What is this Nazi insignia?

Factual Questions
1

Calling all SDMB military experts, World War II wonks, army afficianados, and insignia intelligentsia!

A co-worker has brought in a cloth cap bearing a Nazi insignia and an accompanying insignia. Can you help identify it?

The cap is a folded black cap, peaked in front and back, similar to the Luftwaffe cap pictured here (circa 1962).

There is no piping on the cap, as shown in the picture.

About where the piping would be is a patch depicting a golden eagle with wings outspread, bearing in its claws a circle with the swastika on it.

Below that is a square patch oriented on the diagonal (as on the Luftwaffe cap shown). The insignia on the patch looks amazingly like the depicted cap: three concentric circles about the same size as the sample. Instead of being yellow, orange and black (as in the photo) they are blue, white and red — strangely similar to the logo of the Royal Air Force.

However, it is not an RAF patch added later; it clear that this is an original patch. The lining inside the cap was not disturbed to add any new patches, the thread color is the same, and the patch is the same shaped-square-turned-on-the-diagonal-with-a-circle as on the Luftwaffe picture. The proportions of the circles is also distinctly different from the RAF logo; the center circle is larger.

Any ideas?

2

Does it look like one of these: http://www.atthefront.com/g_insig_luftcap.htm

3

Does it look like this?

http://www.hessenantique.com/Army_Enlisted_M38_Field_cap_p/hegh014.htm

It’s a Heer field cap for enlisted men.

4

Is there a chance that the “blue” on the insignia was/is supposed to be black?

A black garrison cap sounds as if it was tank-related. Does it look like the one on this page? (minus the piping, that’s for officers)

5

And the concentric circles would be black, white, and red. Here are some more pictures of enlisted men sidecaps. Any of them look familliar?

http://users.skynet.be/vonweyersberg/Schiffchen.htm

6

It looks like the EM Luftwaffe insignia in Terminus Est’s link, but the eagle is gold, not silver.

The insignia is correct in Captain Amazing’s first link but the diagonal square and cap are both black.

The insignia is also correct on kellner’s link, but the cap is of a different shape.

I suspect the proper cap and color is the Heer 40 EM Panzer cap in Amazing’s second link.

Thanks, everybody! That was quick.