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Your right palm should stay face up to the sky as you swing through the shot.
If you are looking to hit a bunker shot the main priority is to get height with that shot, so that the ball comes out of the bunker and up over the lip. To achieve this, you must keep your club face open or aiming up to the sky as you play the shot. If your club face turns downwards towards the ground you will find that you hit a much lower trajectory shot, that does not necessarily have the height to get out of the bunker. It is really important during a bunker shot that the right hand and your right palm, stay facing the sky as you play the shot.
Initially, you need to achieve a really good set up that promotes a high trajectory ball flight. Look at the handle of your golf club, or the grip. You will see you have the name of the grip, or the manufacturer, on the centre of the grip, or you have a grip aid on there. You want to rotate this over to the right slightly, if you are a right handed golfer, so rotate it to the right of centre. This now opens your golf club face for you so it is even more lofted. Now place your hands on the club with the name off centre to the right. It is crucial that you rotate the handle and then hold the club in order to maintain the additional loft that you have placed on the club face, so ensure you follow this process in this order – rotate the handle to the right, then place your hands on the grip, with the name off centre to the right.
You should now notice that the club face is aiming more to the right than usual, so you need to rotate that club face back round to the target so that it is aiming at the target, which means that you need to rotate your feet over to the left enough so that the club face aims at the target once more. Once you have done this take your stance up by splitting your feet to about shoulder width apart and play the ball from the middle of the stance. Now set your hands up so that they are over the ball and the shaft of the club is pointing at your belly button.
To make an effective swing from this position, you now need to hinge your wrists very quickly on the back swing and as you hinge your wrists, your right palm wants to face the sky because it really shows that the club face is very open which will allow you to achieve a high shot. As you swing the club head back down towards the ball, work on keeping the palm of your right hand up towards the sky and allow the club to drop into the sand one to two inches before the ball. The club is going to drop into the sand and slide through the sand and under the ball as you keep your right palm up to the sky.
As you play through the sand and come back out of it, work on rotating your body towards the target, with your right palm still up towards the sky. That will allow the club face to really slide under the ball with the club face pointing up to the sky and will allow the club face to be very, very lofted, giving you a very high shot out of the bunker.
A good drill to work on if you struggle with this is to swing the club very slowly without hitting the ball, through the sand. Allow the club to swing back and then swing down into the sand. Work on getting the club face to then carry the sand on it, through the impact position and into your follow through, rather than allowing the club face to turn over and dump the sand off the club face, back into the bunker. Work on hitting the sand and then carrying it into your follow through position with the sand still on the face of the golf club. This shows that you have got your club face pointing up at the sky and your right palm will also pointing up at the sky because you held the club face open as you played the shot.
If you work on doing that you should find that you start hitting much higher bunker shots and that you escape from the bunker in one go, saving yourself a lot of shots when you are next out on the course.
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Letting go of the club handle through impact would cause the club head to slow down too aggressively and would result in bunker shots being left in the bunker.
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Too much tension in the right hand at impact would cause a lack of control and finesse which could result in poor distance control.
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If you allow your right palm to rotate over through impact, when playing a bunker shot, it will cause the club face to de-loft and also to rotate left of the target. This will produce a lower flighted golf shot, that will not escape the bunker lip and you will end up needing to hit a further bunker shot and seeing your score increase.