter-head. For values of h.sub.i down to 2.5 millimetre, the minimum spin rate S is preferably +5.0%. For preference, the height h.sub.c may be less than 10 millimetre, or, more preferably, not more than 7 millimetre, and the value of (K.sup.2/p) may for preference be not less than 5 or, more especially, 8 millimetre. The distance p is preferably at least 10 millimetre and less than 35 millimetre but more preferably less than 30 millimetre.

[0012] For preference a putter-head according to the invention is provided with shaft attachment means that provides additional compliance to rotation of the head of up to .+-.0.5 degrees relative to the shaft to enable achievement of vertical gear effect. Head rotation about the heel-toe axis may also be increased by arranging that stiffness of the shaft where it attaches to the putter-head is minimised. This is achieved by ensuring that the shaft deformation during impact is predominately in bending or twisting mode rather than in axial compression or elongation mode. Thus for preference, a putter-head according to the invention may be provided with shaft attachment means wherein the axis of the shaft-attachment means is horizontally displaced d millimetre either side of the horizontal heel-toe axis through the centre of mass. To optimise the imparted topspin properties of the assembled putter, d should be ideally zero or less than r, where r is the radius of the putter shaft at the shaft-attachment means. It is also advantageous for the horizontal displacement (measured in any direction) of the shaft-attachment means from the centre of mass of the putter-head to be less than the radius of gyration K. Putter-heads in accordance with the present invention will now be described, by way of example, with reference to the accompanying drawings, in which:

[0013] FIGS. 1 to 3 are front-elevation, rear-elevation and plan view respectively of a first putter-head according to the invention;

[0014] FIG. 4 is a sectional side-elevation of the first putter-head taken on the line IV-IV of FIG. 3;

[0015] FIG. 5 is a perspective view from the rear of the first putter-head;

[0016] FIGS. 6a and 6b are, respectively, diagrammatic views of the centre section of the first putter-head and a golf ball at impact, in two different circumstances;

[0017] FIG. 7 is a sectional side-elevation of a second putter-head according to the invention;

[0018] FIG. 8 is illustrative of a form of hosel that may be used in the putter-heads of FIGS. 1 to 5 and FIG. 7;

[0019] FIGS. 9a and 9b are, respectively, sectional views of use of the hosel of FIG. 8 in providing two different angles of lie of the putter-shaft; and

[0020] FIG. 10 is in further illustration of a feature of the hosel of FIG. 8.

[0021] Referring to FIGS. 1 to 5, the putter-head 1, comprises an impact-face flange 2 and a base 3. The base 3, which forms the major part of the putter-head 1, defines the heel 4, the toe 5 and the sole 6 of the head 1, and incorporates a shaft-hosel 7. The flange 2 is of an unusually thin section for a putter-head, being for example of 4 millimetre or less in thickness, yet establishes a rigid interface between the impact face 8 and the base 3. This rigidity is important in ensuring that impacts on the middle or upper part of the face 8 do not deflect the flange 2 relative to the base 3, but instead rotate the entire head 1 fully about its centre of mass 9. This in turn ensures that the putter-head 1 behaves as a rigid body during impact, and parameters such as imparted ball spin and velocity are accurately predictable and fully achieved.

[0022] In one construction of the putter-head 1 of FIGS. 1 to 5, the desired rigidity and mass properties are realised by casting it of 316 stainless steel or a similar alloy. In an alternative construction, the impact flange 2 is provided as a separate part of titanium, aluminium or magnesium alloy or of a high modulus composite. The main requirement is that the flange 2 has a mass which is a small proportion of the overall mass of the putter-head 1, yet provides a rigid interface between the golf ball and the base 3 at impact. This allows-the centre of mass 9 to be positioned close to the bottom surface or sole 6, and some distance from the face 8. The height h, of centre of mass 9 above the sole 6 is preferably less than 10 millimetre or, more preferably, not more than 7 millimetre since this limits the amount of negative loft required.

[0023] A very high value of p, the distance of centre of mass 9 behind the impact face 8, produces high sidespin and directional errors under offset impacts. This undesirable characteristic can be reduced by increasing the moment of inertia of the head 1 about the vertical axis, but increase of this moment affects playing control and/or requires the mass of the head 1 to be excessive. As a result, it is preferable to limit the distance p to be less than 35 millimetre, but, more preferably, less than 30 millimetre. Small values of p are disadvantageous in putter-heads of the present invention since they severely limit vertical gear effect, and accordingly, it is preferred to adopt a construction for which p is at least 10 millimetre.

[0024] By way of modification of the putter-head of FIGS. 1 to 5, the impact face 8 may be formed by material which is softer than that of the flange 2 and which is provided as a layer, or as an insert, bonded to the flange 2 for reducing vibration and noise intensity (so as to give a so-called `soft-feel`). However, it is disadvantageous to have the entire structure of the flange 2 in soft material as this reduces topspin imparted by vertical gear-effect.

[0025] The putter-head of FIGS. 1 to 5 and its action will now be described in further detail with reference to FIGS. 6a and 6b which are, respectively, diagrammatic representations of the centre section of the putter-head 1 at the instant of impact with a golf ball 13 resting on a putting surface 14, in two different circumstances.

[0026] As illustrated in exaggerated form in FIGS. 6a and 6b, the impact face 8 of the putter-head 1 is of curved profile transversely of the heel-toe axis only, and has a lower, curved half 15 that has a loft angle .alpha. degrees which increases with increase in height, progressively from a negative value at the sole 6, through zero to a positive value .alpha..sub.MAX where it merges into the upper half 16 of the face 8. The upper half 16 is flat and has a loft angle of .alpha..sub.MAX so as to be tangential to the lower half 15 where they merge; accordingly, the loft of the impact face 8 increases monotonically throughout its full height upwardly from the sole 6.

[0027] As represented only in FIG. 6a, the centre of mass 9 of the putter-head 1 is located at distance p millimetre behind the impact face 8 and at a height h.sub.c millimetre above the sole 6. The centre of impact of the face 8 with the ball 13 (which is a playing variable with random error) is shown as occurring at height ha above the sole 6 in the circumstances of FIG. 6a but at height h.sub.b in the circumstances of FIG. 6b.

[0028] The main effect required of the impact is to launch the golf ball 13 with linear velocity substantially along the intended line of putt and preferably with a slight positive (upward) elevation angle. The upward trajectory is often provided by a small amount of loft (typically +3 degrees) on the impact-face of a putter. Moreover, most golfers adopt an approximate `pendulum swing` in putting, in which the putter-head is swung about a substantially horizontal axis with the swing rotation axis and the putter shaft axis in (or nearly so) a common plane that is substantially parallel to the heel-toe axis of the putter-head. The main variable with this type of swing is the position of the ball in relation to the vertical arc followed by the putter-head. For preference, impact with the ball occurs at or just beyond the bottom of the arc (on the upward part of the arc), but in practice may occur before or later than this.

[0029] In the circumstances represented in FIG. 6a, impact takes place at the bottom of the arc, where the putter-head trajectory is horizontal (shown by arrow 17a). Impact in such circumstances generally occurs at mid-height, within the upper part 15 of the impact face 8. The loft angle .alpha..sub.MAX applies provided the clearance 18a between the putting surface 14 and the sole 6 is not more than the radius of the ball 13 less the height of the curved lower half 16 of the impact face 8. If the ground-to-sole clearance 18a is more than this, the height of contact will increase and may disadvantageously rise above the horizontal equator of the ball 13 and consequently launch the ball 13 with a slight negative elevation trajectory. This type of putting stroke is rare except with players of less than moderate skill and typifies poor putter control. Nevertheless it is preferred that excessive negative ball trajectory is avoided by providing that the region on the impact-face where the loft is negative is limited to the lower 12 millimetre, or more preferably the lower 9 millimetre.

[0030] FIG. 6b represents the circumstances in which impact occurs at a point beyond the bottom of the pendulum arc where the putter-head trajectory (depicted by arrow 17b) has positive elevation. The ball launch trajectory in these circumstances is dependent on the combination of trajectory elevation angle and the loft angle at impact; the latter is generally slightly negative and varies both with the ground clearance 18b and the elevation angle of the trajectory 17b. Provided the sum of putter-head trajectory angle and loft angle at impact point is greater than -20% of the trajectory elevation angle, the ball launch elevation angle will be positive.

[0031] Thus, the ball is still given a slight lift for impacts in the lower (negative loft) region of the impact-face 8 provided the bottom of the pendulum arc is kept low as before.

[0032] The aim of the present invention is to provide a putter-head that imparts topspin on the ball from all pendulum-swing putts but also provides high probability of imparting positive lift on the ball at impact.

[0033] It is known that two mechanisms impart spin with club-on-ball impact in golf, namely eccentric impact, commonly known as `gear-effect`, and oblique impact which is most commonly experienced as backspin due to club-face loft. The gear-effect realised with a putter-head is dependent on the condition that the line of impact (that is, the line normal to the impact surfaces at the point of impact) is offset from the centre of mass of the head. It follows that the condition for gear-effect with the putter-head of the present invention is also dependent on the loft angle of the impact face at the point of impact.

[0034] The offset distance h between the line of impact and the centre of mass 9 is given by: h=h.sub.i-h.sub.c-p.times.sin(.alpha..sub.i) (1)

[0035] where h.sub.c and h.sub.i are, respectively, the height (millimetre) of the centre of mass 9 and the impact point above the bottom-most part, the sole 6, of the putter-head, and .alpha..sub.i (degrees) is the loft angle of the putter face 8 at the point of impact (positive for upward tilt).

[0036] The value of spin attainable with gear-effect is known from Newtonian dynamics assuming that the putter-head and golf ball behave as free rigid bodies at impact, and is given, as a percentage, by: S.sub.G=(250.times.h)/[(3.2+70.times.M).times.(K.sup.2/p)+p] (2) where M is the putter-head mass (kilogram), K is the radius of gyration for rotation about the horizontal heel-toe axis through the centre of mass (millimetre) and S.sub.G is the ratio (expressed as a percentage) of the peripheral velocity of the ball due to rotation, to its linear or translational velocity.

[0037] It is found that S.sub.G is highly dependent on the term (K.sup.2/p) in equation (2). A low value of this term, such as 5 (millimetre) gives a very high vertical gear effect, which in turn requires high negative loft to overcome the tendency for backspin at low impact heights. It is also the case that most conventional putter-heads (especially low cost, one-piece cast heads) have values of (K.sup.2/p) of 10 to 20 or so, and golfers are familiar and more attuned to this weight distribution. It is thus an aim with the putter-head of the invention to arrange that (K.sup.2/p) is at least more than 5 millimetre, but preferably 8 millimetres or more.

[0038] Further, golfers are not used to putters having very low inertia about the heel-toe axis (or about any other axis). Such low-inertia putters can feel less `solid` to play with, which is disadvantageous.

[0039] It is accordingly preferable that the value of the heel-toe inertia, namely, (M.times.K.sup.2), is not less than 25 kilogram-millimetres.sup.2 or, more preferably, is greater than 30 kilogram-millimetres.sup.2.

[0040] For vertical gear effect to impart topspin rather than backspin, the value of h must be positive. This is exemplified in FIG. 6a where the line of impact 19a (collinear with the centre of the ball 13 and the impact point) passes above the centre of mass 9.

[0041] With pendulum-swing putts the putter-head elevation trajectory is always parallel to the sole 6 and therefore the spin imparted due to oblique impact is a function of the impact-face loft .alpha..sub.i but not trajectory, and is given by: S.sub.L=(-0.76.times..alpha..sub.i)/[1+0.04.times.(p/K).sup.2]

[0042] where S.sub.L denotes the spin ratio (expressed as a percentage and defined as for S.sub.G) as a function of loft. It is to be noted that positive loft imparts negative spin or backspin and negative loft imparts topspin.

[0043] Conveniently, it is practical to provide negative loft, which in turn imparts topspin, in the lower half 16 of the impact-face 8 and this compensates for the fact that the height h defined in equation (1) normally becomes negative for small values of hi. This is depicted in FIG. 6b where the line of impact 19b is shown to pass below the centre of mass 9.

[0044] The value of height h can in practice be kept positive even for zero impact-height h.sub.i by arranging that: h.sub.c-p.times.sin(.alpha..sub.i)

[0045] remains positive. However, this option requires severely negative loft, especially for smaller values of distance p and thus undesirably imparts negative ball-launch trajectory rather than the desired lift. It is thus much more preferable to arrange that the sum of S.sub.L and S.sub.G is positive at least for putts above the lower limit of useful impact height, for example above 5 millimetres or 2.5 millimetres. It is preferable that the minimum spin rate is +2.5%, or more preferably +5.0%, above 5 millimetres, but below this down to 2.5 millimetres, it is very desirably +5.0%.

[0046] Since the diameter of the impact footprint (that is, the contact deformation area) is usually at least 5 millimetres (except for very low-velocity putts), impacts at heights below 2.5 millimetres encroach onto the lower lip of the impact face. In these circumstances, an impact will `top` the ball, giving abundant topspin but at the expense of erratic length and direction control.

[0047] It can be seen from equations (1) to (3) that a number of putter-head parameters determine spin rate, namely p, h.sub.c, M, K and .alpha..sub.i (which is a function of impact height). Typical value ranges of these parameters for blade-style putters according to the invention, are given in Table I. TABLE-US-00001 TABLE I p 10 to 18 millimetres h.sub.c 6 to 10 millimetres M 0.31 to 0.36 kilogram K 10 to 13 millimetres

[0048] For mallet-style putters the values for distance p and radius of gyration K are generally larger than those for blade-style putters. Table II below gives an example of a putter-head based on FIGS. 1 to 5. TABLE-US-00002 TABLE II h.sub.i .alpha..sub.i S.sub.G S.sub.L S.sub.G + S.sub.L (mm) (deg) (%) (%) (%) 2.5 -7.5 -2.4 +5.3 +2.9 5 -5.0 -0.5 +3.5 +3.0 12 +2.0 4.9 -1.4 +3.5 p = 16 millimetres h.sub.c = 6.8 millimetres M = 0.32 kilogram K = 11.6 millimetres .alpha..sub.MAX = 2.0 degrees (h.sub.i > 12 millimetres)

[0049] It is found in practice that the position of the shaft hosel 7 has a strong influence on the putter-head rotation about the heel-toe axis during the very short duration of impact (less than one millisecond). It has been found experimentally that if distance d is the horizontal offset between the shaft attachment axis and the heel-toe axis, topspin performance is enhanced when d is zero and that increasing d reduces the imparted topspin. In order to optimise the imparted topspin properties of the assembled putter, d should be ideally zero, or, more generally, less than the radius r of the putter-shaft.

[0050] A further advantage of positioning the shaft coupling close to the centre of mass of the putter-head is that shaft vibrations due to eccentric impact are minimised. In this respect, it is advantageous that the axis of the means for attachment of the shaft passes close (preferably not more than K millimetres) to the centre of mass of the putter-head (as distinct from the heel-toe axis through this centre).

[0051] FIG. 7 shows a sectional side-elevation of a putter-head 20 that is generally the same as the putter-head of FIGS. 1 to 5 except that the impact face in this case comprises an upper, flat-face portion 21 and a lower, flat-face portion 22. The upper portion 21 has typically zero or positive loft whereas the lower portion 22 has negative loft; differences in loft-are exaggerated in FIG. 7. The upper and lower portions 21 and 22 join one another in a horizontal junction 23 (which is parallel to the heel-toe axis and thus normal to the plane of FIG. 7). The loft angle of the impact face accordingly changes abruptly at the junction 23, but the effective loft actually experienced for impacts on or near the junction 23 changes only gradually as the point of impact is moved through the junction 23, owing to the softness of the cover material of the ball. More particularly, the softness results in the impact force being distributed above and below the junction 23 with the result that the effective loft tends to a value intermediate the lofts of the two flat-face portions 21 and 22; the junction 23 can be chamfered or rounded to enhance the distribution. The change in loft may also be made more gradual by reducing the hardness of the impact surface, for example by using an elastomer insert instead of a steel face as depicted in FIG. 7.

[0052] FIG. 8 shows a sectional view of an alternative form of hosel involving a male stub 30 and an annular recess 31 concentric with it. The axis 32 of stub 30 is inclined at the desired lie angle relative to the horizontal for attachment of the putter-shaft. Attachment of the shaft is carried out by applying a thixotropic adhesive within the hollow tip of the shaft and then placing the shaft-tip over the stub 30 to locate within the surrounding annular recess 31; the adhesive desirably has good gap-filling properties and may, for example, be the `E3332` epoxy adhesive sold under the registered trade mark PERMABOND. The recess 31 is typically only 2 to 3 millimetres deep and serves to centre the shaft-tip relative to the stub 30.

[0053] The dimensions of the stub 30 and recess 31 are such that the shaft can be fitted at different angles relative to the concentric position so as to allow for different lie preferences. This is illustrated by FIGS. 9a and 9b, FIG. 9a showing adoption of an `upright` lie for shaft 33 on the stub 30 in which the shaft 33 is inclined at an angle of 78 degrees to the horizontal. FIG. 9b on the other hand, shows adoption of a `flat` lie in which the shaft 33 is inclined at an angle of 66 degrees to the horizontal.

[0054] Referring again to FIG. 8, the seating plane at the bottom of the annular recess 31 is shown by dashed line 34, and intentionally not square to the axis 32 but is instead tilted towards the horizontal so that the tip of the shaft 33 rests on nominally one point on the plane containing line 34. This arrangement is shown more clearly in FIG. 10 where the tip of shaft 33 touches line 34 at only one point 35. It is arranged that this point 35 is located on the heel-toe axis 36.

[0055] At impact, the putter-head rotates about the heel-toe axis 36. This arrangement provides very high compliance to putter-head rotation relative to the shaft 33 about the heel-toe axis 36 since the rim of the shaft 33 is decoupled from the putter-head body via the cured adhesive material of relatively low modulus, and the only direct contact with the putter-head is at the one point 35 on the axis 34 of rotation.

Claims

1-20. (canceled)

21. A putter-head for imparting a positive rate (S) of topspin on a golf ball for impacts with the ball throughout a range of impact height (h.sub.i) extending above 5 millimeter from the bottom of the putter-head, wherein the head has a center of mass located at a distance p millimeter behind its impact face and a height h.sub.c millimeter above the bottom of the head, a mass M kilogram and a radius of gyration K millimeter about the heel-toe axis through the center of mass, and the loft (.alpha.) of the impact face increases monotonically with height from 5 to 15 millimeter above the bottom of the putter-head, and wherein: K.sup.2/p>5 (a) and S=S.sub.G+S.sub.L (b) where the spin rates S.sub.G and S.sub.L expressed as percentages, are as follows: S.sub.G=(250.times.h)/[(3.2+70.times.m).times.(K.sup.2/p)+p] S.sub.L=(-0.76.times..alpha..sub.i)/[1+0.04.times.(p/K).sup.2] for which: h=h.sub.i-h.sub.c-p.times.sin(.alpha..sub.i) and .alpha..sub.i degrees is the impact-face loft at height h.sub.i millimeter.

22. The putter-head according to claim 21, wherein the loft (.alpha..sub.15) at 15 millimeter above the bottom of the head is at least 3 degrees larger than the loft (.alpha..sub.5) at 5 millimeter above the bottom of the head.

23. The putter-head according to claim 22, wherein .alpha..sub.15 is at least 5 degrees larger than .alpha..sub.5.

24. The putter-head according to claim 23, wherein .alpha..sub.15 is at least 7 degrees larger than .alpha..sub.5.

25. The putter-head according to claim 21, wherein S is at least +2.5%.

26. The putter-head according to claim 25, wherein S is at least +5.0%.

27. The putter-head according to claim 21, wherein the head also imparts a positive rate (S) of topspin of at least 5.0% for impacts with the ball throughout a range of impact height (h.sub.i) extending above 2.5 millimeter from the bottom of the putter-head.

28. The putter-head according to claim 21, wherein h.sub.c is less than 10 millimeter.

29. The putter-head according to claim 28, wherein h.sub.c is not more than 7 millimeter.

30. The putter-head according to claim 21, wherein the ratio K.sup.2/p is more than 5 millimeter.

31. The putter-head according to claim 30, wherein the ratio K.sup.2/p is not less than 8 millimeter.

32. The putter-head according to claim 31, wherein p is at least 10 millimeter.

33. The putter-head according to claim 32, wherein p is less than 35 millimeter.

34. The putter-head according to claim 33, wherein p is less than 30 millimeter.

35. The putter-head according to claim 21, including shaft-attachment means and wherein a putter-shaft is attached to the head via the shaft-attachment means and the horizontal offset of the axis of the shaft from the heel-toe axis is less than the radius of the shaft at the shaft-attachment means.

36. The putter-head according to claim 35, wherein the shaft-attachment means has zero horizontal offset from the heel-toe axis.

37. The putter-head according to claim 35, wherein the horizontal displacement of the shaft-attachment means from the center of mass is less than the radius of gyration K.

38. The putter-head according to claim 21, wherein the impact face includes an upper, flat portion having positive loft.

39. The putter-head according to claim 21, wherein the impact face includes a lower portion which is curved and has loft that increases from a negative value to a positive value upwardly from the bottom of the head.

40. The putter-head according to claim 21, wherein the impact face includes a lower, flat portion having negative loft.