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Notes
on
the
Control
of
an
Aircraft
with
Throttle
Only
There
are
a
few
(rare)
examples
of
ﬂight
control
system
failures
that
left
aircraft
with
no
elevator
control.
In
these
cases,
pilots
have
attempted
to
control
the
vertical
position
of
the
aircraft
using
thrust
changes
only.
This
turns
out
to
be
very
hard
to
do,
because
the
resulting
dynamics
are
hard
for
a
pilot
to
control.
Below,
we
derive
the
dynamics
of
an
aircraft
under
those
conditions.
To
simplify
the
problem,
we
use
the
phugoid
approxima
tion
.
In
the
phugoid
approximation,
the
aircraft
is
treated
as
a
point
mass,
and
the
pitching
dynamics
of
the
aircraft
are
ignored.
Furthermore,
only
the
motion
of
the
aircraft
in
the
vertical
plane
(the
longitudinal
motions)
are
considered.
The
states
of
the
aircraft
are
then
h
=
altitude
of
aircraft
v
=
velocity
of
aircraft
(1)
γ
=
ﬂight
path
angle
of
aircraft
The
ﬂight
path
angle
of
the
aircraft
is
the
angle
of
the
velocity
vector
with
respect
to
horizontal,
with
a
positive
γ
indicating
that
the
velocity
vector
is
above
the
horizon.
The
dynamics
of
the
aircraft
can
be
fairly
easily
derived,
using
only
Newton’s
laws,
and
a
little
aerodynamics.
First,
ﬁnd
h
˙
,
the
rate
of
change
of
the
altitude.
h
˙
is
determined
completely
by
kinematics,
so
that
h
˙
=
v
sin
γ
(2)
Next,
v
˙
is
the
rate
of
change
of
the
velocity
vector,
which
is
the
acceleration
of
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This note was uploaded on 01/28/2012 for the course AERO 16.01 taught by Professor Markdrela during the Fall '05 term at MIT.
 Fall '05
 MarkDrela

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