Hodograph
From Wikipedia, the free encyclopedia
A hodograph is diagram giving a vectorial representation of the movement of a body or a fluid. The position of any plotted data on such a diagram is proportional to the velocity of the moving particle. It is also called a velocity diagram. It appears to have been used by James Bradley, but for its practical development is mainly from Sir William Rowan Hamilton, who published an account of it in the Proceedings of the Royal Irish Academy in 1846.
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[edit] Applications
It is used in physics, astronomy and fluid mechanics to plot deformation of material, motion of planet or any other data that involves the velocities of different part of a body.
[edit] Meteorology
In meteorology, hodographs are used to plot winds from sounding of the Earth's atmosphere. It is a polar diagram where wind direction is indicated by the angle from the center axis and its strengh by the distance from the center. In the figure to the right, at the bottom one finds values of wind at 4 heights above ground. They are plotted by the vectors 
to 
. One has to notice that direction are plotted as mentionned is the upper right corner.
With the hodograph and thermodynamic diagrams like the tephigram, meteorologists can calculate:
- Wind shear: The lines uniting the extremeties of successive vectors represent the variation in direction and value of the wind in a layer of the atmosphere. Wind shear is important information in the development of thunderstorm and future evolution of wind at these levels.
- Turbulence: wind shear indicate the possible turbulence that would cause a hazard to aviation.
- Temperature advection: change of temperature in a layer of air can be calculated by the direction of the wind a that level and the direction of the wind shear with the next level. In the northern hemisphere, warm air is to the right of a wind shear between levels in the atmosphere. The opposite is true in the southern one (see thermal wind). So in the example hodograph, the wind
from southwest meet the right side of the wind shear which means a warm advection and thus warming of the air at that level.
[edit] Further reading
- Feynman's Lost Lecture — The Motion of Planets Around the Sun by David L. Goodstein & Judith R. Goodstein (ISBN 0-393-03918-8, W.W.Norton & Company: New York, 1996). In this book the hodograph is used to geometrically derive elliptical (Keplerian) orbits from Newton's laws of motion and gravitation.
[edit] External links
- The Hodograph - Dr. James B. Calvert, University of Denver
