How is the response time index (RTI) measured?

The response time index (RTI) is a crucial measurement in fire protection engineering, specifically regarding the performance of sprinkler systems. It is fundamentally defined as the time it takes for a fire to be detected and a response initiated. The RTI is measured in meters-seconds to the half power (usually expressed as m·s^0.5). This particular unit incorporates the distance from the sprinkler head to the fire source, factoring in the time it takes for heat to travel through air. The square root relationship reflects a nuanced understanding of the interaction between the fire's heat release rate and the sprinkler's response, allowing for a detailed assessment of how quickly the system can activate in reaction to heat from a fire.

Using this measurement helps engineers and designers to assess and compare the sensitivity and effectiveness of various sprinkler models under different conditions. The other options provided do not adequately represent how RTI is measured, as they involve different units and principles that do not correspond to the behavior of fire and sprinkler systems.