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LVLH mode


#: 127295 S1/U.S. Space Program
28-Apr-89 18:50:06
Sb: #LVLH Confusion
Fm: John Wilson 72300,2475
To: [F] ALL

I have a question about the LVLH (local vertical/local horizontal) designation
of a vehicle in space.

As my understanding of it is, the LVLH "mode" is used as a point of reference.
For example, if the space shuttle were to move in it's position, let's say a
minus y translation, it would be relative the the imaginary axis of the shuttle
itself. This would be because the attitude of the shuttle changes quite often,
and at any point in time, it could be anywhere, relative to the position of the
Earth (which is also rotating). So, the LVLH would give an easier way for
motion in space. An astronaut in the MMU would find it easier to move relative
to him/herself, rather than a position on the Earth. I assume that the MMU
would make a reference local to the MMU, and not the shuttle?

I believe that the shuttle enters LVLH mode just after completion of the roll
maneauver. Is this because it is in an attitude similar to when it inserts
into Earth orbit, or for ease of calculation?

If my assumption is correct (which is open for debate <g>), my question is
this: when does a vehicle enter the LVLH mode, and why then?

( John )----------------[GO ATLANTIS!]------------>=-

* Reply: 127397

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#: 127397 S1/U.S. Space Program
01-May-89 00:47:46
Sb: #127295-#LVLH Confusion
Fm: John Bradbury 71121,2457
To: John Wilson 72300,2475 (X)

John,

Let me see if I can help. LVLH is really a 3-dimensional Cartesian coordinate
system, just like the inertial coordinate system or any other 3-D Cartesian
(XYZ) coordinate system. Unlike the inertial coordinate system, though, it is
not fixed with respect to the distant stars; it rotates over time with respect
to the stars.

The origin in the LVLH coordinate system is located at the spacecraft's center
of mass. Therefore, the origin of the LVLH system moves with the spacecraft as
it travels around the Earth (or whatever body is being orbited by the
spacecraft).

The Z axis is positive in the direction of the center of the Earth along the
geocentric radius vector to the spacecraft; hence it is in the vertical
direction with respect to the point on the surface of the Earth immediately
below the spacecraft ("local vertical"). As the spacecraft moves, this vector
also moves, but it is always vertical.

The X axis is perpendicular to the Z axis, lies in the spacecraft's orbital
plane, and is positive in the direction of vehicle motion. Thus, it is always
parallel to the ground immediately below the spacecraft ("local horizontal").
Again, as the spacecraft moves, the X axis also moves, but it is always
horizontal. The Y axis is normal to the orbital plane and completes the
right-handed orthogonal coordinate system.

Note that LVLH does not take into account any rotating that the surface of the
Earth may do about the Earth's axis. It is not an "Earth-fixed" coordinate
system, as would be used during approach and landing.

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#: 127398 S1/U.S. Space Program
01-May-89 00:48:04
Sb: #127397-#LVLH Confusion
Fm: John Bradbury 71121,2457
To: John Bradbury 71121,2457 (X)

[Continued]

Now, it is true that the shuttle's movements must be commanded in the orbiter
body coordinate system, which is almost constantly rotating with respect to
most other coordinate systems such as inertial or LVLH. The body coordinate
system has its origin at the shuttle's center of mass (same as LVLH), but its X
axis is along the orbiter structural body X axis and is positive in the
direction of the nose of the orbiter; its Z axis is parallel to the orbiter
plane of symmetry, is perpendicular to the X axis, and is positive in the
direction of the wheels; and its Y axis completes the right-handed orthogonal
system (i.e. it's out the right wing).

But commanding movement is a flight control problem (how do I get where I want
to go?). Guidance (where do I want to go?) may be done in whatever coordinate
system is convenient, as long as the commands are converted to body coordinates
before they are sent to the autopilot. "Convenient" usually means whatever
system yields guidance algorithms that are easy to understand and/or easy to
compute either a closed-form solution or a numerical solution. For certain
guidance problems, the LVLH coordinate system yields a convenient algorithm,
such as tracking the center of the Earth. LVLH also provides an easily
understood reference for a pilot who may have to fly the shuttle with respect
to the Earth, where it makes a difference whether you are heads-up or
heads-down. There is actually an on-orbit flight control mode called LVLH
mode, where the digital autopilot maintains the current LVLH attitude, but in
actuality it is getting its commands from a guidance algorithm.

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#: 127399 S1/U.S. Space Program
01-May-89 00:48:24
Sb: #127398-#LVLH Confusion
Fm: John Bradbury 71121,2457
To: John Bradbury 71121,2457 (X)

[Continued]

I am not sure what coordinate system is used for MMU operations, but I suspect
it may be the same one used for rendezvous operations which is essentially
LVLH. But ascent guidance operations prior to MECO are all done in either the
inertial or boost reference coordinate system, not LVLH. One of the ADI's
(attitude/direction indicator) is usually set to LVLH mode to display the
current LVLH attitude of the shuttle, but it is not used for vehicle control
unless perhaps the crew takes over manual flight control.

All of the first stage guidance calculations (through SRB separation) are done
in the boost reference coordinate system, which is a fixed inertial coordinate
system with origin at the center of the Earth. Its Z axis is parallel to the
gravity gradient vector at the launch site at a fixed time and is positive in
the direction of gravity; its X axis is parallel to the launch site meridian
and is positive north; and its Y axis completes the right-handed orthogonal
system and is positive east. The X-Y plane is normal to the launch site
gravity gradient vector. It is very definitely not the same as LVLH.

Ascent second stage guidance calculations are done in the inertial coordinate
system. I can give you the exact definition if you want it, but you may be
getting tired of them by now!

Now, I'm not sure that I have really answered your question, but I think you're
confusing coordinate systems with control modes (or maybe I'm confused by your
question). If this is indeed the case, then yes, your assumption is incorrect.
If not, maybe I've given you enough information so that you can ask the
question again in different terms to which I can relate.

John

* Replies: 127428, 127433

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#: 127428 S1/U.S. Space Program
01-May-89 11:41:04
Sb: #127399-LVLH Confusion
Fm: John Wilson 72300,2475
To: John Bradbury 71121,2457 (X)

So, isn't that way I basically said? <grin*4> I think that it will take me a
few moments to digest & absorb this, but I think that it does answer my
question. I will let you know if I get more confooosed! <grin>

Thanks for your input! I appreciate your answer.

( John )----------------->=-

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#: 127433 S1/U.S. Space Program
01-May-89 12:57:38
Sb: #127399-#LVLH Confusion
Fm: John Wilson 72300,2475
To: John Bradbury 71121,2457 (X)

John,

Let me see if this has soaked into my thick skull! <g>

1. I presume that LVLH is only used when a vehicle (if I can use that term
here) is orbiting another object (planet, asteroid, etc.)?

2. The LVLH system does not make reference to a fixed part of the (in this
case) shuttle. It makes no difference the attitude that the shuttle is
in, with respect to LVLH.

3. The Body Coordinate system is fixed on the shuttle. ie, the x-axis always
refers to the area along the body of the orbiter, running from the nose
to the tail.

4. So, any motion or guidance in this system would relate to the actual
shuttle physically. For example, moving forward, which moves the shuttle
along the positive x-axis.

5. Any motion or guidance in the LVLH system relates directly to the
Earth (although not to any fixed point, like Norfolk, Va.). So, if you
moved along the negative z axis, you would be moving yourself into a
higher Earth orbit. Whereas a move along the negative z axis in the body
coordinate system would move you up, with specific respect to the shuttle.

6. I'd be interested in hearing about the inertial system also.

I think that I have an understanding, but we'll se how I did on points #1 to
#5. I may not be able to explain what I understand here, so please bear with
my attempt at relating what I understand.

Thanks for your help!

P.S. Sounds like you know a little bit about this stuff! <grin>

* Reply: 127461

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#: 127461 S1/U.S. Space Program
01-May-89 23:36:41
Sb: #127433-#LVLH Confusion
Fm: John Bradbury 71121,2457
To: John Wilson 72300,2475 (X)

John,

1, 2, and 3: all correct.

4: partial credit; moving forward moves the shuttle *in the direction of* the
positive X-axis and is referred to as a +X translation, but since the origin of
the body coordinate system is the shuttle's center of mass and you are moving
it with you, you really aren't moving along the X body axis. However, what you
say would be true for an astronaut moving in the payload bay.

5: same comment as on 4 with regard to moving "in the direction of" instead of
"along" a body axis, but we won't penalize you twice for the same mistake!
<grin>. You are correct about moving along the -Z LVLH axis. I would also add
that your statement about motion in the LVLH system not being related to any
fixed point on the Earth is a key distinction; such motion *is* relative to a
point on the Earth, but a constantly changing point (the one immediately below
the shuttle at any given instant) rather than a fixed one.

I'll give you an A- on this one! <grin> I know what you mean about not being
able to explain what you understand; I work with these coordinate systems
quite often and I know how to work with them intuitively, but explaining them
to someone else is another matter! I did refer to some documentation to make
sure I didn't tell any lies! I hope my explanations were helpful, and feel
free to ask for clarification or to ask other questions.

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#: 127462 S1/U.S. Space Program
01-May-89 23:36:58
Sb: #127461-#LVLH Confusion
Fm: John Bradbury 71121,2457
To: John Bradbury 71121,2457 (X)

[Continued]

6: When I said "the inertial coordinate system", I was being imprecise,
although the usage of the term is common on the shuttle project. There are
many inertial coordinate systems, according to the following definition: "a
system whose coordinate axes are fixed, relative to the stars, at infinite
distances. That is, the rotation rates about all axes, relative to the stars,
are zero." The one I was referring to is properly known as the
Aries-mean-of-1950 Cartesian coordinate system, or M50 for short. Its origin
is the center of the earth. It is fixed at a certain point in time, called the
epoch. The epoch for M50 is the beginning of Besselian year 1950 or Julian
ephemeris date 2433282.423357. The X-Y plane is the mean earth's equator of
epoch. The X-axis is directed toward the mean vernal equinox of epoch
(commonly referred to as the direction of the first point of Aries in 1950).
The Z-axis is directed along the earth's mean rotational axis of epoch and is
positive north. The Y-axis completes the right-handed orthogonal system.
(Now, aren't you sorry you asked? <grin>)

LVLH and body coordinate systems are pretty easy to relate to a physical
situation. M50 is not so easily related, and in fact most of the time I don't
worry about what it means in a physical sense except when dealing with things
like pointing vectors for stars (which are also in the M50 system). The sign
of the Z-component does tell you whether you are in the northern or southern
hemisphere, though.

John

* Replies: 127468, 127488

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#: 127468 S1/U.S. Space Program
02-May-89 07:49:49
Sb: #127462-#LVLH Confusion
Fm: John Wilson 72300,2475
To: John Bradbury 71121,2457 (X)

Ok, now, let's see what I have here.

4. Yes, moving "along" the x-axis (translation) does make more sense.

5. Relative to a point. Yes, ok, relative to *a* point, but not the *Same*
point. Twice the same mistake, eh? Just wanted to see if you were paying
attention! <Grin> Would it be relative to the center of the Earth. Or,
should I ask if the axis extends outwards to pass through the center of
the Earth? 6. Ok, I've heard of this one. (doesn't mean I understand it
as you do, but
I've heard of it! <grin>)

I think that I have a handle on LVLH now. I was interpreting it as a "mode"
that the shuttle went into, and the local meant that everything was local to,
or referred to the shuttle itself. More like the body coordinate system, but
kind of a fuzzy interpretation of that also.

I think I understand it *much* better now.

Thank you very much! I'll give you an A+ for your efforts. An "A" for your
excellent knowledge and research, and the "+" because of the subject your
talking to! <g>

( John )------------------------------>=-

* Reply: 127498

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#: 127498 S1/U.S. Space Program
02-May-89 22:24:01
Sb: #127468-LVLH Confusion
Fm: John Bradbury 71121,2457
To: John Wilson 72300,2475 (X)

John,

Yes, that's it; motion in the LVLH system is relative to a point on the
surface of the earth, but the motion itself changes which point the motion is
relative to. (There is an exception if you're rising or falling in the
direction of the Z-axis, but that is actually a degenerate system since there
is no unique orbital plane [the position and velocity vectors are on the same
line]).

Yes, the motion would be relative to the center of the earth, since the Z-axis
is along the geocentric radius vector to the spacecraft (and that means the
vector from the center of the earth to the spacecraft). However, the concept
of LVLH is most meaningful with respect to points on the surface of the earth,
rather than with respect to a point about which the coordinate system itself
rotates (assuming the spacecraft is orbiting the earth). It wouldn't be
meaningful to extend the Z-axis beyond the center of the earth, since it is
defined to be positive toward the center of the earth, but it does extend *to*
the center of the earth.

You're welcome, and thank YOU! Feel free to ask such questions any time!

John

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