As a rocket flies through the air,
it both
translates
and
rotates.
The rotation occurs
about a point called the center of gravity. The
center of gravity is the average location of the
weight
of the rocket. The mass and weight are distributed
throughout the rocket, and for some problems, it is important to know
the distribution. But for rocket trajectory and
maneuvering,
we need to be concerned with only the total weight and the location
of the center of gravity.
How would you determine the location of the
center of gravity?
Calculating cg
A model rocket is a combination of many
parts;
the nose cone, payload, recovery system, body tube,
engine,
and fins.
Each part has a weight associated with it which you can
estimate, or calculate, using Newton's
weight equation:
w = m * g
where w is the weight, m is the mass, and
g is the gravitational constant which is 32.2 ft/square
sec in English units and 9.8 meters/square sec in metric units
on the surface of the
Earth.
On the
Moon and
Mars,
the gravitational constant and the resulting weight is less than
on Earth.
To determine the center of gravity
cg,
we choose a reference location,
or reference line. The cg is determined relative to this reference
location.
The total weight of the
model rocket is simply the sum of all the
individual weights of the components. Since the center of gravity is
an average location of the weight, we can say that the weight of the
rocket W times the location cg of the center of gravity
is equal
to the sum of the weight w of each component times the distance d
of that component from the reference location:
W * cg = [w * d](nose) + [w * d](recovery) + [w * d](engine) + ...
The center of gravity is the massweighted average of the component
locations.
Components' Location
On the slide, we show the weight and distance of the nose cone
from the reference line. A similar distance can
be determined for each component
relative to the reference line. How do we determine the distance d?
Using the nose cone as an example,
the "distance" of the nose dn is the distance of the
cg of the nose relative to the reference line.
So we have to
be able to calculate or determine the cg of the nose cone
and each of the other rocket components.
For some simple shapes, finding the cg, or average location
of the weight, is quite simple. For example, when viewed perpendicular
to the axis, the body tube is rectangular. The cg is
on the axis, halfway between the end planes. For other shapes,
like the nose cone, determining the cg of the component is
not so simple. There is a technique for
determining the cg of any general shape, and the
details of this technique is given on another
page.
Determining cg Mechanically
For a small model rocket, there is a simple mechanical way to determine
the cg for each component or for the entire
rocket:

For simple geometries
we just balance the component or the entire rocket using
a string or an edge. The point at which the component or rocket
is balanced is the center of gravity. This is just like balancing a
pencil on your finger! Obviously, we could not use this procedure
for a large rocket like the Space Shuttle, but it works quite well
for a model.

Another, more complicated way, is to hang the model from some
point, for example, the corner of a fin, and drop a weighted
string from the same point. Draw a line on the rocket along the
string. Repeat the procedure from another point on the rocket, the
nose, for example. You now have two lines drawn on the rocket.
The cg is the point where the lines intersect. This
procedure works well for irregularly shaped objects that are hard
to balance. The problem with this procedure is that the cg
can fall outside the body for complex geometries.
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