## How Do Birds Compare?

## Opening

# How Do Birds Compare?

Predict the range where you think all birds have Strouhal numbers that are close to each other.

Predict the range where you think all birds have Strouhal numbers that are close to each other.

As you solve today's problems, use the problem-solving process.

- Understand the problem situation.
- Represent the situation.
- Answer the question.
- Check that the mathematical answer makes sense.

Create a graph showing the Strouhal numbers for different birds and bats and then compare the data to the Strouhal number for a dolphin.

- Create a graph that shows the given Strouhal numbers for the following birds and bats.
- Woodpecker: 0.22
- Albatross: 0.25
- Fruit bat: 0.40
- Pigeon: 0.20
- Hummingbird: 0.259
- Swan: 0.20
- Osprey: 0.23
- Free-tailed bat: 0.31
- Starling: 0.30

- What is the range of Strouhal numbers for the birds and bats represented on the graph?
- Represent the Strouhal numbers on the vertical axis using the numbers 0 to 0.5 (in 0.1 increments). Place the names of the birds and bats along the horizontal axis.

The dolphin has a cruising speed of 15 meters per second, an amplitude of 3 meters, and a flapping frequency of 1.5 beats per second.

- Predict whether the dolphin’s Strouhal number will fall within the range you calculated for the birds and bats.
- Calculate the Strouhal number for the dolphin and compare it to your prediction.

Prepare a presentation of your findings. Justify all your findings with mathematical explanations.

- How could Strouhal numbers help you design a flying robot?
- Consider how the Strouhal numbers for flying and swimming animals are related.
- If you were designing a flying robot, how could this relationship help you with your design? Consider wing amplitude, frequency, and flying speed.

Take notes about other classmates’ graphs, and their use of the problem-solving process.

Write a reflection about the ideas discussed in class today. Use the sentence starter below if you find it to be helpful.

**The strategy I used to find the range of the Strouhal numbers for birds and bats is…**