What is the relationship between true airspeed and groundspeed when determining wind speed?

True airspeed (TAS) and groundspeed are interconnected when considering the effects of wind on an aircraft's performance. Groundspeed is the actual speed of the aircraft over the ground, while true airspeed is the speed of the aircraft through the air mass.

In calm winds, there are no external wind forces acting on the aircraft. Therefore, true airspeed and groundspeed are equal as the aircraft is moving directly through the smooth air without any assistance or resistance from wind. This scenario serves as a baseline measurement, allowing pilots to accurately gauge performance without the complexities introduced by varying wind conditions.

The other options present scenarios influenced by wind effects that do not apply when there are no winds to consider. Thus, the relationship where groundspeed equals true airspeed in calm winds accurately captures the condition described in the question. Understanding this baseline is vital for further calculations involving wind, as any variations from calm conditions will indicate differences between TAS and groundspeed due to headwinds or tailwinds.