# The Coordinate Axes Of Apollo-Saturn: Part 2

In my previous post on this topic, I described how flight engineers working on the Apollo programme assigned XYZ coordinate axes to the Saturn V launch vehicle and to the two Apollo spacecraft, the Command/Service Module (CSM) and the Lunar Module (LM). This time, I’m going to talk about how these axes came into play when the launch vehicle and spacecraft were in motion. At various times during an Apollo mission, they would need to orientate themselves with an axis pointing in a specific direction, or rotate around an axis so as to point in a new direction. These axial rotations were designated roll, pitch and yaw, and the names were assigned in a way that would be familiar to the astronauts from their pilot training. To pitch an aircraft, you move the nose up or down; to yaw, you move the nose to the left or right; and to roll, you rotate around the long axis of the vehicle.

These concepts translated most easily to the axes of the CSM (note the windows on the upper right surface of the conical Command Module, which indicate the orientation of the astronauts while “flying” the spacecraft):

With the astronauts’ feet pointing in the +Z direction as they looked out of the windows on the -Z side of the spacecraft, they could pitch the craft by rotating it around the Y axis, yaw around the Z axis, and roll around the X axis.

The rotation axes of the LM were similarly defined by the position of the astronauts:

Looking out of the windows in the +Z direction, with their heads pointing towards +X, they yawed the LM around the X axis, pitched it around the Y axis, and rolled it around the Z axis.

For the Saturn V, the roll axis was obviously along the length of the vehicle, its X axis.

But how do you decide which is pitch and which is yaw, in a vehicle that is superficially rotationally symmetrical? It turns out that the Saturn V was designed with a side that was intended to point down—its downrange side, marked by the +Z axis, which pointed due east when the vehicle was on the launch pad. This is the direction in which the space vehicle would travel after launch, in order to push the Apollo spacecraft into orbit—and to do that it needed to tilt over as it ascended, until its engines were pointing west and accelerating it eastwards. So the +Z side gradually became the down side of the vehicle, and various telemetry antennae were positioned on that side so that they could communicate with the ground. You’ll therefore sometimes see this side referred to as the “belly” of the space vehicle. And with +Z marking the belly, we can now tell that the vehicle will pitch around the Y axis, and yaw around the Z axis.

If you have read my previous post on this topic, you’ll know that the astronauts lay on their couches on the launch pad with their heads pointing east.* So as the space vehicle “pitched over” around its Y axis, turning its belly towards the ground, the astronauts ended up with their heads pointing downwards, all the way to orbit. This was done deliberately, so that they could have a view of the horizon during this crucial period.

But the first thing the Saturn V did, within a second of starting to rise from the launch pad, was yaw. It pivoted through a degree or so around its Z axis, tilting southwards and away from the Launch Umbilical Tower on its north side. Here you can see the Apollo 13 space vehicle in the middle of its yaw manoeuvre:

This was carried out so as to nudge the vehicle clear of any umbilical arms on the tower that had failed to retract.

Then, once clear of the tower, the vehicle rolled, turning on its vertical X axis. This manoeuvre was carried out because, although the belly of the Saturn V pointed east, the launch azimuth could actually be anything from 72º to 108º, depending on the timing of the launch within the launch window. (See my post on How Apollo Got To The Moon for more about that.) Here’s an aerial view of the two pads at Launch Complex 39, from which the Apollo missions departed, showing the relevant directions:

An Apollo launch which departed at the start of the launch window would be directed along an azimuth close to 72º, and so needed to roll anticlockwise (seen from above) through 18º to bring its +Z axis into alignment with the correct azimuth, before starting to pitch over and accelerate out over the Atlantic.

Once in orbit, the S-IVB stage continued to orientate with its belly towards the Earth, so that the astronauts could see the Earth and horizon from their capsule windows. This orientation was maintained right through to Trans-Lunar Injection (TLI), which sent the spacecraft on their way to the moon.

During the two hours after TLI, the CSM performed a complicated Transposition, Docking and Extraction manoeuvre, in which it turned around, docked nose to “roof” with the LM, and pulled the LM away from the S-IVB.

This meant that the X axes of CSM and LM were now aligned but opposed—their +X axes pointing towards each other. But they were also oddly rotated relative to each other. Here’s a picture from Apollo 9, taken by Rusty Schweickart, who was outside the LM hatch looking towards the CSM, where David Scott was standing up in the open Command Module hatch.

The Z axes of the two spacecraft are not aligned, nor are they at right angles to each other. In fact, the angle between the CSM’s -Z axis and the LM’s +Z axis is 60º. This odd relative rotation meant that, during docking, the Command Module Pilot, sitting in the left-hand seat of the Command Module and looking out of the left-hand docking window, had a direct line of sight to the docking target on the LM’s “roof”, directly to the left of the LM’s docking port.

Once the spacecraft were safely docked, roll thrusters on the CSM were fired to make them start rotating around their shared X axis. This was called the “barbecue roll” (formally, Passive Thermal Control), because it distributed solar heating evenly by preventing the sun shining continuously on one side of the spacecraft.

Once in lunar orbit, the LM separated from the CSM and began its powered descent to the lunar surface. This was essentially the reverse of the process by which the Saturn V pushed the Apollo stack into Earth orbit. Initially, the LM had to fire its descent engine in the direction in which it was orbiting, so as to cancel its orbital velocity and begin its descent. So its -X axis had to be pointed ahead and horizontally. During this phase the Apollo 11 astronauts chose to point their +Z axis towards the lunar surface, so that they could observe landmarks through their windows—they were flying feet-first and face-down. Later in the descent, as its forward velocity decreased, the LM needed to rotate to assume an ever more upright position (-X axis down) until it came to a hover and descended vertically to the lunar surface. So later in the powered descent, Armstrong and Aldrin had to roll the LM around its X axis into a “windows up” position, facing the sky. Then, as the LM gradually pitched into the vertical position, with its -X axis down, the +Z axis rotated to face forward, giving the astronauts the necessary view ahead towards their landing zone.

Finally, at the end of the mission, the XYZ axes turn out to be important for the re-entry of the Command Module (CM) into the Earth’s atmosphere. The CM hit the atmosphere blunt-end first, descending at an angle of about 6º to the horizontal. But it was also tilted slightly relative to the local airflow, with the +Z edge of its basal heat-shield a little ahead of the -Z edge. This tilt occurred because the centre of mass of the CM was deliberately offset very slightly in the +Z direction, so that the airflow pushed the CM into a slightly tilted position. This tilt, in turn, generated a bit of lift in the +Z direction—which made the Command Module steerable. It entered the atmosphere with its +Z axis pointing upwards (and the astronauts head-down, again, with a view of the horizon through their windows). The upward-directed lift prevented the CM diving into thicker atmosphere too early, and reduced the rate of heating from atmospheric compression.

Later in re-entry, the astronauts could use their roll thrusters to rotate the spacecraft around its X axis, using lift to steer the spacecraft right or left, or even rolling it through 180º so as to direct lift downwards, steepening their descent if they were in danger of overshooting their landing zone.

* As described in my previous post on this topic, the coordinate axes of the CSM were rotated 180º relative to those of the Saturn V—the astronauts’ heads pointed in the -Z direction of the CSM, but the +Z direction of the Saturn V.

I’m missing out a couple of steps here, in an effort to be succinct. (I know, I know … that’s not like me. Take a look at NASA Technical Memorandum X-58040 if you want to know all the details.)

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