In the 1991 Gulf War, the Patriot missile defense system failed due to round off
ID: 2255731 • Letter: I
Question
In the 1991 Gulf War, the Patriot missile defense system failed due to round off error. The troubles stemmed from a computer that performed the tracking calculations with an internal clock whose integer values in tenths of a second were converted to seconds by multiplying by a 24-bit binary approximation to one tenth:
0.110 0.000110011001100110011002
(a) Convert the binary number to a decimal. Call it x.
(You may use Maple convert command: > x:=convert(0.00011001100110011001100,decimal,binary)
(b) What is the absolute error in this number; i.e., what is the absolute value of the difference between x and 0.1?
(c) What is the time error in seconds after 100 hours of operation (i.e., |3,600,000(0.1-x)|)?
(d) During the 1991 war, a Scud missile traveled at approximately MACH 5 (3750 miles per hour). Find the distance that a Scud missile would travel during the time error computed in (c).
Explanation / Answer
Part a
Converting binary value to decimal
x = convert(0.00011001100110011001100,decimal,binary) = 0.099999904632568359375
Part b
absolute error = |(0.1 - x)| = 0.000000095367431640625
Part c
time error after 100 hours = 100 hrs * absolute error
100hrs = 3600000 tenths of a sec; absolute error = 0.000000095367431640625
time error = 3600000 * 0.000000095367431640625 = 0.34332275390625 secs
Part d
speed of missile = 3750 miles per hour = 3750 / 3600 miles per second = 1.041667 miles per second
distance travelled in time error = speed * time error
distance = 1.041667 miles/sec * 0.34332275390625 secs = 0.35763 miles = 0.575 kms