364
11 Locomotion of Marine Animals
Table 11.2: Drag coefficients for some marine organisms (adapted from Chamberlain, 1991; Vogel, 1994)
Animal
Re
Cd
Area
Cephalopod, Nautilus
100,000
0.48
v
Sturgeon, Acipenser fulvescens
0.0053
w
Trout, Salmo gairdneri
50,000-200,000 0.015
w
Mackerel, Scomber
100,000
0.0043
w
Mackerel, Scomber
175,000
0.0052
w
Saithe, Pollachius virens
500,000
0.005
w
Pike, Esox sp.
0.008
w
Sea lion, Zalophus californ.
2,000,000
0.0041
w
Seal, Phoca vitulina
1,600,000
0.004
w
so called 'plan form area', or 'profile area' are also used as a measure of surface,
S. It is area that one would see from above.
Outline of Elongated Body Theory. When a fish swims at a constant speed
in a straight line its momentum is constant and any momentum given to the
water in one direction must be balanced by an equal momentum in the opposite
direction. Many marine animals use this principle of propulsion by giving the
fluid backward momentum. Let the animal velocity be U; the corresponding
thrust is F, and a backward fluid velocity induced by the animal is - U'. Thus,
the accelerated mass of fluid (in unit time) due to thrust F becomes F/U', and
the kinetic energy given to the fluid (in unit time) is 1/2(F /U')U,2 = FU' /2.
This is the wasted power used for driving the fluid backwards and it is not used
for driving the animal forward. The useful power is simply Fdx/dt = FU. A
measure of the efficiency of the propulsion mechanism is known as Froude
efficiency (Alexander, 1977):
useful power
U
Froude efficiency =
-
.
useful power + powerlost to fluid U + ~U'
(11.23)
Thus, the efficiency becomes higher when the animal accelerates a large mass
of fluid (per unit time) to a low velocity (small U'), rather than accelerating a
small mass to a high velocity (high U').
Aquatic organisms swim by transferring momentum from moving portions
of their body to the fluid surrounding them. The amount of generated thrust
depends on the rate at which the animal transfers momentum. The complicated mechanism underlying the exchange of momentum depends on size and
11 Locomotion of Marine Animals
Table 11.2: Drag coefficients for some marine organisms (adapted from Chamberlain, 1991; Vogel, 1994)
Animal
Re
Cd
Area
Cephalopod, Nautilus
100,000
0.48
v
Sturgeon, Acipenser fulvescens
0.0053
w
Trout, Salmo gairdneri
50,000-200,000 0.015
w
Mackerel, Scomber
100,000
0.0043
w
Mackerel, Scomber
175,000
0.0052
w
Saithe, Pollachius virens
500,000
0.005
w
Pike, Esox sp.
0.008
w
Sea lion, Zalophus californ.
2,000,000
0.0041
w
Seal, Phoca vitulina
1,600,000
0.004
w
so called 'plan form area', or 'profile area' are also used as a measure of surface,
S. It is area that one would see from above.
Outline of Elongated Body Theory. When a fish swims at a constant speed
in a straight line its momentum is constant and any momentum given to the
water in one direction must be balanced by an equal momentum in the opposite
direction. Many marine animals use this principle of propulsion by giving the
fluid backward momentum. Let the animal velocity be U; the corresponding
thrust is F, and a backward fluid velocity induced by the animal is - U'. Thus,
the accelerated mass of fluid (in unit time) due to thrust F becomes F/U', and
the kinetic energy given to the fluid (in unit time) is 1/2(F /U')U,2 = FU' /2.
This is the wasted power used for driving the fluid backwards and it is not used
for driving the animal forward. The useful power is simply Fdx/dt = FU. A
measure of the efficiency of the propulsion mechanism is known as Froude
efficiency (Alexander, 1977):
useful power
U
Froude efficiency =
-
.
useful power + powerlost to fluid U + ~U'
(11.23)
Thus, the efficiency becomes higher when the animal accelerates a large mass
of fluid (per unit time) to a low velocity (small U'), rather than accelerating a
small mass to a high velocity (high U').
Aquatic organisms swim by transferring momentum from moving portions
of their body to the fluid surrounding them. The amount of generated thrust
depends on the rate at which the animal transfers momentum. The complicated mechanism underlying the exchange of momentum depends on size and