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Air Resistance Formula
Name: Jeffrey F.
Status: student
Age: 20s
Location: N/A
Country: N/A
Date: 2000-2001
Question:
My question concerns the force equation for air
resistances, specifically, the quadratic drag equation: F=.5DrCV^2
Replies:
I developed a derivation for this equation by using the concepts
presented in the development of the ideal gas laws relating pressure to
the motion of the gas molecules bouncing off the container walls.
However, it seemed to me that it was necessary to ignore the
translational motion of the air molecules when calculating the impulse
experienced by an object due to the change in momentum of the air
molecules. Only when ignoring the translation motion of the air
molecules does my equation integrate into the above equation.
Is the translational motion associated with the air molecules ignored
in that equation? If so, how can it even be valid?
When dealing with fluids on the molecular level, it is important to separate
translational motion of the fluid from the random vibrations of individual
molecules. The 400 m/s motion of a nitrogen molecule due to its temperature
is a random vibration. Consider air without significant wind. There are
just as many air molecules moving north as south, and just as fast. So long
as the moving object is much slower than the vibrational speed of the
molecules, the effects of vibrational motion will balance.
Any variation due viscosity is within the initial constant, C. It is not
actually a constant. "C" can be anywhere from 0.4 to 1 in common
situations. A slightly more viscous fluid will have a slightly higher value
of C. The major effect of temperature is within the density. A higher
temperature results in a lower density. The "constant" also accounts for
effects such as shape of the moving object. For a given situation, however,
C will be fairly constant so long as the object speed doesn't vary a great
deal.
I am aware that the equation will provide a good approximation of drag
when the fluid is moving slowly compared to the speed of the object.
My concern is that the motion of the air is usually much faster than the
speed of an object traveling through it. At about 26 degrees Celsius, A
Nitrogen
molecule travels somewhere in the ball park of 400 m/s. I feel that the
equation is
not adequate because it does not seem to incorporate the notion that the
speed of the
fluid is very high. The equation also seems to ignore the viscosity of air
itself.
I feel that the dynamics of a fluids are still a mystery, an I am just
looking for a little insight.
It is important to realize that many equations used in science are
approximations. The drag force is useful when the object moving
through the air is moving much faster than the air itself. When in a
fluid with a
large current, a scientist must view the motion relative to the fluid. True
drag is more complicated, depending on factors such as aerodynamics and
temperature. The drag equation is a very good approximation if the
fluid is not moving too fast or is not too thick. The equation can not be
used
with honey as the fluid.
Kenneth Mellendorf
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Update: June 2012
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