During the
flight
of a model rocket
small gusts of wind,
or thrust instabilities can cause the rocket to "wobble", or change
its attitude in flight. Like any object in flight, a model rocket
rotates
about its center of gravity cg,
shown as a yellow dot on the figure. The rotation causes the axis of
the rocket to be inclined at some angle a to the flight path. Whenever
the rocket is inclined to the flight path,
a lift force is generated by the rocket body
and fins, while the aerodynamic drag remains
fairly constant for small inclinations.
Lift and drag both act through the center of
pressure cp of the rocket, which is shown as the black and yellow dot in
the figure.
On this slide we show three cases for which the flight direction
is exactly vertical. In the center of the figure, the rocket is undisturbed
and the axis is aligned with the flight direction. The drag of the rocket
is along the axis and there is no lift generated.
On the left of the figure, a
powered rocket has had the nose of the
rocket perturbed to the right. On the right of the figure,
a coasting
rocket has had the nose of the rocket perturbed to the left. We
denote the angle in both cases by the symbol a. Considering the
powered rocket case, we see that a lift force is generated and directed towards
the right or downwind side of the rocket. On the coasting rocket
case, the lift is directed towards the left, also the downwind side
of the rocket. For the powered case, both the lift and the drag
produce counter-clockwise
torques,
or twists, about the center of
gravity; the tail of the rocket will swing to the right under the action
of both forces and the nose will move to left. For the coasting case,
both lift and drag produce clockwise torques about the center of
gravity; the tail of the rocket will swing to the left under the action
of both forces and the nose will move to the right. In both cases, the
lift and the drag forces move the nose back towards the flight
direction. Engineers call this a restoring force because the
forces "restore" the vehicle to its initial condition and the
rocket is determined to be stable.
A restoring force exists for this model rocket because the center
of pressure is below the center of gravity. If the center of pressure
is above the center of gravity, the lift and drag forces maintain
their directions but the direction of the torque generated by the
forces is reversed. This is called a de-stabilizing force. Any
small displacement of the nose generates forces that cause the
displacement to increase. The
conditions
for a stable rocket are that the center of
pressure must be located below the center of gravity.
There is a relatively simple test that you can use on a model rocket to
determine the stability. Tie a string around the body tube at the
location of the center of gravity. Be sure to have the parachute and
the engine installed. Then swing the rocket in a circle around you
while holding the other end of the string. After a few revolutions,
if the nose points in the direction of the rotation, the rocket is
stable and the center of pressure is below the center of gravity. If
the rocket wobbles, or the tail points in the direction of rotation,
the rocket is unstable. You can increase the stability by lowering
the center of pressure, increasing the fin area, for example, or by raising the
center of gravity, adding weight to the nose.
NOTE: Modern
full scale rockets
do not usually rely on
aerodynamics for stability. Full scale rockets
pivot
their exhaust nozzles
to provide stability and control. That's why you don't see fins on a
Delta, Titan, or Atlas booster.
Guided Tours
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Guidance System:
-
Rocket Rotation:
-
Rocket Modeler II:
Activities:
Paper Rocket: Grade 6-10
Pencil Rocket: Grade 6-10
Related Sites:
Rocket Index
Rocket Home
Exploration Systems Mission Directorate Home