Here is an Angle of Attack (AoA) sensor I took from here. If you are interested to know the AoA detail, just click the link. You may see what is inside it. But not sure what airplane's AoA sensor it was, he didn't mentioned it, but he said from Soviets' airplane. And my question is, why is the trailing edge is not smooth and gradually reduce the tip, not just like wings trailing edge? I mean, in the trailing edge there will be curl or eddy's current. Why didn't it make symmetrical between the leading edge and its trailing edge so it will smoothly release the air?
From a couple of patents it seems it's a preferred shape – example:
In cross-section, the vane 4 preferably has a wedge shape as shown in FIG. 3 with a narrow or knife-like leading edge.
But why is it preferred?
A 1971 paper on AOA sensor design references a 1967 paper that compared various shapes, which says the single wedge shape is inferior but remains popular due to "vague intuitive reasoning," citing a 1935 work that I'm yet to find. Also a streamlined shape would have bad characteristics because a streamlined shape "is meant to diminish aerodynamic action" at low angles of attack.
So, a streamlined shape is not good, a flat plate is better, and the wedge shape is popular but not for any particularly good reason, and supposedly works well enough.
Also from the 1971 paper, the drag force is negligible and "does not appear in the equation of vane response."
Much google-fu later, another research undertaken by NASA (1976) tested various flat plates of various aspect ratios (among other shapes), with no mention of the cross section. Oscillation damping according to that report is a function of arm length, and is independent of airspeed.
Lenschow, D. H. "Vanes for sensing incidence angles of the air from an aircraft." Journal of Applied Meteorology and Climatology 10.6 (1971): 1339-1343. p. 1340.
Wieringa, J. "Evaluation and design of wind vanes." Journal of Applied Meteorology and Climatology 6.6 (1967): 1114-1122. p. 1120.
Barna, P. S., and Gary R. Crossman. Experimental studies on the aerodynamic performance and dynamic response of flow direction sensing vanes. No. REPT-75-T7. NASA, 1976.
The shape seems to be a combination of a wedge and a parachute, which would adjust rapidly to a change in airflow and have structural strength.
A cone has 10 times more drag than an airfoil, and, importantly, a sharp leading edge that will respond instantly to a change in airflow.
The wedge/drag combination minimizes reading lag from inertial acceleration, allowing for heavier and stronger construction. It looks like a meat cleaver, and will likely last as long too. This would be an important consideration flying through frozen precipitation, such as hail.
A slight "boat tailing" or rounding of the trailing edge, along with the mass of the vane, would render reading fluctuations from trailing edge turbulence much less than the "steering" effect of drag and the leading edge "wedge". In short, the design is rugged and reliably works.