Apollo 13 - Midcourse Corrective Burn with LM Engine

Hi All!

I was hoping someone could clarify how the last burn worked using the
LM to correct the trajectory for the entry corridor.

Mind you, the question evolves from the Apollo 13 movie, which of
course may be inaccurate on this event.

a. When deciding on an attitude reference point for controlling the
burn, a roll maneuver was made to put the earth in view for the COAS.
It's a minor question here, but performing such a maneuver without
planning it first seems odd. For in reading the flight journals, both
the crew and MC would plan roll attitude adjustments quite carefully,
i.e. PTC. Did the crews of Apollo roll at will?

b. With the earth in the LM window, firing the LM would impart a +x
vector (LM), almost 90 degrees out of plane with their trajectory. If
this actually happened, then is it accurate to say that the burn was
meant to correct their altitude, or H-dot?

Regards,

Richard Brideau

In article ,
Richard Brideau wrote:
I was hoping someone could clarify how the last burn worked using the
LM to correct the trajectory for the entry corridor.
Mind you, the question evolves from the Apollo 13 movie, which of
course may be inaccurate on this event.

In general, the movie should not be taken as gospel. It gets the spirit
right, but plays fast and loose with the facts now and then, to simplify
complex situations and keep things exciting.
--
MOST launched 1015 EDT 30 June, separated 1046, | Henry Spencer
first ground-station pass 1651, all nominal! |

Allow me to get my $0.02 in, and also correct some misinformation.
Though I wasn't involved with working the Apollo 13 problem at all (I
had returned to college during that time), I was involved in much of the
early trjectory work on Apollo, including study of the issue of aborts
from failed missions, and design of the "fast return" trajectories.

For the record, though I do agree with other comments that the movie
over-simplified the issue somewhat, I think they got most of the ideas
right. My understanding is that there were two main burns, rather than
one. That's in addition to the corrections for reenty angle. The first
buwn was on the outbound leg, to put the spacecraft back onto a free
return (circumlunar) trajectory (ironically, 13 was the first mission
_NOT_ to start out on a free return). The second, after passing the
moon, was a burn directly towards the earth, to speed up the return trip
(part of the fast return scheme). I believe that's probably the reason
the reentry communication blackout time was longer than expected; they
were going faster than usual.

First, in the very early days of Apollo, much effort was expended on
dealing with the issue of what to do if things go south. What happens,
for example, if communications with MC was lost, _AND_ so was the flight
computer? What could the astronauts do to get home by dead reckoning?
One of the German scientists (sorry, can't recall which one) spent a lot
of time working up nomographs (Germans _LOVED_ nomographs) that the
astronauts could follow, doing everything manually. Needless to say, all
such plans involved lining up the earth, moon, etc. in various windows.
During the actual flights, communications with MC were so good that the
notion of dead reckoning pretty much got forgotten, but the capability
was always there. AFAIK, the nomographs remained in the mission manual
as a last resort -- one that was never needed, even on 13.

Second, I must correct Doug concerning perigee vs. entry angle. He says

... Yes, the hypothetical "vacuum perigee" would
affect the angle of the trajectory at EI, but they weren't really
figuring on the basis of the vacuum perigee, but of the angle. So the
calculations were made against an optimum entry corridor angle and not
against an altitude or a rate of altitude change.

In reality, the two are pretty much synonomous. Lower vacuum perigee,
and you increase entry angle. Raise it, and you decrease angle. Raise
it too much, and you miss the earth entirely. It's much easier to do
the math based on perigee, and I imagine that's the way it was done.

Thirdly, there's a pretty neat relationship that makes things easy
here. While the orbit relative to the earth can be considered to be an
ellipse, it's such a highly elliptical one (eccentricity OTOO 0.98 or
so) that, for all practical purposes, it can be considered to be a
parabola. One of the characteristics of the parabolic orbit is that the
perigee is _SOLELY_ dependent upon the angular momentum. Increase
angular momentum, and you raise the perigee; decrease it, and you lower
it.

This makes things relatively easy, because you can add or remove angular
momentum by the simple expedient of applying the burn at right angles to
the radius vector (_BUT_ -- to correct a misconception by Richard -- in
the plane of the orbit). If you're only concerned -- as the MC guys
were at that point -- in getting the crew back alive, you don't have to
get fancy with computer-controlled burns; just decrease angular
momentum. Gene Kranz said that he was shooting for a splashdown in the
ocean, and he didn't much care which one, and that was exactly the right
attitude at that point.

Finally, to correct one last point: I'm about 99.44% sure that the
window Lovell was lining up the earth in was the _SIDE_ window of the
LM, not the front one. The front one wouldn't make any sense. Again,
you want to align the vehicle so that the thrust axis is perpendicular
to the radius vector. In simple terms, that means "look out the side
window and keep the earth in the center of it." The beauty of this
manuever is that it doesn't matter much if your attitude isn't perfect;
the cosine effect still gives you most of the thrust in the right
direction, and the only effect any radial component has is to change the
longitude at reentry. But, again, you want to change angular momentum,
so the burn needs to be done in the plane of the orbit.

Hope this helps

Jack

"Doug..." wrote:

In article ,
says...
Hi All!

I was hoping someone could clarify how the last burn worked using the
LM to correct the trajectory for the entry corridor.

Mind you, the question evolves from the Apollo 13 movie, which of
course may be inaccurate on this event.

a. When deciding on an attitude reference point for controlling the
burn, a roll maneuver was made to put the earth in view for the COAS.
It's a minor question here, but performing such a maneuver without
planning it first seems odd. For in reading the flight journals, both
the crew and MC would plan roll attitude adjustments quite carefully,
i.e. PTC. Did the crews of Apollo roll at will?

In general, the Apollo spacecraft could be moved in attitude without
affecting its trajectory. Attitudes were specified in the flight plan
for a nominal mission, but the crew could (and did) maneuver to suit its
own purposes. The Command Module Pilot could (and did) maneuver the
spacecraft from the navigation station in the Lower Equipment Bay, for
that matter, using the computer and not the Rotational Hand Controller to
effect the attitude changes.

On Apollo 13 after the accident, this was a little different, in that the
only way to change attitudes in some axes using *just* the LM thrusters
was to use the Translational Hand Controller (THC) function -- in other
words, fire thrusters that were NOT paired with counter-thrusters to
cancel any translational force. This would, indeed, affect the
trajectory. So, while Apollo crews in general *could* "roll at will" if
they had a reason (but mostly didn't, to conserve RCS fuel), on Apollo 13
they tried to keep the attitude control maneuvering to a minimum. The
only reason they changed attitude on Apollo 13 on the way home was to
accomplish mid-course corrections.

And one other thing -- if you pointed the LM so its windows faced the
earth, "roll" (as defined in the LM axis system) is the one axis through
which you could rotate 360 degrees and never lose sight of the earth.
Roll was the motion in which your windows remained pointing the same way.
Pitch moved the windows up and down against a fixed reference point, and
yaw moved the windows side to side. That's the least complex way of
describing it that I can think of.

b. With the earth in the LM window, firing the LM would impart a +x
vector (LM), almost 90 degrees out of plane with their trajectory. If
this actually happened, then is it accurate to say that the burn was
meant to correct their altitude, or H-dot?

It depended on *where* in the LM window the earth was located. And the
out-of-plane vector, which was critically important, depended on the
direction in relation to the trajectory the LM engine bell was pointed.

Note that, unlike in the movie, Lovell was *not* the person who came up
with the Earth-in-the-COAS means of setting the correct attitude for the
DPS midcourse burn on the way home. The flight guidance controllers in
the Trench determined the right attitude, and dusted off a procedure that
was invented during Apollo 8 training to get to the right attitude.
(Lovell, having been there when the procedure was invented during Apollo
8 training, and knowing that the controllers had said that this was a
last-ditch procedure to be used when the crew "had nothing left to lose,"
commented when hearing the plan on Apollo 13 "I hope the guys in the back
room who thought this up knew what they were doing...")

Had the trajectory been steepening and not shallowing, for example,
instead of aligning the COAS cross-hairs on the horns of the crescent
Earth, they would have flipped it 180 degrees and aligned it in tangent
to the curve of the lit side of the Earth. (In other words, what
mattered was whether the horns of the crescent pointed "right" or "left"
in the COAS.) Remember, you could still move 360 degrees in the LM's
roll axis and still be pointing the windows at the Earth.

Finally -- H-dot was a measure of *change* in altitude, not a direct
measure of altitude. The controllers were trying to adjust the *angle*
at which the CM would intersect the upper atmosphere, not the altitude --
the altitude for entry interface was set at 400,000 feet, and unless the
trajectory shallowed WAY outside of the corridor, it would hit that
altitude at some point. Yes, the hypothetical "vacuum perigee" would
affect the angle of the trajectory at EI, but they weren't really
figuring on the basis of the vacuum perigee, but of the angle. So the
calculations were made against an optimum entry corridor angle and not
against an altitude or a rate of altitude change.

I hope that helped...

--

Do not meddle in the affairs of dragons, for | Doug Van Dorn
thou art crunchy and taste good with ketchup |

Jack Crenshaw wrote in message ...

Gene Kranz said that he was shooting for a splashdown in the
ocean, and he didn't much care which one, and that was exactly the right
attitude at that point.

Interesting –what were the factors that made them unable to pick? Was
there not enough time for MC to work the precision, given the awkward
configuration of the spacecraft (Having the LM attached & using the LM
decent engine). Was the crew too constrained on time to perform an
alignment?

Finally, to correct one last point: I'm about 99.44% sure that the
window Lovell was lining up the earth in was the _SIDE_ window of the
LM, not the front one. The front one wouldn't make any sense. Again,
you want to align the vehicle so that the thrust axis is perpendicular
to the radius vector. In simple terms, that means "look out the side
window and keep the earth in the center of it."

I find something here that is questionable with Doug's response, and
yet still unresolved with yours as well. Wouldn't a burn from the LM,
perpendicular to the radial vector allow the crew to set the
spacecrafts attitude to use the LMP window, and utilize the COAS? It
seems to me it would; perhaps I'm misunderstanding the orientation of
the radial vector.

Richard

In article , Richard
Brideau wrote:
Jack Crenshaw wrote in message
...

Gene Kranz said that he was shooting for a splashdown in the
ocean, and he didn't much care which one, and that was exactly the right
attitude at that point.

Interesting –what were the factors that made them unable to pick? Was
there not enough time for MC to work the precision, given the awkward
configuration of the spacecraft (Having the LM attached & using the LM
decent engine). Was the crew too constrained on time to perform an
alignment?

(disclaimer - I am not now, nor have I ever been, Gene Kranz)

I don't think it was so much "unable to pick" as taking the attitude
that, if your Cunning Plan brought them back safely to the South
Pacific, then go with it - you could worry about getting them *out* of
the South Pacific later. Let's face it, it's not as if they wouldn't be
able to mobilise half of most navies by getting Nixon to make some phone
calls :-)

MCC could manage with sufficient precision - indeed, we've already seen
just how good that precision was - but there was no sense, in those
first hours/days, of worrying about something that came right at the end
until you got there.

--
-Andrew Gray

In article ,
says...
Jack Crenshaw wrote in message ...

Gene Kranz said that he was shooting for a splashdown in the
ocean, and he didn't much care which one, and that was exactly the right
attitude at that point.

Interesting –what were the factors that made them unable to pick? Was
there not enough time for MC to work the precision, given the awkward
configuration of the spacecraft (Having the LM attached & using the LM
decent engine). Was the crew too constrained on time to perform an
alignment?

Finally, to correct one last point: I'm about 99.44% sure that the
window Lovell was lining up the earth in was the _SIDE_ window of the
LM, not the front one. The front one wouldn't make any sense. Again,
you want to align the vehicle so that the thrust axis is perpendicular
to the radius vector. In simple terms, that means "look out the side
window and keep the earth in the center of it."

I find something here that is questionable with Doug's response, and
yet still unresolved with yours as well. Wouldn't a burn from the LM,
perpendicular to the radial vector allow the crew to set the
spacecrafts attitude to use the LMP window, and utilize the COAS? It
seems to me it would; perhaps I'm misunderstanding the orientation of
the radial vector.

The LM didn't really have a side window. It had two windows that pointed
forward and angled down, and a top window that pointed directly up, along
the plus-X axis.

Remember, the axis references changed between the LM and the CSM. If you
point the thrust axis of the LM perpendicular to the trajectory of the
stack, you *can* easily have the LM windows pointed directly forward, at
the earth. Because the LM front windows point out along the LM's plus-Z
axis (IIRC).

--

Do not meddle in the affairs of dragons, for | Doug Van Dorn
thou art crunchy and taste good with ketchup |