Maths encyclopedia and lessons  
Search

Mathematics Encyclopedia and Lessons

 
     
 

Lessons

Popular
Subjects

algebra
arithmetic
calculus
equations
geometry
differential equations
trigonometry
number theory
probability theory
more
 

References

applied mathematics
mathematical games
mathematicians
more
 
 

Denny's paradox

In the study of animal locomotion, Denny's paradox refers to the apparent impossibility of surface-dwelling animals such as the water strider generating enough propulsive force to move. It is named for Mark Denny .

If capillary waves are assumed to generate the momentum transfer to the water, the animal's legs must move faster than the phase speed cm of the waves, given by

c_m=\left(4g\sigma/\rho\right)^{1/4}

where g is the gee, σ is the strength of surface tension, and ρ the density of water. For standard conditions, this works out to be about 0.23 m/s.

Infant water striders' legs move at speeds much less than this and, according to this physical picture, cannot move. For a resolution of Denny's paradox, see water strider.

01-04-2007 01:18:14
The contents of this article are licensed from Wikipedia.org
under the GNU Free Documentation License. How to see transparent copy