Frames for tennis rackets

14.3.1 Frames for tennis rackets

Rackets utilizing the latest engineering materials have increased the capacity of the professional player to make strokes over a remarkable range of pace and spin. At an amateur level, their introduction has made the sport more accessible by providing a greater tol- erance for error and by easing beginners’ problems. For many years, hardwoods, such as ash, maple and okume, were used in the laminated construction of

racket frames. The standard area was 70 in 2 . Although damping capacity was excellent, their temperature- and humidity-dependent behaviour could be awkward: wear and warping problems were commonly accepted. The introduction of tubular-section aluminium alloy and steel frames in the 1960s enabled designers to

Figure 14.1 Schematic representation of cell wall structure in wood, showing various layers and their differing

break through the barriers imposed by the use of wood, orientations of cellulose microfibrils. M.L. D middle layer,

and tennis boomed. In the 1970s, ‘large-head’ rack-

P D primary wall, S1 D outer layer of secondary wall, ets of different shape with a larger area of 105 in S2 D middle layer of secondary wall, S3 D innermost layer

came into vogue. The greater stiffness and strength of secondary wall, HT D helical thickening, W D warty

enabled string tensions to be raised and the effective layer (from Butterfield and Meylan, 1980: by permission of

playing area, the so-called ‘sweet spot’, was consider- Kluwer Academic Publishers, Norwell, MA, USA) .

ably increased. The ‘sweet spot’ is the central portion

408 Modern Physical Metallurgy and Materials Engineering of the stringed area where the vibrational nodes are

is not greatly different from that of thermoplastic minimal, or zero, when the ball is struck. A mishit of

alone.) The fusible core was made of Bi –Sn alloy, the ball outside this area generates undesirable vibra-

C lower than the melting tions and, quite apart from spoiling the accuracy and

m.p. 138.5 °

C, some 130 °

point of the polymeric matrix phase. (Being thermally power of the subsequent shot, can cause the player to

conductive, the core acted as a heatsink and remained develop the painful and debilitating muscular condition

intact.) The core was slowly melted out in an oil bath known as ‘tennis elbow’. Despite their merits, alloy

⊲ 150 ° C⊳ and later reused, leaving a central cavity in the frames had insufficient damping capacity and failed to

frame which could be filled with vibration-damping, displace wooden frames.

low-density polyurethane foam. (The melt-out process In the next stage of evolution, during the 1970s,

also had the beneficial effect of relieving stresses in composite frames were developed which used

the frame.) The mould/core design allowed the flowing polyester, epoxy or phenolic resin matrices in a

composite to form strong tubular pillars in the frame variety of combinations with continuous fibres of E-

through which the strings could be threaded. The wall glass, carbon and aramid (Kevlar); although more

thickness of the frame was 2.5 mm. The cycle time for costly than alloy frames, they had better damping

core preparation, injection moulding and core melt-out capacity. ‘Mid-size’ composite rackets with a strung

2 area of 80–100 in was only 3 minutes per frame. The balanced handle came into favour. The generally was given a leather grip and filled with medium- accepted manufacturing method was to lay-up the

density polyurethane foam. Injection-moulded frames continuous fibres in a frame mould, surround them

of this type, using a short-fibre composite, were much with thermosetting resin, compression mould, cure,

stronger than laminated wood frames and as strong surface finish and drill string holes.

as, often stronger than, ‘conventional’ continuous-fibre These ‘conventional’ composite frames were costly

composite frames. 1

to produce and used material that was twice as dense as a laminated wood frame. In 1980, the world market

14.3.2 Strings for tennis rackets

in tennis rackets was 55% wood, 30% composite and 15% metal. In the same year, injection moulding of

Significant string properties include retention of elas- hollow ‘mid-size’ frames (Figure 14.2) was pioneered

ticity and tension, impact efficiency, directional control (Haines et al., 1983). This method directly challenged

of the ball, resistance to ultraviolet radiation, gamma the ‘conventional’ manufacturing route for composites.

radiation, abrasion, moisture, creep, chemical agents, In the original patented process, a composite mix of

etc. String tension is a subject of prime importance to 30% v/v short carbon fibres (PAN) and polyamide

thermoplastic (nylon 66) was injected into a complex 1 For the racket and manufacturing process, Dunlop Sports frame mould carrying an accurately located central

Co. Ltd, UK, won the 1981 Design Council Award. This core. (Rheological studies have shown that, at high

racket type was used by champions Steffi Graf and John shear rates, the viscosity of the fibre-laden mixture

McEnroe.

Frame section based on hollow rectangle for optimum utilization of material properties to

Holes in frame allow Moulded plastic grip ferrule achieve desired strength

Hard-wearing epoxy paint,

silk screen printed

foam to pass through

and stiffness

cosmetics, and acid

and form handle

catalyzed lacquer finish

Individual pillars

High-quality

moulded around

leather grip

each string hole to

End cap

give added strength and ease of stringing

Low-density PU foam in head shafts

Medium-density PU foam in

Groove round head for string protection

and also under grip Low-density PU foam

Handle available in

handle end of frame

various sizes

helps dampen vibration All sharp edges and imparts balance

removed

Figure 14.2 Injection-moulded frame and handle of tennis racket (from Haines et al., 1983: by permission of the Council of the Institution of Mechanical Engineers) .

Materials for sports 409 tennis players and, because of its intrinsic time depen-

capable of travelling a distance of some 220–240 m. dence, much study and debate. It is contended that

The shaft of a club bends and twists elastically during some ready-strung rackets, as purchased, are already

the complete swing and, after impact, vibrations travel slack.

at the speed of sound along the shaft toward the Ox-gut, the traditional string material, is very effec-

grip. The much-quoted ‘feel’ of a club tends to be a tive. However, a greater rebound velocity can be

highly subjective judgement; for instance, in addition imparted to the ball by using synthetic materials of

to transmitted vibrations, it usually takes into especial higher elastic modulus, such as nylon. Each nylon

account the sound heard after the instant of impact. string, typically 1.3 mm diameter, is a braid composed

A mishit occurs if the striking face of the head is of plaited and intertwined bundles of strong fibres.

imperfectly aligned, horizontally and vertically, with After immersion in an elastomeric solution, the string

the ball; a fair proportion of drives fall into this is given a polymeric coating to protect it from moisture

category. The desired ‘sweet spot’ of impact lies at the and wear. Rebound velocity is, of course, also directly

point where a line projected from the centre of gravity influenced by string tension, which, depending upon

of the head meets the striking face perpendicularly. racket type and personal preference, can range from a

Off-centre impact (outside the ‘sweet spot’) rotates the force of 200 N to more than 300 N. Another promis-

large head of a ‘wood’ about its centre of gravity, ing material for strings, initially supplied in the form of

causing the ball to either hook sidespin (toed shot) yarn (Zyex, Victrex), is polyether-etherketone (PEEK).

or slice sidespin (heeled shot) in accordance with the well-known ‘gear effect’.

The intrinsic difficulties of achieving distance, accu-

14.4 Golf clubs

racy and consistency have challenged golf players for

14.4.1 Kinetic aspects of a golf stroke

centuries and continue to do so. One beneficial effect of the new materials recently adopted for club heads

Consider the violent but eventful history of an effective and shafts has been to make this demanding sport drive with a golf club (Horwood, 1994). Figure 14.3

accessible to a wider range of player ability e.g. senior shows how the bending moment of the shaft varies

citizens. Despite golf being frequently described as a with time during the 2 second period of the stroke. (A

triumph of art over science, concerted efforts are being bending moment of 1 N m is equivalent to a deflection

made to explain and rationalize its unique physical of about 13 mm at the end of the shaft.) In this

aspects in engineering and scientific terms (Cochran, particular test, toward the end of its downward swing

1994). Such research activities, which are commer- and prior to impact, the shaft deflected backwards and

cially stimulated, have led to the realization that many then forwards, the club head reaching a swing speed

phenomena attending the impact of club upon ball are

still imperfectly understood. One consequence is that, of contact between head and ball was approximately

at impact of 42.5 m s 1 (95 miles h 1 ). The period

at a practical level, equipment makers apply a variety

0.5 ms. After a well-executed stroke, the driven golf of testing methods that are often unco-ordinated and ball, aided aerodynamically by its surface dimples, is

potentially confusing: there appears to be a need for

16 Impact with ball

Shaft bent forwards

4 of down swing

− 2 Planar bending moment N

Shaft bent backwards

− 8 Oscillations due to back swing

Time in seconds

Figure 14.3 Shaft bending in typical swing of golf club (after Horwood, 1994) .

410 Modern Physical Metallurgy and Materials Engineering standard testing procedures for shafts, club heads, etc.

device seeks to retain the desired damping capacity of to be established internationally.

CFRP while giving an overall balance similar to that of a steel shaft.

14.4.2 Golf club shafts

The main categories of golf club are (i) wood- type clubs (‘woods’), comprising wooden ‘woods’

The principal design parameters for a shaft are weight, and metal ‘woods’, (ii) iron-type clubs (‘irons’) and bending stiffness, bend point and torsional stiffness.

(iii) putters. Materials used for club heads range For a given head weight, lightening the shaft reputedly

from hardwoods to alloys (stainless steel, titanium makes the swing faster and hence gives some increase

alloy, aluminium alloy, copper alloy) and composites in ball speed and distance. Figure 14.3 has already

(CFRP). There has been a tendency for club heads to indicated the violent forward and backward bending

get larger and for shafts to get longer. that occurs in the plane of swing during a drive.

Professional golfers and players with a rapid, compact swing favour very stiff shafts. The bend point (also

14.4.3 Wood-type club heads

called the flex point or kick point) of a shaft is ‘Woods’ have the bulkiest shape and the largest front generally taken as the region where the minimum

to back dimension. The traditional wooden ‘wood’ radius of curvature occurs during bending. A butt-

club heads, which are still highly regarded, are made flexible shaft has a high bend point (near the grip) and

from either persimmon (date-plum tree) or maple (lam- suits long hitters. Conversely, a tip-flexible shaft has a

inated). These two hardwoods have similar cell struc- low bend point (near the head) and suits weaker hitters.

ture, density and hardness. Their capacity for damping

A low bend point also increases the dynamic loft of vibrations is excellent. Manufacture involves 120–200 the struck ball. During a drive shot, the shaft tends

manual operations and is skill demanding. In a prelimi- to twist a few degrees (as well as bend) because the

nary curing process, the wood structure is impregnated centre of gravity of the club head and the long axis of

with linseed oil in order to make it waterproof and the shaft are offset. Torsional stiffness (wrongly called

hard. A striking face and a sole plate, both metal- ‘torque’) helps the striking face to remain ‘square’

lic, are inserted and a central cavity filled with cork. during impact. Long hitters tend to favour torsionally

The head is protectively coated with polyurethane and stiff (‘low torque’) shafts.

finally weighs about 200 g. As with all club heads,

A typical driver, total weight 350 g, comprises the principal design variables are size, shape, loca-

a grip (50 g), steel shaft (100 g) and head (200 g). tion of the centre of gravity and mass distribution. For

A variety of materials, including alloy steel, alu- instance, the cork insert helps to displace mass to the minium alloy (7075), Ti–6Al –4V alloy and com-

outside of the head to give some degree of ‘peripheral posites, have been used for the hollow shafts. Car-

weighting’, a feature which reduces the twisting action bon, Kevlar, glass, boron and silicon carbide fibres

of off-centre shots i.e. outside the ‘sweet spot’. have been used as ‘reinforcement’ in shaft compos-

In the 1970s, metallic ‘woods’ made from alloys ites. Both epoxy and alloy matrices have been used

became available as drivers. Materials ranged from

e.g. 7075 aluminium alloy C 17%v/v short SiC fibres. stainless steel to the light alloys of aluminium and The main advantages of hollow CFRP shafts, loosely

titanium. Nowadays 17Cr–4Ni stainless steel is a pop- termed ‘graphite’ shafts, is their relative lightness

ular choice. Compared to traditional wooden ‘woods’, (about 60 g) and high damping capacity. They are

alloy heads are easier to make and repeatable quality made by (i) wrapping prepreg sheets of carbon fibre

is more easily achieved, largely because of the intro- around tapered mandrels, (ii) filament winding around

duction of investment casting. In this modern version

a mandrel or (iii) resin transfer moulding (RTM) in of the ancient ‘lost wax’ process, which is eminently which resin is forced around a carbon fibre sleeve.

suitable for high m.p. alloys that cannot be diecast, a Reproducing exactly the same bending characteristics

thin refractory shell is formed around a wax pattern. from shaft to shaft is a difficult, labour-intensive task

The wax is melted to leave a cavity which serves as and demands considerable care and skill. Quality was

a detailed mould for molten steel. The precision cast- not always assured with the early CFRP shafts. With

ings are welded to form a thin-walled, hollow shell. CFRP, torsional stiffness and the location of the bend

The central cavity is usually filled with low-density point can be manipulated by varying the textural form

foam. Compared with wooden ‘woods’, the moment and lay-up of the graphite filaments. In this respect,

of inertia is greater and the centre of gravity is located steel shafts, which represent the principal competition

closer to the striking face. The shell construction gives to the more recently introduced CFRP shafts, are more

peripheral weight distribution away from the centre restricted. However, they can match CFRP for specific

of gravity of the head. In a recent design the cen- stiffness and strength. Paradoxically, irons with ‘heavy

tre of gravity has been lowered by locating dense graphite’ shafts are now available: addition of expen-

Cu/W inserts in the sole, e.g. Trimetal clubs. Over- sive boron fibres to the CFRP near the shaft tip allows

all, such innovative features confer a greater tolerance

a lighter club head to be used. The net effect is to allow for mishits. For instance, a greater moment of inertia the balance point of the club to be shifted 40 –50 mm

reduces twisting of the head when impact is off-centre higher up the shaft and away from the club head. This

and also reduces spin.

Materials for sports 411 Composite ‘woods’ have been made from CFRP.

to draw a heavy longbow. 3 The mystique of the long- These heads, which emphasize lightness and strength,

bow and its near-optimum design have intrigued engi- are similar in shape and style to classic wooden heads

neers and scientists; their studies have greatly helped and have a similar placing of the centre of gravity. Typ-

in providing a theoretical basis for modern designs of ically, they have wear-resistant alloy sole plates and a

bows and arrows (Blyth & Pratt, 1976). foam-filled core. Compression moulding or injection moulding are used in their manufacture.

14.5.2 Bow design

A bow and its arrows should be matched to the strength and length of the archer’s arm. A well-designed bow

acts as a powerful spring and transfers stored strain The relatively narrow heads for ‘irons’ are usually

14.4.4 Iron-type club heads

energy smoothly and efficiently to the arrow. As the made from steels and copper alloys which are shaped

archer applies force and draws the bowstring from by either hot forging or investment casting. Stainless

the braced condition (which already stores energy) materials include 17Cr–4Ni and AISI Types 431 and

through a draw distance of about 35 cm, additional 304. As an alternative to the traditional blade-type

energy is stored in the two limbs (arms) of the bow. In head, ‘cavity-back irons’ provide peripheral weighting.

general, increasing the length of the bow reduces stress In a recent innovation, a non-crystalline zirconium-

and increases the potential for energy storage. Upon based alloy 2 containing Cu, Ti, Ni and Be has been

release of the bowstring, stored energy accelerates the used for the heads of irons (and putters). This alloy

arrow as well as the string and the two limbs of the has high specific strength and good damping capacity

of loose may be taken simply as the kinetic energy and can be successfully vacuum cast in a glassy state

of the arrow divided by work expended in drawing without the need for ultra-fast freezing rates.

the bow. Alternatively, allowance can be made for the energy-absorbing movement of the two limbs, as in the Klopsteg formula: