The most important parts are in a)
and b) at the top of the figure. In a) we see a change in
orientaton of the spinning mass, which results in no change in length
of the H vector (as would have occurred with a change of angular
velocity, omega). The H vector simply points in a different
direction. In b) we see the initial and final states of H,
and the change ("delta"-denoted by a triangle, H).
most important part to remember is that any change in Angular Momentum
requires application of a Torque, so Delta-H must
represent the torque required to change the angular momentum from the
first state to the second
. Hold that thought.
equations are shown for those who are interested, but the only required
parts to pay attention to now are at the bottom of the figure.
This shows a "cross product" of the Angular Momentum vector
and the Precession
Omega-p. Omega-p represents the rate of
change of the angle theta shown in a) and b). The figure at
the bottom right shows the relation of the 3 vector quantities in
space. Here we need to make careful note of several points:
Omega-p and H are all at right angles to one another.
Applying a torque to an axis perpendicular to H results in a
rotation about an axis that is perpendicular to both the H and T
vectors. Or, if the system is rotated, a reaction torque is
created perpendicular to the plane of rotation.
is non-zero only while the angle theta is changing. Once the
angle stops changing, there is no T. Also, the faster the
angle changes, the larger T becomes.
- We can look at
b) above to determine the direction of the torque for a given rotation
theta. Simply draw the Momentum change vector from the
initial to final position ("delta-H"), and then apply the right hand
Now we can apply this to a glider during
the glider lifts the pilot, the rear of the harness pivots down, which
changes the angular Momentum vector as shown in the figure.
H1 represents the angular moment during the pilot's run, as
shown in the earlier figure. H2 represents the angular
momentum while the pilot is stabilized in a climb. Between
these two states there is a change in the angle theta, resulting in the
change in angular momentum, delta-H. During the time this
angle is changing (and only
during this time), there is a gyroscopic torque being generated as
shown. We can point our thumb in the direction of the delta-H
vector and from the direction of our fingers we determine that this
torque is such as to cause a yaw to the right of the glider.
forces are a plausible explanation for the reports of many pilots of a
tendency to the right wing to "dip" during takeoff. If this
is indeed the explanation, then the dip is not directly caused by the
, but is rather a result of the glider yawing.
That is, the glider yawing to the right causes the right wing
to drop back, and left wing to move forward, resulting in decreased
lift on the right wing and increased lift on the left wing, which in
turn causes a roll (or 'dip') to the right.
are further implications to this:
effect is very short lived (only while the pilot/harness is changing
- It will be minimized with ample airspeed,
as a slight yaw when both wings are well above stall will likely have a
much smaller impact. Indeed, it may only be noticeable when there is a sudden
pitch rotation of the harness, as when someone attempts to 'pop' the glider off the ground.
As this is poor technique in any case, the gyroscopic force may play a slight role
in making a bad takeoff worse.
Comparisons to PPG
and Gyroscopic precession will be much more noticeable on a PPG:
a Powered Paraglider, there are two risers, so engine torque will load
one riser move heavily than the other, tending to induce a constant
turn. Because of the single strap on a flphg, this effect is
- The prop axis on a flphg is quite
long, and changes angles only relatively slowly, thus gyroscopic forces
will be comparatively low, compared to a PPG. On a PPG the
prop axis is coupled directly to the pilot's upper body, and even
turning his body to look behind him, or bend over, will cause
considerable change in the Momentum Vector orientation, resulting in
large precession torques on the pilot's body.