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Yokogeri means Side kick. This one is another of the 'basics' but it's probably the hardest of the three (the others being Maegeri and Mawashigeri). Also sometimes called 'Sokoto' or 'Sokoto Fumikomi' or some combination or abbreviation of all three. Like Maegeri, there are a couple of different techniques to performing Yokogeri.

Unless you have thigh muscles like the hydraulics off a piece of civil engineering hardware you may as well forget this one. Basicly it involves lifting the leg straight out to the side and clouting your opponent on the way up. 'Easiest' to perform off the front leg, whereby you simply turn your rear foot 90° outwards, twist your hips and shoulders to a side facing position and lift your front leg straight out from the hip. To kick off the rear leg requires a swinging-twisting motion - but be careful with your hip joints. Aside from the difficulty in actually hitting your target (he would probably need to be leaning forward quite a bit) this move is a bit risky on the knees. The impact force must be almost solely comprised of transfer of momentum - the energy transferred from the speed of your foot - and minimal force, preferably none. If you continue to apply force from your hip after impact, you risk hurting your knee, because the joint is taking strain sideways, which it is not designed for. Of course this means that to hit with any real power you have to get you leg moving at quite some speed. Having suitably criticised this technique, I will say this about it - it is terrific for strengthening your hips with a view to improving your Side and Round kicks. If you stand and do maybe 20 of these off each leg before you train you will quickly get very strong thighs. You can hold onto a partner if you keep falling over (though it's better to try to improve your balance on your own). This technique should be performed with the body up straight, not leaning back, otherwise you lose the benefit of the excercise.

This technique is executed by bringing a leg up with the knee bent, turning the straight leg 90° so the body is side facing, and then extending the bent leg in the direction of the target with the foot on its side. The end position is the same as that for Yokokeage, but the impact is a thrust from the hip. To work from the rear leg you must first bring the leg up to the coiled position before extending the leg.

This is another thrusting kick, like Yokokekomi, but instead of first bringing the leg up to a coiled position, it instead follows a straight path to the target. As such it is faster than the Kekomi technique but loses some of the power. The twisting of the straight leg is essential and occurs as the kicking leg travels towards the target.

There are a number of different strike zones for Yokogeri. The most well known is probably Sokoto which is Japanese for the blade of the foot (the outer edge). It takes some practice to be able to kick with this part of the foot and many people prefer Kakato - the heel. You can also use the entire sole of the foot (Chusoku). Most beginners start with Chusoku and then graduate up to Kakato before someone nags them into using Sokoto. Though I've never seen it written anywhere, of practised by anyone, I've found that Josokutei (the ball of the foot) works very well too, particularly for Yokogeri.

Here are some thoughts on these techniques:

Choosing between Yokokekomi and Yokogeri
In Karate there are two key principles which result in powerful moves. Force and momentum. Momentum is the combination of the speed and weight of an object. In terms of Karate, you cannot change the weight of your leg (well not during the course of a fight anyway), but you can alter the speed. Thus to maximise the momentum you must make the speed as high as possible. Upon impact some of the kinetic energy in your foot and leg is transferred into the target. The actual physics is quite complex, but basicly the faster your foot goes, the more damage it causes and the more it hurts. Momentum alone is pretty feeble though in comparison to the effects of force. Force is what happens when you work your muscles. If you put your hand on someone's chest and then push them back you are applying a force. Up until you make contact, force only goes to accelerating your arm/leg/whatever (thereby increasing the speed and thus momentum). When you make contact however, if you can still apply force then you can do even more damage, and also increase the liklihood of off-balancing your opponent.
The kekomi technique is better for force because in the coiled position several strong leg muscles are fully extended. These muscles are designed for pushing heavy things around (namely your body when walking etc) and whilst being good for accelerating your leg, are better employed when shoving something, eg your opponent. The point when the muscles are strongest is when the leg is half extended, so if you make contact at this point, not only will the leg have a fair bit of momentum but you will still have a half-leg-extension's worth of force still to use, and unless your opponent is very heavy, they are likely to describe a beautiful parabolic arc through the air onto the ground a few metres infront of you. Of course according to Newton, whatever forces are exerted by your leg, equal and opposite forces are exerted by the target on you, so if you aren't putting a bit of weight behind the kick (ie leaning in) then you can expect a similar flying lesson. Onlookers will obviously be rather amused by the seeming explosion of two combatants who didn't have an adequate grasp of mechanics.
Alternatively there's the Yokogeri. This is more of a momentum weapon, particularly if used off the rear leg. You have a much greater distance with which to accelerate the kick and you have the swinging motion to assist you. Further, because the leg is never fully coiled, you don't have the same force opportunities as you have with Yokokekomi.

More physics
Many beginners cannot see the sense in using the blade of the foot. The answer is simple: pressure. As your physics teacher no doubt will have told you, pressure is inversely proportional to the area over which force is applied. This means the smaller the area of your foot you boot someone with the more it hurts. It's why sharp things stick into you if you stand on them, or why even a very light girl (or boy I suppose) standing on your foot hurts like hell if they're wearing stilettos. So using a small, hard area of your foot such as the ball, keel or blade increases the effectiveness of the kick. However, it is imortant to train well before attempting to kick something in this way, because you need strong ankles. If you have weak ankles then they may twist and then the full force of the kick is absorbed by your ankle. Not fun.

Double side-kicks
Attempt this technique: Perform Sokoto Yokogeri followed by Kakato Yokokekomi off the same leg (initially the rear leg) without placing the leg down in between. Work this technique against a bag or shield and attempt to first maximise the impact momentum on the first kick and then maximise the force on the second. You should have the bag holder move slightly towards you for the second kick (but have a mat placed behind you if you think you may fall over).

This is good too: Working off the front leg perform multiple Yokokekomis working each of the strike zones in turn. For extra nail-biting thigh agony try holding each kick out fully extended with the foot in the relevant position for half a second each time. Get a high grade to check each of your foot positions.