Note: this post may not make much sense unless you have already read Part 1 (1). Even then, I make no promises…
In Part 1, we considered the use of the overpowered Gemini retrorockets and the even more overpowered Gemini-B retrorockets for de-orbiting those spacecraft. Despite the obvious nature of their designations, it appears the retrorockets were sized for launch escape purposes, but were conveniently available for de-orbiting when the spacecraft made it safely to orbit. De-orbiting by use of the Gemini retros resulted in a faster return from orbit than the theoretical minimum capability provided by the Orbital Attitude and Maneuvering System thrusters would have provided, with the added advantage of depleting the explosive solid fuel rockets instead of letting them burn and explode during re-entry.
The discussion and calculations in Part 1 assumed that the de-orbiting thrust was delivered exactly into the direction of travel, in what is the most efficient application of that thrust. However, in practice, the Gemini retro maneuver involved an element of pitch. If Gemini-B had ever flown it might also have involved an element of yaw.
First, note that NASA oriented its Gemini spacecraft slightly nose-down (“pitch down”) during retrofire, apparently to help the command pilot maintain the proper attitude by keeping the Earth’s horizon at the top edge of his forward-looking window. I have calculated that the nose-down pitch angle for manned Gemini in four cases was about 21 degrees. This angle allowed the pilots to confirm visually that their retro attitude was correct: in those early years of the space age it was not unheard of for spacecraft to have significant errors in the direction they were pointed for retrofire. The nose-down pitch presumably allowed them to confirm that the flow of the earth’s surface past the Gemini’s nose was the same on the left and right sides, and thus that they were correctly oriented “blunt-end forward” (yes, that is what they called it; it even had an acronym: “BEF”) so the retrothrust slowed them down and they fell out of orbit.
Nose-down pitch of 21 degrees at retrofire would deliver less effective thrust directly opposite the orbital motion, thus extending the travel time in the de-orbit arc. However, the downward component of the thrust would have “pushed” the orbit lower, making it more elliptical and shortening the time and distance traveled to entry interface. A purely downward push would have produced a new low point, or perigee, about ¼ of the way around the Earth, and a new high point, or apogee, about half an orbit after that.
My math skills only allow me to calculate simple orbit changes from thrusting directly forward or backward. I might be able to struggle through the calculations for a purely upward or downward maneuver. But the combination of the two is beyond me. Luckily, I was able to enlist Ryan Whitley of NASA JSC to mathematically model an inclusive set of Gemini and Gemini-B de-orbit cases. Along the way he helped me understand my own questions better.
I will present the results from the case of a circular orbit at 344 kilometers (186 nautical miles, 214 statute miles), but we also modeled elliptical orbits of 344 by 148 km. (186 x 80 n.mi., 214 x 92 st. mi.) and 256 by 144 km. (138 x 78 n. mi., 159 x 90 st. mi.). The circular orbit provides the most challenging scenario; the elliptical orbits represent likely reconnaissance orbits early and late in the 30-day mission whose intentionally-low perigees are already very close to the threshold for atmospheric entry.
The Gemini de-orbit maneuvers combining retrograde thrust and nose-down pitch produced a terminal orbit designed to intersect the atmosphere—and thus initiate re-entry—at its low point about ¼ of the way around the globe. This orbit had a slightly flattened angle of entry into the atmosphere and slightly increased the entry velocity compared to the nose-horizontal case (see Table 1).
Table 1. Effects of Nose-down Pitch and Yaw on Gemini Descent Orbit Characteristics
Second, there is a simple solution to the problem (if it really is a problem) of Gemini-B having 50% more retrorocket thrust than Gemini: waste the excess thrust.
By trigonometry, aiming the Gemini-B sideways (this is called “yaw”) by 48 degrees—that is, just over halfway between parallel to its direction of travel and perpendicular to its direction of travel—before its six retrograde rockets fired would still have produced the same orbital deceleration as Gemini would have achieved by firing its four retro rockets directly backwards. Achieving the same atmosphere re-entry velocity and flight path angle (the angle of intersection with the atmosphere) as Gemini had would keep re-entry thermal loads within the qualification limits validated during testing. Those limits were validated by Gemini spacecraft #2 in two separate suborbital flights, first for NASA’s Gemini program in January 1965 and then for the Air Force’s Gemini-B development program in November 1966.
There is no reason the Gemini-B/MOL flights would not have continued the practice of nose-down pitch established during NASA’s ten manned Gemini missions, to provide the same assurance. Assuming deorbiting was to take place on the southbound leg (called the descending node) of a polar orbit, Ryan’s model showed that aiming the Gemini-B’s 50% excess retrograde thrust to one side or the other with a yaw of 132 degrees (which is 48 degrees less than the usual 180 degrees of yaw, that is, aiming directly backwards to the direction of flight) while maintaining Gemini’s 21-degree nose-down pitch would have produced a re-entry essentially identical to a typical Gemini re-entry except that its landing point would be moved 84 kilometers (53 statute miles) either to the east or the west of its polar orbital track (Table a). In both cases, the capsule would have intersected the upper atmosphere at the official re-entry altitude of 400,000 feet (122 kilometers, 76 miles) at an angle of no more than 1.3 degrees and a velocity of 7,872 meters per second (see Table 2).
Table 2. Effects of Nose-down Pitch and Yaw on Gemini and Gemini-B Descent Orbit Characteristics
All that would seem to be required is to tell the recovery forces which way the Gemini-B would be aiming so they could position themselves appropriately to the east or west of the polar orbit ground track.
But wait—there’s more. The effect on Gemini-B would have been even further complicated by the geometry of the retrorockets’ mounting in the adapter module. They would all have been mounted at or below the module’s left-right centerline (see Figure 1) because the top half of the module would have accommodated the transfer tunnel from the Gemini-B cabin back to the MOL. Remember that plug hatch in the heat shield I mentioned in Part 1? It would have opened up into the transfer tunnel to allow the pilots to transit in shirtsleeves from their capsule to their habitat for their month-long mission without ever passing through the vacuum of outer space (2). The NASA Gemini retrorocket arrangement could not have been used because, among other reasons, one arm of its cross-shaped braces would have interfered with that tunnel.
Figure 1. Retrograde rockets in NASA Gemini (4 retrorockets) and Air Force Gemini-B (6 retrorockets) illustrating the central symmetrical arrangement in Gemini and the asymmetrical off-center arrangement in Gemini-B. Note that the Gemini retrorockets are viewed from the top while those of the Gemini-B are viewed from the bottom. (If this figure looks familiar, it was previously Figure 3 in Part 1.)
I estimated that this arrangement of the Gemini-B retrorockets would have required the command pilot to aim about 25 degrees nose down, compared to 21 degrees for Gemini, to keep the direction of the thrust through the spacecraft’s center of mass in the same relative direction as on Gemini (see Figure 2). Early in the Space Age, there had already been considerable nervousness about making sure the retro thrust was delivered in the correct direction, compounded by the fact that the Gemini-B may have also required a unique decision about whether to aim left or right of the ground track. If I were a MOL planner, I might well have decided that the 21-degree nose-down pitch was already well-established by Gemini and that the small loss (9% by trigonometry) in retro thrust due to the 4-degree offset would not have had a significant effect on the velocity change delivered by the six retro rockets.
Figure 2. Thrust vectors of Gemini-B retrorockets (approximated graphically).
I don’t know if the 48-degree yaw or the 25-degree nose-down pitch were ever established as standard procedure for Gemini-B; maintaining the standard Gemini yaw of 180 degrees and 21-degree nose-down pitch during Gemini-B retrofire would have produced a flight path angle still within acceptable limits and only a slightly higher entry velocity, so the 48-degree yaw may not even have been evaluated. Maybe there is one among the 825 MOL documents (3) declassified in October 2015 that confirms or refutes my hypothesis, but I have not found it yet.
This has been a circuitous disquisition on some arcane aspects of an almost invisible aspect of a cancelled space program from five decades ago; it certainly justifies the “crypto” and “trivio” parts of this blog’s name, as well as the “astro.” However, these are the details that lure me to this type of in-depth analysis. If you have read this, I thank you for your patience and congratulate you on knowing something that practically nobody else in the world knows, or even knows they don’t know.
Acknowledgements
My thanks to Ryan Whitley of NASA Johnson Space Center for doing the calculations, and to Roger Balettie, Jorge Frank, Jonathan McDowell and Jim Oberg for their patience and good humor in educating me about orbital mechanics.
References.
- “A Jones for MOL #11: Retroactivity of MOL (Part 1),” http://www.astrocryptotriviology.com/blog/2016/6/18/a-jones-for-mol-11-the-retroactivity-of-mol-part-1 (accessed July 23, 2016).
- “A Jones for MOL #3: Down the hatches,” http://www.astrocryptotriviology.blogspot.com/2012_09_01_archive.html (accessed Oct. 4, 2015) and “A Jones for MOL #7: Hatches? We Don’t Need No Stinking Hatches!” http://www.astrocryptotriviology.blogspot.com/2012_12_01_archive.html (accessed Oct. 4, 2015).
- National Reconnaissance Office, Declassified Records, Index, Declassified Manned Orbiting Laboratory (MOL) Records, http://www.nro.gov/foia/declass/MOL.html (accessed July 23, 2016).