While the debate about the effectiveness of the Patriot Missile in the 1991 Gulf War continues, most observers believe its hit rate was closer to 10 percent than to 90 percent. The failure to stop Scud missiles in one Iraqi missile attack resulted in the death of 28 American soldiers in their barracks in Dhahran, Saudi Arabia.
The Maths Error: Numbers too Big for the Software Program
In late March 1992, the U.S. General Accounting Office’s report to Congress on the Patriot’s problems was identified as an error in the software, which used the target missile’s velocity and time elapsed to calculate the target position. As the report explained the program was not designed to fit the size of the numbers involved:
‘Time is kept continuously by the system’s internal clock in tenths of seconds but is expressed as an integer or whole number (e.g., 32, 33, 34 . . .). The longer the system has been running, the larger the number representing time. To predict where the Scud will next appear, both time and velocity must be expressed as real numbers. Because of the way the Patriot computer performs its calculations and the fact that its registers are only 24 bits long, the conversion of time from an integer to a real number cannot be any more precise than 24 bits. This conversion results in a loss of precision causing a less accurate time calculation. The effect of this inaccuracy on the [system’s] calculation is directly proportional to the target’s velocity and the length that the system has been running.’ Consequently, performing the conversion after the Patriot computer system has been running continuously for extended periods causes the [system’s estimated Scud position] to shift away from the center of the target, making it less likely that the target will be successfully intercepted’.
Mathspig Blog 