Topics: History Of Physics - Richard Feynman

Richard Feynman

Born: 11 May 1918 in Far Rockaway, New York, USA

Died: 15 Feb 1988 in Los Angeles, California, USA

Richard Feynman's parents were Melville Feynman and Lucille Phillips. Melville was born into a Jewish family in Minsk, Belarus, and emigrated with his parents to the United States when he was five years old. He was a business man who tried, not too successfully, many different types of business. It is clear that his talents were not in business but rather in science which was the subject that fascinated him but he never had the opportunity to make a career from it. Lucille Phillips was born in the United States into a Jewish family. Lucille's father had emigrated from Poland and her mother also came from a family of Polish immigrants. She trained as a primary school teacher but married Melville in 1917 before taking up a profession.

After their marriage Lucille and Melville Feynman moved into a Manhattan apartment and, in the following year, their first child Richard was born. Melville wanted his first child to be a son and he also wanted him to become a scientist so, overjoyed when he got the son he wanted, he did all he could to interest Richard in science throughout his childhood. Gleick writes [6]:-

Melville's gift to the family was knowledge and seriousness. Humour and storytelling came from Lucille.

Tragedy struck the family when Richard was five years old for Lucille and Melville had a second son who died when four weeks old. It meant that a sadness fell over the household which must have greatly affected the young Richard. After this, he remained an only child until his sister Joan was born when he was nine years old. The family moved several times during these years but when Richard was ten they settled in Far Rockaway.

Richard, or Ritty as his friends called him, learnt a great deal of science from Encyclopaedia Britannica and taught himself elementary mathematics before he encountered it at school. He also set up a laboratory in his room at home where he experimented with electricity. In particular he wired circuits with light bulbs, he invented a burglar alarm, and he took radios apart to repair damaged circuits. When he entered Far Rockaway High School his interests were almost entirely mathematics and science. He found little liking for arts type subjects at this time [4]:-

I always worried about being a sissy; I didn't want to be too delicate. To me, no real man ever paid any attention to poetry and such things.

At school Feynman approached mathematics in a highly unconventional way. Basically he enjoyed recreational mathematics from which he derived a large amount of pleasure. He studied a lot of mathematics in his own time including trigonometry, differential and integral calculus, and complex numbers long before he met these topics in his formal education. Realising the importance of mathematical notation, he invented his own notation for sin, cos, tan, f (x) etc. which he thought was much better than the standard notation. However, when a friend asked him to explain a piece of mathematics, he suddenly realised that notation could not be a personal matter since one needed it to communicate. He really enjoyed mathematics competitions and was a real star in his school. In his final year at Far Rockaway High School he won the New York University Math Championship.

After leaving school he applied to several universities to study there. One would have expected every university to which he applied would enthusiastically offer him a place but it was not that easy. Although his grades in mathematics and science were outstanding, he had performed much less well in other subjects. There was also the "problem" that he was a Jew, which really was a problem in the United States at this time with universities having quotas on the number of Jews they admitted. He sat an entrance examination for Columbia University and they turned him down. He never quite forgave them for charging him 15 dollars and then rejecting him. He was accepted, however, by the Massachusetts Institute of Technology.

He entered MIT in 1935 and, after four years study, obtained his B.Sc. in 1939. He went there to study mathematics but, although he found the courses easy, he became increasingly worried by the abstraction and lack of applications which characterised the course at this time. He read Eddington's Mathematical Theory of Relativity while in his first year of studies and felt that this was what he wanted from mathematics. His mathematics lecturers presented him with the view that one did mathematics for its own sake so Feynman changed courses, taking electrical engineering. Very quickly he changed again, this time moving into physics. It is interesting to think that had Feynman taken the mathematics course at Cambridge which Hoyle took around the same time, he would have found it exactly what he wanted.

The physics course that Feynman took at MIT was not the standard one. He took Introduction to Theoretical Physics, a class intended for graduate students, in his second year. There was no course on quantum mechanics, a topic that Feynman was very keen to study, so together with a fellow undergraduate, T A Welton, he began to read the available texts in the spring of 1936. Returning to their respective homes in the summer of 1936 the two exchanged a series of remarkable letters as they tried to develop a version of space-time where (quoted from one of the letters - see [6]):-

... electrical phenomena [are] a result of the metric of a space in the same way that gravitational phenomena are.

By 1937 Feynman was reading Dirac's The principles of quantum mechanics and seeing how his highly original ideas fitted into Dirac's approach. In fact Dirac became the scientist who Feynman most respected throughout his life.

We mentioned above that Feynman went home for his vacations. In fact he applied for summer jobs at the Bell Telephone Laboratories every summer but was always refused a position there despite the highest recommendations. Although it can never be proved, there seems no other reason that he would be turned down other than that he was Jewish.

As he approached the end of his remarkable four undergraduate years at MIT he began to think about studying for his doctorate. Since he had been so happy at MIT and also believing it to be the leading institution, he approached the head of physics, John Slater, requesting that he stay on to take a Ph.D. course. Slater told him that for his own good he had to move and he suggested Princeton.

Despite the personal recommendation that Harry Smyth at Princeton received from Slater, it was not obvious that Feynman would be accepted. He had the best grades in physics and mathematics that anyone had seen, but on the other hand he was close to the bottom in history, literature and fine arts. He had one other thing going against him - namely that he was Jewish. Smyth wrote:-

Is Feynman Jewish? We have no definite rule against Jews but have to keep their proportion in our department reasonably small because of the difficulty of placing them.

After further letters from Slater, Feynman was accepted by Princeton. His doctoral work at Princeton was supervised by John Wheeler, and after finding the first problem that Wheeler gave him rather intractable, he went back to ideas he had thought about while at MIT. The first seminar that he gave at Princeton was to an audience which included Einstein, Pauli and von Neumann. Pauli said at the end [4]:-

I do not think this theory can be right ...

In retrospect, Feynman thought that Pauli must have seen difficulties at once, for after Feynman had spent a long time working on it, he too thought that it was not satisfactory. However, he then went on to develop a new approach to quantum mechanics using the principle of least action. He replaced the wave model of electromagnetics of Maxwell with a model based on particle interactions mapped into space-time. Gleick writes [6]:-

This was Richard Feynman nearing the crest of his powers. At twenty-three ... there was no physicist on earth who could match his exuberant command over the native materials of theoretical science. It was not just a facility at mathematics (though it had become clear ... that the mathematical machinery emerging from the Wheeler-Feynman collaboration was beyond Wheeler's own ability). Feynman seemed to possess a frightening ease with the substance behind the equations, like Einstein at the same age, like the Soviet physicist Lev Landau - but few others.

He received his doctorate from Princeton in 1942 but before this time the United States had entered World War II.

Feynman worked on the atomic bomb project at Princeton University (1941-42) and then at Los Alamos (1943-45). When he was approached during his final year of research to take part in the project his first reaction had been a very definite no since he was entering the final stages of work for his thesis at the time [4]:-

... I went back to my thesis - for about three minutes. Then I began to pace the floor and think about the thing. The Germans had Hitler and the possibility of developing an atomic bomb was obvious, and the possibility that they would develop it before we did was very much of a fright.

Feynman began work on the Manhattan project at Princeton developing a theory of how to separate Uranium 235 from Uranium 238, while his thesis supervisor Wheeler went to Chicago to work with Fermi on the first nuclear reactor. Wigner, in Wheeler's absence, advised Feynman to write up his thesis and after Wheeler and Wigner examined the work he received his doctorate in June 1942.

Feynman had a difficult personal problem at this time. His girlfriend of many years, Arlene Greenbaum, had been diagnosed as having tuberculosis and his family opposed their marriage. Shortly after he was awarded his doctorate Feynman married Arlene with no family members present. Shortly after his marriage Feynman went to the newly constructed Los Alamos site to work on the atomic bomb project. His remarkable abilities soon led to him being appointed as head of the theoretical division. Arlene died in 1945 just before the first test of the bomb. Feynman would marry twice more and have two children with his third wife.

After World War II, in the autumn of 1945, Feynman was appointed as a professor of theoretical physics at Cornell University. At first he devoted himself to teaching and put his research aside. The pressure of the work at Los Alamos, together with the personal stress of watching his wife's health decline, had taken its toll. He wrote [4]:-

If you're teaching a class, you can think about the elementary things that you know very well. These things are kind of fun and delightful. It doesn't do any harm to think them over again. Is there a better way to present them? The elementary things are easy to think about; if you can't think of a new thought, no harm done; what you thought about it before is good enough for the class. If you do think of something new, you're rather pleased that you have a new way of looking at it.

He received offers of posts at other universities but felt that as a non-researcher he could not even consider them. Suddenly the desire to undertake research hit him again and he returned to the quantum theory of electrodynamics that he was working on before World War II.

In 1950 Feynman accepted a position as professor of theoretical physics at the California Institute of Technology. Since he had already planned a sabbatical leave before receiving the offer, he was able to arrange to spend the first ten months of his new appointment in Brazil. He remained at Cal tech for the rest of his career, being appointed Richard Chace Tolman Professor of Theoretical Physics there in 1959.

Feynman's main contribution was to quantum mechanics, following on from the work of his doctoral thesis. He introduced diagrams (now called Feynman diagrams) that are graphic analogues of the mathematical expressions needed to describe the behaviour of systems of interacting particles. He was awarded the Nobel Prize in 1965, jointly with Schwinger and Tomonoga:-

... for fundamental work in quantum electrodynamics, with deep-ploughing consequences for the physics of elementary particles.

Other work on particle spin and the theory of 'partons' which led to the current theory of quarks were fundamental in pushing forward an understanding of particle physics.

In early 1979 Feyman's health had deteriorated and he had surgery for stomach cancer. This was very successful and his doctors believed that he would not suffer a recurrence. After his recovery he enjoyed the limelight as a famous public figure, a role which was enhanced when the book [4] became a surprise best seller. His final major task was as a member of a committee set up to investigate the cause of the explosion on the space shuttle Challenger on Tuesday 28 January 1986. The fascinating story of the science and politics of this investigation is told in Feyman's own words in [5]. It was a very difficult time for Feyman since throughout the investigation his health was deteriorating. Near the end of 1987 cancer was found again in his abdomen. After his death, Chandler wrote on 17 February 1988 in [17]:-

Feynman, who died at the University of California at Los Angeles Medical Center after an eight-year battle with abdominal cancer, was a popular and energetic lecturer who, despite his illness, continued to teach at the California Institute of Technology until two weeks ago.

Feynman's books include many outstanding ones which evolved out of lecture courses. For example Quantum Electrodynamics (1961) and The Theory of Fundamental Processes (1961), The Feynman Lectures on Physics (1963-65) (3 volumes), The Character of Physical Law (1965) and QED: The Strange Theory of Light and Matter (1985).

In [6] Gleick described Feynman's approach to science:-

So many of his witnesses observed the utter freedom of his flights of thought, yet when Feynman talked about his own methods not freedom but constraint ... For Feynman the essence of scientific imagination was a powerful and almost painful rule. What scientists create must match reality. It must match what is already known. Scientific creativity, he said, is imagination in a straitjacket ... The rules of harmonic progression made for Mozart a cage as unyielding as the sonnet did for Shakespeare. As unyielding and as liberating - for later critics found the creator's genius in the counterpoint of structure and freedom, rigour and inventiveness.

Feynman received many honours for his work. He was elected to the American Physical Society, the American Association for the Advancement of Science, the National Academy of Science, and the Royal Society of London. Among the awards he received were the Albert Einstein Award (1954) and the Lawrence Award (1962).

As to Feynman's character, he was described in [17] as follows:-

He was widely known for his insatiable curiosity, gentle wit, brilliant mind and playful temperament.

Gleick [6] describes him as:-

... mystifyingly brilliant at calculating, strangely ignorant of the literature, passionate.

Article by: J J O'Connor and E F Robertson

August 2002

MacTutor History of Mathematics


Richard P. Feynman

The Nobel Prize in Physics 1965

Banquet Speech

Richard P. Feynman's speech at the Nobel Banquet in Stockholm, December 10, 1965

Your Majesty, Your Royal Highnesses, Ladies and Gentlemen.

The work I have done has, already, been adequately rewarded and recognized.

Imagination reaches out repeatedly trying to achieve some higher level of understanding, until suddenly I find myself momentarily alone before one new corner of nature's pattern of beauty and true majesty revealed. That was my reward.

Then, having fashioned tools to make access easier to the new level, I see these tools used by other men straining their imaginations against further mysteries beyond. There, are my votes of recognition.

Then comes the prize, and a deluge of messages. Reports; of fathers turning excitedly with newspapers in hand to wives; of daughters running up and down the apartment house ringing neighbor's doorbells with news; victorious cries of "I told you so" by those having no technical knowledge - their successful prediction being based on faith alone; from friends, from relatives, from students, from former teachers, from scientific colleagues, from total strangers; formal commendations, silly jokes, parties, presents; a multitude of messages in a multitude of forms.

But, in each I saw the same two common elements. I saw in each, joy; and I saw affection (you see, whatever modesty I may have had has been completely swept away in recent days).

The prize was a signal to permit them to express, and me to learn about, their feelings. Each joy, though transient thrill, repeated in so many places amounts to a considerable sum of human happiness. And, each note of affection released thus one upon another has permitted me to realize a depth of love for my friends and acquaintances, which I had never felt so poignantly before.

For this, I thank Alfred Nobel and the many who worked so hard to carry out his wishes in this particular way.

And so, you Swedish people, with your honors, and your trumpets, and your king - forgive me. For I understand at last - such things provide entrance to the heart. Used by a wise and peaceful people they can generate good feeling, even love, among men, even in lands far beyond your own. For that lesson, I thank you. Tack!

From Les Prix Nobel en 1965, [Nobel Foundation], Stockholm, 1966

Copyright © The Nobel Foundation 1965

Feynman's Appendix to the Rogers Commission Report on the Space Shuttle Challenger Accident

Personal observations on the reliability of the Shuttle, by R. P. Feynman


It appears that there are enormous differences of opinion as to the probability of a failure with loss of vehicle and of human life. The estimates range from roughly 1 in 100 to 1 in 100,000. The higher figures come from the working engineers, and the very low figures from management. What are the causes and consequences of this lack of agreement? Since 1 part in 100,000 would imply that one could put a Shuttle up each day for 300 years expecting to lose only one, we could properly ask "What is the cause of management's fantastic faith in the machinery?"

We have also found that certification criteria used in Flight Readiness Reviews often develop a gradually decreasing strictness. The argument that the same risk was flown before without failure is often accepted as pted again and again, sometimes without a sufficiently serious attempt to remedy them, or to delay a flight because of their continued presence.

There are several sources of information. There are published criteria for certification, including a history of modifications in the form of waivers and deviations. In addition, the records of the Flight Readiness Reviews for each flight document the arguments used to accept the risks of the flight. Information was obtained from the direct testimony and the reports of the range safety officer, Louis J. Ullian, with respect to the history of success of solid fuel rockets. There was a further study by him (as chairman of the launch abort safety panel (LASP)) in an attempt to determine the risks involved in possible accidents leading to radioactive contamination from attempting to fly a plutonium power supply (RTG) for future planetary missions. The NASA study of the same question is also available. For the History of the Space Shuttle Main Engines, interviews with management and engineers at Marshall, and informal interviews with engineers at Rocketdyne, were made. An independent (Cal Tech) mechanical engineer who consulted for NASA about engines was also interviewed informally. A visit to Johnson was made to gather information on the reliability of the avionics (computers, sensors, and effectors). Finally there is a report "A Review of Certification Practices, Potentially Applicable to Man-rated Reusable Rocket Engines," prepared at the Jet Propulsion Laboratory by N. Moore, et al., in February, 1986, for NASA Headquarters, Office of Space Flight. It deals with the methods used by the FAA and the military to certify their gas turbine and rocket engines. These authors were also interviewed informally.

Solid Rockets (SRB)

An estimate of the reliability of solid rockets was made by the range safety officer, by studying the experience of all previous rocket flights. Out of a total of nearly 2,900 flights, 121 failed (1 in 25). This includes, however, what may be called, early errors, rockets flown for the first few times in which design errors are discovered and fixed. A more reasonable figure for the mature rockets might be 1 in 50. With special care in the selection of parts and in inspection, a figure of below 1 in 100 might be achieved but 1 in 1,000 is probably not attainable with today's technology. (Since there are two rockets on the Shuttle, these rocket failure rates must be doubled to get Shuttle failure rates from Solid Rocket Booster failure.)

NASA officials argue that the figure is much lower. They point out that these figures are for unmanned rockets but since the Shuttle is a manned vehicle "the probability of mission success is necessarily very close to 1.0." It is not very clear what this phrase means. Does it mean it is close to 1 or that it ought to be close to 1? They go on to explain "Historically this extremely high degree of mission success has given rise to a difference in philosophy between manned space flight programs and unmanned programs; i.e., numerical probability usage versus engineering judgment." (These quotations are from "Space Shuttle Data for Planetary Mission RTG Safety Analysis," Pages 3-1, 3-1, February 15, 1985, NASA, JSC.) It is true that if the probability of failure was as low as 1 in 100,000 it would take an inordinate number of tests to determine it ( you would get nothing but a string of perfect flights from which no precise figure, other than that the probability is likely less than the number of such flights in the string so far). But, if the real probability is not so small, flights would show troubles, near failures, and possible actual failures with a reasonable number of trials. and standard statistical methods could give a reasonable estimate. In fact, previous NASA experience had shown, on occasion, just such difficulties, near accidents, and accidents, all giving warning that the probability of flight failure was not so very small. The inconsistency of the argument not to determine reliability through historical experience, as the range safety officer did, is that NASA also appeals to history, beginning "Historically this high degree of mission success..."

Finally, if we are to replace standard numerical probability usage with engineering judgment, why do we find such an enormous disparity between the management estimate and the judgment of the engineers? It would appear that, for whatever purpose, be it for internal or external consumption, the management of NASA exaggerates the reliability of its product, to the point of fantasy.

The history of the certification and Flight Readiness Reviews will not be repeated here. (See other part of Commission reports.) The phenomenon of accepting for flight, seals that had shown erosion and blow-by in previous flights, is very clear. The Challenger flight is an excellent example. There are several references to flights that had gone before. The acceptance and success of these flights is taken as evidence of safety. But erosion and blow-by are not what the design expected. They are warnings that something is wrong. The equipment is not operating as expected, and therefore there is a danger that it can operate with even wider deviations in this unexpected and not thoroughly understood way. The fact that this danger did not lead to a catastrophe before is no guarantee that it will not the next time, unless it is completely understood. When playing Russian roulette the fact that the first shot got off safely is little comfort for the next. The origin and consequences of the erosion and blow-by were not understood. They did not occur equally on all flights and all joints; sometimes more, and sometimes less. Why not sometime, when whatever conditions determined it were right, still more leading to catastrophe?

In spite of these variations from case to case, officials behaved as if they understood it, giving apparently logical arguments to each other often depending on the "success" of previous flights. For example. in determining if flight 51-L was safe to fly in the face of ring erosion in flight 51-C, it was noted that the erosion depth was only one-third of the radius. It had been noted in an experiment cutting the ring that cutting it as deep as one radius was necessary before the ring failed. Instead of being very concerned that variations of poorly understood conditions might reasonably create a deeper erosion this time, it was asserted, there was "a safety factor of three." This is a strange use of the engineer's term ,"safety factor." If a bridge is built to withstand a certain load without the beams permanently deforming, cracking, or breaking, it may be designed for the materials used to actually stand up under three times the load. This "safety factor" is to allow for uncertain excesses of load, or unknown extra loads, or weaknesses in the material that might have unexpected flaws, etc. If now the expected load comes on to the new bridge and a crack appears in a beam, this is a failure of the design. There was no safety factor at all; even though the bridge did not actually collapse because the crack went only one-third of the way through the beam. The O-rings of the Solid Rocket Boosters were not designed to erode. Erosion was a clue that something was wrong. Erosion was not something from which safety can be inferred.

There was no way, without full understanding, that one could have confidence that conditions the next time might not produce erosion three times more severe than the time before. Nevertheless, officials fooled themselves into thinking they had such understanding and confidence, in spite of the peculiar variations from case to case. A mathematical model was made to calculate erosion. This was a model based not on physical understanding but on empirical curve fitting. To be more detailed, it was supposed a stream of hot gas impinged on the O-ring material, and the heat was determined at the point of stagnation (so far, with reasonable physical, thermodynamic laws). But to determine how much rubber eroded it was assumed this depended only on this heat by a formula suggested by data on a similar material. A logarithmic plot suggested a straight line, so it was supposed that the erosion varied as the .58 power of the heat, the .58 being determined by a nearest fit. At any rate, adjusting some other numbers, it was determined that the model agreed with the erosion (to depth of one-third the radius of the ring). There is nothing much so wrong with this as believing the answer! Uncertainties appear everywhere. How strong the gas stream might be was unpredictable, it depended on holes formed in the putty. Blow-by showed that the ring might fail even though not, or only partially eroded through. The empirical formula was known to be uncertain, for it did not go directly through the very data points by which it was determined. There were a cloud of points some twice above, and some twice below the fitted curve, so erosions twice predicted were reasonable from that cause alone. Similar uncertainties surrounded the other constants in the formula, etc., etc. When using a mathematical model careful attention must be given to uncertainties in the model.

Liquid Fuel Engine (SSME)

During the flight of 51-L the three Space Shuttle Main Engines all worked perfectly, even, at the last moment, beginning to shut down the engines as the fuel supply began to fail. The question arises, however, as to whether, had it failed, and we were to investigate it in as much detail as we did the Solid Rocket Booster, we would find a similar lack of attention to faults and a deteriorating reliability. In other words, were the organization weaknesses that contributed to the accident confined to the Solid Rocket Booster sector or were they a more general characteristic of NASA? To that end the Space Shuttle Main Engines and the avionics were both investigated. No similar study of the Orbiter, or the External Tank were made.

The engine is a much more complicated structure than the Solid Rocket Booster, and a great deal more detailed engineering goes into it. Generally, the engineering seems to be of high quality and apparently considerable attention is paid to deficiencies and faults found in operation.

The usual way that such engines are designed (for military or civilian aircraft) may be called the component system, or bottom-up design. First it is necessary to thoroughly understand the properties and limitations of the materials to be used (for turbine blades, for example), and tests are begun in experimental rigs to determine those. With this knowledge larger component parts (such as bearings) are designed and tested individually. As deficiencies and design errors are noted they are corrected and verified with further testing. Since one tests only parts at a time these tests and modifications are not overly expensive. Finally one works up to the final design of the entire engine, to the necessary specifications. There is a good chance, by this time that the engine will generally succeed, or that any failures are easily isolated and analyzed because the failure modes, limitations of materials, etc., are so well understood. There is a very good chance that the modifications to the engine to get around the final difficulties are not very hard to make, for most of the serious problems have already been discovered and dealt with in the earlier, less expensive, stages of the process.

The Space Shuttle Main Engine was handled in a different manner, top down, we might say. The engine was designed and put together all at once with relatively little detailed preliminary study of the material and components. Then when troubles are found in the bearings, turbine blades, coolant pipes, etc., it is more expensive and difficult to discover the causes and make changes. For example, cracks have been found in the turbine blades of the high pressure oxygen turbopump. Are they caused by flaws in the material, the effect of the oxygen atmosphere on the properties of the material, the thermal stresses of startup or shutdown, the vibration and stresses of steady running, or mainly at some resonance at certain speeds, etc.? How long can we run from crack initiation to crack failure, and how does this depend on power level? Using the completed engine as a test bed to resolve such questions is extremely expensive. One does not wish to lose an entire engine in order to find out where and how failure occurs. Yet, an accurate knowledge of this information is essential to acquire a confidence in the engine reliability in use. Without detailed understanding, confidence can not be attained.

A further disadvantage of the top-down method is that, if an understanding of a fault is obtained, a simple fix, such as a new shape for the turbine housing, may be impossible to implement without a redesign of the entire engine.

The Space Shuttle Main Engine is a very remarkable machine. It has a greater ratio of thrust to weight than any previous engine. It is built at the edge of, or outside of, previous engineering experience. Therefore, as expected, many different kinds of flaws and difficulties have turned up. Because, unfortunately, it was built in the top-down manner, they are difficult to find and fix. The design aim of a lifetime of 55 missions equivalent firings (27,000 seconds of operation, either in a mission of 500 seconds, or on a test stand) has not been obtained. The engine now requires very frequent maintenance and replacement of important parts, such as turbopumps, bearings, sheet metal housings, etc. The high-pressure fuel turbopump had to be replaced every three or four mission equivalents (although that may have been fixed, now) and the high pressure oxygen turbopump every five or six. This is at most ten percent of the original specification. But our main concern here is the determination of reliability.

In a total of about 250,000 seconds of operation, the engines have failed seriously perhaps 16 times. Engineering pays close attention to these failings and tries to remedy them as quickly as possible. This it does by test studies on special rigs experimentally designed for the flaws in question, by careful inspection of the engine for suggestive clues (like cracks), and by considerable study and analysis. In this way, in spite of the difficulties of top-down design, through hard work, many of the problems have apparently been solved.

A list of some of the problems follows. Those followed by an asterisk (*) are probably solved:

1. Turbine blade cracks in high pressure fuel turbopumps (HPFTP). (May have been solved.)

2. Turbine blade cracks in high pressure oxygen turbopumps (HPOTP).

3. Augmented Spark Igniter (ASI) line rupture.*

4. Purge check valve failure.*

5. ASI chamber erosion.*

6. HPFTP turbine sheet metal cracking.

7. HPFTP coolant liner failure.*

8. Main combustion chamber outlet elbow failure.*

9. Main combustion chamber inlet elbow weld offset.*

10. HPOTP subsynchronous whirl.*

11. Flight acceleration safety cutoff system (partial failure in a redundant system).*

12. Bearing spalling (partially solved).

13. A vibration at 4,000 Hertz making some engines inoperable, etc.

Many of these solved problems are the early difficulties of a new design, for 13 of them occurred in the first 125,000 seconds and only three in the second 125,000 seconds. Naturally, one can never be sure that all the bugs are out, and, for some, the fix may not have addressed the true cause. Thus, it is not unreasonable to guess there may be at least one surprise in the next 250,000 seconds, a probability of 1/500 per engine per mission. On a mission there are three engines, but some accidents would possibly be contained, and only affect one engine. The system can abort with only two engines. Therefore let us say that the unknown suprises do not, even of themselves, permit us to guess that the probability of mission failure do to the Space Shuttle Main Engine is less than 1/500. To this we must add the chance of failure from known, but as yet unsolved, problems (those without the asterisk in the list above). These we discuss below. (Engineers at Rocketdyne, the manufacturer, estimate the total probability as 1/10,000. Engineers at marshal estimate it as 1/300, while NASA management, to whom these engineers report, claims it is 1/100,000. An independent engineer consulting for NASA thought 1 or 2 per 100 a reasonable estimate.)

The history of the certification principles for these engines is confusing and difficult to explain. Initially the rule seems to have been that two sample engines must each have had twice the time operating without failure as the operating time of the engine to be certified (rule of 2x). At least that is the FAA practice, and NASA seems to have adopted it, originally expecting the certified time to be 10 missions (hence 20 missions for each sample). Obviously the best engines to use for comparison would be those of greatest total (flight plus test) operating time -- the so-called "fleet leaders." But what if a third sample and several others fail in a short time? Surely we will not be safe because two were unusual in lasting longer. The short time might be more representative of the real possibilities, and in the spirit of the safety factor of 2, we should only operate at half the time of the short-lived samples.

The slow shift toward decreasing safety factor can be seen in many examples. We take that of the HPFTP turbine blades. First of all the idea of testing an entire engine was abandoned. Each engine number has had many important parts (like the turbopumps themselves) replaced at frequent intervals, so that the rule must be shifted from engines to components. We accept an HPFTP for a certification time if two samples have each run successfully for twice that time (and of course, as a practical matter, no longer insisting that this time be as large as 10 missions). But what is "successfully?" The FAA calls a turbine blade crack a failure, in order, in practice, to really provide a safety factor greater than 2. There is some time that an engine can run between the time a crack originally starts until the time it has grown large enough to fracture. (The FAA is contemplating new rules that take this extra safety time into account, but only if it is very carefully analyzed through known models within a known range of experience and with materials thoroughly tested. None of these conditions apply to the Space Shuttle Main Engine.

Cracks were found in many second stage HPFTP turbine blades. In one case three were found after 1,900 seconds, while in another they were not found after 4,200 seconds, although usually these longer runs showed cracks. To follow this story further we shall have to realize that the stress depends a great deal on the power level. The Challenger flight was to be at, and previous flights had been at, a power level called 104% of rated power level during most of the time the engines were operating. Judging from some material data it is supposed that at the level 104% of rated power level, the time to crack is about twice that at 109% or full power level (FPL). Future flights were to be at this level because of heavier payloads, and many tests were made at this level. Therefore dividing time at 104% by 2, we obtain units called equivalent full power level (EFPL). (Obviously, some uncertainty is introduced by that, but it has not been studied.) The earliest cracks mentioned above occurred at 1,375 EFPL.

Now the certification rule becomes "limit all second stage blades to a maximum of 1,375 seconds EFPL." If one objects that the safety factor of 2 is lost it is pointed out that the one turbine ran for 3,800 seconds EFPL without cracks, and half of this is 1,900 so we are being more conservative. We have fooled ourselves in three ways. First we have only one sample, and it is not the fleet leader, for the other two samples of 3,800 or more seconds had 17 cracked blades between them. (There are 59 blades in the engine.) Next we have abandoned the 2x rule and substituted equal time. And finally, 1,375 is where we did see a crack. We can say that no crack had been found below 1,375, but the last time we looked and saw no cracks was 1,100 seconds EFPL. We do not know when the crack formed between these times, for example cracks may have formed at 1,150 seconds EFPL. (Approximately 2/3 of the blade sets tested in excess of 1,375 seconds EFPL had cracks. Some recent experiments have, indeed, shown cracks as early as 1,150 seconds.) It was important to keep the number high, for the Challenger was to fly an engine very close to the limit by the time the flight was over.

Finally it is claimed that the criteria are not abandoned, and the system is safe, by giving up the FAA convention that there should be no cracks, and considering only a completely fractured blade a failure. With this definition no engine has yet failed. The idea is that since there is sufficient time for a crack to grow to a fracture we can insure that all is safe by inspecting all blades for cracks. If they are found, replace them, and if none are found we have enough time for a safe mission. This makes the crack problem not a flight safety problem, but merely a maintenance problem.

This may in fact be true. But how well do we know that cracks always grow slowly enough that no fracture can occur in a mission? Three engines have run for long times with a few cracked blades (about 3,000 seconds EFPL) with no blades broken off.

But a fix for this cracking may have been found. By changing the blade shape, shot-peening the surface, and covering with insulation to exclude thermal shock, the blades have not cracked so far.

A very similar story appears in the history of certification of the HPOTP, but we shall not give the details here.

It is evident, in summary, that the Flight Readiness Reviews and certification rules show a deterioration for some of the problems of the Space Shuttle Main Engine that is closely analogous to the deterioration seen in the rules for the Solid Rocket Booster.


By "avionics" is meant the computer system on the Orbiter as well as its input sensors and output actuators. At first we will restrict ourselves to the computers proper and not be concerned with the reliability of the input information from the sensors of temperature, pressure, etc., nor with whether the computer output is faithfully followed by the actuators of rocket firings, mechanical controls, displays to astronauts, etc.

The computer system is very elaborate, having over 250,000 lines of code. It is responsible, among many other things, for the automatic control of the entire ascent to orbit, and for the descent until well into the atmosphere (below Mach 1) once one button is pushed deciding the landing site desired. It would be possible to make the entire landing automatically (except that the landing gear lowering signal is expressly left out of computer control, and must be provided by the pilot, ostensibly for safety reasons) but such an entirely automatic landing is probably not as safe as a pilot controlled landing. During orbital flight it is used in the control of payloads, in displaying information to the astronauts, and the exchange of information to the ground. It is evident that the safety of flight requires guaranteed accuracy of this elaborate system of computer hardware and software.

In brief, the hardware reliability is ensured by having four essentially independent identical computer systems. Where possible each sensor also has multiple copies, usually four, and each copy feeds all four of the computer lines. If the inputs from the sensors disagree, depending on circumstances, certain averages, or a majority selection is used as the effective input. The algorithm used by each of the four computers is exactly the same, so their inputs (since each sees all copies of the sensors) are the same. Therefore at each step the results in each computer should be identical. From time to time they are compared, but because they might operate at slightly different speeds a system of stopping and waiting at specific times is instituted before each comparison is made. If one of the computers disagrees, or is too late in having its answer ready, the three which do agree are assumed to be correct and the errant computer is taken completely out of the system. If, now, another computer fails, as judged by the agreement of the other two, it is taken out of the system, and the rest of the flight canceled, and descent to the landing site is instituted, controlled by the two remaining computers. It is seen that this is a redundant system since the failure of only one computer does not affect the mission. Finally, as an extra feature of safety, there is a fifth independent computer, whose memory is loaded with only the programs of ascent and descent, and which is capable of controlling the descent if there is a failure of more than two of the computers of the main line four.

There is not enough room in the memory of the main line computers for all the programs of ascent, descent, and payload programs in flight, so the memory is loaded about four times from tapes, by the astronauts.

Because of the enormous effort required to replace the software for such an elaborate system, and for checking a new system out, no change has been made to the hardware since the system began about fifteen years ago. The actual hardware is obsolete; for example, the memories are of the old ferrite core type. It is becoming more difficult to find manufacturers to supply such old-fashioned computers reliably and of high quality. Modern computers are very much more reliable, can run much faster, simplifying circuits, and allowing more to be done, and would not require so much loading of memory, for the memories are much larger.

The software is checked very carefully in a bottom-up fashion. First, each new line of code is checked, then sections of code or modules with special functions are verified. The scope is increased step by step until the new changes are incorporated into a complete system and checked. This complete output is considered the final product, newly released. But completely independently there is an independent verification group, that takes an adversary attitude to the software development group, and tests and verifies the software as if it were a customer of the delivered product. There is additional verification in using the new programs in simulators, etc. A discovery of an error during verification testing is considered very serious, and its origin studied very carefully to avoid such mistakes in the future. Such unexpected errors have been found only about six times in all the programming and program changing (for new or altered payloads) that has been done. The principle that is followed is that all the verification is not an aspect of program safety, it is merely a test of that safety, in a non-catastrophic verification. Flight safety is to be judged solely on how well the programs do in the verification tests. A failure here generates considerable concern.

To summarize then, the computer software checking system and attitude is of the highest quality. There appears to be no process of gradually fooling oneself while degrading standards so characteristic of the Solid Rocket Booster or Space Shuttle Main Engine safety systems. To be sure, there have been recent suggestions by management to curtail such elaborate and expensive tests as being unnecessary at this late date in Shuttle history. This must be resisted for it does not appreciate the mutual subtle influences, and sources of error generated by even small changes of one part of a program on another. There are perpetual requests for changes as new payloads and new demands and modifications are suggested by the users. Changes are expensive because they require extensive testing. The proper way to save money is to curtail the number of requested changes, not the quality of testing for each.

One might add that the elaborate system could be very much improved by more modern hardware and programming techniques. Any outside competition would have all the advantages of starting over, and whether that is a good idea for NASA now should be carefully considered.

Finally, returning to the sensors and actuators of the avionics system, we find that the attitude to system failure and reliability is not nearly as good as for the computer system. For example, a difficulty was found with certain temperature sensors sometimes failing. Yet 18 months later the same sensors were still being used, still sometimes failing, until a launch had to be scrubbed because two of them failed at the same time. Even on a succeeding flight this unreliable sensor was used again. Again reaction control systems, the rocket jets used for reorienting and control in flight still are somewhat unreliable. There is considerable redundancy, but a long history of failures, none of which has yet been extensive enough to seriously affect flight. The action of the jets is checked by sensors, and, if they fail to fire the computers choose another jet to fire. But they are not designed to fail, and the problem should be solved.


If a reasonable launch schedule is to be maintained, engineering often cannot be done fast enough to keep up with the expectations of originally conservative certification criteria designed to guarantee a very safe vehicle. In these situations, subtly, and often with apparently logical arguments, the criteria are altered so that flights may still be certified in time. They therefore fly in a relatively unsafe condition, with a chance of failure of the order of a percent (it is difficult to be more accurate).

Official management, on the other hand, claims to believe the probability of failure is a thousand times less. One reason for this may be an attempt to assure the government of NASA perfection and success in order to ensure the supply of funds. The other may be that they sincerely believed it to be true, demonstrating an almost incredible lack of communication between themselves and their working engineers.

In any event this has had very unfortunate consequences, the most serious of which is to encourage ordinary citizens to fly in such a dangerous machine, as if it had attained the safety of an ordinary airliner. The astronauts, like test pilots, should know their risks, and we honor them for their courage. Who can doubt that McAuliffe was equally a person of great courage, who was closer to an awareness of the true risk than NASA management would have us believe?

Let us make recommendations to ensure that NASA officials deal in a world of reality in understanding technological weaknesses and imperfections well enough to be actively trying to eliminate them. They must live in reality in comparing the costs and utility of the Shuttle to other methods of entering space. And they must be realistic in making contracts, in estimating costs, and the difficulty of the projects. Only realistic flight schedules should be proposed, schedules that have a reasonable chance of being met. If in this way the government would not support them, then so be it. NASA owes it to the citizens from whom it asks support to be frank, honest, and informative, so that these citizens can make the wisest decisions for the use of their limited resources.

For a successful technology, reality must take precedence over public relations, for nature cannot be fooled.

Source: University of Missouri - Kansas City

Richard Feynman