A bit late to the dance, so to speak. The term LW Survival Machete was coined by the late Tom Johnson in his Vol III from long ago. I knew Tom somewhat well as he asked me to write the chapter on police sidearms for his volume IV. When first viewing the blade in his book, I realized that the blade bore the acceptance stamp of the Ordnungspolizei, so it could not be LW issue. The blade pictured in Vol III was owned by Jerry Drake, a collector from Michigan. Jerry had a copy of a wartime issue of "Die Woche" magazine which contained an article about LW equipment for downed aircraft in winter time. That is from where the above photo and where the idea of the blade was LW originated. Here is another photo from that article.
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I eventually bought Jerry's Buschmesser (machete) shown here an recognizable by the dented scabbard, as well as the magazine with the article.
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I added several more to my collection over the years in researching the subject, some with scabbard, some without; commercial and police marked.
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I never found a LW marked example but concluded that the unmarked examples were simply a commercial contract purchased by the LW. On the other hand, the Eagle B marked examples were from a police contract to supply survival equipment for the Police Air Squadron which operated several dozen aircraft on both the eastern and western front. My curiosity satisfied, I have since disposed of that small collection.