Patriot Missile Failure

Updated 15 Sep 2026

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What it is
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  a real-world case study (Dhahran, Saudi Arabia, February 25, 1991) where an accumulated floating-point truncation error caused a US Patriot missile battery to fail to intercept an incoming Iraqi Scud missile, resulting in 28 deaths
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Root cause chain
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  the radar's internal clock tracked time in units of $0.1$ seconds, using a 24-bit register
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  $0.1_{10}$ is a repeating binary fraction and cannot be represented exactly — truncating it at 24 bits introduces an error of about $9.536743 \times 10^{-8}$ seconds per tick
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  the battery had been running continuously for over 100 hours (3,600,000 ticks) before the incident, accumulating a total time drift of about $0.3433$ seconds
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  the incoming Scud traveled at roughly Mach 5 ( $\approx1676$ m/s); in $0.3433$ s it covers about $575$ meters
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  this shifted the missile's apparent position outside the radar's tracking "range gate," causing the system to discard it as a false target and abort interception
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Significance
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  Ties together Machine Epsilon, binary representation limits, and cumulative rounding error into a single consequential, real-world failure — the same $9.5367\times10^{-8}$ per-tick error magnitude that shows up abstractly in the Chopping vs Rounding worked example
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Related
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  Chopping vs Rounding
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  Machine Epsilon

Linked references 3