What do you call tower crane in German? It is a noun.
I found a corresponding Wikipedia page named Kran. I am now wondering whether to use Kran, Drehkran or Turmdrehkran.
My hypothesis: Kran is a hypernym, Turmdrehkran is what I am looking for.
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Most of the population — especially small children who are generally fascinated by construction sites — would not think twice and call the thing in the image a Kran.
However, you are correct that the word Kran is indeed a hypernym and can subsume different types of cranes. If you want to be 100 % specific, use Turmkran or Turmdrehkran. Do not use those terms outside of industry fairs or specialised companies that sell, rent or buy these things as you will be looked at with confusion. (‘Ach, Sie meinen Kran!’)
Interesting question: Basically, you are right.
However, note that outside of professional circles, Turmdrehkran and Drehkran may not be known.
On the other hand, it is my impression that when you say Kran, the first association that most people will have is that of a tower crane. Rather than Drehkran, the word Mobilkran (mobile crane) will be commonly understood. Therefore, you could say that if a Kran is not explicitly called Mobilkran, the default assumption will be that you are talking about a tower crane.