Drag

Drag is a force caused by the dynamic action of a fluid that acts in the direction of the freestream fluid flow. Generally, a drag is a resistance force - a force that slows the motion of a body moving through a fluid. The drag force is computed using the coefficient of drag, the fluid density, the projected area of the body or the surface area of the body oriented perpendicular to the fluid flow, and is the relative velocity of the body with respect to the fluid.

The coefficient of drag is a unitless number that serves as an index of the amount of drag an object can generate. Its size depends on the shape and orientation of a body relative to the fluid flow, with long, streamlined bodies generally having lower coefficients of drag than blunt or irregularly shaped objects. For example the frontal drag on a speed skater is approximately 0.26, in comparison, the vertical drag on a parachutist falling with the parachute fully opened is 1.20. Does this make sense to you?

The formula for the total drag force demonstrates the exact way in which each of the identified factors affects drag. If the coefficient of drag, the fluid density, and the projected area of the body remain constant, drag increases with the square of the relative velocity of motion. This relationship is referred to as the theoretical square law. According to this law, if cyclists double their speed and other factors remain constant, the drag force opposing them increases fourfold. The effect of drag is more consequential when a body is moving with a high velocity, which occurs in sports such as cycling, speed skating, downhill skiing, the bobsled, and the luge.

Increase or decrease in the fluid density also results in a proportional change in the drag force. Because air density decreases with increasing altitude, many world records set at the 1968 Olympic Games in Mexico City where the elevation is 2250 m may have been partially attributable to the reduced air resistance acting on the competitors. Mathematical model-based estimates indicate that the reduction in drag attributable to the lesser air density in Mexico City accounts for 0.08 seconds of performance time in the 100 m sprint and 0.16 seconds of race time in the 200 m event. Bob Beamon's noteworthy long jump performance of 8.9 m during the games was 2.4 cm longer than if the same jump had been performed at sea level. Theoretical calculations indicate that because air density decreases more than VO₂max with increasing altitude, the ideal altitude for cycling performance should be 4000 m.

In swimming, research indicates that drag varies with the anthropometric characteristics of the individual swimmer, as well as with the stroke used. Researchers distinguish between passive drag, which is generated by the swimmer's body size, shape, and position in the water, and active drag, which is associated with the swimming motion. Elite swimmers generate much less active drag than average swimmers through superior stroke technique. Older swimmers tend to generate more drag than younger swimmers, and sprinters tend to incur more drag than long distance swimmers). Furthermore, better swimmers appear to be able to increase swimming speed while simultaneously reducing drag or showing only a small increase.

Three forms of resistance contribute to the total drag force. The component of resistance that predominates depends on the nature of the fluid flow immediately adjacent to the body.

Surface Drag

One component of the total drag is known as surface drag or skin friction. Skin friction is derived from the sliding contacts between successive layers of fluid close to the surface of a moving body. The layer of fluid particles immediately adjacent to the moving body is slowed because of the shear stress the body exerts on the fluid. The next adjacent layer of fluid particles moves with slightly less speed because of friction between the adjacent molecules, and the next layer is affected in turn. The number of layers of affected fluid becomes pro gressively larger as the flow moves in the downstream direction along the body. The entire region within which fluid velocity is diminished be cause of the shearing resistance caused by the boundary of the moving body is the boundary layer. The force of the body exerts on the fluid in creating the boundary layer results in an oppositely directed reaction force exerted by the fluid on the body. This reaction force is known as skin friction.

Several factors affect the magnitude of skin friction drag. It increases proportionally with increases in the relative velocity of fluid flow, the surface area of the body over which the flow occurs, the roughness of the body surface, and the viscosity of the fluid. Skin friction is always one component of the total drag force acting on a body moving relative to a fluid, and it is the major form of drag present when the flow is primarily laminar.

Among these factors, the one that a competitive athlete can readily alter is the relative roughness of the body surface. Athletes can wear tight-fitting clothing composed of a smooth fabric rather than loose-fitting clothing or clothing made of a rough fabric. A 10% reduction of drag occurs when a speed skater wears a smooth spandex suit as opposed to the traditional wool outfit. A 6% decrease in air resistance results from cyclists using appropriate clothing, including sleeves, tights, and smooth covers over the laces of the shoes. The long cotton socks and loose shorts and singlets commonly worn by runners are particularly aerodynamically inefficient. Smoothing the running shoe and laces and either covering or shaving body hair reduces drag on runners by as much as 10%. Competitive male swimmers and cyclists often shave body hair to reduce skin friction. Can you think of any other "tricks" that athletes will attempt to reduce surface drag?

The other factor affecting skin friction that athletes can alter in some circumstances is the amount of surface area in contact with the fluid. Carrying an extra passenger such as a cox in a rowing event results in a larger wetted surface area of the hull because of the added weight and, as a result, skin friction drag is increased.

Form Drag

A second component of the total drag acting on a body moving through a fluid is form drag, which is also known as profile drag or pressure drag. Form drag is always one component of the drag on a body moving relative to a fluid. When the boundary layer of fluid molecules next to the surface of the moving body is primarily turbulent, form drag predominates. Form drag is the major contributor to overall drag during most human and projectile motion.

When a body moves through a fluid medium with sufficient velocity to create a pocket of turbulence behind the body, an imbalance in the pressure surrounding the body - a pressure differential - is created (see figure below). At the upstream end of the body where fluid particles meet the body head-on, a zone of relative high pressure is formed. At the downstream end of the body where turbulence is present, a zone of rel ative low pressure is created. Whenever a pressure differential exists, a force is directed from the region of high pressure to the region of low pressure. Take a moment and think of a practical example of this in everyday life. In fact I can think of one example that was part of my chores when I was growing up. Hint: think of house cleaning. Figure it out? Click here to see what I'm thinking of.

Several factors affect the magnitude of form drag, including the relative velocity of the body with respect to the fluid, the magnitude of the pressure gradient between the front and rear ends of the body, and the size of the surface area that is aligned perpendicular to the flow. Both the size of the pressure gradient and the amount of surface area perpendicular to the fluid flow can be reduced to minimize the effect of form drag on the human body. For example, streamlining the overall shape of the body reduces the magnitude of the pressure gradient. Streamlining minimizes the amount of turbulence created and hence minimizes the negative pressure that is created at the object's rear. Assuming a more crouched body position also reduces the body's projected surface area oriented perpendicular to the fluid flow.

Competitive cyclists, skaters, and skiers assume a streamlined body position with the smallest possible area of the body oriented perpendicular to the oncoming airstream. Even though the low-crouched aeroposition assumed by competitive cyclists increases the cyclist's metabolic cost as compared to riding in an upright position, the aerodynamic benefit is an over tenfold reduction in drag. Similarly, race cars, yacht hulls, and some cycling helmets are designed with streamlined shapes. The aerodynamic frame and handlebar designs for racing cycles also reduce drag.

Streamlining is also an effective way to reduce form drag in the water. The ability to streamline body position during freestyle swimming is a characteristic that distinguishes elite from sub-elite performers. Using a triathlon wet suit can reduce the drag on a competitor swimming at a typical triathlon race pace of 1.25 m/sec by as much as 14% because the buoyant effect of the wet suit results in reduced form drag on the swimmer.

The nature of the boundary layer at the surface of a body moving through a fluid can also influence form drag by affecting the pressure gradient between the front and rear ends of the body. When the boundary layer is primarily laminar, the fluid separates from the boundary close to the front end of the body, creating a large turbulent pocket with a large negative pressure and thereby a large form drag. In contrast, when the boundary layer is turbulent, the point of flow separation is closer to the rear end of the body, the turbulent pocket created is smaller, and the resulting form drag is smaller.

The nature of the boundary layer depends on the roughness of the body's surface and the body's velocity relative to the flow. As the relative velocity of motion for an object such as a golf ball increases, changes in the acting drag occur. As relative velocity increases up to a certain critical point, the theoretical square law is in effect, with drag increasing with the square of velocity. After this critical velocity is reached, the boundary layer becomes more turbulent than laminar, and form drag diminishes because the pocket of reduced pressure on the trailing edge of the ball becomes smaller. As velocity increases further, the effects of skin friction and form drag grow, increasing the total drag. The dimples in a golf ball are carefully engineered to produce a turbulent boundary layer at the ball's surface that reduces form drag on the ball over the range of velocities at which a golf ball travels.

Another way in which form drag can be manipulated is through drafting, the process of following closely behind another participant in speedbased sports such as cycling and automobile racing. Drafting provides the advantage of reducing form drag on the follower, since the leader partially shelters the follower's leading edge from increased pressure against the fluid. Depending on the size of the pocket of reduced pressure behind the leader, a suctionlike force may also help to propel the follower forward.

Wave Drag

The third type of drag acts at the interface of two different fluids, for example, at the interface between water and air. Although bodies that are completely submerged in a fluid are not affected by wave drag, this form of drag can be a major contributor to the overall drag acting on a human swimmer, particularly when the swim is done in open water. When a swimmer moves a body segment along, near, or across the air and water interface, a wave is created in the more dense fluid (the water). The reaction force the water exerts on the swimmer constitutes wave drag.

The magnitude of wave drag increases with greater up-and-down motion of the body and increased swimming sped. The height of the bow wave generated in front of a swimmer increases proportionally with swim ming velocity, although at a given velocity, skilled swimmers produce smaller waves than less-skilled swimmers, presumably due to better technique (less up-and-down motion). At fast swimming speeds, wave drag is generally the largest component of the total drag acting on the swimmer. For this reason, competitive swimmers typically propel themselves underwater to eliminate wave drag for a small portion of the race in events in which the rules permit it. One underwater stroke is allowed following the dive or a turn in the breaststroke, and a distance of up to 15 m is allowed underwater after a turn in the backstroke. In most swimming pools the lane lines are designed to minimize wave action by dissipating moving surface water.