Since the 1930's aircraft manufacturers have tried to build airplanes with frictionless wings, shaped so smoothly and perfectly that the air passing over them would not become turbulent.


(A) wings, shaped so smoothly and perfectly

(B) wings, wings so smooth and so perfectly shaped

(C) wings that are shaped so smooth and perfect

(D) wings, shaped in such a smooth and perfect manner

(E) wings, wings having been shaped smoothly and perfectly so


Since the 1930's aircraft manufacturers have tried to build airplanes with frictionless wings, shaped so smoothly and perfectly that the air passing over them would not become turbulent.

the second part of the sentence-  "shaped so smoothly and perfectly"- what is this modifying? wings or airplanes? manufacturers have tried to build airplanes with frictionless wings, shaped so smoothly and perfectly that the air passing over them would not become turbulent.
What does "them" refer to? wings or airplanes?.
The subject of both the modifiers is "wings". Options B and E correct this ambiguity by adding the subject "wings" before the dependent clause. 

So A, C, and D are out.


Another error in option C is that - wings that are shaped so smooth and perfect

"shaped" is a verb that should be modified by adverbs and not adjectives. "Smooth" and "perfect" are adjectives. 
shaped so smoothly and perfectly- correct grammatically but distorts the meaning of the sentence. 



E- wings, wings having been shaped smoothly and perfectly so
The use of the perfect participle to modify "wings" is Incorrect.

B- Since the 1930's aircraft manufacturers have tried to build airplanes with frictionless wings, wings so smooth and so perfectly shaped that the air passing over them would not become turbulent.
The use of absolute phrase corrects the ambiguity in the original sentence. 
wings so smooth and so perfectly shaped- "smooth" and perfectly "shaped" -adjectives modify the noun- "wings". Correct.