Dui-Hurigi : essence
The first thing you have to know is how it can produce its big power with good speed. Its speed is closely connected to its power; It means, because it is quick it can be powerful. Generally speaking, speed is an important factor of power.
Look at the left image. The lines represent the orbit of kicking foot from the upside.
The blue line is not the orbit of Dui-chagi but that of Hwae-chuk. The red line is for Dui-chagi. The first thing I have to emphasize is that the main movement of Dui-chagi is the straight one. Look at Dui-chagi(View from Forward) . And compare it with Dui-Hurigi(View from Forward)
For your better understanding of what I emphasize, I have to notice that everyone recognize the kicker spins his or her body for Dui-chagi. Yes, it is right. But you should not attached to the visible thing too much. What you see easiy is not the essence of technique nor of Taekwondo. If you intend to spin as you saw him or her spinning in their kick, you will fail to make good kick. The essential part of technique is in your mind, as TAEKWONDO is the way of mind(3JKY 9-2). Concerned with Dui-chagi, you have to understand that you should intend to make straight kick backward for a good Dui-chagi.
As Dui-chagi moves straight it can touch your opponent quickly. But as far as you intend to kick backward, although you intend to make straight one, you cannot but spin back. That spinning makes big power.
Best Taekwondo Knockouts KO : In order to see the actual effects of this technique.