Which indicator will show 'Zero' when the static port is clogged and during a constant speed climb?

In this scenario, the correct indicator that will show 'Zero' when the static port is clogged during a constant speed climb is indeed the Vertical Speed Indicator (VSI). The VSI measures the rate of climb or descent based on changes in static pressure. When the static port is clogged, the VSI cannot accurately detect changes in atmospheric pressure, leading it to indicate zero, regardless of the aircraft's actual vertical speed.

In a constant speed climb, even though the aircraft is ascending, the VSI would still reflect the incorrect reading of zero due to the lack of pressure information. This is crucial for pilots to understand, as relying on the VSI under such conditions may lead to incorrect assessments of the aircraft's performance.

Air speed indicators, heading indicators, and altitude indicators depend on different principles and sources of information. The airspeed indicator relies on the difference between static pressure and dynamic pressure; the heading indicator operates based on a magnetic compass; and the altitude indicator uses static pressure as well but continues to function normally unless the static port is completely obstructed, which typically affects the VSI before the altitude reading becomes unreliable. Thus, the VSI is the most directly impacted instrument in this specific scenario.