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Did Feynman cite a fallacy about only circles having the same width in all directions as a reason for the Challenger disaster?

Did the Challenger SRBs fail due to design for reuse?Why did the design for Space Shuttle docking change?Challenger disaster: how full was the external tank at the time of destruction?Did all of the Space Shuttles dock with multiple space stations or crewed spacecraft?How much did the fuel for the space shuttle missions cost?Do the solid rocket boosters of the Shuttle and SLS have a self-destruct system and was it activated during the Challenger disaster?Did the medium range KTM tracking cameras for the Shuttle really have a “150 inch lens”?During the Space Shuttle Columbia Disaster of 2003, Why Did The Flight Director Say, “Lock the doors.”?

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15

1

$begingroup$

In a Math Overflow post about mathematical fallacies it was stated that:

Richard Feynman regarded the mistake that a "circle is the only figure which has the same width in all directions" as one reason for the space shuttle Challenger disaster.

I haven't been able to find any references to this myself. Is it an accurate statement and if so, what is it referring to?

space-shuttle challenger

share|improve this question

edited 10 hours ago

DaveInCaz

asked 12 hours ago

DaveInCazDaveInCaz

25011 silver badge77 bronze badges

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• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Thanks. Have you tried asking the poster of that answer what they meant?
  $endgroup$
  – GdD
  12 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
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  @GdD that's a good idea, though it was from 2010 but I can try.
  $endgroup$
  – DaveInCaz
  12 hours ago
  

  
  
  
  


• 
  
  
  

  
  4
  

  
  
  
  
  
  

  
  $begingroup$
  You might want to add an explicit description as to why a "circle is the only figure which as the same width in all directions" is incorrect. Curve of constant width - Wikipedia
  $endgroup$
  – Ray Butterworth
  11 hours ago
  
  
  

  
  
  
  

add a comment
 | 

15

1

$begingroup$

In a Math Overflow post about mathematical fallacies it was stated that:

Richard Feynman regarded the mistake that a "circle is the only figure which has the same width in all directions" as one reason for the space shuttle Challenger disaster.

I haven't been able to find any references to this myself. Is it an accurate statement and if so, what is it referring to?

space-shuttle challenger

share|improve this question

edited 10 hours ago

DaveInCaz

asked 12 hours ago

DaveInCazDaveInCaz

25011 silver badge77 bronze badges

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Thanks. Have you tried asking the poster of that answer what they meant?
  $endgroup$
  – GdD
  12 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @GdD that's a good idea, though it was from 2010 but I can try.
  $endgroup$
  – DaveInCaz
  12 hours ago
  

  
  
  
  


• 
  
  
  

  
  4
  

  
  
  
  
  
  

  
  $begingroup$
  You might want to add an explicit description as to why a "circle is the only figure which as the same width in all directions" is incorrect. Curve of constant width - Wikipedia
  $endgroup$
  – Ray Butterworth
  11 hours ago
  
  
  

  
  
  
  

add a comment
 | 

$begingroup$

In a Math Overflow post about mathematical fallacies it was stated that:

Richard Feynman regarded the mistake that a "circle is the only figure which has the same width in all directions" as one reason for the space shuttle Challenger disaster.

I haven't been able to find any references to this myself. Is it an accurate statement and if so, what is it referring to?

space-shuttle challenger

share|improve this question

edited 10 hours ago

DaveInCaz

asked 12 hours ago

DaveInCazDaveInCaz

25011 silver badge77 bronze badges

$endgroup$

share|improve this question

edited 10 hours ago

DaveInCaz

asked 12 hours ago

DaveInCazDaveInCaz

25011 silver badge77 bronze badges

share|improve this question

edited 10 hours ago

DaveInCaz

asked 12 hours ago

DaveInCazDaveInCaz

25011 silver badge77 bronze badges

asked 12 hours ago

DaveInCazDaveInCaz

25011 silver badge77 bronze badges

asked 12 hours ago

DaveInCazDaveInCaz

25011 silver badge77 bronze badges

2 Answers
2

active

oldest

votes

29

$begingroup$

This was indeed an avenue of investigation for Feynman. From his autobiographical book What Do You Care What Other People Think?:

Then I investigated something we were looking into as a possible contributing cause of the accident: when the booster rockets hit the ocean, they became out of round a little bit from the impact. At Kennedy they're taken apart and the sections... are packed with new propellant... During transport, the sections (which are hauled on their sides) get squashed a little bit - the softish propellant is very heavy. The total amount of squashing is only a fraction of an inch, but when you put the rocket sections back together, a small gap is enough to let hot gases through: the O-rings are only a quarter of an inch thick, and compressed only two-hundredths of an inch!

He then describes the procedure used to ensure the roundness of tanks, which was to check that the diameter was consistent at different angles around the tank - but then notes that this does not guarantee roundness, an arbitrary shape can have the same diameter at multiple different points, and there are even non-circular shapes that have a consistent diameter at every point. Having tank sections slightly out-of-round may have contributed to the O-ring failure, and the method they used to ensure roundness was not theoretically sound, as it relied on an incorrect assumption that a circle is the only shape with a fixed diameter at all points.

share|improve this answer

edited 4 hours ago

answered 12 hours ago

Nuclear WangNuclear Wang

66544 silver badges88 bronze badges

$endgroup$

• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  $begingroup$
  I recently ran across a nice drawing of the circumferential tool used to "round off" the SRB casings during stacking, but I can't seem to find it again, grrrr.
  $endgroup$
  – Organic Marble
  8 hours ago
  

  
  
  
  


• 
  
  
  

  
  9
  

  
  
  
  
  
  

  
  $begingroup$
  As an aside, a good example of a shape which appears to have the same diameter everywhere but which isn't circular is the British 50p coin. They are that shape so coin machines can measure them. A more extreme example is this one.
  $endgroup$
  – Jack B
  5 hours ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  "a little bit for the impact" Was "from" rather than "for" intended, and if so at what point was the typo introduced?
  $endgroup$
  – Acccumulation
  4 hours ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
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  @Acccumulation Yep, good catch - my own transcription error.
  $endgroup$
  – Nuclear Wang
  4 hours ago
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  $begingroup$
  @JackB Good example. You'll notice that most, if not all, non-circular coins in the modern day have an odd number of "sides" for this reason - you can't get a consistent diameter with an even number of "sides" (sides in quotes because the edges aren't straight segments).
  $endgroup$
  – Nuclear Wang
  4 hours ago
  

  
  
  
  

add a comment
 | 

6

$begingroup$

In addition to Nuclear Wang's answer, Feynam also mentions this during PBS Newshour interview with Jim Lehrer.

(the relevant part starting at 7:30)

While he doesn't directly mention the mathematical fallacy, he describes how the width-preserving properties that's usually observed in the automobile industry usage of o-rings, does not necessarily hold true, and how this affected the shuttle.

share|improve this answer

edited 10 hours ago

uhoh

54.4k2626 gold badges214214 silver badges682682 bronze badges

answered 11 hours ago

Hohmannfan♦Hohmannfan

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$endgroup$

add a comment
 | 

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29

$begingroup$

This was indeed an avenue of investigation for Feynman. From his autobiographical book What Do You Care What Other People Think?:

Then I investigated something we were looking into as a possible contributing cause of the accident: when the booster rockets hit the ocean, they became out of round a little bit from the impact. At Kennedy they're taken apart and the sections... are packed with new propellant... During transport, the sections (which are hauled on their sides) get squashed a little bit - the softish propellant is very heavy. The total amount of squashing is only a fraction of an inch, but when you put the rocket sections back together, a small gap is enough to let hot gases through: the O-rings are only a quarter of an inch thick, and compressed only two-hundredths of an inch!

He then describes the procedure used to ensure the roundness of tanks, which was to check that the diameter was consistent at different angles around the tank - but then notes that this does not guarantee roundness, an arbitrary shape can have the same diameter at multiple different points, and there are even non-circular shapes that have a consistent diameter at every point. Having tank sections slightly out-of-round may have contributed to the O-ring failure, and the method they used to ensure roundness was not theoretically sound, as it relied on an incorrect assumption that a circle is the only shape with a fixed diameter at all points.

share|improve this answer

edited 4 hours ago

answered 12 hours ago

Nuclear WangNuclear Wang

66544 silver badges88 bronze badges

$endgroup$

• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  $begingroup$
  I recently ran across a nice drawing of the circumferential tool used to "round off" the SRB casings during stacking, but I can't seem to find it again, grrrr.
  $endgroup$
  – Organic Marble
  8 hours ago
  

  
  
  
  


• 
  
  
  

  
  9
  

  
  
  
  
  
  

  
  $begingroup$
  As an aside, a good example of a shape which appears to have the same diameter everywhere but which isn't circular is the British 50p coin. They are that shape so coin machines can measure them. A more extreme example is this one.
  $endgroup$
  – Jack B
  5 hours ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  "a little bit for the impact" Was "from" rather than "for" intended, and if so at what point was the typo introduced?
  $endgroup$
  – Acccumulation
  4 hours ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  @Acccumulation Yep, good catch - my own transcription error.
  $endgroup$
  – Nuclear Wang
  4 hours ago
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  $begingroup$
  @JackB Good example. You'll notice that most, if not all, non-circular coins in the modern day have an odd number of "sides" for this reason - you can't get a consistent diameter with an even number of "sides" (sides in quotes because the edges aren't straight segments).
  $endgroup$
  – Nuclear Wang
  4 hours ago
  

  
  
  
  

add a comment
 | 

29

$begingroup$

This was indeed an avenue of investigation for Feynman. From his autobiographical book What Do You Care What Other People Think?:

Then I investigated something we were looking into as a possible contributing cause of the accident: when the booster rockets hit the ocean, they became out of round a little bit from the impact. At Kennedy they're taken apart and the sections... are packed with new propellant... During transport, the sections (which are hauled on their sides) get squashed a little bit - the softish propellant is very heavy. The total amount of squashing is only a fraction of an inch, but when you put the rocket sections back together, a small gap is enough to let hot gases through: the O-rings are only a quarter of an inch thick, and compressed only two-hundredths of an inch!

He then describes the procedure used to ensure the roundness of tanks, which was to check that the diameter was consistent at different angles around the tank - but then notes that this does not guarantee roundness, an arbitrary shape can have the same diameter at multiple different points, and there are even non-circular shapes that have a consistent diameter at every point. Having tank sections slightly out-of-round may have contributed to the O-ring failure, and the method they used to ensure roundness was not theoretically sound, as it relied on an incorrect assumption that a circle is the only shape with a fixed diameter at all points.

share|improve this answer

edited 4 hours ago

answered 12 hours ago

Nuclear WangNuclear Wang

66544 silver badges88 bronze badges

$endgroup$

• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  $begingroup$
  I recently ran across a nice drawing of the circumferential tool used to "round off" the SRB casings during stacking, but I can't seem to find it again, grrrr.
  $endgroup$
  – Organic Marble
  8 hours ago
  

  
  
  
  


• 
  
  
  

  
  9
  

  
  
  
  
  
  

  
  $begingroup$
  As an aside, a good example of a shape which appears to have the same diameter everywhere but which isn't circular is the British 50p coin. They are that shape so coin machines can measure them. A more extreme example is this one.
  $endgroup$
  – Jack B
  5 hours ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  "a little bit for the impact" Was "from" rather than "for" intended, and if so at what point was the typo introduced?
  $endgroup$
  – Acccumulation
  4 hours ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  @Acccumulation Yep, good catch - my own transcription error.
  $endgroup$
  – Nuclear Wang
  4 hours ago
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  $begingroup$
  @JackB Good example. You'll notice that most, if not all, non-circular coins in the modern day have an odd number of "sides" for this reason - you can't get a consistent diameter with an even number of "sides" (sides in quotes because the edges aren't straight segments).
  $endgroup$
  – Nuclear Wang
  4 hours ago
  

  
  
  
  

add a comment
 | 

$begingroup$

This was indeed an avenue of investigation for Feynman. From his autobiographical book What Do You Care What Other People Think?:

Then I investigated something we were looking into as a possible contributing cause of the accident: when the booster rockets hit the ocean, they became out of round a little bit from the impact. At Kennedy they're taken apart and the sections... are packed with new propellant... During transport, the sections (which are hauled on their sides) get squashed a little bit - the softish propellant is very heavy. The total amount of squashing is only a fraction of an inch, but when you put the rocket sections back together, a small gap is enough to let hot gases through: the O-rings are only a quarter of an inch thick, and compressed only two-hundredths of an inch!

He then describes the procedure used to ensure the roundness of tanks, which was to check that the diameter was consistent at different angles around the tank - but then notes that this does not guarantee roundness, an arbitrary shape can have the same diameter at multiple different points, and there are even non-circular shapes that have a consistent diameter at every point. Having tank sections slightly out-of-round may have contributed to the O-ring failure, and the method they used to ensure roundness was not theoretically sound, as it relied on an incorrect assumption that a circle is the only shape with a fixed diameter at all points.

share|improve this answer

edited 4 hours ago

answered 12 hours ago

Nuclear WangNuclear Wang

66544 silver badges88 bronze badges

$endgroup$

share|improve this answer

edited 4 hours ago

answered 12 hours ago

Nuclear WangNuclear Wang

66544 silver badges88 bronze badges

answered 12 hours ago

Nuclear WangNuclear Wang

66544 silver badges88 bronze badges

answered 12 hours ago

Nuclear WangNuclear Wang

66544 silver badges88 bronze badges

6

$begingroup$

In addition to Nuclear Wang's answer, Feynam also mentions this during PBS Newshour interview with Jim Lehrer.

(the relevant part starting at 7:30)

While he doesn't directly mention the mathematical fallacy, he describes how the width-preserving properties that's usually observed in the automobile industry usage of o-rings, does not necessarily hold true, and how this affected the shuttle.

share|improve this answer

edited 10 hours ago

uhoh

54.4k2626 gold badges214214 silver badges682682 bronze badges

answered 11 hours ago

Hohmannfan♦Hohmannfan

13.7k11 gold badge5151 silver badges109109 bronze badges

$endgroup$

add a comment
 | 

6

$begingroup$

In addition to Nuclear Wang's answer, Feynam also mentions this during PBS Newshour interview with Jim Lehrer.

(the relevant part starting at 7:30)

While he doesn't directly mention the mathematical fallacy, he describes how the width-preserving properties that's usually observed in the automobile industry usage of o-rings, does not necessarily hold true, and how this affected the shuttle.

share|improve this answer

edited 10 hours ago

uhoh

54.4k2626 gold badges214214 silver badges682682 bronze badges

answered 11 hours ago

Hohmannfan♦Hohmannfan

13.7k11 gold badge5151 silver badges109109 bronze badges

$endgroup$

add a comment
 | 

$begingroup$

In addition to Nuclear Wang's answer, Feynam also mentions this during PBS Newshour interview with Jim Lehrer.

(the relevant part starting at 7:30)

While he doesn't directly mention the mathematical fallacy, he describes how the width-preserving properties that's usually observed in the automobile industry usage of o-rings, does not necessarily hold true, and how this affected the shuttle.

share|improve this answer

edited 10 hours ago

uhoh

54.4k2626 gold badges214214 silver badges682682 bronze badges

answered 11 hours ago

Hohmannfan♦Hohmannfan

13.7k11 gold badge5151 silver badges109109 bronze badges

$endgroup$

share|improve this answer

edited 10 hours ago

uhoh

54.4k2626 gold badges214214 silver badges682682 bronze badges

answered 11 hours ago

Hohmannfan♦Hohmannfan

13.7k11 gold badge5151 silver badges109109 bronze badges

edited 10 hours ago

uhoh

54.4k2626 gold badges214214 silver badges682682 bronze badges

edited 10 hours ago

uhoh

54.4k2626 gold badges214214 silver badges682682 bronze badges

answered 11 hours ago

Hohmannfan♦Hohmannfan

13.7k11 gold badge5151 silver badges109109 bronze badges

answered 11 hours ago

Hohmannfan♦Hohmannfan

13.7k11 gold badge5151 silver badges109109 bronze badges