Kicking downward? Your referring to chopping the kick downward at the target i assume. My opinion, your leg kicks should always be thrown by chopping the kick from high to low. That said, a chopping kick can be thrown mid or high as well, if you have the flexibility necessary it is a great way to throw high kicks, chop the shin inside or over the guard.
Technical aspects that really create the chop in the kick.
1. you have to get up on the ball of the pivot foot on the post leg, with a slight bend in the leg. But you must remain heavy on the post leg, if you hop or come up light on the toe the kick will flatten out and you cant get your hips turned over as far.
2. as you turn into the kick throw the point of the shoulder (on kicking leg) and point of the hip (also on kicking leg) down and outside of the opponent (if both orth and kicking at lead leg, throw the point of shoulder/hip just outside of opponents rear foot.). You should almost feel like your falling forward, this is where the arm swing comes in for the counterbalance as the hip drives through (please, lets not get into swing or dont swing, to chop a kick, you swing the arm.... period!)
3. The important part in creating the power and downward trajectory is to keep your upper body over top your hips, if you lean back, come up high on the toes, or pull away the kick trajectory begins to plane out, get your upper body over your hips and drive the shoulder/hip down and across your opponent. Your upper body should actually be closer to your opponent when the kick lands than when in began (for a low kick). Ideally, your shoulders are below your opponents and your head is outside his power hand (assuming orth).
4. Make sure your turning through the kick on the pivot foot, the hip should be out in front of the shin that makes contact. When you turn the kick over think about trying to get the heel of the post foot pointing at the centerline of your opponent, almost turning your backside toward him when making contact. The trick to really chopping down on a kick is to get the hips/shoulders/upperbody through about 80% of the rotation before the shin makes contact. Anytime your shin gets out in front of the hip, the kick loses power and the upper body is in a position to be easily countered. Got to get through the kick, commit to it or dont throw it. Stay as heavy on the post leg as you can when pivoting and let your hips carry the kick through. Watch Thiago Alves throw a low kick, he does it exceptionally well.
As for chopping high kicks, similar technique only it does require you to lean back and really turn the kick over late in the rotation, your back is basically facing the opponent when kick lands. See pic below, maybe that helps. Again, you want to keep your upper-body over your hips as long as possible, even on the high kick, the difference in throwing it higher is just coming up higher on the post leg and turning the hips over later. Instead of throwing the hip/shoulder across your opponent, your basically throw them straight down at your post leg as your hips start to turn, why you end up pulling back more on the high kick.
