Editing Strouhal number (section)

===Animal locomotion===
In swimming or flying animals, Strouhal number is defined as

:<math> \text{St} = \frac{f}{U} A, </math>
where,
: ''f'' = oscillation frequency (tail-beat, wing-flapping, etc.),
: ''U'' = flow rate,
: ''A'' = peak-to-peak oscillation amplitude.

In animal flight or swimming, [[propulsive efficiency]] is high over a narrow range of Strouhal constants, generally peaking in the 0.2 < St < 0.4 range.<ref name="TaylorNudds2003" /> This range is used in the swimming of dolphins, sharks, and bony fish, and in the cruising flight of birds, bats and insects.<ref name="TaylorNudds2003" /> However, in other forms of flight other values are found.<ref name="TaylorNudds2003" /> Intuitively the ratio measures the steepness of the strokes, viewed from the side (e.g., assuming movement through a stationary fluid) – ''f'' is the stroke frequency, ''A'' is the amplitude, so the numerator ''fA'' is half the vertical speed of the wing tip, while the denominator ''V'' is the horizontal speed. Thus the graph of the wing tip forms an approximate sinusoid with aspect (maximal slope) twice the Strouhal constant.<ref name="Corum2003" />

==== Efficient motion ====
The Strouhal number is most commonly used for assessing oscillating flow as a result of an object's motion through a fluid. The Strouhal number reflects the difficulty for animals to travel efficiently through a fluid with their cyclic propelling motions. The number relates to propulsive efficiency, which peaks between {{val|70|-|80|u=%}} when within the optimal Strouhal number range of {{val|0.2|to|0.4}}. Through the use of factors such as the stroke frequency, the amplitude of each stroke, and velocity, the Strouhal number is able to analyze the efficiency and impact of an animal's propulsive forces through a fluid, such as those from swimming or flying. For instance, the value represents the constraints to achieve greater propulsive efficiency, which affects motion when cruising and aerodynamic forces when hovering.<ref name="Taylor"/>

Greater reactive forces and properties that act against the object, such as viscosity and density, reduce the ability of an animal's motion to fall within the ideal Strouhal number range when swimming. Through the assessment of different species that fly or swim, it was found that the motion of many species of birds and fish falls within the optimal Strouhal range.<ref name="Taylor"/> However, the Strouhal number varies more within the same species than other species based on the method of how they move in a constrained manner in response to aerodynamic forces.<ref name="Taylor"/>

=====Example: Alcid=====
The Strouhal number has significant importance in analyzing the flight of animals since it is based on the streamlines and the animal's velocity as it travels through the fluid. Its significance is demonstrated through the motion of [[Auk|alcids]] as it passes through different mediums (air to water). The assessment of alcids determined the peculiarity of being able to fly under the efficient Strouhal number range in air and water despite a high mass relative to their wing area.<ref name="Lapsansky"/> The alcid's efficient dual-medium motion developed through natural selection where the environment played a role in the evolution of animals over time to fall under a certain efficient range. The dual-medium motion demonstrates how alcids had two different flight patterns based on the stroke velocities as it moved through each fluid.<ref name="Lapsansky"/> However, as the bird travels through a different medium, it has to face the influence of the fluid's density and viscosity. Furthermore, the alcid also has to resist the upward-acting buoyancy as it moves horizontally.