# Resistance, Drag, and Hydro-dynamics

 ©allensswimwear.co.uk Water is 1000 times more resistant than air. In fact, 91% of a person's energy is lost through drag. Therefore, swimmers need to maximize their streamline and reduce the surface area of the human body traveling through the water. The reduced surface area will decrease the resistance and drag. Resistance is the opposing force in water, much like the force of friction.

## Streamlining Form:

In order for swimmers to maximize their speeds, they need to minimize the surface area in which they will be traveling through the water. A larger body will move slower through the water because its larger surface area will create greater resistance. The equation for Resistance is:

R = 1/2 DpAv^2

• p is the density of the water, which depends on the temperature. The density of water is 1 x 10^3 kg/m^3.
• A is the surface area of the body traveling through the water.
• v is the velocity of the body traveling through the water.
• D is the constant for the viscosity of the fluid.
• The smaller the velocity the more linear the equation is. Since the velocity is squared it exponentially affects resistance so it is important to minimize the surface area as much as possible. Minimizing surface area is achieved by tightening the body to resemble a torpedo. Each motion in the water decreases the swimmer's energy and efficiency. Resistance and power increase by squares and sometimes cubes, so to increase speed by ten percent, the energy loss due to swimming would be thirty-three percent. Thus to reiterate, you need to minimize surface area to achieve maximum velocity. Note that the fastest human swimmer will be traveling 4 miles per hour which is 2 meters per second.

 ©abcnews.com The fabric of the Speedo fast-skin suit was designed to be similar to the skin of a shark. A shark was chosen because sharks are mammals with a large surface area, but still have a very fast velocity. Water will travel at differently along the different curves of any object traveling through the water. Therefore, the sharks skin is very hydrodynamic because there are different scale-like patterns, which are situated in different areas of the sharks body to accommodate for the waters movement along the curves of the body. Sharks do not follow the theory that the larger the surface area, the greater resistance. The speedo swimsuits cover the entire body, except hands and feet to minimize drag. It has the design of the sharks skin impeded into the material to make the swimmer more hydrodynamic. For this same reason, swimmers wear swim caps so that drag will be lessened on the surface of the head.

# Buoyancy

Buoyancy is the net upward force which acts on the swimmer because as the depth of the water increases, so does the pressure. So the pressure beneath the swimmer is greater than the pressure above. This is the reasoning behind floatation. The magnitude of the buoyant force is:

F = Wfluid

• F is the net upward force
• Wfluid is the weight of fluid displaced.
• At the surface, there is less resistance because fluid is more resistant than air. It is to the swimmer's advantage to be more buoyant and stay closer to the surface. In order for an object to float the buoyant force needs to be greater or equal to the weight of the water.

To establish more buoyancy swimmers try to "press the T." The horizontal part of the T is the shoulders and the vertical part is the spine. In all swimmeres the upper body is more buoyant because it has a greater surface area, which causes the lower body to sink and not be streamlined. The chest is pressed down because this causes the hips to rise. Pressing the T eliminates this effect and causes the swimmer to be parallel to the surface. Water is 773 times more dense than air. This causes swimmers to float. The higher up a swimmer is in the water, the less water he/her is swimming through. The less water a swimmer displaces will cause him to swim "on top" of the waters surface.

# Propulsion

Swimmers are propelled through the water by a combination of kicking the legs and pulling water with the arms. The arms are used as levers to propel the swimmer through the water. The drag force is opposite the direction of the pulling arm. The greater the flexion in the ankle and the knee joints gives swimmers a greater propulsion because of the greater range of motion to propel the swimmers through the water. The ability of swimmers to hyperextend their knees and ankles provides swimmers with more undulation and a great propulsion through the water. Swimmers have a highest speed when pushing off the walls.

The lift forces arise from a difference in pressure as the fluid travels further and faster around the more curved side of the foil than the less curved side. Thus, a swimmer's hand could act as a foil because the back of the hand is more curved than the front. To generate lift by the Bernoulli Principle the hand should be sculled so that the angle between the hand plane and line of motion of the hand is small. This generates forces, which are mostly lift rather than drag. Thus, swimmers should scull their hands to move most efficiently. The curved motion of the hands means that the force from the arms can act over a greater distance and cause the swimmer to move further per stroke. Since swimming is so inefficient because of the resistance of the water, it is advantageous to increase the power per stroke instead of trying to maximize the number of strokes. To further maximize this propulsion force, the fingers should be together so that the surface area on the levers is maximized and the most water is pulled. While underneath the water, the most efficient motion is undulation with the arms stretched over head in a streamline fashion and the legs together. Together, the legs can create a greater magnitude of force against the water because of their greater surface area.

## What propels swimmers the most their arms or legs?

To kick 100 meters it takes 80 seconds. When kicking, a swimmer can travel at a velocity of 1.25 m/s. To pull 100 meters it takes 60 seconds. When pulling, a swimmer can travel at a velocity of 1.6 m/s. To swim 100 meters with both the arms and the legs it would take 50 seconds. When swimming using both the arms and the legs, a swimmer has a velocity of 2 m/s. The arms therefore generate more propulsion than the legs. The propulsion generated by the legs is 62%. The propulsion generated by the arms is 83%. The ratio of pull to kick is 1.3, meaning that the pull is 1.3 times greater than the kick. Water applies a force perpendicular to each surface of the swimmer's body.

F = PA

The force acting perpendicular to the surface of the swimmer's body is equal to the pressure acting on the swimmer mulitiplied by the surface area. For example, if the Pressure acting on the back of a swimmer's hand 1.3 x 10^5 Pa and the surface area of the back of the hand is 8.3 x 10^-3 m^2 then the equation F = PA would yield:

F = (1.3 x 10^5 Pa) * (8.3 x 10^-3 m^2) = 1079 N.

©Tara Koff, Eddy Matkovich and Kristin McPhillips

This site is a course requirement for Physics 24 at UNC Chapel Hill

Last Updated: April 15, 2004