Aerodynamics in Sports

Introduction
Sports one of the most visible applications of the principles of physics but sadly it is rarely ever associated with the latter. A time when computers decide which team based on previous statistics taking into account physics too might lead to a better understanding of the game and a better process to develop your game.

    Aerodynamic principles affect the flight of a sports ball as it travels through the air. From the design of dimples on a golf ball or the curved flight path of a tennis, cricket or baseball,

aerodynamics affects speed, motion (position and placement) and ultimately athletic

performance.

The aerodynamics of several different sports balls, including baseballs, golf balls, tennis balls,

cricket balls, volleyballs and soccer balls are discussed with the help of recent wind tunnel

measurements and theoretical analyses. An overview of basic sports ball aerodynamics as well as

some new flow visualization data and aerodynamic force measurements are presented and

discussed. The materials include explanations of basic fluid dynamics principles, such as

Bernoulli's theorem, circulation, the four flow regimes a sphere or a sports ball encounters, and

laminar and turbulent boundary layers. The effects of these specific mechanisms on the behavior

and performance of sports balls are demonstrated. The specific aerodynamics of the strategic

pitches, serves, kicks and strokes used in each sport are described. In particular, the effects of

surface roughness and spin on the behavior of the boundary layers and the critical Reynolds

number are discussed here.

For spinning balls, the Magnus effect, which is responsible for producing the side or lift force, is

discussed in detail, as well as the conditions under which a negative or reverse Magnus effect can

be created. It is interesting to note that except for golf and cricket, the ball in all the other games

included in the present discussion undergoes a flight regime when the ball is not spinning. The

role of the surface roughness, especially if it can be used to generate an asymmetric flow,

becomes even more critical for these cases. This assignment compares and contrasts the unique

aerodynamic characteristics of a variety of sports balls.

Aerodynamics plays a prominent role in defining the flight of a ball that is struck or thrown

through the air in almost all ball sports. The main interest is in the fact that the ball can be made

to deviate from its initial straight path, resulting in a curved, or sometimes an unpredictable,

flight path. Lateral deflection in flight, commonly known as swing, swerve or curve, is well

recognized in baseball, cricket, golf, tennis, volleyball and soccer. In most of these sports, the

lateral deflection is produced by spinning the ball about an axis perpendicular to the line of

flight. In the late 19th century, Lord Rayleigh credited the German scientist, Gustav Magnus, with

the first true explanation of this effect and it has since been universally known as the Magnus

effect. This was all before the introduction of the boundary layer concept by Ludwig Prandtl . It was soon recognized that the aerodynamics of sports balls was strongly dependent on the detailed development and behavior of the boundary layer on the ball's surface.

A side force, which makes a ball swing through the air, can also be generated in the absence of

the Magnus effect. In one of the cricket deliveries, the ball is released with the seam angled,

which creates the boundary layer asymmetry necessary to produce swing. In baseball, volleyball

and soccer there is an interesting variation whereby the ball is released without any spin imparted

to it. In this case, depending on the seam or stitch orientation, an asymmetric, and sometimes

time-varying, flow field can be generated, thus resulting in an unpredictable flight path. Almost

all ball games are played in the Reynolds Number range of between about 40,000 to 400,000.

The Reynolds number is defined as, Re = Ud/v, where U is the ball velocity, d is the ball

diameter and v is the air kinematic viscosity. It is particularly fascinating that, purely through

historical accidents, small disturbances on the ball surface, such as the stitching on baseballs and

cricket balls, the felt cover on tennis balls and patch-seams on volleyballs and soccer balls, are

about the right size to affect boundary layer transition and development in this Re range.

Basic Aerodynamic Principles

       Let us first consider the flight of a smooth sphere through an ideal or inviscid fluid. As the flow

accelerates around the front of the sphere, the surface pressure decreases (Bernoulli equation)

until a maximum velocity and minimum pressure are achieved half way around the sphere. The

reverse occurs over the back part of the sphere so that the velocity decreases and the pressure

increases (adverse pressure gradient). In a real viscous fluid such as air, a boundary layer, defined

as a thin region of air near the surface, which the sphere carries with it is formed around the

sphere. The boundary layer cannot typically negotiate the adverse pressure gradient over the back

part of the sphere and it will tend to peel away or "separate" from the surface. The pressure

becomes constant once the boundary layer has separated and the pressure difference between the

front and back of the sphere results in a drag force that slows down the sphere. The boundary

layer can have two distinct states: "laminar", with smooth tiers of air passing one on top of the

other, or "turbulent", with the air moving chaotically throughout the layer. The turbulent

boundary layer has higher momentum near the wall, compared to the laminar layer, and it is

continually replenished by turbulent mixing and transport. It is therefore better able to withstand

the adverse pressure gradient over the back part of the sphere and, as a result, separates relatively

late compared to a laminar boundary layer. This results in a smaller separated region or "wake"

behind the ball and thus less drag. The "transition" from a laminar to a turbulent boundary layer

occurs when a critical sphere Reynolds number is achieved.

   The flow over a sphere can be divided into four distinct regimes (2). These regimes are

illustrated in Fig. 1, in which the drag coefficient (CD) is plotted against the Reynolds number

(Re). The drag coefficient is defined as, CD = D/(0.5pU2A), where D is the drag force, p is the air

density and A is the cross-sectional area of the sphere. In the subcritical regime, laminar

boundary layer separation occurs at an angle from the front stagnation point (6S) of about 80° and

the CD is nearly independent of Re. In the critical regime, the CD drops rapidly and reaches a

minimum at the critical Re. The initial drop in CD is due to the laminar boundary layer separation

location moving downstream (0S = 95°). At the critical Re, a separation bubble is established at

this location whereby the laminar boundary layer separates, transition occurs in the free-shear

layer and the layer reattaches to the sphere surface in a turbulent state. The turbulent boundary

layer is better able to withstand the adverse pressure gradient over the back part of the ball and

separation is delayed to 0S = 120°. In the supercritical regime, transition occurs in the attached

boundary layer and the CD increases gradually as the transition and the separation locations creep

upstream with increasing Re. A limit is reached in the transcritical regime when the transition

location moves all the way upstream, very close to the front stagnation point. The turbulent

boundary layer development and separation is then determined solely by the sphere surface

roughness, and the CD becomes independent of Re since the transition location cannot be further

affected by increasing Re.

    Earlier transition of the boundary layer can be induced by "tripping" the laminar boundary layer

using a protuberance (e.g. seam on a baseball or cricket ball) or surface roughness (e.g. dimples

on a golf ball or fabric cover on a tennis ball). The CD versus Re plot shown in Fig. 2 contains

data for a variety of sports balls together with Achenbach's  curve for a smooth sphere. All

these data are for non-spinning test articles, and all except the cricket ball, were held stationary in

wind tunnels for the drag measurements. The cricket ball was projected through a wind tunnel

test section and the drag determined from the measured deflection. For the smooth sphere, the CD

in the subcritical regime is about 0.5 and at the critical Re of about 400,000 the CD drops to a

minimum of about 0.07, before increasing again in the supercritical regime. The critical Re, and

amount by which the CD drops, both decrease as the surface roughness increases on the sports

balls. The specific trends for each of the sports balls are discussed below in the individual ball 

sections.

In a viscous flow such as air, a sphere that is spinning at a relatively high rate can generate a flow

field that is very similar to that of a sphere in an inviscid flow with added circulation. That is

because the boundary layer is forced to spin with the ball due to viscous friction, which produces

a circulation around the ball, and hence a side force. At more nominal spin rates, such as those

encountered on sports balls, the boundary layers cannot negotiate the adverse pressure gradient

on the back part of the ball and they tend to separate, somewhere in the vicinity of the sphere

apex. The extra momentum applied to the boundary layer on the retreating side of the ball allows

it to negotiate a higher pressure rise before separating and so the separation point moves

downstream. The reverse occurs on the advancing side and so the separation point moves

upstream, thus generating an asymmetric separation and an upward deflected wake, as shown in

Following Newton's 3 Law of Motion, the upward deflected wake implies a downward

(Magnus) force acting on the ball. Now the dependence of the boundary layer transition and

separation locations on Re can either enhance or oppose (even overwhelm) this effect. Since the

effective Re on the advancing side of the ball is higher than that on the retreating side, in the

subcritical or (especially) supercritical regimes, the separation location on the advancing side

will tend to be more upstream compared to that on the retreating side. This is because the CD

increases with Re in these regions, thus indicating an upstream moving separation location.

However, in the region of the critical Re, a situation can develop whereby the advancing side

winds up in the supercritical regime with turbulent boundary layer separation, whereas the

retreating side is still in the subcritical regime with laminar separation. This would result in a

negative Magnus force, since the turbulent boundary layer on the advancing side will now

separate later compared to the laminar layer on the retreating side. Therefore, a sphere with

topspin for example, would experience an upward aerodynamic force. So in order to maximize

the amount of (positive) Magnus force, it helps to be in the supercritical regime and this can be

ensured by lowering the critical Re by adding surface roughness (e.g. dimples on a golf ball).

Tennis Ball Aerodynamics

              Most of the recent research work on tennis ball aerodynamics was inspired by the introduction of a slightly larger "oversized" tennis ball (roughly 6.5% larger diameter). This decision was instigated by a concern that the serving speed in (men's) tennis had increased to the point where the serve dominates the game. The main evidence for the domination of the serve in men's tennis has been the increase in the number of sets decided by tie breaks at the major tournaments

Some recent experimental studies of tennis ball aerodynamics have revealed the very important

role that the felt cover plays. Fig. 6 shows a photograph of the smoke flow visualization

over a 28-cm diameter tennis ball model that is held stationary (not spinning) in a wind tunnel.

The first observation is that the boundary layer over the top and bottom of the ball separates

relatively early, at 0S ~ 80° to 90°, thus suggesting a laminar boundary layer separation. However,

since the flow field did not change with Re (up to Re = 284,000), it was presumed that transition

had already occurred and that a (fixed) turbulent boundary layer separation was obtained over the

whole Re range tested, thus putting the ball in the transcritical flow regime. Although the felt

cover was expected to affect the critical Re at which transition occurs, it seemed as though the

felt was a more effective boundary layer trip than had been anticipated. The fact that the

boundary layer separation over the top and bottom of the non-spinning ball was symmetric

leading to a horizontal wake was, of course, anticipated since a side force (upward or downward)

is not expected in this case.

In the second round of testing, spin was imparted to the ball by rotating the support rod. In Fig. 3,

the ball is spun in a counter-clockwise direction to simulate a ball with topspin. The wind tunnel

conditions corresponded to a standard tennis ball velocity of 39 m/s (87 mph) and spin rate of 72

revs/sec (4320 rpm); this would represent a typical second serve in men's professional tennis. In

Fig. 3, the boundary layer separates earlier over the top of the ball compared to the bottom. As

193discussed above, this results in an upward deflection of the wake behind the ball and a downward (Magnus) force acting on it which would make it drop faster than a non-spinning ball. By

imparting spin to the ball, tennis players use this effect to make the ball curve; the direction and

amount of movement is determined by the spin axis and the spin parameter (S). Spin about a

near-vertical axis is imparted to gain sideways movement whereas topspin and underspin (or

backspin) are used to control the trajectory length (shorter for topspin, longer for underspin).

Drag measurements on non-spinning tennis balls (simulating a perfectly flat serve) revealed that,

for the most part, the flow over new tennis balls was indeed transcritical, with a relatively high

value for the drag coefficient (CD = 0.6), higher than any other sports ball data shown in Fig. 2.

In the transcritical regime, the turbulent boundary layer separation location has moved all the

way up to the region of the ball apex, as shown in Fig. 6. Since almost all of the total drag on a

bluff body, such as a round ball, is accounted for by pressure drag, it was proposed that the

maximum CD on a very rough sphere should not exceed 0.5 . However, on a tennis ball, apart

from providing a rough surface, the felt cover is also a porous (drag-bearing) coating since the

"fuzz" elements themselves experience pressure drag. This additional contribution was thus

termed: "fuzz drag." Since the fuzz elements come off as the ball surface becomes worn, the ball

CD should also decrease, and that is precisely what was observed in the data for the used ball

(Fig. 2). The used ball appears to be in the supercritical regime with a critical Re ~ 100,000.

One of the more intriguing trends in the (new) tennis ball drag measurements was the increase in

CD with decreasing Re. The higher levels of CD at the lower Re (80,000 < Re < 150,000) were

attributed to the dependence of fuzz element orientation on flow (or ball) velocity and the

stronger dependence of CD on Re at the very low fuzz element Re. The recently approved

oversized tennis ball CD was found to be comparable to that for the standard-sized balls.

However, the drag on the oversized balls is higher by virtue of the larger cross-sectional area and

so the desired effect of "slowing down the game" (increased ball flight time) will be achieved.

Cricket Ball Aerodynamics

       In India cricket has been a religion which has been extensively studied. On each delivery, the ball can have a different trajectory, varied by changing the pace (speed), length, line or, most subtly of all, by moving or "swinging" the ball through the air so that it drifts sideways. The actual construction of a cricket ball and the principle by which the faster bowlers swing the ball is unique to cricket. A cricket ball has six rows of prominent stitching along its equator, which makes up the "primary" seam. Each hemisphere also has a line of internal stitching forming the "quarter" or "secondary" seam. These primary and quarter seams play a critical role in the aerodynamics of a swinging cricket ball .Fast bowlers in cricket make the ball swing by a judicious use of the primary seam. The ball is released with the seam at an angle to the initial line of flight. Over a certain Reynolds number range, the seam trips the laminar boundary layer into turbulence on one side of the ball whereasthat on the other (nonseam) side remains laminar. As discussed above, by virtue of its increased energy, the turbulent boundary layer, separates later compared to the laminar layer and so a pressure differential, which results in a side force, is generated on the ball. In Fig. 7, the seam has tripped the boundary layer on the lower surface into turbulence, evidenced by the chaotic nature of the smoke edge just downstream of the separation point. On the upper surface, a smooth, clean edge confirms that the separating boundary layer is in a laminar state. Note how the laminar

boundary layer on the upper surface has separated relatively early compared to the turbulent layer

on the lower surface. The asymmetric separation of the boundary layers is further confirmed by

the upward deflected wake, which implies that a downward force is acting on the ball.

When a cricket ball is bowled, with a round arm action as the laws insist, there will always be

some backspin imparted to it as the ball rolls-off the fingers as it is released. In order to measure

the forces on spinning cricket balls, cricket balls were rolled along their seam down a ramp and

projected into a wind tunnel through a small opening in the ceiling. The aerodynamic forces

were evaluated from the measured deflections. At nominally zero seam angle there was no

significant side force, except at high velocities when local roughness, such as an embossment

mark, starts to have an effect by inducing transition on one side of the ball. However, when the

seam was set at an incidence to the oncoming flow, the side force started to increase at about U =

15 m/s (34 mph). The side force increased with ball velocity, reaching a maximum of about 30%

of the ball's weight before falling-off rapidly. The critical velocity at which the side force started

to decrease was about 30 m/s (Re = 140,000). This is the velocity at which the laminar boundary

layer on the nonseam side undergoes transition and becomes turbulent. As a result, the

asymmetry between the boundary layer separation locations is reduced and the side force starts to

decrease. The CD curve for the cricket ball in Fig. 2 seems to indicate that transition has started

to occur at Re < 140,000. For those tests, the (non-spinning) ball was released with the seam

angled at 20° and it was found that the ball rotated due to the aerodynamic moment about the

vertical axis and thus the seam caused relatively early transition on both sides of the ball. Also,

these data suggest that as the critical Re is approached, the CD for spinning balls will not fall-off

as abruptly as that for non-spinning balls. On spinning balls, the transition occurs in stages led by

the advancing side where the effective Re is higher. Also, note that for balls with discrete

roughness (seam on cricket ball and baseball), the spin axis and rotation rate also play an

important role in determining the ball aerodynamics.

The maximum side force was obtained at a bowling speed of about 30 m/s (67 mph) with the

seam angled at 20° and the ball spinning backwards at a rate of 11.4 revs/s. Trajectories of a

cricket ball, computed using the measured forces, resulted in a parabolic flight path with a

maximum deflection of 0.8 m; this compared extremely well with field measurements. The

computed data also helped to explain the phenomenon of "late" swing. Since the flight paths are

parabolic, late swing is in fact "built-in" whereby 75% of the lateral deflection occurs over the

second half of the flight from the bowler to the batsman. A used ball with a rough surface can be

made to "reverse swing" at relatively high bowling speeds. Due to the rough surface, transition

occurs relatively early (before the seam location) and symmetrically. The seam acts as a fence,

thickening and weakening the turbulent boundary layer on that (seam) side which separates early

compared to the turbulent boundary layer on the nonseam side. Therefore, the whole asymmetry

is reversed and the ball swings towards the nonseam side.

Volleyball and Soccer Ball Aerodynamics

         In recent years, there has been an increased interest in the aerodynamics of volleyballs and soccer balls. In volleyball, two main types of serves are employed: a relatively fast spinning serve

(generally with topspin), which results in a downward Magnus force adding to the gravitational

force or the so-called "floater" which is served at a slower pace, but with the palm of the hand so

that no spin is imparted to it. An example of a serve with topspin is shown in Fig. 8. The

measured flight path implies that the downward force (gravity plus Magnus) probably does not

change significantly, thus resulting in a near-parabolic flight path. The floater has an

unpredictable flight path, which makes it harder for the returning team to set up effectively.

In soccer, the ball is almost always kicked with spin imparted to it, generally backspin or spin

about a near-vertical axis, which makes the ball curve sideways. The latter effect is often

employed during free kicks from around the penalty box. The defending team puts up a "human

wall" to try and protect a part of the goal, the rest being covered by the goalkeeper. However, the

goalkeeper is often left helpless if the ball can be curved around the wall. A recent spectacular

example of this type of kick was in a game between Brazil and France in 1997 . The ball

initially appeared to be heading far right of the goal, but soon started to curve due to the Magnus

effect and wound up "in the back of the net." A "toe-kick" is also sometimes used in the free

kick situations to try and get the "knuckling" effect.

For both these balls, the surface is relatively smooth with small indentations where the "patches"

come together, so the critical Re would be expected to be less than that for a smooth sphere, but

higher than that for a golf ball. As seen in Fig. 2, that is indeed the case for a non-spinning

volleyball with a critical Re of about 200,000. The typical serving speeds in volleyball range

from about 10 m/s to 30 m/s and at Re = 200,000, U = 14.5 m/s. So it is quite possible to serve at

196a speed just above the critical (with turbulent boundary layer separation) and as the ball slows

through the critical range, get side forces generated as non-uniform transition starts to occur

depending on the locations of the patch-seams. Thus, a serve that starts off on a straight flight

path (in the vertical plane), may suddenly develop a sideways motion towards the end of the

flight. Even in the supercritical regime, wind tunnel measurements have shown that side force

fluctuations of the same order of magnitude as the mean drag can be developed on non-spinning

volleyballs, which can cause the "knuckling" effect .

CONCLUSION :

 Though I have discussed the applications of aerodynamics in only a few of the more popular sports, every sport makes use of the principles of aerodynamics. Aerodynamics is not only seen in sports but in every aspect of life. From the way we walk to the way we have evolved aerodynamics has played an unimaginable role.

References :

·         http://www.aviation-for-kids.com/the-baseball-flight.html

·         http://www.seas.upenn.edu/~meam211/slides/aero.pdf

·         http://iweb.tms.org/ED/01-5085-185.pdf

·         http://www.topendsports.com/biomechanics/areodynamics.htm