Airspeed change in wind shear

Question

The instrument questions I’m studying say that a decreasing tailwind will increase airspeed. I can’t wrap my head around why this would be the case.

Answer 1

Let's consider a simple example: you fly at a true airspeed (TAS) of 100 kt with a tailwind (TW) of 20 kt. This would result in a ground speed (GS) of

$$ \text{GS} = \text{TAS} + \text{TW} = 100 \, \text{kt} + 20 \, \text{kt} = 120 \, \text{kt} $$

In a wind shear, the tailwind suddenly decreases to just 10 kt. Due to the inertia of the aircraft, the ground speed cannot change instantaneously. Therefore, your TAS is now suddenly higher:

$$ \text{GS} = \text{TAS} + \text{TW} \; \Leftrightarrow \; \text{TAS} = \text{GS} - \text{TW} = 120 \, \text{kt} - 10 \, \text{kt} = 110 \, \text{kt} $$

If the aircraft was in trim, it will return to its trimmed airspeed eventually (assuming no pilot action). So this is just a short term in increase.