"Wobble Angle": Characteristics of 11 Apollo-derived Artificial-Gravity Space Station Designs (1963)

"Zero-G and I feel fine" — astronaut John Glenn, the first American to reach Earth orbit, during his five-hour flight on board Mercury-Atlas 6 spacecraft Friendship 7, 20 February 1962. Image credit: NASA.

In early May 1963, Robert Mason and William Ferguson, engineers at the NASA Manned Spacecraft Center (MSC) in Houston, Texas, completed a study of 11 artificial-gravity Earth-orbital laboratory designs. Some might have argued that NASA engineers had better things to do. After all, for two years the space agency's main goal had been to land a man on the Moon and return him safely to the Earth before the Soviet Union did, and the U.S. program still lagged behind its Soviet counterpart.

When the MSC engineers completed their study, the U.S. record for weightless space endurance was held by Wally Schirra, the third American to reach Earth orbit. During the Mercury-Atlas 8 mission (3 October 1962), he racked up a little less than nine hours of weightless experience. About a week after Mason and Ferguson completed their study, Gordon Cooper would set a new record by orbiting the Earth for about 34 hours during the Mercury-Atlas 9 mission (15-16 May 1963).

The world record for weightless space endurance at the time was, however, held by cosmonaut Andriyan Nikolayev, whose Vostok 3 spacecraft lifted off from Baikonur Cosmodrome on 11 August 1962. He orbited the Earth 64 times in 3 days, 22 hours, and 28 minutes, and landed on 15 August 1962. Apart from assurances that Nikolayev was in good health, the Soviet Union shared little information about his physical condition during or after his flight.

Lack of data on human responses to continuous weightlessness goes a long way toward explaining why NASA continued to study Earth-orbiting laboratories two years after President John F. Kennedy made the Moon a major U.S. goal on 25 May 1961. It seemed prudent to some to retain the option to launch a laboratory for studies of human health in weightlessness at least until astronauts could live in space for a period of time equal to the duration of an Apollo lunar landing mission.

Lack of data also explains why Mason and Ferguson studied artificial-gravity laboratory designs. If it were found that humans could not withstand weightlessness for long periods, then it would become necessary to establish a lab in space where the human health effects and engineering requirements of spin-induced acceleration — which is what "artificial gravity" is — could be examined.

There were also policy reasons for studying Earth-orbital laboratories. Before President Kennedy put NASA on course for the Moon, an Earth-orbiting lab had been central to the agency's plans for the 1960s. Some engineers believed that the laboratory should have remained NASA's first priority after Project Mercury, and they looked for opportunities to turn back the clock.

By the end of 1962, the probable cost of the lunar program had become increasingly clear. Grumbling had begun in Congress, placing pressure on Kennedy, who in turn placed pressure on NASA brass to contain space program costs. It seemed possible that the Apollo lunar goal might be found wanting by either Kennedy or, if he lost his bid for reelection in November 1964, by his successor. If so, the reasoning went, NASA might do well to have on hand a plan for an Apollo-derived Earth-orbiting laboratory as a cheap replacement for the lunar program.

In all but one of their 11 designs, Mason and Ferguson had the laboratory and crew reach orbit together; the astronauts would ride in a modified Apollo Command and Service Module (CSM) spacecraft atop the lab's drum-shaped Mission Module (MM). CSM modifications included a much-shortened Service Module (SM) with only enough propulsion, power, and life-support capability for the trip to the lab's 300-mile-high operational orbit and return to Earth.

Mason and Ferguson focused their study on the extent of the shift in the laboratory spin axis that astronaut movement parallel to the spin axis would produce. They called that shift the "wobble angle."

This illustration from Mason and Ferguson's paper depicts the "wobble angle." The line marked "Z" corresponds to the spin axis, which passes through the center of gravity of the orbiting laboratory. The Z at the top would, if the laboratory's spin remained entirely stable, always point directly at the Sun. Astronaut movement parallel to the Z line would, however, cause the spin axis to shift along the curving line labeled "Spin-axis trace." In this design, which corresponds to Laboratory Design 1 below, astronauts would need to contend with a wobble angle of up to 43°. Mason and Ferguson likened this motion to the "rolling of a ship."

The MSC engineers assumed that the orbiting laboratory MM and other structure, habitation and science equipment, and the modified CSM would together weigh about 15 tons. Of that, five tons were allotted to the CSM. All of their designs retained the Saturn IB rocket second stage, the S-IVB, for use as a counterweight. With its liquid hydrogen/liquid oxygen propellants spent, the S-IVB stage would weigh 10 tons.

Mason and Ferguson set the spin rate at a maximum of four rotations per minute. At that rate, and at a distance of 40 feet from the spin axis, the acceleration an astronaut would feel would vary by 15% between their feet and their head, with maximum acceleration being felt at their feet, farthest from the spin axis. Maximum acceleration would be limited to one Earth gravity; minimum acceleration would not fall below one lunar gravity (0.2 Earth gravities).

The 11 images that follow each include two views. The laboratory launch configuration is on the left and orbital configuration is on the right. In all but two of the images, the Z axis/spin axis points at the viewer in both views; for Laboratory Designs 8 and 9, the Z axis in the launch configuration view is turned 90° relative to the orbital configuration view.

Laboratory Design 1: the first Mason and Ferguson artificial-gravity lab design is the simplest, though it also has one of the greatest maximum wobble angles (about 43°). Crew couches in the CSM are at the minimum distance (40 feet) from the spin axis (Z), but the entire two-deck MM is too near the spin axis to avoid a variation in acceleration level between astronaut head and feet greater than 15%. Equipment weight is 12,496 pounds, structure weight is 7504 pounds, and pressurized volume is 2504 cubic feet. Thrusters located at the ends of the lab would expend 52.9 pounds of propellant to start it spinning at a rate of four rotations per minute.

Laboratory Design 2:  An alternate method of solar array deployment improves stability (wobble angle slightly more than 9°) by increasing lab width and mass along the Y axis. Structure weight is 8235 pounds and equipment weight is 11,765 pounds. Pressurized volume is 2505 cubic feet. Unfortunately, no part of the CSM or MM is far enough from the spin axis to avoid a greater than 15% variation in acceleration level between astronaut head and feet. Thrusters expend 55.3 pounds of propellant to spin up the laboratory. 

Laboratory Design 3:  Equipment modules of unspecified function deploy along the Y axis; this helps to reduce maximum wobble angle to about 3.5°. Structure weight including the equipment modules is 12,492 pounds. Equipment weight — 7508 pounds — is the least of any of the designs. Pressurized volume is 2396 cubic feet. No part of the CSM or MM is far enough from the spin axis to avoid a greater than 15% variation in acceleration level between astronaut head and feet. Thrusters expend just 49.7 pounds of spin-up propellant. 

Laboratory Design 4: A tunnel between the CSM and the MM places the CSM crew couches 43.3 feet from the spin axis. Unfortunately, the maximum distance from the spin axis within the MM is just 18.3 feet. Placing the relatively massive CSM far from the spin axis and relatively narrow structure along the Y axis contribute to a wobble angle of nearly 44°. Structure weight is 8687 pounds and equipment weight is 11,313 pounds. Pressurized volume is 2396 cubic feet. Thrusters expend 50.7 pounds of propellant to spin up the laboratory. 

Laboratory Design 5: The tunnel linking the CSM and MM is extendable, increasing CSM crew couch distance from the spin axis to 52.9 feet. The wobble angle is identical to that of Design 4. Structure weight is 8290 pounds and equipment weight is 11,710 pounds. Pressurized volume is 2400 cubic feet. The MM entirely surrounds the spin axis; in theory, an astronaut at the spin axis would be weightless while the station spun around them. No part of the MM is far enough from the spin axis to avoid a greater than 15% variation in acceleration level between astronaut head and feet. Thrusters expend 65.7 pounds of propellant to spin up the laboratory. 

Laboratory Design 6: Both the CSM and the MM telescope away from the spin axis. The 45° maximum wobble angle is the greatest of the 11 designs. Structure weight is 7505 pounds and equipment weight is 11,765 pounds. Pressurized volume is just 1633 cubic feet, the least of any of the designs. About half the MM is far enough from the spin axis to avoid a greater than 15% variation in acceleration level between astronaut head and feet. Thrusters expend 68.3 pounds of propellant to spin up the lab. 

Laboratory Design 7 is similar to Design 6, but its modified solar array configuration increases its width and mass along the Y axis, reducing its maximum wobble angle to slightly less than 29°. Structure weight is 7869 pounds, equipment weight is 12,131 pounds, and pressurized volume is 1743 cubic feet. Thrusters expend 68.3 pounds of propellant to spin up the laboratory.

Laboratory Design 8 combines features of Designs 3 and 7 to achieve a wobble angle of slightly less than 2.5°. A new feature of this design is a docking port for a visiting modified CSM at the spin axis (Z). In many artificial-gravity station designs, docking ports at the spin axis rotate spin "backwards" so that they appear to remain still, facilitating docking. Mason and Ferguson gave no indication that their design would include a counter-spun docking port, however. Structure weight is 12,169 pounds, equipment weight is only 7831 pounds, and pressurized volume — without a second CSM — is 2048 cubic feet. All of the CSM and nearly all of the MM are far enough from the spin axis to avoid a greater than 15% variation in acceleration level between astronaut head and feet. Thrusters expend 66.9 pounds of propellant to spin up this design. 

Laboratory Design 9 includes new structural elements: a "fork" and cables that permit the spent S-IVB stage to be pivoted 90° relative to its launch axis. This reduces the wobble angle to slightly less than 1° — the least of any of the 11 designs. Unfortunately, no part of the CSM or MM is far enough from the spin axis to avoid a greater than 15% variation in acceleration level between astronaut head and feet. Structure weight is 8306 pounds and equipment weight, 11,694 pounds. Pressurized volume is 3118 cubic feet. Thrusters expend 64 pounds of spin-up propellants.

Laboratory Design 10 employs a "rigid support" and cables to pivot the spent S-IVB stage 90° relative to its launch axis. Maximum wobble angle is 1°. The CSM crew couches and part of the MM are far enough from the spin axis to avoid a greater than 15% variation in acceleration level between astronaut head and feet. Structure weight is 8120 pounds and equipment weight is 11,880 pounds. Pressurized volume is 2400 cubic feet. Thrusters would expend 71.8 pounds of propellants to spin up this design.

Laboratory Design 11 includes no CSM in its launch configuration view because structure and equipment weight is too great. The large MM is extendible. The CSM is displayed in the orbital configuration view as it would appear after it launched separately and docked with the MM in orbit. The pivoted S-IVB stage and the solar panel arrangement help to compensate for the large MM, yielding a wobble angle only slightly greater than Design 9. Structure weight is 14,047 pounds and equipment weight is 15,953 pounds. Pressurized volume is by far the greatest of the 11 designs (3828 cubic feet), as is the amount of spin-up propellant required (116.1 pounds). Spin-up would take place after the CSM arrived. All parts of CSM and MM are far enough from the spin axis to avoid a greater than 15% variation in acceleration level between astronaut head and feet. 

Source

Project Apollo Conceptual Rotating Space Vehicle Designs Using Apollo Components for Simulation of Artificial Gravity, NASA Project Apollo Working Paper No. 1073, NASA Manned Spacecraft Center, 8 May 1963.

More Information

Space Station Resupply: The 1963 Plan to Turn the Apollo Spacecraft into a Space Freighter

To "G" or Not to "G" (1968)

"A True Gateway": Robert Gilruth's June 1968 Space Station Presentation

A Forgotten Rocket: The Saturn IB