The parts of the paddle are the blade, shaft, throat, and drip rings. The blade has two sides called the power face and the non-power face. The power face is the concave (scooped out) side. This is usually where the manufacturer prints the logo. Most blades have an asymmetrical shape with the widest part of the blade on top. This shape provides for extra efficiency during the forward stroke. The throat connects the blade to the shaft. When paddling, the drip rings are placed on the shaft about 6" from the throat. The drip rings are there simply to keep some water from dripping on the paddler. They are not intended as guides for hand placement.
Take the paddle in both hands and center it. Hold it out in front of you and look at the blades. You should be looking at the power face, with the widest part of the blade on top. If your paddle is feathered and made for right-hand control, then your right blade will be perpendicular to the ground (and if left, the opposite). If your paddle is non-feathered, then both blades will be perpendicular to the ground.
The spacing of the grip should be fairly wide. Start with your hands spaced slightly wider than your shoulder. As you gain experience and comfort, you may modify this to your personal taste.
This "standard" grip is seldom changed when using "Euro" style paddles (Greenland paddling technique is another matter, not for discussion here). Even when paddling in reverse, the grip doesn't change. Maintaining the same grip has the advantage of keeping you ready for any eventuality.
When paddling, resist the temptation to hold the paddle in a death grip. Keep your hands as loose as is consistent with what you're doing. For example, you can completely open your upper hand during a forward stroke, and cradle the paddle shaft between thumb and forefinger while pushing it forward. At the same time, you can pull the lower paddle shaft back with four fingers while relaxing your thumb. Relaxed hands minimize tension, fatigue, and physical stress.
A kayak paddle has two blades. Usually, one blade will be in the water, working to control the kayak, and the other blade will be somewhere in the air. We will call the working blade the onside blade, and the hand nearest it the onside hand. The opposite blade and hand will be called offside.
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The three main types of paddle stroke are the propulsion strokes, turning strokes and support strokes. Propulsion strokes move the kayak from one point to another. Turning strokes are used to change course. We use support strokes mainly to keep from capsizing. As you progress, you will find that you will blend these three types of strokes instinctively.