Generating power in your elbow strikes is all in the hips. Just like with many strikes, power is generated from the ground up. Let's take for example the horizontal elbow.
From a standard ready position, if you're going to throw a horizontal elbow with the front hand the action would go like this:
1) Drop your fist and raise your elbow so that your forearm is parallel to your chin.
2) Pivot the heel of your front foot outward to facilitate the turning of your hips toward the opponent just like you would with a lead hook. This will allow a fuller rotation of your hips to generate power.
3) The rotation of your hips should begin the rotation of your shoulders toward the taget. You want a good compact rotation as this generates the majority of the power, but you don't want to overexaggerate the swing to upset your balance.
4) On that rotation, you want to swing your elbow accross horizontally in a compact, chopping manner. It will be short, no more than 90 degrees from the side of your body into your target.
5) Coincide the swing with a shift of weight forward onto your front leg by pushing off your rear leg and dipping into your front leg a small amount (2 or 3 inches). Since elbows are used primarily on the inside (where the range won't facilitate true power punches, you need not slide your front foot forward.
6) Connect with the target with the point of your elbow and chop into it by about 2 inches.
A few things to consider when throwing an elbow (this or any elbow):
- Do not clench your fist when throwing an elbow. This tenses the arm musculature, and impedes the speed of the movement.
- Keep your non striking hand up as if your in range to elbow someone, they can elbow you back. Some advocate that you bring the back of the open non-striking hand up in front of your forehead. Some texts advocate that your keep it close to your chin as you would in a standard boxing stance. I think this one can be compromised, by bringing your open hand up to the level of your brow. This way, you can still defend any incoming elbow strikes, while still having your arm accessible to defending any strikes that may be launched toward your body.
- Try to connect with the point of your elbow as this is the hardest joint in your arm (the second hardest in the body, after your heel). Hitting higher up will disperse a lot of the striking force, and you'll make contact with the softer musculature of your forearm. Also, hitting with the point of the elbow will ensure the likelihood of cutting your opponent which is one of the side effects of a well thrown elbow.
A simple drill to help develope power in your elbows is this:
1) With a heavy bag (or a partner with a shield or pads), stand in front of the target with your hands up at shoulder level like your holding the lapels of a jacket and your elbows out.
2) Without removing your hands, swing your body with the rotation of your hips and shoulders and make contact to the target with your elbow. You are doing this without any arm movement in order to train the movement of your legs and hips.
3) At the end of the swing, push of your rear leg slightly and transfer your weight forward onto your front leg. This will teach to commit body mass into the strike.
Remember: Force = Mass X Acceleration. It will take a while to build ample amounts of speed in your movements, but it will take even longer to train the body to move in a way to commit full mass into the strikes. I'll break down the nuances for other elbow strikes when time permits. I hope this helps.