Some of the Problems and Their Solutions, Continued
Q. How were the design shear strength parameters and other soil properties estimated based on available pre-Surveyor information?
A. This was perhaps our biggest challenge. As indicated previously, the Moon has virtually no atmosphere (atmospheric pressure <10-12 mm of mercury). Therefore, the surface of the Moon is being constantly bombarded by meteorites and micrometeorites. These two conditions were thought to have a major effect on the lunar soil’s shear strength parameters. Comminution of geologic materials by meteorite bombardment in an ultrahigh vacuum results in molecularly clean fracture surface, i.e., there are no water or gas molecules to adhere to the freshly cleaved surfaces. The implication of that type of mechanical weathering is that soil particles can bond molecularly with each other (cohere) and with other materials (adhere). The strength of that bond provides an earth-like effective cohesion or adhesion. Les and I observed something analogous to that phenomenon in our laboratory studies. The problem was to estimate the magnitude of such cohesion. To this end we reverted back to the Lunar Orbiter photos that showed boulder tracks, e.g., Figure 2. By enhancing the photo images and with a knowledge of variables such as geometric scale and the sun angle, Grumman’s air photo interpreters were able to estimate the size of the boulders and, even more importantly, the width and depth of the tracks that they had left in the soil.
In the meantime, Les and I obtained a narrow range of values for the friction angle of the simulated lunar soil (a basaltic silty sand) from the results of direct shear tests performed in Grumman’s Soil Laboratory under terrestrial conditions. We assumed that the lunar environment had little or no effect on friction angle based on our observations of crater slopes in the Lunar Orbiter photos. Les and I then used all of this information in analyses based on the theory of plasticity to back-calculate the cohesion required for a boulder of given size (and weight) to create the corresponding impression as observed in the photo. As expected, the value of cohesion was greater for the lunar soil than for a terrestrial soil with the same gradation. Once the shear strength parameters had been determined in this way, a bearing capacity analyses could be performed for the proposed size and shape of candidate LM footpads. Although the analyses suggested that the anticipated static loads on the footpads would not result in a bearing capacity failure, the LM designers introduced a sophisticated shock-absorber system in each of the four the legs of the LM consisting of crushable honeycombed infills that would prevent impact loads from reaching the footpads. We also performed settlement analyses based on a plasticity model that we had developed. Although I don’t recall the exact values, I remember that the results of these analyses showed that the anticipated settlements were well below the limit required to satisfy Criterion I. Figure 5 shows the extent of settlement of the LM footpad and the apparent cohesion of the lunar soil as demonstrated by the vertical-sanding footprints.
Buzz Aldrin standing by one of the Eagle’s foil-wrapped footpads. (A tiny image of Neil Armstrong taking the photograph can be seen on Aldrin’s reflective faceplate.) The slightly arms-out stance derives from the pressurized suit. A plaque on the landing stage, which is still on the Moon, is engraved: “Here men from the planet Earth first set foot upon the Moon, July 1969, A.D. We came in peace for all mankind.” (NASA photo)
Q. What are the effects of the Moon’s reduced gravity on solutions to conventional geotechnical engineering problems here on earth?
A. The effect of the Moon’s reduced gravity (1/6 of that on the Earth) on soil-structure interaction was relatively straightforward to evaluate and was easily accounted for by modifying gravity-dependent terms in any structural and/or geotechnical equations that are used conventionally to solve problems on earth, e.g., the γ-term in the bearing capacity equation.
Q. What are the effects of the Moon’s unique environmental conditions on lunar solutions to other conventional engineering problems here on earth?
A. Because there is virtually no atmosphere on the Moon, there is nothing to retain ambient “air” temperatures. Therefore, objects on the surface of the Moon experience virtually instantaneous temperature changes of up to 356º C (640º F) over a very short distance, i.e., between the sunlit and shaded areas on any surface. Scientists and engineers had to evaluate this phenomenon on the integrity of items manufactured on earth, such the LM itself, the astronauts’ space suits, etc. Another unanticipated problem was adhesion of the lunar dust to materials manufactured on earth. The Apollo 11 astronauts reported that every time they returned to the LM, much of the exterior surface of their spacesuits was covered by dust. The same with tools that they were using outside of the LM. This phenomenon was probably due to molecular bonding between the earth-manufactured objects and the molecularly clean surfaces of the lunar soil particles as described previously.
Q. How do you determine the magnitude of differential settlements that could occur between any two of the four legs of the LM and assure that such differential settlements do not cause the vertical axis of the LM to be more than 15 degrees from true vertical?
A. You don’t. But there were some very good reasons why we were not overly concerned with this potential problem. First of all, the Apollo 11 landing site was chosen to be in the area of the Moon known as the Sea of Tranquility. Figure 6 shows the area to be relatively smooth and free of large craters and their associated debris. Second, although all of the complex maneuvers related to this journey (rocket burns, midcourse corrections, etc.) were computer controlled, even those directly related to the descent itself (the LM was “launched” from the orbiting command module with the landing trajectory computer-controlled), the astronauts, all of whom were veteran military pilots, insisted that the actual landing be controlled by the crew. They felt, and rightly so, that they could make a last minute decision, if necessary, to avoid a potential hazard, such as a large boulder or the edge of a crater. Since this aspect of the lunar landing was still not fully resolved up to the time of liftoff, I think it is appropriate to go into a little more detail here on the landing itself because the answer thus far seems rather flippant for a question whose answer has such serious consequences. The following paragraphs are excerpted from:
The LM was equipped with what was, for the time, a sophisticated on-board computer that did much of the routine work of flying the spacecraft. During all but the final moments of the approach, flying the proper trajectory was a matter of analyzing navigation data from inertial and radar systems and then subtly adjusting the thrust and pointing of the LM engine. It was a labor-intensive task and a job well suited to computer control. Not until after “pitchover” occurred, i.e., when the spacecraft rotated from 60 degrees off vertical to 20 degrees did the astronauts’ roles become more than that of monitor-and-backup.
The Apollo 11 landing site at an altitude of approximately 9 miles, one orbit before descent was begun. Tranquility Base is near the shadow line, a little to the right of center. (NASA photo)
Each of the astronauts had a small, double-paned, triangular window in front of him. On the inner surface of each pane in Armstrong’s window, there was a long vertical scale marked in degrees and, at right angles to it, a similar but shorter horizontal scale. At pitchover, Armstrong positioned himself so that the vertical scales were aligned; and Aldrin read a computer output to him that indicated just where he should look on the scale to see the computer’s intended landing point. In principle, if he didn’t like the spot, he could pulse the pistol-grip hand controller forward or back or to either side and thereby tell the computer to move the target a small amount in the indicated direction. According to plan, Aldrin was to give Armstrong an “angle” every few seconds until, at an altitude of about 500 feet, the window targeting scheme lost its usefulness and Armstrong took over complete manual control for the final descent.
However, once Aldrin had given him an initial target angle, Armstrong realized that the computer controls were taking the LM into a field of boulders on the northeast shoulder of a crater the size of a football field. Although the site selection team had picked a smooth patch of ground, the state of the art of spacecraft guidance at the time of Apollo 11 wasn’t nearly as refined as it would be for the later missions. Nowhere on the Moon are craters of that size more than a few kilometers apart and, for this first landing, the NASA flight engineers were not yet ready to fine-tune the approach trajectory to much better than about eight kilometers east or west of the target point and about two kilometers north or south. The Apollo 11 “landing ellipse” contained dozens of craters a hundred meters across or more, and the important point is that the LM had plenty of range so that Armstrong could avoid even the largest of them.
There was no doubt in Armstrong’s mind about not landing in the boulder field if he could avoid it. It wasn’t essential that he land the LM perfectly upright. A tilt of up to 15 degrees would cause no particular problem with the launch back to the SM. However, if the exhaust nozzle or one of the landing struts hit a large boulder, there would be a good chance of sustaining structural damage. Two minutes after pitchover and about two minutes prior to the landing, Armstrong took action. He decided to overfly the crater and land well to the west of it. There was clearly not enough time to give the computer an update via the hand controller since the Landing Point Designator (LPD) was designed for fine tuning and what Armstrong needed was a big change. So he switched to manual control, pitched the LM forward, and began to fly the vehicle like a helicopter. Within seconds, he had slowed his rate of descent from about twenty feet per second down to about three and flew the LM about 1100 feet west beyond the craters and the boulders
While Armstrong flew the LM toward a good landing spot, his attention was totally focused on the job at hand. Aldrin did virtually all the talking; and he, too, was all business. He read the computer output to Armstrong, giving him their altitude, their rate of descent and their forward speed. Back at mission control in Houston it was obvious that the landing was taking longer than planned. Indeed, with each passing second there was mounting concern about how much fuel remained. Because of uncertainties in both the gauges in the tanks and the estimates that could be made from telemetry data on the engine firing, the amount of time remaining until the fuel ran out was uncertain by about 20 seconds. If they got too low, mission control in Houston would have to order an abort.
Drama was the last thing that any one wanted for the first landing. The event itself was exciting enough. Finally, Armstrong found a place that he liked and he began to reduce his forward velocity and let the LM ease down toward the surface. As they came down through 75 feet, mission control radioed that they had sixty seconds of fuel left. In the cabin, Aldrin had already seen a warning light telling him the same thing. But they were close now and it was just a matter of easing themselves down. Armstrong had reduced almost all of their forward velocity by now. As they began to kick up dust with the engine exhaust, Armstrong asked Aldrin to confirm that they were still moving forward a little. He wanted to land on the surface that he could see in front of them, rather than on ground he couldn’t see behind them. Aldrin gave him the confirmation that he wanted and, eight seconds later, they saw the blue contact light on the control panel. The ten-foot-long probes that dangled from the landing gear had touched the Moon. A second or two later the engine shut off and they were down on the surface of the Moon.
In hindsight, it gives me a feeling of great accomplishment when I look at Figures 1 and 5 and see the astronauts and their footprints on the lunar surface. It is not hard to imagine how proud and yet humbled Les Karafiath and I felt when we realized that due in part to our efforts the LM did not sink into the lunar dust more than the few inches we had predicted, that the attitude of the LM’s vertical axis was much less than the critical value of 15 degrees, and that the lip of the SM’s exhaust nozzle was well above the lunar surface.