The Art of Fly-Fishing

Norman Maclean's novella—"A River Runs Through It"—begins with the statement: "In our family, there was no clear line between religion and fly-fishing." Many fishing enthusiasts feel that fly-fishing is at least an art, if not a spiritual endeavor. What is so special about fly-fishing?

Fly-fishing uses tiny yarn and feather lures that resemble actual flies in order to trick fish into thinking that there is a meal at the end of the line. A fly-fisherman casts the line so that the lure lands delicately on the water just as a fly would. The form is very important and difficult to master, which is one reason that fly-fishing has a reputation for being as much an art as a sport.

While one can fly-fish for many fish species, including bluegill, bass, pike, and tarpon, trout are the species most often associated with fly-fishing. Trout are known for their picky eating habits, so fly-fishing is an effective way of tricking them into biting the lure.

• Read a tribute to the sport in ENN's feature: "fly-fishing."

As U.S. rivers become ever more polluted and dams disrupt natural waterways, trout and other fish species are at risk in their natural habitats. As a group, fly-fishermen are generally concerned about the environment. They recognize that if fish populations are depleted, they will have no fish to catch.

The Nature Conservancy (TNC) is an organization that owns stretches of Silver Creek in Idaho. Only fly-fishing is allowed on TNC property, and anglers must release any fish that they catch.

• Read about how another group of fishermen is helping study the impact of acid rain on fish populations in the CNN article: "Virginia anglers fish for clues to acid rain."

Learn about the Problem

When casting a flyline, fishermen try to attain a graceful parabola that imitates a fly's motion over the water. The path and landing of the line are important, in order to convince the fish that the lure is a real fly.

• You can analyze parabolic motion in the Tangible Math activity, Parabolic Motion of Animals.
  
  
• For additional work with parabolas, see the Destination Math activities, Algebra I, Course 2: Graphing Parabolas and Analyzing Properties of Parabolas.

Think about the Problem

Consider the equation for vertical motion of a fly-fishing lure:

y = at² + bt + c

where
  y = the vertical distance above the ground
  t = time
  and a, b, and c are parameters dependent on the particular cast.

The line moves horizontally from left to right along the x-axis at the same time as it moves vertically according to the equation.

Describe how each of the following factors might affect the values of a, b, and c:

• the length of the rod
  
  
• the weight of the lure
  
  
• the height of the angler
  
  
• the velocity with which the line is cast
  
  

• Students may be curious about fly-fishing, even if they do not intend to fish themselves. They can learn about the basics at Beginner's Netguide to Flyfishing.
  
  
  
• Fishing enthusiasts fly-fish on lakes as well as in streams and rivers. The Great Lakes Information Network offers information about the environment, ecosystem, economy, and tourism of the Great Lakes.
  
  
• Students can encounter other aspects of parabolas in the following activities and sites:
  
  
  • Tangible Math: The Trajectory of a Ball: This activity explores the graph of a parabola and the trajectory of a basketball attached to an equation of the form y = ax² + bx + c.
    
    
    
    
  • Parabola: This page summarizes important points about parabolas.