370
a
-..wave velocity U w
b
11 Locomotion of Marine Animals
forward velocity V
-.
/ r b ,
--~_\ -.
,
I
X
- ;
Fig. 11.2: Diagram of forces acting on swimming flagella: a flagella propels itself at
speed U, b force components on tail segment
The total thrust generated by a wavy flagellum can be represented as the sum of
the forces produced by many small cylindrical segments (Fig. 11.2). Assuming
that a particular segment is oriented at an angle, (), to the horizontal plane,
the thrust, FT , produced by that segment becomes:
(11.41)
As the drag coefficient C~n) is always greater than c~t), an inclined cylinder
moving through a fluid generates a force normal to the direction of motion.
This simple method of calculation of the thrust is known as the resistive theory,
developed originally by Gray and Hancock (1955). There are a number of
extensions of the resistive theory to some flagellar waveforms and other motile
structures, some of which are listed by Holberton (1977). For example, for a
plane sine wave on a smooth flagellum propelling a spherical body, Gray and