posted on Sep, 10 2004 @ 11:46 PM
For those who have more time on their hands can solve for the correct rate of descent, provided one knows the exact dimension and weight of the probe
returning to earth.
What follows below is a small excerpt from NASA's website.
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An object which is falling through the atmosphere is subjected to two external forces. One force is the gravitational force, expressed as the weight
of the object. The other force is the air resistance, or drag of the object. The motion of any object can be described by Newton's second law of
motion, force F equals mass m times acceleration a:
F = m * a
which can be solved for the acceleration of the object in terms of the net external force and the mass of the object:
a = F / m
Weight and drag are forces which are vector quantities. The net external force F is then equal to the difference of the weight W and the drag D
F = W - D
The acceleration of a falling object then becomes:
a = (W - D) / m
The drag force depends on the square of the velocity. So as the body accelerates its velocity and the drag increase. It quickly reaches a point where
the drag is exactly equal to the weight. When drag is equal to weight, there is no net external force on the object and the object falls at a constant
velocity as described by Newton's first law of motion. The constant velocity is called the terminal velocity .
We can determine the value of the terminal velocity by doing a little algebra and using the drag equation. Drag depends on a drag coefficient, Cd the
air density, r the square of the velocity V and some reference area A of the object:
D = Cd * r * V ^2 * A / 2
At terminal velocity, D = W. Solving for the velocity, we obtain the equation
V = sqrt ( (2 * W) / (Cd * r * A) )
The terminal velocity equation tells us that an object with a large cross-sectional area or a high drag coefficient falls slower than an object with a
small area or low drag coefficient. A large flat plate falls slower than an a small ball with the same weight. If we have two objects with the same
area and drag coefficient, like two identically sized spheres, the lighter object falls slower. This seems to contradict the findings of Galileo that
all free falling objects fall at the same rate with equal air resistance. But Galileo's principle only applies in a vacuum, where there is NO air
resistance and drag is equal to zero.
The drag coefficient is a number which aerodynamicists use to model all of the complex dependencies of drag on shape, inclination, and some flow
conditions. The drag coefficient Cd is equal to the drag D divided by the quantity: density r times reference area A times one half of the velocity V
squared.
Cd = D / (.5 * r * V^2 * A)
This slide shows some typical values of the drag coefficient for a variety of shapes. The values shown here were determined experimentally by placing
models in a wind tunnel and measuring the amount of drag, the tunnel conditions of velocity and density, and the reference area of the model. The drag
equation given above was then used to calculate the drag coefficient. The projected frontal area of each object was used as the reference area. A flat
plate has Cd = 1.28, a wedge shaped prism with the wedge facing downstream has Cd = 1.14, a sphere has a Cd that varies from .07 to .5, a bullet Cd =
.295, and a typical airfoil Cd = .045.
We can study the effect of shape on drag by comparing the values of drag coefficient for any two objects as long as the same reference area is used
and the Mach number and Reynolds number are matched. All of the drag coefficients on this slide were produced in low speed (subsonic) wind tunnels and
at similar Reynolds number, except for the sphere. A quick comparison shows that a flat plate gives the highest drag and a streamlined symmetric
airfoil gives the lowest drag, by a factor of almost 30! Shape has a very large effect on the amount of drag produced. The drag coefficient for a
sphere is given with a range of values because the drag on a sphere is highly dependent on Reynolds number. Flow past a sphere, or cylinder, goes
through a number of transitions with velocity. At very low velocity, a stable pair of vortices are formed on the downwind side. As velocity increases,
the vortices become unstable and are alternately shed downstream. As velocity is increased even more, the boundary layer transitions to chaotic
turbulent flow with vortices of many different scales being shed in a turbulent wake from the body. Each of these flow regimes produce a different
amount of drag on the sphere. Comparing the flat plate and the prism, and the sphere and the bullet, we see that the downstream shape can be modified
to reduce drag.
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Don't forget, the exact speed would also hinge on the rate of rotation of the probe returning to earth (X-Y axis) since that would increase and
decrease the aerodynamics of the object. These numbers would probably be very insignificant. This is where the Cd, or Drag Coefficient, comes into
place.
I'll wait 'till the movie comes out....
NVBadBoy
[edit on 11-9-2004 by NVBadBoy]