http://science.ksc.nasa.gov/shuttle/missions/51-l/docs/rogers-commission/Appendix-F.txt
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! [] 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.
Каждому математическому экономисту выбить на скрижалях и читать вслух до достижения просветления.
(кому лень читать текст по ссылке, речь идет об уплотнительном кольце в корпусе твердотопливного ускорителя, из-за которого, по современным представлениям, взорвался Челленджер).
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! [] 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.
Каждому математическому экономисту выбить на скрижалях и читать вслух до достижения просветления.
(кому лень читать текст по ссылке, речь идет об уплотнительном кольце в корпусе твердотопливного ускорителя, из-за которого, по современным представлениям, взорвался Челленджер).