Before revision:  Sci.  770 (2019), 88--94] and  provide a 2-tree which does not allow any drawing with such bounded ratio . On the other hand, when the ratio is restricted to adjacent edges only, we provide a procedure that for any 2-tree yields a drawing with the ratio arbitrarily close to 4.
After revision:  Sci.  770 (2019), 88--94] and provide a 2-tree which does not admit a planar straight-line drawing with a ratio bounded by r. When the ratio is restricted to adjacent edges only, we provide a procedure that for any 2-tree yields a drawing with the ratio arbitrarily close to 4.