This page introduces students to different kinds of flight by comparing birds with different wing profiles to common airplanes with similar shapes (and modes of flying). Students will recognize that differently shaped wings are
suited to different kinds of flying.

Topics introduced are Wing Load and Wing Ratio; these ideas describe the mathematics
that determine a bird's flying speed, efficiency, and maneuverability. These topics lend themselves to a math activity, described below.



The costs of flight are influenced by the relationship between total wing area
and body mass. In other words, how many grams of mass each unit area of
wing surface must carry.

To achieve and maintain flight, a bird has to have tremendous muscles. Over
30 percent of a hummingbird's weight is in its flight muscles. In fact, the
flapping motion is one of the most strenuous activities in the entire animal
kingdom. The heavier the bird, the more difficult is flight.

The top weight range of flying birds is about 20 - 30 pounds. Examples are
mute swans, California condors, and some pelicans. The Andean Condor
weighs 30 lbs., while Bee Hummingbird is only 1.95 grams.

Birds use a great amount of energy for flight, almost 15 times as much as
when perched on a branch resting. To fuel their muscles, birds eat
high-energy foods and store much of the energy as fat. These energy
reserves are used when food is scarce as well as by migratory birds
that fly non-stop over vast distances of water.

Consider the lifestyle of a bird. It must hunt for food, travel, protect itself
from predators, and raise a family. Add to these activities, the high
amount of energy needed for flight. It is no wonder that birds limit their
flying. In fact there are over 35 species of birds that no longer fly and
many more that only fly rarely. When not on a hunt to fill their stomachs,
even our everyday birds limit their flying to conserve energy.


To build on wing load and aspect ratio equations students will solve for
variables practicing with teacher utilizing given data
of another bird or set measures given the following formulas:

Bird Weight / Wing Area=Load

Length / Width=Ratio

After completing practice sessions, teacher will then assign students to plot the
variables working backwards with the formulas/measures to gain the correct
variables, or forward to obtain the answer. The educator can obtain independent
measures for a different species of bird or can utilize the corresponding
measures for the Wandering Albatross, our selected species, plugging in the
following data:

Median weight of a Wandering Albatross = 20 lbs. which equals 9,072 grams
Wing Load = 1.7 grams/cm² (given)

Bird Weight / Wing Area = Load

Solving for Wing area:

  1. 9072 grams / A = 1.7 grams/cm²
  2. 9072 grams = 1.7 grams/cm² (A)
  3. 9072 grams / 1.7 grams/cm² = A
  4. A = Wing Area = 5336.5 cm²
  5. Wing area (wing area = wing length * wing width) = 5,336.5 cm²
  6. 9,072 grams/5,336.5 cm² = 1.7 grams/cm² wing load

Wing Area = Wing Length * Wing Width

Length of a Wandering Albatross Wing = 340 cm
Wing area of a Wandering Albatross = 5,336.5 cm²

Solving for Wing width of a Wandering Albatross:

  1. 5,336.5 cm² = 340 cm * w (wing width)
  2. 5,336.5 cm²/340cm = w (wing width)
  3. 15.7 cm = w (wing width for Wandering Albatross)
  4. 5,336.5 cm² = 340cm * 15.7 cm

Wing Length/Wing Width = Wing Ratio

Wing Length of a Wandering Albatross = 340 cm
Wing width of a Wandering Albatross = 15.7 cm

Solving for Wing ratio:

  1. Wing length / wing width = Wing ratio
  2. 340cm / 15.7cm. = r
  3. r = 21.7
  4. Wing ratio = 21.7

Another activity that students may participate in is the paper wings project.


  • ½ sheet of paper cut lengthwise
  • Ruler
  • Tape


  1. Fold paper in half widthwise.
  2. Tape top edge of the paper so that it is about ½ inch from the
    bottom edge. A curve will be created.
  3. Slide the wing over the ruler, curved side facing you, seam
    facing you.
  4. Hold the ruler in front with the wing hanging down and blow
    straight across the folded seam
  5. The papers will lift because of Bernoulli's principal.


There is lower air pressure on top of the paper because the air is moving faster. Higher air pressure on the bottom pushes up on the wing.

  Hunters & Hunted
  What's for Lunch?
  How's the Water
  Beaks are Tools
  Backyard Birdfeeder
Shapes & Sizes
  Lift Off
  A Big Enough Wing
  Migration Hopscotch
  Sing Out Loud
  Virtual Incubator
  Dance of Love
  On the Egg
  Becoming a Bird
  The Big Deal: The Feather
  Dead or Alive
  Are Birds Dinosaurs?

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