I am beginning an experiment with my honors physics
students dealing with drag. I know of 2 models for the force of
air-resistance - one that is proportional to the speed squared and one
proportional to the velocity. I know little of the specifics of these
forces, except that the density of the air and cross-sectional area of
the object are included in them.
I am going to use model rockets to test our models for which I know drag
doesn't greatly affect. Do you know where I can find more about these
forces? There are constants involved that depend on the objects shape and
it would be nice not to have to find them, but to know them ahead of time.
Thanks for your question -- it sounds like a great lesson. Sorry to say you
know more than I. When I was teaching Physics, I found 'physics teacher'
magazine had some good suggestions. Maybe check out some back issues and
use the search word 'rockets' or 'drag' and see what you get.
Let me take a try at your question. I think I understand what you are
searching for, and it might be easier than you think.
Aerodynamic drag affects any object moving through the air. It is defined as
the sum of parasitic drag and induced drag. The latter is a byproduct of the
production of lift. The lift from an airfoil does not operate in direct
opposition to gravity, but rather perpendicular to the chord line of the wing
... meaning that it has a vertical component (opposing gravity) and a
horizontal component (opposing the thrust). The horizontal component is
considered to be drag - induced drag. In the case of your rockets... what
luck... there is no lift-producing airfoil and therefore (I think) no induced
drag. This drag is the drag that you referred to as being proportional to
speed. (Actually it is inversely proportional because at higher speed the
airfoil has a lower angle of attack and therefore a smaller horizontal
component - induced drag, that is.) A long way to saying that I think in your
project, you can ignore this variety of drag.
Parasitic drag increases with the square of speed. I expect that if you find a
means of measuring this, you will develop a nice exponential curve on your
graph. Each rocket will have come constant based on its design, but this will
only change the position of your graph line, not the shape.
Should be an interesting project.
You might want to find a book in the library - Modern Airmanship, by Van
(sp?). I seem to recall him treating this subject in his book. If you want a
graph of the summation of the two drags, you can find it in a book called
Aviation Fundamentals published by Jeppesen, Sanderson (one of many places).
Best of Luck.
You should be able to find information on "Drag Coefficient" values for
various shapes and in different flow regimes in textbooks on Fluid
Mechanics. Both empirical relations and experimental graphs are
available. Drag force depends on velocity, frontal area, and the drag
coefficient. The latter has a value typically in the 0-3 range depending
on the shapes the fluid Reynolds number. Introductory text on fluid
mechanics such as (Introduction to Fluid Mechanics by John and Haberman)
will give you a quick start on this topic.
All the Best.
Ali Khounsary, Ph.D.
Advanced Photon Source
Argonne National Laboratory
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Update: June 2012