Movement through fluids

Introduction

One of the strongest effects on the morphology (body shape) of animals is through the interaction with the physical requirements of their environment. In particular, the need to move efficiently has produced drastic effects on animal form. Efficient motion benefits the organism in a variety of ways, for example, by decreasing energy costs and/or increasing speed (important for both predators and prey). One of the areas where this is most obvious is in movement through fluid environments. The term fluid applies to both liquids and gases since these objects are able to flow, meaning that organisms moving through both air and water are subject to the physics of fluids. When the fluid is moving relative to an object in the fluid, the object is acted on by a drag force. The relative nature of the motion is important – it can be caused by motion of a body through motionless fluid, movement of fluid past a stationary body, or a combination of both the body and the fluid moving. The drag force is in the same direction as the relative movement of the fluid.

Three factors determine the amount of drag force on a particular object in a given fluid:

1.  The drag coefficient – this is a particular value for each object that has to be determined by experiment, and can vary somewhat with the object’s velocity.

2.  The cross-sectional area of the object – the measurement of the largest area that the object presents perpendicular to the direction of the motion (figure 1).

Figure 1: Motion of an object in a fluid. The dashed line indicates the plane that would indicate the cross-sectional area for this object.

3.  The velocity of the object – the faster the object is moving, the more drag it experiences.

Biophysics of Movement through Fluids

When moving through air, the drag force is generally minor, until high speeds are reached. This is something that you have experienced when riding in a car with open windows. At slow speeds the amount of air that is moving is minor, but as speed increases so does the amount of air movement, and with it the amount of drag. Due to the greater density of water, drag forces are a major factor for an organism moving through an aquatic environment, even at low speeds. This fact has lead to some of the strongest examples of convergent evolution – evolution that produces very similar morphologies in unrelated species. Among aquatic animals, a particular body shape has evolved in several different lineages of vertebrates due to the strong drag forces present in water. An object moving through an aquatic environment causes the water to flow around the object. As the water moves around the object, it flows in lines parallel to the object (a process known as laminar flow). When the water reaches the back side of the object, if the flow pathways of water interact too abruptly, they produce turbulence, a chaotic mixing of the water flows that increases the drag on an object as it moves (figure 2a). If the water can continue with laminar flow after it passes by then turbulence is decreased (figure 2b). A round object moving through water experiences turbulence quite often, while a teardrop-shaped object experiences less. The amount of turbulence that develops is also affected by the speed of motion, but at any given speed the teardrop shape will experience less. For this reason, evolution has repeatedly produced aquatic organisms that possess this sort of body shape, including fish, dolphins, and aquatic reptiles.

Figure 2: Motion of differently shaped objects through water. Arrows indicate the direction of motion. The blue lines represent the displacement path of the water.

While it is true that organisms moving through air generally encounter less drag and turbulence there is at least one situation where these issues can have important effects on movement: flight. When a bird is flying, the movement of air over its wings is the source of lift to keep the bird in the air. If air flow is too slow or too turbulent, the animal will not be able to keep itself in the air. To address this problem, the wings of flying animals can change shape, taking on a particular shape called an airfoil (figure 3).

Figure 3: cross-section of an airfoil. Blue lines represent movement of air around the wing. The arrow represents the direction of movement.

Figure 3 shows the movement of air over an airfoil; the path of air differs on top and bottom of the airfoil. Partly due to the different paths of airflow, lift is produced. In actuality, this description applies more to a rigid, non-moving wing, like that found on an airplane – the situation is much more complex in animals, and is still being studied in an attempt to develop an understanding of the biophysics. While this explanation is an over-simplification, the basic ideas that we encountered in aquatic organisms apply as well – a particular shape to the body (and the wings) tends to evolve by convergent evolution to produce the minimum amount of drag during flight. The effects of convergent evolution can be seen in the wings of birds, bats, and pterosaurs, the only vertebrates to develop true flight.

During flight, the angle of the wing as it moves through the air has important implications for the ability of the wing to provide lift. The angle of attack is the amount that the wing deviates from a horizontal line. As this angle goes up, the risk of turbulence increases (figure 4).

Figure 4: angle of attack. As the angle of attack increases, turbulent airflow increases. Blue lines represent movement of air around the wing. The arrow represents the direction of movement.

Unfortunately, as a flying object comes in to land, the angle of attack must increase, and the velocity of flight must decrease. These two factors together tend to increase turbulence, causing an increase in drag, making it very difficult for flight to be maintained. To avoid crashing, planes use a structure called a flap to maintain laminar flow and prevent turbulence. Bird wings have a similar structure called an alula (figure 5) that serves the same function. The wings of bats have a similar ability, showing another example of convergent evolution in action.

Figure 5: the alula is visible on the leading edge of this wing, serving to maintain laminar flow as the bird prepares to land.

Additional Readings

Fish, F.E. and Lauder, G.V. 2006. Passive and active flow control by swimming fishes and mammals. Annual Review of Fluid Mechanisms. 38: 193-224.

Halliday, D., Resnick, R., and Walker, J. 1993. Fundamentals of physics, extended, 4th ed. John Wiley & Sons, Inc. New York.

Kardong, K.V. 2006. Vertebrates: comparative anatomy, function, evolution, 4th ed. McGraw Hill. New York.

Koehl, M.A.R. 1996. When does morphology matter? Annual Review of Ecology and Systematics. 27: 501-542.

Pettersson, L.B. and Hedenstrom, A. 2000. Energetics, cost reduction and functional consequences of fish morphology. Proceedings: Biological Sciences. 267: 759-764.

Walker, J.A., and Westneat, M.W. 2000. Mechanical performance of aquatic rowing and flying. Proceedings: Biological Sciences. 267: 1875-1881.

Experiment

In this activity you will be studying the effects of body shape on drag. Specifically, you will take various body designs of similar masses and try to determine which factors are most important in producing an efficient swimming body shape.

Needed materials

1.  Tea candles (4)

2.  Swim tank (this should be assembled by your instructor before you arrive in lab)

3.  Fishing line with leaders attached

4.  Various objects to attach to your candles to change their area

5.  Stopwatch

6.  Calipers

In this exercise, you will build various models using the tea light as a base and adding various pieces of plastic or other material to the candle to vary its cross-sectional area. By testing the ability of different body plans to “swim” through the water, you can test your understanding of the dynamics of movement through a viscous substance like water. The design of the apparatus is shown below in figure 1.

Figure 1: basic apparatus for experiment.

By attaching the test object to a string running down to a movement mass, the test object will “swim” across the container until it strikes the opposite wall. This will allow you to time the movement of the test object and make relative comparisons between different body shapes. You should note that the movement mass is held above the bottom of the container by fishing line. This is to prevent friction with the bottom of the container from affecting the movement of the object. You will also attach a “stabilizing mass” to the opposite end of the test mass to prevent it from moving too quickly. You will want to check with your instructor for the amounts that you start these masses with. You may want to experiment with them – an object that moves too quickly may provide inaccurate data just like one that moves too slowly.

Procedure

1.  You should work with a group of students to form a group of 3-5 students.

2.  For each group, students should get a container, enough material to build four test objects, one movement mass, and one stabilizing mass.

3.  Use the screws provided by your instructor to attach the fishing line leaders to your first test object (a single tealight candle). Pull the candle out of its aluminum holder. There is an aluminum piece attached to the bottom of the wick. By putting the candle back into its aluminum holder backwards (figure 2), you will have two metal pieces to attach to your screws, and the candle should be held more tightly.

Figure 2 - Tealight candle. A) Candle in its holder. B) Candle out of its holder, showing the aluminum piece on the bottom of the candle.

4.  Assemble your movement and stabilizing mass as instructed.

5.  Build your other test objects. The students in each group should decide on the shape of their test objects before they begin building them. As part of this process, you should develop hypotheses about how the different shapes will move through the water and why that is the case. Once you have decided on the appropriate shapes, you should build each one using a candle as your starting point. Begin by inserting a screw with a loop to into each side of the candle – these will serve as the point to attach the line that pulls on the test object (figure 3)

Figure 3 – Candle with eye screws attached

6.  Use glue to attach the projections to the candle (figure 3). When you attach material to your movement object, you’ll want to make sure that the pieces are as even as possible. You should attach your projections to the same side of the candle (although you can use either side). The “front” of the candle will be the screw that is attached to the candle holder, not the side with the wick of the candle, as this might cause additional drag, which could distort your results.

Figure 4: A test object with projections attached to the “front” of the candle

7.  Weigh the movement mass, stabilizing mass, and the test objects. Record these values on the data sheet.

8.  Use the calipers to measure the size of each candle and projections that are attached to it, perpendicular to the direction the object will be moving. Use this to calculate the cross-sectional area for each object. Sketch a diagram of each object with the appropriate measurements on the data sheet.

9.  Measure the length of the container. You should only measure the space between the pulleys as the object can only move through this distance (figure 5). You may also need to adjust this based on the actual distance the test object can move, as the fishing line leaders may further limit the distance the object can move.

Figure 5 – container with length indicated

10.  Attach one end of the string to the movement mass and the other end to the stabilizing mass. The movement and stabilizing masses should be suspended over the edge of the lab bench so that when the test object is released the movement mass will drop downward and pull the test object through the water. (figure 6)

Figure 6 – container with movement and stabilizing masses attached

11.  Fill the container with water so that it will easily cover the test object (the amount of water needed will vary with the size of the container).

12.  Designate one group member to each of the following jobs:

  1. Timer
  2. Data recorder
  3. Releaser
  4. Observer

13.  The releaser will take the test object to be tested, pull it to the end of container opposite the pulley and hold it there. You will want to be sure that you pull on the string, as opposed to pulling on the object itself, as this runs the risk that the string will detach. You want to be sure that the object is at the same point for each trial.

14.  The releaser will release the test object and say “start” so that the timer can start the stopwatch.

15.  The observer will need to watch the motion of the object, and describe that motion, making note of factors such as:

  1. Whether or not the test object moved constantly
  2. If the test object moved in a straight line or if it “tumbled”
  3. Any other factors that could have affected the motion of the object.

16.  When the test object reaches the opposite side of the container, the releaser says “stop” so the timer can stop the stopwatch.

17.  The data recorder records all the data for the trial.