As a model rocket flies through the air,
aerodynamic forces act on all parts of the
rocket. In the same way that the weight of
all the rocket components acts through the center
of gravity cg, the aerodynamic forces act through a single
point called the center of pressure cp. How do you determine
the location of the center of pressure?
Calculating cp
You can
calculate
the center of pressure. But, in general, this is
a complicated procedure requiring the use of calculus. The
aerodynamic forces are the result of
pressure variations
around the
surface of the rocket. In general, you must determine the
integral of the pressure times the unit normal, times the area, times
the distance from a reference line. Then divide by the integral of
the pressure times the unit normal, times the area. Lot's of work!
For a model rocket, there are some simplifying assumptions that we
can use to make this task much easier. Model rockets are fairly
symmetric about the axis of the rocket. This allows us to reduce the
full three dimensional problem to a simple, two dimensional cut
through the axis of the rocket. For model rockets, the magnitude of
the pressure variation is quite small. If we assume that the pressure
is nearly constant, finding the average location of the pressure
times the area distribution reduces to finding just the average
location of the projected area distribution.
Simplified Calculation of cp
The figure shows a simplified version of the calculation
procedure that you can use to calculate the cp of a model rocket.
We assume that we already know the
projected area and location, relative to some
reference location, of each of the major
parts
of the rocket:
the nose, body tube, and fins. The projected area A of the rocket is
the sum of the projected area a of the components.
A = a(nose) + a(tube) + a(fins)
Since the center of
pressure is an average location of the projected area, we can
say that the area of the whole rocket times the location of the
center of pressure cp is equal to the sum of the
projected area of each
component times the distance d of that component from the reference
location.
A * cp = [a * d](nose) + [a * d](tube) + [a * d](fins)
The "location" of each component is the distance of each
component's center of pressure from the reference line. So you
must calculate or determine the center of pressure of each
of the components. For example, the projected area of the body tube
is a rectangle. The center of pressure is on the axis, half way
between the end planes.
Mechanically determining cp
For a model rocket, there is a simple mechanical way to determine
the center of pressure for each component or for the entire rocket.
Make a two dimensional tracing of the shape of the component, or
rocket, on a piece of cardboard and cut out the shape. Hang the cut
out shape by a string, and determine the point at which it balances.
This is just like balancing a pencil with a string! The point at which the
component, or rocket, is balanced is the center of pressure. You
obviously could not use this procedure for a very large rocket like
the Space Shuttle. But it works quite well for a model.
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