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87-408: The most significant difference between clubs of the same type is loft , or the angle between the club's face and the vertical plane. It is loft that is the primary determinant of the ascending trajectory of the golf ball, with the tangential angle of the club head's swing arc at impact being a secondary and relatively minor consideration (though these small changes in swing angle can nevertheless have

174-547: A central mass . In control theory , a trajectory is a time-ordered set of states of a dynamical system (see e.g. Poincaré map ). In discrete mathematics , a trajectory is a sequence ( f k ( x ) ) k ∈ N {\displaystyle (f^{k}(x))_{k\in \mathbb {N} }} of values calculated by the iterated application of a mapping f {\displaystyle f} to an element x {\displaystyle x} of its source. A familiar example of

261-699: A free fall frame which happens to be at ( x , y ) = (0,0) at  t  = 0. The equation of motion of the projectile in this frame (by the equivalence principle ) would be y = x tan ⁡ ( θ ) {\displaystyle y=x\tan(\theta )} . The co-ordinates of this free-fall frame, with respect to our inertial frame would be y = − g t 2 / 2 {\displaystyle y=-gt^{2}/2} . That is, y = − g ( x / v h ) 2 / 2 {\displaystyle y=-g(x/v_{h})^{2}/2} . Now translating back to

348-413: A "condition of competition". Wedges that conform to the new standard are often marketed as "CC" or "Condition of Competition" wedges; this moniker is likely to fall into disuse as players upgrade clubs and the use of non-conforming irons diminishes. Notes Bibliography [REDACTED] Media related to Golf clubs (equipment) at Wikimedia Commons Trajectory A trajectory or flight path

435-407: A 9-iron and a lower and longer trajectory than a gap wedge . Though technically a wedge , pitching wedges are generally treated as if they were numbered irons . This is for a number of reasons: first, before the term "wedge" became common for high-loft short irons, the pitching wedge was actually numbered as the "10-iron" of a matched set, and to this day it follows the normal loft progression of

522-410: A combination of high-lofted woods (up to 7-wood) and hybrids to replace the 5, 6 and 7-irons, allowing these players to achieve greater carry distances with slower swings. Putters are a special class of clubs with a loft not exceeding ten degrees, designed primarily to roll the ball along the grass, generally from a point on the putting green toward the hole. Contrary to popular belief, putters do have

609-469: A compromise to club-makers after imposing and enforcing a 460cc volume limit on these same club heads. Many recently developed woods have a marked "trampoline effect" (a large deformation of the face upon impact followed by a quick restoration to original dimensions, acting like a slingshot), resulting in very high ball speeds and great lengths of tee shots. As of 1 January 2008, the USGA and R&A have settled on

696-589: A driver, instead using a 3-wood for tee shots and making up the difference on the approach using a lower-lofted iron. The most common omissions are the "long irons", numbered from 2 to 5, which are notoriously difficult to hit well. The player can supplement the gaps in distance with either higher-numbered woods such as the 5 and even the 7-wood, or may replace the long irons with equivalently-numbered hybrid clubs. If hybrids are used, higher-lofted woods are often omitted as redundant, but ladies' and seniors' sets commonly feature both hybrids and high-lofted woods, omitting

783-406: A flat-topped "putter grip". This disqualifies many chipper designs, but there are some USGA-conforming chippers, and non-conforming designs can still be used for informal play. The shafts of the woods were made of different types of wood before being replaced by hickory in the middle of the 19th century. The varieties of woods included ash , purpleheart , orangewood , and blue mahoe . Despite

870-406: A full swing to produce high-altitude shots such as approaches to the green or lifting the ball over trees. They are also commonly used to "lay up" in front of a hazard or to create a better lie for the next shot, and for recovery from firmer rough or sometimes from sand when the ball is lying on top of the surface. The loft of a particular pitching wedge follows the progression of the numbered irons of

957-583: A futile hypothesis by practical-minded investigators all through the Middle Ages in Europe . Nevertheless, by anticipating the existence of the vacuum , later to be demonstrated on Earth by his collaborator Evangelista Torricelli , Galileo was able to initiate the future science of mechanics . In a near vacuum, as it turns out for instance on the Moon , his simplified parabolic trajectory proves essentially correct. In

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1044-678: A given range d h {\displaystyle d_{h}} . The angle θ {\displaystyle \theta } giving the maximum range can be found by considering the derivative or R {\displaystyle R} with respect to θ {\displaystyle \theta } and setting it to zero. which has a nontrivial solution at 2 θ = π / 2 = 90 ∘ {\displaystyle 2\theta =\pi /2=90^{\circ }} , or θ = 45 ∘ {\displaystyle \theta =45^{\circ }} . The maximum range

1131-521: A loft (often 5° from truly perpendicular at impact) that helps to lift the ball from any indentation it has made. Newer putters also include grooves on the face to promote roll rather than a skid off the impact. This increases rolling distance and reduces bouncing over the turf. Putters are the only class of club allowed to have certain features, such as two striking faces, non-circular grip cross-sections, bent shafts or hosels, and appendages designed primarily to aid players' aim. Present in some golfers' bags

1218-443: A low, medium or high kick; a low kick means the shaft will store energy closer to the club head, which means the club head can twist more but also allows for higher club head speeds. A high kick shaft will store energy closer to the grip; such a shaft will feel firmer when swinging it and will give better control over direction, but the same strength swing will flex the shaft less, which will reduce club-head speed. Widely overlooked as

1305-625: A matched set. Irons are typically grouped according to their intended distance (which also roughly corresponds to their shaft length and thus their difficulty to hit the ball); in the numbered irons, there are long irons (2–4), medium irons (5–7), and short irons (8–9), with progressively higher loft angles, shorter shafts, and heavier club heads. As with woods, "irons" get their name because they were originally made from forged iron. Modern irons are investment-cast out of steel alloys, which allows for better-engineered "cavity-back" designs that have lower centers of mass and higher moments of inertia, making

1392-418: A one-piece "sleeve" made of rubber, synthetic or composite material that is slid over the shaft and secured with an adhesive. These sleeve grips allow club makers and golfers to customize the grip's diameter, consistency (softness/firmness) and texturing pattern to best fit the player. Clubs with an outer "wrap" of leather or leather-like synthetic still typically have a "sleeve" form underneath to add diameter to

1479-434: A part of the club, the shaft is considered by many to be the engine of the modern club head. Shafts range in price from a mere US$ 4 to over US$ 1200. Current graphite shafts weigh considerably less than their steel counterparts (sometimes weighing less than 50 grams (1.8 oz) for a driver shaft), allowing for lighter clubs that can be swung at greater speed. Beginning in the late 1990s, custom shafts have been integrated into

1566-411: A particle of mass m {\displaystyle m} , moving in a potential field V {\displaystyle V} . Physically speaking, mass represents inertia , and the field V {\displaystyle V} represents external forces of a particular kind known as "conservative". Given V {\displaystyle V} at every relevant position, there

1653-499: A player is positioned so as to catch it as it descends, he sees its angle of elevation increasing continuously throughout its flight. The tangent of the angle of elevation is proportional to the time since the ball was sent into the air, usually by being struck with a bat. Even when the ball is really descending, near the end of its flight, its angle of elevation seen by the player continues to increase. The player therefore sees it as if it were ascending vertically at constant speed. Finding

1740-479: A putt, which is more difficult with a lofted iron due to a difference in lie angle. Most chippers have a loft greater than 10 degrees, which is the maximum loft permitted by the Rules of Golf for a club to be classed as a putter, so these clubs are actually classed as irons. To be legal for sanctioned play, a chipper cannot have any feature that is defined in the rules as allowable only on putters, e.g. two striking faces or

1827-415: A putter may have two such faces if their characteristics are the same, and they are opposite each other. Page 127 of the USGA rules of golf states: A putter is a club with a loft not exceeding ten degrees designed primarily for use on the putting green. Therefore, any double sided club with a loft greater than 10 degrees is not legal. The trim ring, usually black (It may have additional trim colors), that

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1914-460: A reasonably good approximation, although if a comet passes close to the Sun, then it is also influenced by other forces such as the solar wind and radiation pressure , which modify the orbit and cause the comet to eject material into space. Newton's theory later developed into the branch of theoretical physics known as classical mechanics . It employs the mathematics of differential calculus (which

2001-506: A regulation that limits the acceptable "trampoline effect" to a coefficient of restitution (COR)—a measurement of the efficiency of the transfer of energy from the club head to the ball—of .830. Other large scale USGA rulings involve a 1990 lawsuit, and subsequent settlement, against Karsten Manufacturing, makers of the PING brand, for their use of square, or U-grooves in their immensely popular Ping Eye2 irons. The USGA argued that players who used

2088-531: A set. They are primarily utilized from the tee box and, on longer holes, may be employed for the second or even third shot. The largest wood, often referred to as the driver or one wood, is frequently crafted from hollow titanium and incorporates feather-light shafts. The length of the woods has been increasing in recent decades, and a typical driver with a graphite shaft is now 45.5 inches (1,160 mm) long. The woods may also have very large heads, up to 460 cm (28 cu in) in volume (the maximum allowed by

2175-451: A significant influence on launch angle when using low-lofted clubs). The impact of the club compresses the ball, while grooves on the club face give the ball backspin . Together, the compression and backspin create lift . The majority of woods and irons are labeled with a number; higher numbers usually indicate shorter shafts and higher lofts, which give the ball a higher and shorter trajectory. Woods are long-distance clubs, meant to drive

2262-400: A subclass of irons with greater loft than the numbered irons (generally starting at 47°–48° of loft, above the 9-irons of 44°–45°), and other features such as high-mass club heads and wide soles that allow for easier use in tricky lies. Wedges are used for a variety of short-distance, high-altitude, high-accuracy "utility" shots, such as hitting the ball onto the green ("approach" shots), placing

2349-554: A trajectory is the path of a projectile, such as a thrown ball or rock. In a significantly simplified model, the object moves only under the influence of a uniform gravitational force field . This can be a good approximation for a rock that is thrown for short distances, for example at the surface of the Moon . In this simple approximation, the trajectory takes the shape of a parabola . Generally when determining trajectories, it may be necessary to account for nonuniform gravitational forces and air resistance ( drag and aerodynamics ). This

2436-486: A uniform downwards gravitational force we consider two bodies orbiting with the mutual gravitation between them, we obtain Kepler's laws of planetary motion . The derivation of these was one of the major works of Isaac Newton and provided much of the motivation for the development of differential calculus . If a projectile, such as a baseball or cricket ball, travels in a parabolic path, with negligible air resistance, and if

2523-431: A variety of shots from all over the course, from the tee box on short or dog-legged holes, to the fairway or rough on approach to the green, to tricky situations like punching through or lobbing over trees, getting out of hazards, or hitting from tight lies requiring a compact swing . Most of the irons have a number from 1 to 9 (the numbers in most common use are from 3 to 9), corresponding to their relative loft angle within

2610-521: Is a deliberately low upper limit such as four clubs, or three clubs plus putter, with a typical load being a wood or hybrid, middle iron, wedge and putter, although often with significant variation between players with regards to which specific clubs are favored in each role. The ruling authorities of golf, The R&A (formerly part of The Royal and Ancient Golf Club of St Andrews ) and the United States Golf Association (USGA), reserve

2697-414: Is a large gap but not unplayable). Other clubs may be omitted as well. On courses where bags must be carried by the player, the player may take only the odd-numbered irons; without the 4, 6 or 8 irons (the 3 is sometimes removed instead of the 4) the bag's weight is considerably reduced. Carrying only a driver, 3-wood, 4-hybrid, 5-7-9 irons, pitching and sand wedges, and a putter reduces the number of clubs in

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2784-442: Is a maximum, it is not a minimum; players are free to use any lesser number of clubs they prefer, so substitutions for the common omissions above are not always made; a player may simply choose to play without a 5-wood or 2–4 irons, instead using a 4-wood and moving directly to their 5-iron as desired distance decreases (a 4-wood in a skilled golfer's hands averages 200 yards; a 5-iron in the same player's hands would be about 160, which

2871-491: Is a tapered steel tube or a series of stepped steel tubes in telescopic fashion. This has improved the accuracy of golfers. The grips of the clubs are made from leather or rubber. The shaft is a tapered tube made of metal (usually steel) or carbon fiber composite (referred to as graphite). The shaft is roughly 0.5 inches (13 mm) in diameter near the grip and from 34 to 48 inches (86 to 122 cm) in length. Shafts weigh from 45 to 150 grams (1.6 to 5.3 oz), depending on

2958-465: Is a very versatile club. Being on the cusp between numbered irons and wedges, the pitching wedge has generally accepted uses falling into either class. Used with a "full swing" similar to a short iron, a golfer can produce a high-trajectory shot that carries between 80–130 yards (73–119 m) (depending on a variety of factors such as swing and club design), then "bites" with little or no roll after initial impact. Used with an abbreviated "chipping" motion,

3045-411: Is a way to infer the associated force that would act at that position, say from gravity. Not all forces can be expressed in this way, however. The motion of the particle is described by the second-order differential equation On the right-hand side, the force is given in terms of ∇ V {\displaystyle \nabla V} , the gradient of the potential, taken at positions along

3132-494: Is for players with a slower swing speed (70–79 mph (113–127 km/h)), and the stiffer shafts, such as S-Flex and X-Flex (Stiff and Extra-Stiff shafts) are reserved only for those players with an above average swinging speed, usually above 100 mph (160 km/h). Some companies also offer a "stiff-regular" or "firm" flex for players whose club speed falls in the upper range of a Regular shaft (90–100 mph (140–160 km/h)), allowing golfers and club makers to fine-tune

3219-419: Is found directly on top of the hosel on many woods and irons. The ferrule is mostly decorative, creating a continuous line between the shaft and the wider hosel, but in some cases it can form part of the securing mechanism between hosel and shaft. Ferrules of differing weights can fine-tune the center of mass of the overall club head, but for these minute adjustments, screw-in weighted inserts at specific points on

3306-422: Is not practicable to define 'plain in shape' precisely and comprehensively." These two rules are used as the basis for most of the more specific rules of Appendix II, including that no club may have a concave face (1931) and various rules defining what is "traditional" about the shapes of specific clubs, while allowing for the progression of technology. The "traditional and customary" rule was originally used to ban

3393-543: Is perpendicular to it ( parallel to the gravitational field lines ). Let g {\displaystyle g} be the acceleration of gravity . Relative to the flat terrain, let the initial horizontal speed be v h = v cos ⁡ ( θ ) {\displaystyle v_{h}=v\cos(\theta )} and the initial vertical speed be v v = v sin ⁡ ( θ ) {\displaystyle v_{v}=v\sin(\theta )} . It will also be shown that

3480-402: Is the chipper , a club designed to feel like a putter but with a more lofted face, used with a putting motion to lift the ball out of the higher grass of the rough and fringe and drop it on the green, where it will then roll like a putt. This club replaces the use of a high-lofted iron to make the same shot, and allows the player to make the shot from a stance and with a motion nearly identical to

3567-422: Is the acceleration due to gravity). The range , R , is the greatest distance the object travels along the x-axis in the I sector. The initial velocity , v i , is the speed at which said object is launched from the point of origin. The initial angle , θ i , is the angle at which said object is released. The g is the respective gravitational pull on the object within a null-medium. The height , h ,

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3654-506: Is the focus of the discipline of ballistics . One of the remarkable achievements of Newtonian mechanics was the derivation of Kepler's laws of planetary motion . In the gravitational field of a point mass or a spherically-symmetrical extended mass (such as the Sun ), the trajectory of a moving object is a conic section , usually an ellipse or a hyperbola . This agrees with the observed orbits of planets , comets , and artificial spacecraft to

3741-464: Is the greatest parabolic height said object reaches within its trajectory In terms of angle of elevation θ {\displaystyle \theta } and initial speed v {\displaystyle v} : giving the range as This equation can be rearranged to find the angle for a required range Note that the sine function is such that there are two solutions for θ {\displaystyle \theta } for

3828-447: Is the path that an object with mass in motion follows through space as a function of time. In classical mechanics , a trajectory is defined by Hamiltonian mechanics via canonical coordinates ; hence, a complete trajectory is defined by position and momentum , simultaneously. The mass might be a projectile or a satellite . For example, it can be an orbit — the path of a planet , asteroid , or comet as it travels around

3915-403: Is then R max = v 2 / g {\displaystyle R_{\max }=v^{2}/g\,} . At this angle sin ⁡ ( π / 2 ) = 1 {\displaystyle \sin(\pi /2)=1} , so the maximum height obtained is v 2 4 g {\displaystyle {v^{2} \over 4g}} . To find

4002-400: Is zero when θ = π / 2 = 90 ∘ {\displaystyle \theta =\pi /2=90^{\circ }} . So the maximum height H m a x = v 2 2 g {\displaystyle H_{\mathrm {max} }={v^{2} \over 2g}} is obtained when the projectile is fired straight up. If instead of

4089-455: The range is 2 v h v v / g {\displaystyle 2v_{h}v_{v}/g} , and the maximum altitude is v v 2 / 2 g {\displaystyle v_{v}^{2}/2g} . The maximum range for a given initial speed v {\displaystyle v} is obtained when v h = v v {\displaystyle v_{h}=v_{v}} , i.e.

4176-567: The traditional and customary form and make . The club must be composed of a shaft and a head and it may also have material added to the shaft to enable the player to obtain a firm hold (see 3 below). All parts of the club must be fixed so that the club is one unit, and it must have no external attachments." In addition, Appendix II-4a states, regarding club heads, that "the club head must be generally plain in shape . All parts must be rigid, structural in nature and functional. The club head or its parts must not be designed to resemble any other object. It

4263-443: The "flop wedge" or FW, 64°–68°). Hybrids are a cross between a wood and an iron, giving these clubs the wood's long distance and higher launch, with the iron's familiar swing. The club head of a hybrid has a wood-inspired, slightly convex face, and is typically hollow like modern metal woods to allow for high impulse on impact and faster swing speeds. The head is usually smaller than true woods, however, not extending as far back from

4350-560: The Eye2 had an unfair advantage in imparting spin on the ball, which helps to stop the ball on the putting greens. The USGA utilized John L. Saksun , founder of Canadian golf company Accuform Golf, as a consultant to set up methods of measuring the unique grooves and determining PING's compliance with the rulings. Saksun, by proposing a cost-effective solution to help PING change the design of subsequent Eye2s, saved PING hundreds of millions. PING subsequently withdrew their US$ 100 million lawsuit against

4437-403: The USGA in sanctioned events; drivers with even larger club-head volumes are available for long-drive competitions and informal games). The shafts range from senior to extra-stiff depending upon each player's preference. Irons are clubs with a solid, all-metal head featuring a flat angled face, and a shorter shaft and more upright lie angle than a wood, for ease of access. Irons are designed for

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4524-863: The USGA. Ping’s older clubs were "grandfathered in" and allowed to remain in play as part of the settlement. However, the USGA has begun phasing in a ban on square grooves in golf. Manufacturers were required to discontinue noncompliant clubs by January 1, 2011. According to the USGA, as January 1, 2010, professional golfers on one of the top tours, or those attempting to qualify for one of the three Open Championships (since then four) will need to use new conforming wedges (those without square grooves). Moreover, those who plan to qualify for any other USGA championship (Amateur championships—under 18, Amateur, over 25, and over 50 in both sexes, and four-ball, along with international team championships), will need new conforming wedges by 2014. In addition, this regulation includes IGF and USGA-sanctioned regional amateur events as well, as

4611-418: The adhesive cures, it creates a very strong bond between grip and shaft and the grip is usually impossible to remove without cutting it off. The hosel is the portion of the club head to which the shaft attaches. Though largely ignored by players, hosel design is integral to the balance, feel and power of a club. Modern hosels are designed to place as little mass as possible over the top of the striking face of

4698-405: The analysis that follows, we derive the equation of motion of a projectile as measured from an inertial frame at rest with respect to the ground. Associated with the frame is a right-hand coordinate system with its origin at the point of launch of the projectile. The x {\displaystyle x} -axis is tangent to the ground, and the y {\displaystyle y} axis

4785-687: The angle giving the maximum height for a given speed calculate the derivative of the maximum height H = v 2 sin 2 ⁡ ( θ ) / ( 2 g ) {\displaystyle H=v^{2}\sin ^{2}(\theta )/(2g)} with respect to θ {\displaystyle \theta } , that is d H d θ = v 2 2 cos ⁡ ( θ ) sin ⁡ ( θ ) / ( 2 g ) {\displaystyle {\mathrm {d} H \over \mathrm {d} \theta }=v^{2}2\cos(\theta )\sin(\theta )/(2g)} which

4872-475: The average female player's height and swing speed. Variations on this basic set abound; several club options usually exist for almost any shot depending on the player's skill level and playing style, and the only club universally considered to be indispensable is the putter. Some consider the modern deep-faced driver to be equally irreplaceable; this is cause for some debate, as professional players including Tiger Woods have played and won tournaments without using

4959-411: The average golfer's clubhead speed. (Professionals now also use similar designs, preserving the gap in hitting distance between the amateur golfer and the pro.) As a result the loft of the pitching wedge decreased along with the numbered irons from a traditional loft of between 48–54° to between 45–50°, similar to that of an older 8-iron. Many pitching wedges have a loft close to 50°. The pitching wedge

5046-417: The bag to 9; this is a common load-out for a "Sunday bag" taken to the driving range or to an informal game. A skilled player can usually overcome the lesser selection of club lofts by reducing their swing speed on a lower-loft iron and/or placing the ball further forward in their stance to get the same carry distance and/or launch angle as the next higher loft number. Another increasingly common informal format

5133-506: The ball a great distance down the fairway towards the hole. They generally have a large head and a long shaft for maximum club speed. Historically, woods were made from persimmon wood, although some manufacturers—notably Ping —developed laminated woods. In 1979, TaylorMade Golf introduced the first wood made of steel. Even more recently, manufacturers have started using materials such as carbon fiber , titanium , or scandium . Although most "woods" in golf are constructed from various metals,

5220-443: The ball accurately on the fairway for a better shot at the green ("lay-up" shots), or hitting the ball out of hazards or rough onto the green (chipping). There are five main types of wedges, with lofts ranging from 45° to 64°: pitching wedge (PW, 48–50°), gap wedge (GW, also "approach", "attack", "utility", or "dual" wedge, typically 52–54°), sand wedge (SW, 55–56°), lob wedge (LW, 58°–60°), and ultra lob wedge (sometimes called

5307-447: The club can produce short (25–45 yd (23–41 m)) "lob" or "approach" shots. And with a "putting" motion, the club can lift the ball over rough or fringe onto the putting green from a short distance to the pin (10–25 yd (9.1–22.9 m)). This last kind of stroke is commonly called a "bump and run" and can be done with many other irons, generally with a loft equal or higher than a 7-iron. These clubs are most commonly used with

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5394-417: The club easier to hit and giving better distance than older forged "muscle-back" designs. Forged irons with less perimeter weighting are still seen, especially in sets targeting low-handicap and scratch golfers, because this less forgiving design allows a skilled golfer to intentionally hit a curved shot (a "fade" or "draw"), to follow the contour of the fairway or "bend" a shot around an obstacle. Wedges are

5481-401: The club head are usually used instead. The rules of golf limit each player to a maximum of 14 clubs in their bag. Strict rules prohibit sharing of clubs between players that each have their own set (if two players share clubs, they may not have more than 14 clubs combined), and while occasional lending of a club to a player is generally overlooked, habitual borrowing of other players' clubs or

5568-479: The club, which lowers the center of gravity of the club for better distance. Each head has one face which contacts the ball during the stroke. Putters may have two striking faces, as long as they are identical and symmetrical. Some chippers (a club similar in appearance to a double-sided putter but having a loft of 35–45 degrees) have two faces, but are not legal. Page 135 of the 2009 USGA rules of golf states: The club head must have only one striking face, except that

5655-450: The club-making process. These shafts will, within a given flex rating, address specific criteria, such as to launch the ball higher or lower or to adjust for the timing of a player's swing to load and unload the shaft at the correct moments of the swing for maximum power. Whereas in the past each club could come with only one shaft, today's club heads can be fitted with dozens of different shafts, each with slight variation in behavior, creating

5742-405: The everyday "wrap"-style grip are generally bought and installed by a clubsmith. Re-gripping used to require toxic, flammable solvents to soften and activate the adhesive, and a vise to hold the club steady while the grip was forced on. The newest replacement kits, however, use double-sided tape with a water-activated adhesive that is slippery when first activated, allowing easier installation. Once

5829-557: The face, and the lie and shaft length are similar to an iron giving similar swing mechanics. These clubs generally replace low-numbered irons in a standard set (between 2 and 5, most commonly 3–4), which are typically the hardest clubs in a player's bag to hit well. By doing so they also generally make higher-lofted woods redundant as well. However, some manufacturers produce "iron replacement" sets that use hybrid designs to replace an entire set of traditional irons, from 3 to pitching wedge. Sets designed for less muscular players commonly feature

5916-436: The flex for a stronger amateur-level player. At impact, the club head can twist as a result of torque applied to the shaft, reducing accuracy as the face of the club is not square to the player's stance. The ability of a shaft to twist along its length due to this torque is fundamentally a function of the flex of the shaft itself; a stiffer shaft will also torque less. To counter torque in more flexible shafts, club makers design

6003-584: The grip and give it its basic profile. According to the rules of golf , all club grips must have the same cross-section shape along their entire length (the diameter can vary), and with the exception of the putter, must have a circular cross-section. The putter may have any cross section that is symmetrical along the length of the grip through at least one plane; "shield" profiles with a flat top and curved underside are common. Grips may taper from thick to thin along their length (and virtually all do), but they are not allowed to have any waisting (a thinner section of

6090-613: The grip surrounded by thicker sections above and below it) or bulges (thicker sections of the grip surrounded by thinner sections). Minor variations in surface texture (such as the natural variation of a "wrap"-style grip) are not counted unless significant. Advances in materials have resulted in more durable, longer-lasting soft grips, but nevertheless grips do eventually dry out, harden, or are otherwise damaged and must be replaced. Replacement grips sold as do-it-yourself kits are generally inexpensive and of high quality, although custom grips that are larger, softer, or textured differently from

6177-417: The head not to be square at impact, resulting in lower accuracy. Most shaft makers offer a variety of flexes. The most common are: L/W (Lady/Women's), A/I (Soft Regular, Intermediate or Senior), R (Regular), S (Stiff), and X (Tour Stiff, Extra Stiff or Strong). A regular flex shaft is generally appropriate for those with an average head speed (80–94 mph (129–151 km/h)), while an A-Flex (or senior shaft)

6264-425: The inertial frame the co-ordinates of the projectile becomes y = x tan ⁡ ( θ ) − g ( x / v h ) 2 / 2 {\displaystyle y=x\tan(\theta )-g(x/v_{h})^{2}/2} That is: (where v 0 is the initial velocity, θ {\displaystyle \theta } is the angle of elevation, and g

6351-399: The initial angle is 45 ∘ {\displaystyle ^{\circ }} . This range is v 2 / g {\displaystyle v^{2}/g} , and the maximum altitude at the maximum range is v 2 / ( 4 g ) {\displaystyle v^{2}/(4g)} . Assume the motion of the projectile is being measured from

6438-507: The introduction of steel club shafts (patented in 1910), as that material was not traditional for shafts; that specific ban was rescinded in 1924 by the USGA (the R&;A would continue to ban steel shafts until 1929), and steel would become universal until the development of graphite shafts whose introduction was less controversial. The "plain in shape" rule was more recently bent to allow for non-traditional driver club head shapes, such as squares, as

6525-406: The long irons entirely in favor of the lofted woods, and replacing the mid-irons (5–7) with hybrids. The combination allows for higher launch angles on the long-distance clubs, which gives better distance with slower swing speeds. Where a club is omitted and not replaced with a club of similar function, players may add additional clubs of a different function such as additional wedges. While 14 clubs

6612-547: The material and length. Shafts are quantified in a number of different ways. The most common is the shaft flex. Simply, the shaft flex is the amount that the shaft will bend when placed under a load. A stiffer shaft will not flex as much, which requires more power to flex and "whip" through the ball properly (which results in higher club speed at impact for more distance), while a more flexible shaft will whip with less power required for better distance on slower swings, but may torque and over-flex if swung with too much power causing

6699-405: The numbered irons. Also, even though it has been named a wedge, many matched iron sets for retail sale include the pitching wedge even when not including other wedges. Finally, the loft of modern irons has been reduced compared to older designs. This is both to compensate for cavity-back iron designs that launch the ball higher for a given loft, and to increase the distance carried by each club for

6786-433: The place from which the ball appears to rise steadily helps the player to position himself correctly to make the catch. If he is too close to the batsman who has hit the ball, it will appear to rise at an accelerating rate. If he is too far from the batsman, it will appear to slow rapidly, and then to descend. Pitching wedge A pitching wedge is a wedge used to hit a shot with higher and shorter trajectory than

6873-415: The potential for a much better fit for the average golfer. The grip of the club is attached to the opposite end of the shaft from the club head, and is the part of the club the player holds on to while swinging. Originally, the grip was composed of one or more leather strips wrapped around the shaft. The leather outer wrap on a grip is still seen on some clubs, most commonly putters, but most modern grips are

6960-534: The right to define what shapes and physical characteristics of clubs are permissible in tournament play. The current rules for club design, including the results of various rulings on clubs introduced for play, are defined in Appendix II of the Rules of Golf. The overarching principle of club design used by both authorities is defined in Appendix II-1a, which states: "The club must not be substantially different from

7047-621: The same set, and these sets can have subtle differences in the loft progression and starting loft of the set, so the loft of pitching wedges can vary widely between sets. The loft of a pitching wedge generally falls between 42 and 49 degrees, but the launch angle and the average carry distance of the club between sets are typically similar. Pitching wedges can also have between zero and 10 degrees of bounce , though most pitching wedges have very low bounce (only 2 or 3 degrees) as other wedges like gap wedges or sand wedges are more traditionally suited for play out of hazards or soft lies where high bounce

7134-452: The shafts with varying degrees of torque through their length, particularly along the thinnest part of the shaft where it joins with the club head. This results in a point at which the shaft is most flexible, called the "kick point"; above that point the increasing diameter of the shaft makes it more rigid, while below that point the shaft is reinforced internally to reduce torquing of the club head. Shafts have typically been classified as having

7221-455: The sharing of a single bag of clubs slows play considerably when both players need the same club. The most common set of men's clubs is: The above set is only 12 clubs; these (or equivalent hybrid substitutes) are found in virtually every golf bag. To this, players typically add two of the following: Women's club sets are similar in overall makeup, but typically have higher lofts and shorter, more flexible shafts in retail sets to accommodate

7308-413: The strength of hickory, the long-nose club of the mid nineteenth century was still prone to breaking at the top of the back swing. The club heads were often made from woods including apple , pear , dogwood , and beech in the early times until persimmon became the main material. Golf clubs have been improved and the shafts are now made of steel, titanium, other types of metals or carbon fiber. The shaft

7395-407: The term "woods" persists to characterize their general shape and intended use on the golf course. Contemporary woods commonly feature a graphite shaft paired with a predominantly hollow head made of titanium, composite materials, or steel. This design emphasizes light weight, enabling faster club-head speeds. Woods, being the longest and most powerful clubs, typically consist of three to four options in

7482-402: The trajectory. This is the mathematical form of Newton's second law of motion : force equals mass times acceleration, for such situations. The ideal case of motion of a projectile in a uniform gravitational field in the absence of other forces (such as air drag) was first investigated by Galileo Galilei . To neglect the action of the atmosphere in shaping a trajectory would have been considered

7569-401: Was also initiated by Newton in his youth). Over the centuries, countless scientists have contributed to the development of these two disciplines. Classical mechanics became a most prominent demonstration of the power of rational thought, i.e. reason , in science as well as technology. It helps to understand and predict an enormous range of phenomena ; trajectories are but one example. Consider

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