Spaceflight Insider

Jack Crenshaw: the space pioneer you never heard of

The crew portrait of Apollo 13. Commander Jim Lovell, Command Module Pilot Jack Swigert, Lunar Module Pilot Fred Haise. Photo Credit: NASA

The crew portrait of Apollo 13. Commander Jim Lovell, Command Module Pilot Jack Swigert, Lunar Module Pilot Fred Haise. Photo Credit: NASA

Despite their scientific justification of gaining samples of the lunar regolith, the Apollo expeditions had two objectives laid down by President John F. Kennedy in 1961: to land a man on the Moon and return him safely to the Earth. A critical part of the second objective, returning safely to the Earth, was a trajectory that would bring the spacecraft back from the Moon and re-enter Earth’s atmosphere.

Dr. Jack Crenshaw was one of the pioneers in designing the figure-8 trajectory which became known as the free-return trajectory. The early Moon missions set off for our closest celestial neighbor in the free-return trajectory which, if uncorrected, would loop them around the Moon and return them straight to Earth.

In order to orbit the Moon and land on it, the Apollo spacecraft’s Service Propulsion System (SPS) engine had to fire in order to slow the vehicle down and settle into lunar orbit. Delicate calculations were needed in order to ensure the orbit would not bring the craft into a collision with the lunar mountains.

Jack Crenshaw. Photo Credit: Jack Crenshaw

Crenshaw. Photo Credit: Jack Crenshaw

Crenshaw graduated from Auburn in 1958 and applied to the National Advisory Committee for Aeronautics (NACA)—the precursor to NASA. He received a reply with NACA letterhead—with the “C” crossed out and replaced by an “S”. That was Crenshaw’s first introduction to the U.S. space agency.

Crenshaw joined NASA Langley in April of 1959, where he was slated to work with one of the wind tunnels. Crenshaw protested that he was a physicist and knew nothing about aerodynamics. He asked where he could use his expertise in advanced dynamics. From there, was placed in the Theoretical Mechanics Division with Clint Brown.

Later that year, Brown created the Lunar Trajectory Group, led by Bill Michael, which was to study lunar trajectories for manned and unmanned missions (and they were all ‘manned’ in that era). The team in which Crenshaw found himself included Bob Tolson, John “Gap” Gapcynski, and Wilbur Mayo. They were tasked with designing a mission based on the old Scout solid-propellant rocket, to send a “Brownie” class camera to photograph the far side of the Moon.

“We wanted a circumlunar trajectory because we wanted to take a photograph of the back side of the Moon and (unlike the Russians, who used a TV camera) recover the film,” Crenshaw said. “Later, we used the circumlunar trajectory in Apollo because we wanted a fail-safe return to Earth—even in missions that were nominally intended for landings—in case something went wrong (as it did in Apollo 13).”

As Crenshaw says on his website: “When Scout’s projected payload at the Moon went from a few hundred pounds, through zero and negative, those plans were abandoned. However, the effort left us more than ready for Apollo when it came along.”

Bill Michael came across a paper by Hans Lieske and Bob Buchheim of RAND Corp., who had studied the circumlunar trajectory. Michael asked Crenshaw to study it in more detail, using a computer simulation of the Restricted Three-Body Problem. The study was later expanded to include a full 3-D, N-body simulation.

Michael and Crenshaw authored the paper Trajectory Considerations for Circumlunar Missions, which was presented at the Institute of Aerospace Sciences 29th Annual Meeting in New York in Jan. of 1961.

“I can’t say for certain that Bill Michael and I—or even Lieske and Buchheim—were the first to ‘invent’ the circumlunar trajectory,” Crenshaw said. “In recent years, I’ve tried very hard to find a copy of Lieske and Buchheim’s paper, but the best I’ve been able to do is a vague reference: Beginnings of space studies and efforts at RAND during the mid-1950s; work with Hans Lieske, Al Lang, and Bob Buchheim.”

Sketch of the Free Return Trajectory. Photo Credit: Karen Wehrstein

Sketch of the Free Return Trajectory. Photo Credit: Karen Wehrstein

Unfortunately, in those days, a lot of research went unpublished. Crenshaw explains, “We were all too busy doing stuff to write it down for posterity. This was especially true on the West Coast, where a lot of studies got passed around, scientist to scientist. Many of the ‘think tanks’ were doing studies for classified USAF programs, which—for reasons I can’t begin to fathom—included missions to Mars.”

The difficulty in plotting a circumlunar trajectory is that it is very sensitive to errors in the initial conditions.

“The chances of Apollo astronauts leaving the Earth, swinging past the Moon, and returning to a safe re-entry/splashdown without midcourse guidance are slim to none,” Crenshaw said. “Even so, by using the circumlunar trajectory (the Free Return) as our baseline, we were giving the astronauts at least a fighting chance of getting home alive.”

During the eventful flight of Apollo 13, when an oxygen tank exploded and the command module Odyssey had to be powered down, Commander Jim Lovell was able to save the mission by applying midcourse corrections manually with no help from the Apollo flight computer.

“Ironically enough,” Crenshaw said, “Apollo 13 was the first Apollo mission that did not leave the Earth on a Free Return trajectory. I’m not sure exactly why, but I expect it was because they needed a different trajectory to reach the landing site in the Fra Mauro highlands.”

In fact, none of the Apollo lunar missions after Apollo 12 used the Free Return trajectory, so that they could better target their landing sites.

“So after the accident, the first thing the Apollo 13 astronauts had to do was to get back on a Free Return trajectory,” Crenshaw said.

After leaving NASA, Crenshaw worked at GE in Daytona, studying abort trajectories. There, he came up with two classes of maneuvers called “Fast Returns”. If a spacecraft did not land on the Moon, it would still have a lot of unspent fuel in both the service module as well as the lunar module. In order to make a faster return trip, that fuel could be used to get home quickly.

Apollo 13 mission patch image credit NASA

The Apollo 13 insignia. Image Credit: NASA

“In the movie Apollo 13, there’s a scene where the Gene Kranz character, played by Ed Harris, first hears of the accident from his trajectory specialist,” Crenshaw relates. “Kranz says, ‘Can we do a fast return?’ Answer: ‘No, we’re too far out for that. We’ll have to get on a free return.’ That exchange struck me because I had designed both trajectories. I thought, ‘These guys just told my life story.'”

It was fortunate, in fact, that the Apollo 13 crew did not attempt the Fast Return. To do so, they would have had to use the SPS engine, which was likely damaged in the explosion. Lighting the damaged engine may well have destroyed the spacecraft.

After his time at NASA, Crenshaw worked for General Electric on their NASA Apollo Study Contract in a small team that was responsible for trajectory work. Lieske, who had studied lunar trajectory and provided the basis for Crenshaw’s and Bill Michael’s 1961 paper, was the systems engineer for trajectories. His job was to supply Lieske with trajectories.

Crenshaw said: “GE has always tended to encourage competition between groups, and the Apollo effort was no exception. During my stay there, there were no less than eight departments, all vying to be THE GE trajectory analysis group. Hans sought to have one of his own and cooked up a devious scheme to get it. One day he offhandedly asked me to look at the problem of Return from the Moon. As far as I know, no one had yet done that one. I said I would, but there was no sense of urgency about it, and we certainly had more pressing problems to study.

“Well, it turned out that Hans was complaining to management that my team wasn’t responsive enough to his needs. He had contracted with another company—Space Technology Labs (STL) in Houston—to study the same problem. His hope was that he would get results from STL before he got them from us, so he could say, ‘See, I’m having to go outside the company because I can’t get trajectories from Crenshaw.’ Somehow or other, my manager heard about the plan. So we jumped on the Return from Moon problem and got the results. Hans never got them from STL. Management found him out, and he was fired.”

A few months later, Crenshaw attended a conference at the American Institute of Aeronautics and Astronautics (AIAA) conference, and he saw that there was a paper by Dr. Paul Penzo on trajectories for Return from the Moon.

“After his presentation, I approached Paul and told him I had also studied the problem,” Crenshaw said. “Over lunch, I told him the story of Hans Lieske and his scheme to use STL as a weapon against me. Paul said, ‘There’s more to the story than you think.’ I asked, ‘How so?’ He said, ‘I was the guy at STL!’.”

Because he had not studied the problem before, Penzo had not been able to produce results on Lieske’s tight schedule, but the problem intrigued him and he continued to study it which brought him to AIAA.

“Paul and I had a good laugh over it, and [we] became fast friends, though we’ve not met since the Apollo days,” Crenshaw said.

According to Crenshaw, Bill Michael was the first to analyze Lunar-Orbit Rendezvous for the Apollo missions.

“He published his work in a NASA Tech Note authored by yours truly,” Crenshaw said. “Thanks to a gee-whiz article in Life Magazine, John Houbolt got credit for that idea, and has been trying ever since to get big-bucks NASA payments for ‘his’ idea.”

In 1962, Crenshaw developed a technique known today as Universal Variable. “Instead of separate sets of equations for elliptic, hyperbolic, and parabolic orbits, this formulation unifies the equations in a single set of new functions I called the Unified Functions. Despite the fact that I published them first—and used them in all my studies for GE—Richard Battin got the credit, and they became known as the Lemmon-Battin functions.”

In 1961, Crenshaw had studied the motion in near-circular orbits and developed a theory for the motion of a spacecraft relative to a reference circular orbit. That technique is widely used today for geostationary missions, and it has become known as the Clohessy-Wiltshire equations.



Collin R. Skocik has been captivated by space flight since the maiden flight of space shuttle Columbia in April of 1981. He frequently attends events hosted by the Astronaut Scholarship Foundation, and has met many astronauts in his experiences at Kennedy Space Center. He is a prolific author of science fiction as well as science and space-related articles. In addition to the Voyage Into the Unknown series, he has also written the short story collection The Future Lives!, the science fiction novel Dreams of the Stars, and the disaster novel The Sunburst Fire. His first print sale was Asteroid Eternia in Encounters magazine. When he is not writing, he provides closed-captioning for the hearing impaired. He lives in Atlantic Beach, Florida.

Reader Comments

But who is Richard Crenshaw in the URL to this article?

Hi Eerik,

It looks like the link is related to Richard, I am not aware that in Jack W. Crenshaw, the W stands for Richard.. 🙂

After all of this year, Dr. Chrenshaw is still active working on trajectory calculations. I have the privelage to work with Dr. Crenshaw. He is my mentor in Aersopace and more importantly my friend.. One thing that the author forgot to mention is that Jack has coined a new acronym for the KISS priciple: Keep It Short and Simple…


Yes, the REAL Hidden Figures not the bogus made up embellished BS that hollyweird has just released.

I was ar Auburn (Alabama Polytechnic Instute) along with Ken Mattingly who was the astronaut who helped to,guide Apollo 13 iback to earth. Both of these guys were the geniuses that set the grading curves for every class. I worked at NASA in Huntsville in 1961 through 1965. We did indeed have computers that were used for any and all calculations. My wife was a secretary there. She, of course was consulted by Werner von Braun when a critical issue arose..(tongue in cheek). I have not seen the HIDDEN FIGURES movie, but from what Izvestia heard, I think it is a total fabrication.

Hello Marvin and Jim,

I would ask you to not have a negative sentiment towards the movie Hidden Figures. I would ask you to actually read the book that the film is based on. The truth is that Americans of all stripes contributed to our Space Program (this is true and is much more so today). The book Hidden Figures by Margot Lee Shetterly and Rise of the Rocket Girls by Nathalia Holt tell of the experiences of some people whom the general public did not know about – I think that is helpful. Hidden Figures is not bogus, but an important part of our shared history.

With respect to Apollo 13, the Command Module was saved by the Lunar Module which functioned as a life boat. The Lunar Module was built in Beth Page, New York. A key person who did calculations on the fuel load and thruster firings of the Lunar Module was a man named Carl Echols (a black man), one of the Lunar Module engineers. He was woken up very early in the morning and told to rush into Grumman Headquarters, and was placed on a phone with Mission Control.

Carl Echols had to give orders over the phone to mission control. Carl’s story was well documented, however he was NOT featured in the movie Apollo 13, though his work was life saving and critical. I should add that an article that discusses him is currently being used as a critique of black Americans. The article is “Giant Step” – It discusses the blacks that worked in NASA, and the social conditions going on in America at that time – Poverty and the Vietnam war. The crux of THAT article is the black Americans in the space program and that their work is largely unnoticed by the general public.

Lastly, I know Mr. Crenshaw’s work – He is an incredible engineer and has written many good articles, specifically in the CMP publications.

In conclusion The Preamble of the Declaration of Independence of our country espoused a hope of a Nation, that I feel we should uphold especially with what we feel inside towards others – so we should have good feelings towards our fellow citizens, even if they are different.

Hidden Figures embellishes on historical events and should therefore not be taken as historical fact. You are asking us to suspend our disgust for Hollywood colorization of the facts in order to support a fabricated gender specific narrative. Sorry…no sale.

Richard Gornik

I knew Carl Echols at Grumman….what a guy!!!

XAVI you are nothing more then
a naive,ignorant,oblivious person
blacks can never be anything
especially engineers of any type what you said is nothing more than liberal propaganda,ruse,deceit,lies,shill,delusional comments making false vouchers claiming he did the things that you mentioned and said. if that was the case how come African blacks are still failing in all black Schools an public schools same thing happens in Haiti Jamaica and Sub Saharan Africa because if they are an or were succeeding in school they would have their own version
of NASA in their own nation’s and Sub continent.

Michael Helton

I don’t doubt that there was a group of colored gals working on computations on the Apollo Program but I have some reservations. I saw the movie and read the book “Hidden Figures” very carefully to find any evidence of the math used and required geometries to do Lunar launch windows — found none. I did those calculations when working for NAA in the mid 1960’s to verify we still had launch windows to get to the Moon when the Apollo capsule was being redesigned due to the Apollo 1 fire. The book is poorly written and centers around racism – not the mathematical processes needed. I wrote the author, but she never responded. I found it interesting that this story (“Hidden Figures”) did not come out to the general public until just after John Glenn died. I never heard of these gals until the story came out after Glenn died, but I do remember the name “Crenshaw” from these days.

I’d like to clarify a couple of points. First, about Hidden Figures: XAVI is right: You have to distinguish between the book by Shetterly and the movie. I thought the book was well done and she gave an EXTENSIVE set of notes and references. Yes, Mike is correct in that Shetterly is obviously focussed on race. She knows nothing at all about technical issues.

OTOH, as a Southern boy from Montgomery, Alabama, I was fascinated by her description of how black families in VA hung together to deal with racism in VA. Even the women’s sororities were all about supporting families.

I also learned (and I think this is definitely true) that the racial attitudes in VA were _WAY_ more hostile to blacks than we ever dreamed of in AL, George Wallace to the contrary.

As a kid, I often saw how important family and God was to the black folks around me. At that time, family was everything. It was a far cry from black life in the inner cities, today — more’s the pity.

OTOH, the _MOVIE_ is, I think, total junk. Like Mike, I looked at some of the equations movie Katherine was putting on the board, and I simply don’t believe they’re real.

For starters, at one point she wrote down a result in kilometers. That would _NEVER_ have happened in 1954 NACA: We always used either ft or nautical miles.

I don’t know what was going on in the making of the movie, but I’m told that they spent more on campaigning for the Academy Award than actually making the movie.

Also, the movie was actually made _BEFORE_ the book. They made the movie; they based it on Shetterly’s early notes.
I suspect that there was some serious “hidden” motives involved in the making of the movie.

Two fact-checks: The movie has a scene where IBM technicians are unable to get the IBM 7094 to work, until one of the West Computing ladies stepped in and fixed the problem with a couple of lines of code.

That could _NEVER_ happen. First, NASA’s first computer was the IBM 650. When I was there in 1959-60, we only had a 702. The 7094 was years away.

Second, IBM field technicians were EXCELLENT at what they did. There’s no way they’d be fumbling around like that.

OTOH, the book and movie were quite correct in that one of the West Computing girls figured out that once computers came along, their value in being able to run spreadsheets on Friden calculators would go the way of the dinosaur.

Bob Tolson was one of my colleagues in the Lunar Trajectory Group, but he was also at NACA starting in 1953. He told me that one of the black ladies absolutely wrote the code for a simulation of the Restricted Three-Body Problem (RTBP). But not for the 7094 or even the 702. It was for the 650, which had a drum memory (core did not exist then).

When I first joined the group, we had a new solver for the RTBP, written in assembly language for the 702. My first job was to validate the program, that it correctly implemented the equations of motion (it did. No errors found).

I have no idea who actually wrote the code, but if you told me that it was the same black computer that wrote the 650 version, I’d believe it in a flash.

One last thought: I’ve written elsewhere that we used to do calculations on a Friden calculator (to 10-digit precision). When I asked my boss Clint Brown what I should do if I had a job too big for me, he said, “Take it to the computer room.”

I naively thought, “Hot Dog! I’m finally going to get to see the Giant Brain everybody’s talking about.” But it turned out to be a roomful of women banging on Fridens!

Over time I took many jobs to the Computer Room, and the women (all white) did a wonderful job.

As recently as two years ago, I never thought of them as doing more than banging on the calculator, I never considered them to be mathematically adept.

My mind was changed when I found that all Computers had to have math degrees. Also, I realized that they weren’t just doing add, subtract, multiply, and divide operations. They also had to know how to use functions like sine,cosine, etc. And log and exp. And a whole lot more, because the aerodynamics problems sometimes involved things like Legenre polynomials and many other weird functions.

And that goes back to the black ladies of West Computing. Think about it. In 1950’s Virginia, what kind of work was a black woman going to do? She could either be a maid or cleaning lady, or she could be a teacher.

To be a teacher, she had to know math.

The Computer ladies that I knew were all white. I had never heard of West Computing; didn’t even dream it existed.

The NACA of the 50’s was lily white, from the managers to the engineers to the wind tunnel techs to the machine-shop guys. Not one single black person in sight. For all I know, even the janitors were all white.

That said, it’s easy to understand why nobody much knew about the West Computing ladies.

Oh, yeah,I almost forgot. Much was made in the movie of how Katherine ran trajectories by hand. They show her doing it all in her head, but that’s ridiculous.

When I first heard all this, I thought that the idea was ridiculous, even if she did it on a calculator. No _WAY_ was she going to do 4th-order Runge-Kutta integration on a calculator.

But then I realized: Who said it had to be RK-4? The simplest way to do numerical integration is Euler’s method, and it absolutely could be done on a calculator. Euler’s method is not accurate enough by modern computer standards, but to use it as a check on the computer’s more accurate results? Yes, it could be done, and I do believe that Katherine Jonson did it.

Get this , this so called Carl Echols is nowhere to be found…LOL…more BS!

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