Swimsuit Technology

In a professional swimming competition, the difference between first and second place can come down to thousandths of a second. Swimmers try to gain any advantage they can, and in 2007 Speedo developed a new suit to help. This suit claimed to eliminate 5% of the drag (resistance of the water on the body) when compared to other suits. The Speedo suit broke countless world records between 2007 and 2009, including 43 at the 2009 World Championships in Rome, Italy. In 2009 the swimming governing body banned the suits, to even the playing field.

Read the basics of swimsuit technology.

Skiing: It’s All About Friction

glide2It’s all about friction. Really. Friction from the snow, friction from the air, friction from the surface of the ski or the clothing you wear.  The physics of skiing is all about how to overcome drag and resistance and allow a skier to slice his/her way down the mountain.  And if Newton’s laws have anything to do with it, a skier who controls friction best has the best chance of winning.

Find out the basics of friction and skiing.

Articles by Marcia Howell

Aerodynamics and Cycling

Cycling has undergone immense changes since its early days.  As science has opened our understanding of aerodynamics, it has driven changes in bicycle composition and design, the clothing worn by the cyclist, and even the positioning of the rider on the bicycle.

These three factors directly correlate to the amount of drag experienced by the cyclist.  In fact, researcher L. Brownlie reported that some styles of baggy clothes cost cyclists 1.17% of their finishing time in a 100-meter race.  Serious cyclists utilize this knowledge by dressing in sleek, close-fitting clothing to optimize their aerodynamics.

How much of a role do aerodynamics play? Learn the basics or read the more technical explanation.

Articles by Cristian Clavijo

Skiing: It’s All About Friction (Basic)

glide3aWhen Bioengineer, Parker Tyler, goes skiing, she probably isn’t thinking about the biology or the physics behind the activity.  Rather, he is enjoying the crisp, cool, mountain air, the clear view of the slope, and the anticipated exhilaration he will feel as she maneuvers to the bottom. She likely doesn’t consider earth’s gravitational force (9.81 m/s), or potential energy, or kinetic energy, or her own mass, or any of those other factors that will contribute to his acceleration.  However, scientists do think about these things and their thinking has affected many facets of the industry from clothing to equipment to style.

It’s all about friction. Really. Friction from the snow, friction from the air, friction from the surface of the ski or the clothing you wear.  The physics of skiing is all about how to overcome drag and resistance and allow a skier to slice his/her way down the mountain.  And if Newton’s laws have anything to do with it, a skier who controls friction best has the best chance of winning.

Back to Parker, her potential energy is greatest at the top of the hill where she perches until the start of her run.  Her body is physically fit and adrenaline is taking over, sending added energy to her muscles, vision center, quick decision making regions of the brain, and the area that controls coordination.  Once she leaves starting position, gravity pushes down, mass pushes down, but the acceleration down the slope kicks in and changes how the forces affect the ride.  Potential energy turns into kinetic energy, or energy of motion, and everything he touches tries to resist and slow the movement.

Since Parker is a wise skier, she wears a GS suit (a sleek, form fitting suit with a minimum of abrasive surface area) and aerodynamic boots, hat (or helmet), gloves, etc.  As she accelerates, she assumes a crouching position to reduce air resistance and tighten the air current close to her body.  His skis are designed specifically for the type of skiing being done, the edges are sharp, and the bottoms are carefully waxed.  The wax waterproofs the skis, prevents them from drying out, and it reduces the wet drag of a kind of “suction” type friction from the snow.

When Parker comes to a curve, the skis will either be eased into the turn with the ski pointed in the same direction as her velocity, making a sharp cut in its wake, or she will choose a skidding type of maneuver where the skis will be forced in the direction she wishes to go, leaning away from the curve at a 45-90 degree optimal angle, and literally plowing snow away from her. Some skis have special designs that scientists have found will decrease the drag and increase the speed these curves can be safely made.  Surely, Parker will have researched and purchased those that fit his style and goals for skiing.

By the time she reaches the bottom, her potential energy is expended, the ensuing kinetic energy is maxed out, and now friction works against him to slow down her acceleration to a stop.  His adrenalin will return to normal levels, and her blood circulation and other systems will begin to function normally once again.  (At least until the next run.)

Research will continue to change the sport of skiing.  And no doubt, the savvy skier will keep tabs on the newest and best ways scientists will come up with to help us beat the forces working against us.

By: Marcia Howell, University of Utah


Energy Transformation for Downhill Skiing. 2012. Retrieved from http://www.physicsclassroom.com/mmedia/energy/se.cfm

The Physics of Skiing. Real World Physics Problems. 2009. Retrieved from http://www.real-world-physics-problems.com/physics-of-skiing.html

Locke, B. 2012. The physics of skiing. Retrieved from http://ffden2.phys.uaf.edu/211_fall2002.web.dir/brandon_locke/Webpage/homepage.htm

Mears, A. 2002. Physics of Alpine Skiing. Retrieved from http://www.suberic.net/~avon/mxphysics/anne/Annie%20Mears.htm

Aerodynamics and Cycling (Basic)

CyclingConsidered to be one of the most exhilarating and efficient human-powered vehicles ever invented, the bicycle continues to find its way into the lives of many Americans and people throughout the world.  Cycling sporting events have exponentially increased in popularity since the day German inventor, Baron Karl von Drais, put two wheels on a wooden frame in 1817 (Ballantine 2001).  Since then, the bicycle has undergone several modifications.  Once engineering technology caught up with the public’s need for speed, cycling was transformed from a field of design guesswork to a scientific research analytical field involving a diverse number of disciplines.

There are many factors that hinder a bicycle from reaching maximum velocities.  Among these are transmission friction, air drag, rolling resistance and inertia forces.  The most significant of these is air drag.  70% – 90% of the resistance experienced by a rider in a high-speed race is due to drag (Brownlie 2010).  Therefore, aerodynamic studies are of paramount importance for better bike design, and several studies have been conducted within the past two decades.

In the most basic definition of air resistance, drag occurs due to a pressure difference between the front and rear of an object, which is in movement relative to its medium (air).  When air hits the rider, it is brought to a stop, creating what engineers refer to as the stagnation point.  At this point, the air splits and moves in opposite directions following “streamlines”, which contour around the rider.  The air sticks to the body of the rider as it moves around him/her.  However, due to a lack of energy, it separates from the body somewhere around the rider’s back.  This separation creates a low-pressure field in the rear of the rider.  This pressure difference between the front and the rear causes a force, which pushes the rider backwards, called drag.

There are two methods to study aerodynamics around a bicycle: mathematically and experimentally.  In the first method, engineers and scientists solve complex systems of equations, which predict air behavior around the rider.  Since some of these equations are too difficult to be solved by hand, computers programs are often used.  Others study drag experimentally.  They put a rider on a bike inside a big tunnel (generally referred to as a wind tunnel), which blows air at high speeds while the rider stays still.  Sensors attached to the rider are able to measure pressure differences and compute drag.  Both methods have advantages and disadvantages, and both are often used in unison.

Different components have been individually tested for drag such as helmets, loose clothing, rider’s position and wheels.  Studies have shown that even seemingly small factors, such as loose clothing, can increase drag significantly during a race.  Bicycle scientists continue to try to find the ultimate rider’s position, the best helmet and the most appropriate clothing to help cycling athletes further improve their performance.

Learn the technical details of aerodynamics and cycling.

By: Cristian Clavijo, University of Utah

Cristian Clavijo is a native of Peru, moved to the US in the 8th grade, and is now a Masters student in Mechanical Engineering at the University of Utah.  As an advocate for the Hispanic underserved population in Utah, Clavijo is involved in educating children and parents on how basic scientific and medical knowledge can help them progress and become collaborators of their communities.  He plans to pursue a PhD in Mechanical Engineering next year.


Ballantine, R. 2001. Richard’s 21st-century bicycle book. The Overlook Press, New York, New York, USA.

Brwonlie, L., P. Ostafichuk, E. Tews, H. Muller, E. Briggs and  K. Franks. 2010. The wind-averaged aerodynamic drag of competitive time trial cycling helmets. Procedia Engineering 2:2419-2424.


Aerodynamics and Cycling (Technical)

At one point almost banned by social and environmental safety national leaders, cycling, in its many forms, has become one of the most competitive international sporting events and is certainly among the top choices for transportation and recreation.  Most people today view cycling as a form of mere exercise or seasonal recreation.  However, for some, cycling is a way of life.  Paul Fournel expressed, “When you get on your first bike you enter a language you’ll spend the rest of your life learning, and you transform every move and every event into a mystery for the pedestrian” (Fournel 2003). What is it about cycling that stirs such feelings or even mania among its faithful devotees? Breath-taking landscapes, memorable sights and smells, the sound of self-induced wind challenging the rider to pedal harder, and physical and mental rejuvenation are some of the reasons.

Fig. 1 Old design of bicycle in the 1800’s.

Though the early roots of first invention designs and legal patents are blurred, there is a clear idea of the road traveled by the bicycle since its advent in the early 1800’s.  Originally known as “pedestrian’s accelerator”, “boneshaker” and “velocipede” (Norcliffe 2001), the bicycle, in its most basic form, consists of two wheels (hence the name of “bi-cycle”), a connecting metal frame, a seat, steering bars and pedals.  However, the first bike, which was invented in Germany by Baron Karl von Drais in 1817, had no pedals (Ballantine 2001).  The rider was expected to propel himself while sitting on the two-wheel frame.  This design, though more efficient than sole human transportation, was quickly and necessarily improved throughout Europe in the following decades (Norcliffe 2001).   The second half of the 19th century saw innumerable changes in the bicycle.  Pedals were co-axially attached to the front wheel.  Big (over 1 meter in diameter) front wheels were later designed to induce higher speeds (see figure 1).  Steel frames were manufactured to provide longevity and durability.  However, despite all these improvements, the bicycle still had not reached its full potential.  By the dawn of the 20th century, problems with turning, safety, cost and weight had driven engineers to design the bicycle as it is known today.

The earliest records of cycling race competitions date back to when the front wheel was almost as tall as the rider.  It was, perhaps, the desire for faster lap times that pushed bicycle engineering to new heights.  Today, there are diverse engineering and science fields involved in the design and technological development of bicycles.

Some of the aspects engineers continue to explore are air resistance, drafting, altitude, hills, rolling resistance, power transmission friction, inertia forces, and braking energy losses.  Air resistance seems to be the single most adverse resistance factor for road race cycling.  The event that revealed the importance of this fact took place in the 1989 Tour de France.  Greg Lemond was 50 seconds behind his competitor in the last stage of the race.  Unlike Greg Lemond however, his competitor did not have an aero helmet, triathlon bars and a back disc wheel.  Greg Lemond was able to beat out his opponent by 58 seconds by the end of the race (Tew and Sayers 1997, Chowdury et al. 2011).  Other similar unbelievable aerodynamic feats were repeated over the next couple of years, which caused aerodynamics to become of interest.

Aerodynamics is a subfield of fluid mechanics, a mechanical and chemical engineering field essential for the analysis of systems in which a fluid is the working medium (Fox et al. 2004).  Aerodynamics deals with the dynamics of gases, especially air interactions with moving objects(Houghton Mifflin Company 1969).  Early studies showed that in a typical training ride, wind resistance accounts for 72% (although numbers up to 90% have been reported (Brownlie et al. 2010, Gibertini et al. 2010) with faster speeds) of the force retarding the forward movement of the rider, the tires 15%, braking losses 8%, and bearing and chain losses 5% (Burke 1986).

Several attempts to improve cycling aerodynamics were made through trial and error.  Unsurprisingly, this approach was ineffective, and engineers had to step in.  There are basically two methods to analyze the aerodynamics of a bicycle: mathematically and experimentally.  In mathematics, certain fluid behavior can be predicted by solving mathematical partial differential equations.  These equations take into account momentum, energy and mass conservation laws, and often are brought together into a system of equations.  One of the most commonly used equations in fluid mechanics is called the Navier-Stokes equation (Tew et al. 1997) shown below:

This equation is a simplified one-dimensional version with several built-in assumptions, and it only represents one given particle of air.  Clearly, airflow around a cyclist involves countless particles of air—it is easy to see why a powerful computer would be necessary to solve the aerodynamics physics around a cyclist.  Engineers and mathematicians have developed different numerical methods to simplify complex systems of equations, so that a computer can solve them in real time.  One such method is Computational Fluid Dynamics (CFD), which is a field in which equations similar to the one described above are discretized by approximating a solution with a system of algebraic equations, which can then be solved on a computer Ferziger and Peric 2002).  Several computational cycling engineers, nationally and abroad, use commercially available CFD packages to solve their designs of interest.

Fig. 2 ANSYS CFD image of air movement (stream lines) seen around cyclist creating pressure difference (drag). (Picture provided by Bike Tech Review)

If using an experimental approach to analyze the aerodynamics of cycling, experiments are usually carried out in a wind tunnel (see figure 3).  A wind tunnel cross section may be small enough (.5m x .25m) to test minor drag (due to clothing, for instance), or big enough (4m x 3.5m) to fit a whole bicycle (Gilbertini et al. 2010, Alam et al. 2010).  Sensors, attached to the rider and bike, are able to pick up pressure changes inside the wind tunnel and thereby measure drag (Iniguez-de-La and Iniguez 2009).  Experimental wind tunnel testing is often preferred over purely computational testing due to the limiting assumptions found in the mathematical equation solvers.  However, performing computational experiments can save a significant amount of time and money.  Often, both mathematic and experimental approaches are used in conjunction and offer comparative results.

Fig. 3 Wind tunnel experiment (picture provided by A2 Wind Tunnel)

When scientists study the aerodynamics of cycling, there are two main types of drag being considered: pressure drag and skin-friction drag.  When air hits an object (rider or bicycle), it splits and travels around the object creating a boundary layer, which is a thin film of compressed air near the surface of the object.  However, the air fails to meet back at the opposite side of the object due to a lack of energy, and the boundary layer separates from the body altogether.  This separation causes a pressure difference between the front and rear of the body thereby causing pressure drag.  The second type of drag (skin-friction or shear) occurs tangentially to the object as the air particles move around it.  This phenomenon can be observed by watching loose clothing of a rider flap with the wind.

There are three major areas of focus for drag studies: drag produced on the rider’s position, on the bike, or on the cyclist’s attire.  Two thirds of the drag experienced is due to the rider position (Kyle and Burke 1984), therefore great efforts have been focused in that area.  There are basically three positions that a rider can adopt while riding: upright position, dropped position and time trial position Burke 1986).  While the upright position provides the greatest comfort, it also induces the greatest drag.  The dropped position (20° angle relative to the horizontal) induces less drag and is generally the most used position while on a race.  In the time trial position, the rider positions his/her back almost completely parallel to the ground, with hands on the low handle bars and both pedals vertically aligned.  This provides the best aerodynamic efficiency and is mainly used during downhill rides.

Great efforts have also been made on bike design.  Lighter frames, thinner tires and aerodynamic wheel spokes are the current fields of interest for bike design.  Different wheel spoke designs—even wheel flap covers—have been tested for drag reduction because reductions of up to 50% have been observed with changes in the spoke design (Houghton Mifflin Company 1969).  While wheel flap covers have shown better aerodynamic characteristics (Karabelas and Markatos 2012), they are often undesirable during side winds.

In addition to the rider’s position and the bike itself, the rider’s attire is also important because loose clothing can generate significant drag.  This is due to the skin-friction drag phenomenon explained above.  It has been reported that tight clothing could save up to 1.17% of the rider’s finishing time in 100 meters (Brownlie 1992).  More meaningful is the drag reduction that can be obtained by use of an aerodynamic helmet.  Differences in overall drag reduction of different commercially available helmets of up to 8% have been reported (Alam et al. 2010).  Another aspect engineers have taken into account more recently is thermal comfort, which, disadvantageously, is inversely proportional to aerodynamic efficiency.  In other words, the more vents a helmet has for cooling, the less aerodynamic it is.  The third variable in the helmet design equation is safety considerations.  Certain helmets have been designed that offer great thermal comfort and good aerodynamic properties, but do not meet safety standards.

Has bicycle technology reached its end?  Or more importantly, are any further drag reductions too minimal to be worth the research effort?  Many opinions differ, but for as long as competitive cycling events still occur, researchers will continue to engineer the latest bicycle and appendages.  While the recreational bicycle rider may not be extremely concerned about which helmet or shorts to buy, it is of utmost interest for the serious race cyclist.

By: Cristian Clavijo, University of Utah
Cristian Clavijo is a native of Peru, moved to the US in the 8th grade, and is now a Masters student in Mechanical Engineering at the University of Utah.  As an advocate for the Hispanic underserved population in Utah, Clavijo is involved in educating children and parents on how basic scientific and medical knowledge can help them progress and become collaborators of their communities.  He plans to pursue a PhD in Mechanical Engineering next year.


Alam, F., H. Chowdhury, Z. Elmir, A. Sayogo, J. Love, and A. Subic. 2010. An experimental study of thermal comfort and aerodynamic efficiency of recreational and racing bicycle helmets. Procedia Engineering 2:2413-2418.

Ballantine, R. 2001. Richard’s 21st-century bicycle book. The Overlook Press, New York, New York, USA.

Brownlie, L. 1992. Aerodynamic characteristics of sports apparel. School of Kinesiology, Simon Fraser University, Burnaby, BC, Canada.

Brownlie, L., P. Ostafichuk, E. Tews, H. Muller, E. Briggs, and K. Franks. 2010. The wind- averaged aerodynamic drag of competitive time trial cycling helmets. Procedia Engineering 2:2419-2424.

Burke, E. R. 1986. Science of cycling. Human Kinetics Publishers, Champaign, Illinois, USA.

Chowdhury, H., F. Alam, and D. Mainwaring. 2011. A full scale bicycle aerodynamics testing methodology. Procedia Engineering 13:94–99.

Ferziger, J. H., and, M. Peric. 2002. Computational methods for fluid dynamics 3rd ed. Springer Publishing Company, New York, New York, USA.

Fournel, P. 2003. Need for the bike. University of Nebraska Press, Lincoln, Nebraska, USA.

Fox, R. W., A. T. McDonald, and P. J. Pritchard. 2004. Introduction to fluid mechanics 6th ed. John Wiley and Sons, Hoboken, New Jersey, USA.

Gibertini, G., G. Campanardi, L. Guercilena, and C. Macchi. 2010. Cycling aerodynamics: wind tunnel testing versus track testing. IFMBE Proceedings 31:10-13.

Houghton Mifflin Company. 1969. The American Heritage Dictionary of the English Language. Houghton Mifflin Company, Boston, Massachusetts, USA.

Iniguez-de-la T., and J. Iniguez. 2009. Aerodynamics of a cycling team in a time trial: does the cyclist at the front benefit? European Journal of Physics 30:1365-1369.

Karabelas, S. J., and N. C. Markatos. 2012. Aerodynamics of fixed and rotating spoked cycling wheels. Journal of Fluids Engineering 134:1-14.

Kyle, C. R. and E. R. Burke. 1984. Improving the racing bicycle. Mechanical Engineering 106:34-35.

Norcliffe, G. 2001. The ride to modernity: the bicycle in Canada. University of Toronto Press, Toronto, Canada.

Tew, G. S. and A. T. Sayers. 1997. Aerodynamics of yawed racing cycle wheels. Journal of Wind Engineering 82:209-222.

From Tee to Fairway: How Physics Affects the Drive, the Club, and the Golf Ball

Golf Ball Velocity

Golf Ball Velocity

The average golfer drives the golf ball with an initial velocity of over 100 miles per hour.  If the player uses a club with a flexible shaft, the act of swinging adds an additional measure of torque as the head of the club also propels forward to connect with the ball.  The head of the club has grooves that increase the friction between the club and the ball, allowing the club to more effectively focus the area of contact.

The optimal angle to hit the ball ranges from about 12 to 20 degrees.  Putting a backspin on the ball increases lift and can add significant distance to the drive.  The dimples on the golf ball itself help reduce drag from the air stream by reducing turbulent air pressure around and behind the ball, shifting the wake further behind the ball, thus allowing for smoother, less resistant flight.   Any combination of these variables contributes to how well the ball overcomes the forces of gravity and air resistance.

Learn the basics of how physics affects golf or read the more technical details here.

Articles by Trevor Stoddard

From Tee to Fairway: The Basics of How Physics Affects the Drive, the Club, and the Golf Ball (Basic)

The motion of a golf ball can be thought of as a projectile, whose trajectory is parabolic and acted upon by gravity.  The initial velocity imparted to the ball by the club head can be broken down into both a horizontal and vertical component.  Numerous scientific studies have identified the optimum launch angle as 11-20° to achieve maximum distance (Erlichson, 1983). Though drivers are typically 8-10° in loft, the flexibility of the graphite driver shafts increases the launch angle through a split second whipping action (Zumerchik, 1997).  Golf clubs have grooves added to their faces to add some friction to the club head, so that momentum is transferred to the ball and backspin is created to generate lift. The difference between a ball with backspin and one without can add up to 100 yards after 2 or 3 seconds of additional flight time (Zumerchik, 1997).

There are several forces that act upon the aerodynamics of a golf ball in flight.  The most recognizable force acting upon a golf ball is gravity, which pulls the ball downward and creates the parabolic trajectory common of projectiles.  Another force on a golf ball is lift, the force that opposes gravity.  When backspin is transferred to the ball from the grooves on the clubhead, the velocity of air on top of the ball (which is moving in the direction of the backspin) is higher than the velocity of air on the bottom of the ball.  To counteract this, the Magnus effect generates lift on the ball and pushes it up.

In addition to gravity and lift, another force acting on a golf ball is drag, or air resistance.  As a golf ball is sent flying through the air, the molecules that come into contact with the front of the ball exert a large pressure force on the front of the ball (drag). Drag slows down the forward velocity of the ball. As the air comes into contact with the front of the golf ball, the fluid motion of the air becomes turbulent.  Turbulent flow can be thought of as smoke from a smoke stack- chaotic and wispy. As the turbulent air swirls around the golf ball, the dimples capture some of the swirls and keep them close to the surface of the golf ball. This means that the boundary layer of air stays close and hugs the ball longer, which means that there is a smaller pressure difference between the front of the ball and the back (when compared to a ball without dimples). The dimples thus allow the golf ball to travel farther than a smooth ball because the golf ball experiences less drag.

By: Trevor Stoddard, University of Utah

Learn more about the technical science behind golf.


Benson, T. (2010) Drag of a Sphere.  National Aeronautics and Space Administration, Date Accessed:  8/10/2012 <http://www.grc.nasa.gov/WWW/k-12/airplane/dragsphere.html>

Bird, R. B., W.E. Stewart and E.N. Lightfoot. 2007. Transport Phenomena, 2nd edition, Wiley & Sons, New York.

Cochran, A. (ed.). 1990. Science and Golf.  New York: Chapman and Hall

Cochran, A. (ed.). 1992. Science and Golf II.  New York: Chapman and Hall

Davies, J.  1949. “The Aerodynamics of Golf Balls.”  Journal of Applied Physics 20: 821-828

Erlichson, H. 1983. “Maximum Projectile Range with Drag and Lift, with Particular Application to Golf.”  American Journal of Physics 51: 357-362.

Jorgensen, T. 1994. The Physics of Golf. New York:  American Institute of Physics

McDonald, W. 1991. “The Physics of the Drive in Golf.”  American  Journal of Physics 59: 213-218

Werner, F. and R. Greig. 2000. How Golf Clubs Work and How to Optimize Their Designs.  Jackson Hole, WY:  Origin Inc.

Wesson, J. 2009. Science of Golf.  New York, Oxford University Press

Williams, D. 1959. “Drag Forces on a Golf Ball in Flight and Its Practical Significance.”  Quarterly Journal of Mechanical Applications of Mathematics XII 3: 387-393

Zumerchik. J. (ed.). 1997. Encyclopedia of Sports Science.

Zumerchik J. 2002. Newton on the tee- a good walk through the science of Golf

History of the golf ball <http://www.golfeurope.com/almanac/history/golf_ball.htm> last accessed 8/10/12

From Tee to Fairway: How Physics Affects the Drive, the Club, and the Golf Ball (Technical)


According to the PGA there are 27 million golfers in the United States (citation).  By understanding the science behind the game, golfers are more likely to improve their scores because they can better understand the errors that they are making.

From Tee to Fairway: The Physics Behind Golf (Projectile Motion)

Projectile motion is the motion of an object that is imparted with an initial velocity (such as hitting a golf ball with a golf club) that moves in a parabolic trajectory that is caused by the effect of gravity on the object.    Initial velocity can be broken into horizontal and vertical components as in Equation (1).

Where the subscript 0 denotes initial, x and y are the directions and i and j are the vector directions (i is in the x-direction and j is in the y-direction).  The initial horizontal and vertical velocities can be determined if the angle the ball is launched from the horizontal,α, is known, given by Equations (2) and (3).

Acceleration due to gravity pulls the golf ball down during flight and as time goes on actually forces the vertical velocity in the downward direction, the components of the golf ball velocity at any given time, t, during its flight are given by Equations (4) and (5).

Where g is the acceleration due to gravity, which is a constant assumed to be -9.8 m/s2 (or 32 ft/s2), and the time t is in seconds.  The magnitude of the velocity is given by Pythagorean’s theorem.

A diagram of these velocity vectors is given in Figure 1.

Figure 1.  Golf ball velocity

The average golfer drives the golf ball with an initial velocity of over 100 miles per hour (Zumerchik, 2002)! This means that the golf ball, if struck at an angle of 12°, will be initially traveling at 87 mph in the horizontal direction and 13 mph in the vertical direction.

Typically the projectile motion equations used to calculate range and height of a golf ball’s flight do not account for drag, and are therefore only estimates as to the true maximum height and range that the golf ball will travel.

Drag force (or air resistance) is the force that acts opposite to an object that is moving through it. When a golf ball is hit, the air molecules flow past the golf ball as the golf ball flies through the air, thus creating a retarding force on the forward motion of the ball known as drag.

In 1949, Davies conducted experiments to determine the magnitude of drag and lift forces that occur on a golf ball by dropping rotating golf balls into a wind tunnel.  Davies found that “drag increased nearly linearly from about 0.06 lb for no spin to about 0.1 lb at 8000 rpm” and that “lift varied with the rotation speed” (Davies, 1949).

In 1959, Williams used the previous findings of Davies and conducted an analysis on golf ball carry as a function of velocity.  Williams showed that the drag force varied linearly with the velocity.  The drag force on a golf ball can be calculated by Equation (7).

Where CD is the drag coefficient, A is the cross-sectional area of the ball, ρ is the air density, and v is the ball velocity (in ft/s).

Williams showed that the drag coefficient can roughly be estimated as 46/v, showing that at higher speeds the drag coefficient drops significantly.  Williams found that the drag force on the golf ball varied linearly with the speed, he found D to be as given in Equation (8).

Where D is in pounds, and 0.000783 represents the constant c, to be discussed.   One note is that Williams’ (1959) calculations used a British ball with a diameter of 1.62 inches compared to the American ball of 1.68 inches.  The easiest calculation is to consider the case of a nonspinning golf ball (no lift) with linear air resistance in calculations of range and height.  The reader is directed to the paper by Erlichson for a more in depth analysis of range calculations that incorporate lift forces into the derivations.

Erlichson (1983) gives the equations for range and height as in Equations (9) and (10).

Where c is 0.000783 lb/(ft/s) and m is in [lb] and g is 32 ft/s2 and t is time, initial velocities are given in ft/s.

Using these equations a golfer could estimate how long they will hit the ball and where it will end up.  Variables such as wind and weather can affect these numbers in reality so they are best used for only estimations on distance.

Several studies have been conducted on the optimum launch angle.  Scottish physicist Alastair Cochran calculated that the optimum launch angle of 20° achieves the longest carries (Cochran, 1990). One needs to take this finding with a grain of salt, however, because the ball will land at a high angle and will have less bounce and roll, unless the grass is wet.

Erlichson (1983) found that the optimum launch angle was around 12-13°, only slightly more lofted than the drivers available on the market, and with the additional loft generated from shaft flex. Zumerchik concludes that anywhere from 12°-20° will give the ball maximum range with only a few yards difference between the different angles. (Zumerchik, 2002)

Golf Clubs: Loft and Grooves

Several forces act on the golf club, such as torque (exerted by the golfer on the club), centrifugal acceleration, and gravity.  Typically golfers can average a whole 4-5 hP of power generated from their golf swings. (Wesson, 2009)

At the top of the backswing, the club head coils because the shaft is flexible and the center of mass is in the clubhead. As the swing moves forward, the shaft of the club coils, unloads, and recoils as the club head attempts to catch up to the wrists during the swing.  At impact between the clubhead and the ball there is a final forward oscillation that creates a snapping effect that increases the velocity of the club head through the ball, and by extension also increases the initial velocity imparted to the golf ball.  It has been found that a “forward shaft flex of about 3.3 degrees can add 8.7 percent to the velocity of the club head” (Jorgensen, 1994).  During the course of the swing, the club oscillates 1.5 times (Zumerchik, 1997).

Werner et al. (2000) conducted a full suite of simulations and experiments on optimizing club designs. Their findings showed that there is an optimum combination of loft angle and center of gravity location, and that an extra-large face provides advantages (Werner et al., 2000) But does the addition of more surface area on the club head create an increased drag on the club head, diminishing initial velocity?

It’s been found that air drag on the shaft and clubhead results in an energy loss of 10% of the energy of the club at impact with the ball.  This results in a reduction of roughly 15 yards in the range of the ball (Wesson, 2009).

When the club head strikes the ball, the grooves on the club head increase the amount of friction at the ball-club head interface, allowing for the ball to have backspin, which increases the lift force.  Without friction, the ball would merely glide up and off the club face.

When the club head comes into contact with the golf ball, some of the energy is lost and is not entirely transferred into velocity of the golf ball. The ratio of the velocity transfer between the club face and golf ball surface is given by the coefficient of restitution.

If a ball hits a surface at a right angle with a speed v and leaves the surface with a speed v’ then the coefficient of restitution is defined by

When bounced off a hard surface, a typical golf ball has a coefficient of restitution of around 0.7.  This means that if the golf ball were dropped from 100 feet above the ground, it would rebound and bounce back 70 feet. The coefficient of restitution is about 1.46 for a driver, 1.3 for a 5 iron, and 1.12 for a 9 iron.  (Zumerchik, 1997).

Why all the dimples: The Fluid Mechanics behind a golf ball in flight

The aerodynamic forces that act on a golf ball in flight are shown in Figure 1.

Figure 1. Forces that Act on a Golf Ball in Flight

Typically golf balls have between 330 and 500 dimples on their Surlyn covers.  Some dimples are round while most golf ball manufacturers have started making their dimples in a variety of hexagonal shapes.  As stated by Euler’s principle (Bird et al, 2007) separation of the boundary layer (the layer of air molecules next to the surface of the golf ball) is likely to occur in regions where the pressure increases in the direction of the flow. The following youtube video gives a good look at a simulation of the boundary layer.

The reason for the large number of dimples on a golf ball is to ensure that the boundary layer does not separate until the back part of the ball.  A smooth sphere will generate a large wake behind the ball, as there is much lower pressure behind the ball than in front.  The air will move to rush into the area of low pressure, exerting a pressure drag force on the ball.  However, as the turbulent air swirls around the golf ball, the dimples capture some of the swirls and keep them close to the surface of the golf ball. Dimples force a turbulent trip at the surface, ensuring a later separation of the boundary layer which decreases the amount of drag force on the ball. Dimples on the golf ball do not reduce the drag at the front of the ball, because the cross-sectional area of the ball is always the same. However, they do decrease the size of the low pressure wake behind the ball, lowering the overall drag force, and improving flight.  An example of this is shown in Figure 2, a simulation run in Fluent between a sphere and a dimpled golf ball.

Figure 2. Fluent simulation showing the pressure field around a smooth sphere and dimpled golf ball. Balls are traveling to the left.

As shown in both cases, the pressure contacting the front face of both balls is large. However, the magnitude of the pressure difference (front side versus back side of the ball) in the sphere case is much greater than in the golf ball case. The large amount of high pressure (red and yellow) pushing against the flight of the ball slows it down much faster than in the golf ball case, where there is less pressure behind the ball.  In addition to this pressure calculation it is of interest to look at the shear stress distribution on the face of both the sphere and modeled golf ball, as shown in Figure 3.

Figure 3. Wall shear stress of both a dimpled golf ball and a sphere modeled in Fluent

As shown in Figure 3, the shear stress on the surface of the sphere (red/orange) covers a greater surface area, showing where the boundary layer separates from the sphere.  The dimples on the golf ball keep the turbulent flow boundary layer close to the golf ball wall and greatly reduce the shear stresses over the golf ball’s surface area.  This means that the golf ball is slowed less.  The boundary layer separation in laminar and turbulent flow is shown in Figure 4, a COMSOL simulation of a sphere in flow.

Figure 4. Boundary layer separation

As shown in Figure 4, in the laminar case with a low Reynolds number (Re=0.1) (top) has no boundary layer separation as the streamlines hug the outside of the ball. This situation is unrealistic for a golf ball because of the high velocities that the golf ball travels at (~200 ft/s) once it is hit  (Zumerchik, 2002).

The second case (middle) shows a smooth ball at a high velocity. There is a large pressure difference between the front and back side of the ball, and the boundary layer separates much earlier than the dimpled sphere case (bottom).  The dimples allow for the boundary layer to hug the ball and boundary layer separation does not occur until the very tail end of the ball. The smaller the blue zone of low pressure behind the ball, the farther the golf ball will fly.

Similar to an air foil, the dimples on a golf ball also allow for a lift force to be exerted on the ball.  Backspin, as generated from the loft of the clubface that strikes the ball, deforms the airflow around the ball and creates a lift force due to the Magnus effect.  The Magnus effect is a phenomenon where a spinning object flying in a fluid creates a whirlpool around itself and experiences a force (in this case, lift) perpendicular to the line of motion.  Because the top of the ball is spinning with the direction of the air, the air on top of the ball moves more rapidly than the air at the bottom of the ball.  The air at the bottom of the ball moves against the wind, and this shifts the pressure behind the ball downward, in the direction of the backspin.  Because of the differing velocities on top and bottom of the ball, there is a resultant force upward known as lift.

The magnus effect can have a large impact in golf. If two golf balls are hit with the same velocity, a ball hit with backspin will stay in the air 2 or 3 seconds longer and may travel 18 to 30 meters farther (Zumerchik, 1997).

Despite the benefits of backspin, the use of too much spin can be a problem because some of the momentum is imparted into the high spin of the golf ball.  As a ball travels faster, it needs less backspin to generate lift. (Zumerchik, 2002).


Golf equipment has evolved over the centuries to increase the distance a ball can travel. By understanding the forces acting on the golf ball, a golfer can maximize his/her performance

By: Trevor Stoddard, University of Utah



Benson, T. (2010) Drag of a Sphere.  National Aeronautics and Space Administration, Date Accessed:  8/10/2012 < http://www.grc.nasa.gov/WWW/k-12/airplane/dragsphere.html>

Bird, R. B., W.E. Stewart and E.N. Lightfoot. 2007. Transport Phenomena, 2nd edition, Wiley & Sons, New York.

Cochran, A. (ed.). 1990. Science and Golf.  New York: Chapman and Hall

Cochran, A. (ed.). 1992. Science and Golf II.  New York: Chapman and Hall

Davies, J.  1949. “The Aerodynamics of Golf Balls.”  Journal of Applied Physics 20: 821-828

Erlichson, H. 1983. “Maximum Projectile Range with Drag and Lift, with Particular Application to Golf.”  American Journal of Physics 51: 357-362.

Jorgensen, T. 1994. The Physics of Golf. New York:  American Institute of Physics

McDonald, W. 1991. “The Physics of the Drive in Golf.”  American  Journal of Physics 59: 213-218

Werner, F. and R. Greig. 2000. How Golf Clubs Work and How to Optimize Their Designs.  Jackson Hole, WY:  Origin Inc.

Wesson, J. 2009. Science of Golf.  New York, Oxford University Press

Williams, D. 1959. “Drag Forces on a Golf Ball in Flight and Its Practical Significance.”  Quarterly Journal of Mechanical Applications of Mathematics XII 3: 387-393

Zumerchik. J. (ed.). 1997. Encyclopedia of Sports Science.

Zumerchik J. 2002. Newton on the tee- a good walk through the science of Golf

History of the golf ball <http://www.golfeurope.com/almanac/history/golf_ball.htm> last accessed 8/10/12


For more information:

  1. DeNevers, Noel, Fluid Mechanics for Chemical Engineers, McGraw-Hill, New York, 2005.
  2. Libii, Josue Njock (2007)  “Dimples and Drag:  Experimental demonstration of the aerodynamics of golf balls.”  American Journal of Physics, 75, 764.
  3. Millne, R. and J. Davies (1992)  “The Role of the Shaft in the Golf Swing.”  Journal of Biomechanics 129:  975-983
  4. Zander, J. and A. Chou (February 1999)  “Max out your ball:  Increasing your launch angle and decreasing your spin rate will help you hit farther.”  Golf Digest 50: 76-80


Tennis Courts and Equipment: How Physics Affects the Speed of Play (Technical)


Technological advancements have played a key role in making power and spin prominent features in the game of tennis.  The transition from wood to composite graphite rackets has produced larger sized rackets (in terms of both head and shafts) with frames that are thicker and lighter (Brody 1997), allowing players to hit harder than ever before. Changes in racket construction have altered the tennis serve, to the point where serves can dominate many tennis matches.  In order to make match points last longer, scientists and athletes have explored ways to slow the serve and restore balance to the game. One approach has been to engineer new types of tennis balls with properties that can counteract the power and speed of the serve (Haake et al. 2000).  Changes in tennis ball construction and interactions between the ball and different types of court surfaces have become primary considerations.

Types of Tennis Court Surfaces

Tennis was first played on natural grass courts.  Modern day grass courts consist of a soil foundation with a seeded turf overlay (Miller 2006).  While grass is still used at Wimbledon, its use has diminished due to the cost associated with high maintenance.

Clay courts gained favorability in the 1950s and consist of a base layer of crushed stone covered with a layer of rough particle material such as crushed brick (Miller 2006). This produces high amounts of friction between the ball and surface, but low amounts of friction between the player and the surface. On a clay court, the player has a tendency to slide, particularly when slowing down or attempting to change their direction of movement (Miller 2006).  Lower injury rates have been associated with players that frequently use clay courts (Dragoo et al. 2010), possibly because of lower impact forces due to the sliding motion.  Currently, the French Open is the only major tennis tournament played on clay.

Acrylic hard courts have rapidly gained popularity since their introduction in the 1940s and are used in two major tennis tournaments, the US Open and the Australian Open.  These courts utilize either asphalt or concrete as the foundation layer, a rubber mid-layer, and a top coating made of an acrylic paint/sand mixture (Miller 2006).  These courts produce the highest amount of friction between the surface and player, and have been associated with the most player injuries when compared to other surfaces (Dragoo et al. 2010).

Tennis Court Surfaces Affect the Speed of the Game

One of the most important considerations in tennis is the influence of the court surface on the ball.  Aside from the force of gravity, a bouncing ball additionally experiences normal and frictional forces (Brody 2003).  The normal force acts perpendicularly to the surface and the frictional (or sliding) force will act parallel to the surface (horizontally). The combination of these forces impacts the bouncing movement of the ball. The amount of friction generated between the ball and court dictates if the court is considered to be “fast” or “slow.”  In particular, the amount of sliding friction that is present, dependent upon the surface type, is of interest.

A “slower” court is one where more friction is generated between the ball and the surface.  Clay, with its rough surface composition, has a high coefficient of friction.  When more frictional contact is produced, the horizontal speed of the ball is reduced.  This reduction in forward motion creates a high vertical bounce. The longer the ball is in the air, the more time a player has to move and react, making clay a “slow” paced court.

A “faster” court produces less friction between the ball and the surface.  Grass, with its firm and slippery (even more so when wet) surface composition has a low coefficient of friction making it a “fast” paced surface.  With less friction, the ball will slide more easily across the surface, and it will retain more of its horizontal speed. This produces a low vertical bounce.  For these reasons, points on “fast” surfaces are often much shorter, as a lower bounce means the player has less time to react and move towards the ball.  In an examination of rally lengths in men’s singles tennis, 66%  of rallies on clay lasted less than six seconds, but this figure increased to 88% on grass courts (Lees 2003).

Engineering of Tennis Balls

In order to engineer tennis balls with more desirable properties, understanding ball construction is important. The two main components of a tennis ball are the core and covering.  The core is typically made of natural rubber that is mixed with powder fillers to produce desirable properties, such as strength and color (Manufacture).  The outer surface is made of cloth material; either of a wool-based fabric (Melton) or less expensive cloth (Needle cloth) that contains more synthetic components (Manufacture).  In addition, most tennis balls are pressurized, and the amount of internal pressure (ranging from 0-15 psi) will be determined based upon the ball type (Miller 2006).

Tennis balls are manufactured through a series of processes. The first of these processes is an extrusion, where the rubber is forced into a cylindrical shape through an application of pressure (Manufacture). The resultant rubber rod is then sectioned into smaller segments.  Subsequent processes include forming the material into a spherical shape (by using a hydraulic press to form two individual hemispheres that are later joined), curing and pressurizing the ball, covering the ball with fabric and finally joining the core and covering together in a molding process that utilizes pressure and heat (Manufacture). The final step is to steam the ball, thus producing a more raised outer covering.  Once finished, balls must pass tests related to mass, size, compression and bounce (ITF 2012).

There are three major categories (types 1-3) of tennis balls, each designed for specific use on set court types to speed up or slow down play.  The weight and rebound of the tennis balls does not change across type.  The standard and most utilized ball type is type 2, as it is suitable for medium paced surfaces.  Type 1 balls are the same size as type 2 balls, but are harder, which is reflected by smaller amounts of forward and reverse deformation, when compared to the type 2 balls (Miller 2006).  Because type 1 balls are considered to be “fast” balls, they are suggested for use on slower surfaces such as clay.

Type 3 balls differ from type 2 balls only in size.  Type 3 balls are typically 6-8 percent larger than type 2 balls (Miller 2006).  As demonstrated by Andrew et al. (2003), Type 3 balls are “slow” and travel through the air more slowly than their standard tennis call counterparts. Since type 3 balls are larger in size, they encounter greater drag (resistance) when traveling through the air. Thus, type 3 balls are suggested for use on faster court surfaces, such as grass, to help slow down the pace of play and reduce the dominance of the serve.  Furthermore, the additional drag associated with type 3 balls also allows for a larger amount of spin to be generated (Blackwell 2007).  Type 3 balls may also be beneficial for new players, as a slower pace allows for more reaction time and increased spin can aid in accuracy.

Although less prevalent, there are also balls designed for use at high altitude.  By changing either the internal pressure of the ball or the elasticity of the core material, high altitude balls can be made to bounce lower than type 2 balls  (Miller 2006).  This is done so that at the lower air density at higher altitude the same bounce height (as that of a type 2 ball at sea level) can be achieved.

Other Tennis Ball Considerations

Despite careful efforts to engineer tennis balls and select a ball that complements court conditions, there are additional factors that impact the speed of the game. One of these is unavoidable ball wear-and-tear, which affects even the most well-engineered tennis balls.

Four distinct phases of tennis ball wear have been identified: new ball, loose fuzz, tufted fuzz, and finally the bald ball (Steele et al. 2006).  The ball covering itself is porous, which creates additional instances of drag (Mheta et al. 2001) when compared to a smooth covering.  As the surface material becomes worn, the “fuzz” on the ball is depleted, and both lift and drag forces are reduced (Goodwill et al. 2004).  The drag coefficient for new tennis balls was found on average to be higher than 0.6. The drag coefficient was reduced to values near 0.5 for worn balls (Mehta et al. 2001). This means that a worn ball will fly faster with less force to push it down when compared to a newer ball, increasing the likelihood that the ball will be hit out of play.

The impacts of a worn ball may be reduced if a player applies spin to the ball. Spin is possible due to the Magnus effect, or a nonsymmetrical distribution of air that flows across the ball surface while it is in flight (Mehta 1985, Miller 2006).  When topspin is applied, some of the air (that is flowing in the same direction as the spin of the ball) will interact with the ball surface longer, which has the effect of deflecting the wake of the ball upwards while other forces act in a downwards direction (Mheta et al. 2001, Miller, 2006). By applying topspin to the ball, a player can help a tennis ball fall to the ground and remain in-bounds.

What Players Should Know

Beginning players may be most successful on clay courts, since the speed of play is likely to be slower, and the player is better able to slide

  • A type 2 ball is most common, but a beginner may consider using a type 3 because of its slower air speeds
  • Old, worn balls do have a noticeable impact on play


By: Lindsay Sanford, University of Utah
Lindsay received her B.S. in Mechanical Engineering from Washington State University and is currently pursuing a PhD degree in Bioengineering. In her spare time, she likes to travel, hike, read, and play with her two year old son.  She is also an avid runner and tennis player.



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