As a matter arising from my long, slow build of a Saturn V model, I became absorbed in the confusing multiplicity of coordinate systems and axes applied to the Apollo launch vehicle and spacecraft. So I thought I’d provide a guide to what I’ve learned, before I forget it all again. (Note, I won’t be talking about all the other coordinate systems used by Apollo, relating to orbital planes, the Earth and the Moon—just the ones connected to the machinery itself. And I’m going to talk only about the Saturn V launch vehicle, though much of what I write can be transferred to the Saturn IB, which launched several uncrewed Apollo missions, as well as Apollo 7.)

First up, some terminology. The Saturn V that sent Apollo on its way to the Moon is called the launch vehicle, consisting of three booster stages, with an Instrument Unit on top, responsible for controlling what the rest of the launch vehicle does. Sitting on top of the launch vehicle, mated to the Instrument Unit, is the spacecraft—all the specifically Apollo-related hardware that the launch vehicle launches. This bit is sometimes also called the Apollo stack, since it will eventually split up into two independent spacecraft—the Lunar Module (LM) and the Command/Service Module (CSM). The combination of launch vehicle and spacecraft (that is, the whole caboodle as it sat on the launch pad) is called the space vehicle.

The easiest set of coordinate axes to see and understand were the position numbers and fin letters which were labelled in large characters on the base of the Saturn V’s first stage, the S-IC. You can see them here, in my own model of the S-IC:

In this view you can see fins labelled C and D, and the marker for Position IIII, equidistant between them.

The numbering and lettering ran anticlockwise around the launch vehicle when looking down from above, creating an eight-point coordinate system of lettered quadrants (A to D) with numbered positions (I to IIII) between them, which applied to the whole launch vehicle. They marked out the distribution of black and white stripes—each stripe occupied the span between a letter and a number, with white stripes always to the left of the position numbers, and black stripes to the right. The five engines of the S-IC and S-II stages were each numbered according to the lettered quadrant in which they lay, with Engine 5 in the centre, Engine 1 in the A quadrant, Engine 2 in the B quadrant, and so on. The curious chequer pattern of the S-IVB aft interstage (the “shoulder” where the launch vehicle narrows down between the second and third stages) is distributed in the lettered quadrants, with A all black, B black high and white low, C white high and black low, and D all white.*

Position II of the launch vehicle was the side facing the Launch Umbilical Tower (LUT), so that side of the Saturn V was dotted with umbilical connections and personnel access hatches, as well as a prominent vertical dashed line painted on the second stage, called the vertical motion target, which made it easy for cameras to detect the first upward movement as the space vehicle left the launch pad. You don’t often get a clear view of the real thing from the Position II side, so I’ve marked up the appropriate view of my model instead, at left.

The two Cape Kennedy launch pads used for Apollo (39A and 39B) were oriented on a north-south axis, with the LUT positioned on the north side of the Saturn V, so Position II faced north. Position IIII, on the opposite side, faced south, looking back down the crawler-way along which the Saturn V had been transported on its Mobile Launcher Platform. Position IIII was also the side that faced the Mobile Service Structure, which was rolled up to service the Saturn V in its launch position, and then rolled away again before launch. And so Position I faced east, which was the direction in which the space vehicle had to travel in order to push the Apollo stack into orbit.

These letters and numbers seem to have been largely a reference for the contractors and engineers responsible for assembling and mating the different launch vehicle stages. Superimposed on them were the reference axes used by the flight engineers, who used them to talk about the orientation and movements of the launch vehicle and the two Apollo spacecraft. These axes were labelled X, Y and Z.

For the launch vehicle, LM and CSM the positive X axis was defined as pointing in the direction of thrust of the rocket engines. So the end with the engines was always -X, and the other end was +X. The +Z direction was defined as “the preferred down range direction for each vehicle, when operating independently”. For the launch vehicle, that’s straightforward—downrange is to the east as it sits on the pad (the direction in which it will travel after launch), so +Z corresponds to Position I, and -Z to Position III. The Y axis was always chosen to make a “right-handed” coordinate system, so +Y points south through Position IIII.

In the image below, we’re looking north. Once the Saturn V has launched it will tip over and head eastwards (to the right) to inject the Apollo stack into orbit.

These axes were actually labelled on the outside of the Instrument Unit (IU), at the very top of the launch vehicle. Here’s one in preparation, with the +Z label flanked by the casings of two chunky directional antennae—a useful landmark I’ll come back to later.

So here’s a summary of all the axes of the Saturn V:

Moving on to the Lunar Module, its downrange direction is the direction in which it travels during landing, when it is orientated with its two main windows facing forward—so +Z points in that direction, out the front. The right-hand coordinate system then puts +Y to the astronauts’ right as they stand looking out the windows.

The landing legs were designated according to their coordinate axis locations. In the descent stage, between the legs, were storage areas called quads—they were numbered from 1 to 4 anticlockwise (looking down), starting with Quad 1 between the +Z and -Y leg. The ascent stage, sitting on top of the descent stage, had four clusters of Reaction Control System (RCS) thrusters, which were situated between the principal axes and numbered with the same scheme as the descent-stage quads.

But it’s not clear that there is a natural downrange direction for the CSM—the +Z direction is defined (fairly randomly, I think) as pointing towards the astronauts’ feet, with -Z therefore corresponding to the position of the Command Module hatch. That places +Y to the astronauts’ right side as they lie in their couches.

The Command Module was fairly symmetrical around its Z axis, and its RCS thrusters were neatly place on the Z and Y axes. Not so the Service Module, which was curiously skewed. Its RCS thrusters, arranged in groups of four called quads, were offset from the principal axes by 7º15′ in a clockwise direction when viewed from ahead (that is, looking towards the pointed end of the CSM).^† The RCS quad next to the -Z axis was designated Quad A; Quad B was near the +Y axis, and the lettering continued in an anticlockwise direction through C and D. I’ve yet to find out why the RCS system was offset in this way, since it would necessarily produce translations and rotations that were offset from the “natural” orientation of the crew compartment, and from the translations and rotations produced by the RCS system of the Command Module.

The Service Module also contained six internal compartments, called sectors, numbered from 1 to 6. These were symmetrically placed relative to the RCS system, rather than the spacecraft’s principal axes. Finally, the prominent external umbilical tunnel connecting the Service Module to the Command Module wasn’t quite on the +Z axis, but offset by 2º20′ in the same sense as the RCS offset.

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So those are the axes for the launch vehicle and spacecraft. But how did they line up when the Saturn V and Apollo stack were assembled? Badly, as it turns out.

First, the good news—all the X axes align, because the spacecraft and launch vehicle are all positioned engines-down for launch, for structural support reasons, if nothing else.

With regard to Y and Z, it’s easy to see the CSM’s orientation on the launch pad. Here’s a view from the Launch Umbilical Tower, which we’ve established (see above) is on the -Y side of the launch vehicle. The tunnel allowing access to the crew hatch of the Command Module (-Z) is on the left, and the umbilical tunnel connecting the Service Module to the Command Module is on the right (+Z), so the CSM +Y axis is pointing towards us.

Oops. The CSM YZ axes are rotated 180º relative to those of the Saturn V launch vehicle.

It’s more difficult to find out the orientation of the Lunar Module within the Apollo stack, since it’s concealed inside the shroud of the Spacecraft/Lunar Module Adapter. Various diagrams depict it as facing in any number of directions relative to the CSM, but David Weeks’s authoritative drawings show it turned so that its +Z and +Y axes align with those of the CSM—facing to the right in the picture above, then, with its YZ axes rotated 180º relative to those of the Saturn V launch vehicle below. We can check that this is actually the case by looking at photographs of the LM when it’s exposed on top of the S-IVB and Instrument Unit, during the transposition and docking manoeuvre. The viewing angles are never very favourable, but the big pair of directional antennae flanking the +Z direction on the IU are useful landmarks (see above).

We can see that the front of the Lunar Module (+Z) is indeed pointing in the opposite direction to the directional antennae marking the +Z axis of the IU and the rest of the launch vehicle. Weeks’s drawing are correct.

So, sitting on the launch pad, the axes of the launch vehicle are pointing in the opposite direction to those of the spacecraft. NASA rationalized this situation by stating that:

A Structural Body Axes coordinate system can be defined for each multi-vehicle stack. The Standard Relationship defining this coordinate system requires that it be identical with the Structural Body Axes system of the primary or thrusting vehicle.

NASA, Project Apollo Coordinate System Standards (June 1965)

So the whole space vehicle used the coordinate system of the Saturn V launch vehicle, and the independent coordinates of the LM and CSM didn’t apply until they were manoeuvring under their own power.

So, beware—there’s real potential for confusion here, when modelling the Apollo-Saturn space vehicle, because different sources use different coordinates; and many diagrams, even those prepared by NASA, do not reflect the final reality.

In Part 2, I write about what happens to all those XYZ axes once the vehicles start moving around.

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* I suspect I’m not the first person to notice that the S-IVB aft interstage chequer can be interpreted as sequential two-digit binary numbers, with black signifying zero and white representing one. Reading the least significant digit in the “low” positions, we have 00 in the A quadrant, 01 in the B quadrant, 10 in C and 11 in D—corresponding to 0, 1, 2, 3 in decimal. (I doubt if it actually means anything, but it’s a useful aide-memoire. Well, if you have a particular kind of memory, I suppose.)
^† See the Apollo Systems Engineering Manual: Service Module And Adapter Structure.