Here's 'the math':
So, "No, your airspeed would not show as 30."
The magnitude of your velocity, and thus your airspeed, would be 21.2 mph. Velocity is not a
scalar value, but a
vector value because your "air velocity" in this situation has two components:
In other words, the
magnitude is your airspeed, and its value is 21.2 mph. Its
direction is shown in the diagram with a crosswind that's perpendicular to the direction of travel. Of course in the 'real world', the crosswind could be at any angle. I have assumed the crosswind to be perpendicular (90 deg) to your direction of travel to make the math easier for me :) I hope it's now clear that the direction of the crosswind relative to your forward velocity will affect your airspeed. This is because your airspeed is just the
magnitude of the resultant (R) velocity, and the Resultant velocity is the vector sum of the forward velocity of your cycle and the crosswind.
Put another way, the airspeed of 21.2 mph is what would be measured by a pitot tube, and by most airspeed sensors. A windsock or vane would measure direction.
IMHO, knowing the airspeed on a cycle might be useful to a training cyclist, but not so much for training and evaluation of progress toward a goal. I say this because relating airspeed to power requires more data. Consider the following:
If you have measured your airspeed and you know your
drag coefficient you can determine the force required to move the cycle. You apply a force to the pedals, and as the cycle moves forward you are said to have done
work. If you do
work over a period of time, you have generated
power. (Some references for your reading pleasure).
In other words, you will run into some complications: Force on the pedals will change depending not ONLY on airspeed, but also on gear selection and incline (among other things). If you cycled the same stretch of road (same incline), with the same gear selection, and the same cadence, then airspeed would be a reasonable indicator of how much power you expended relative to a reference.
But, that's probably neither practical nor meaningful in terms of training, and measuring progress toward a goal. And so my conclusion is not an
answer, but rather my opinion: If you're serious about training, and measuring your progress toward some objective, an airspeed sensor is a poor substitute for a cycling power meter.