@ARIZE had some real good stuff, others too. Flexibility, co-ordination, balance, good technique/snappy technique and accuracy are all key components for fast anything. I like that flexibility is emphasized, because proper and unhindered ROM (range of motion) will let you move faster, especially if you can relax the antagonists (muscles on the opposite site of the direction of the joint you are moving). Dynamic stretching is a great suggestion. Flexibility is rather useless without control though. There's some really good TKD exercises for creating strength and control throughout the entire range of motion of the kick. Anyway, I'll refer to the people who can actually kick well and use a substantial amount of time on it (I'm not one).
I wont mind going over the biomechanics and muscle synergies though. I'll just spitball a bit. First of all you need to be able to brace your core at the right moment, which comes with practice, as it frees up the extremeties to move. The more precise, fast and rightly timed force wise your core bracing is, the more your nervous system will allow your extremeties to more at a higher velocity. It shouldn't really be something you overthink, which is the same for the following. The body can do things at a speed you can't keep up with thought wise. That's why, it's quality repetition after repetition that get's you somewhere.
Which muscles you use, and when, depends on the kick. Let's go with a wide rear MT roundhouse (which you use). I wont include the step that you do and the outward rotation you do with your front foot before kicking, nor the arm swing and counterbalance. Just from the initation of the kick.
- Right hip externally rotates using the rear gluteus maximus (the biggest of the butt muscles) and gluteus medius (butt muscle that externally rotates) and other external rotators
- Left hip internally rotates with a quick contraction and subsequent relaxation of the psoas major and tensor fasciae latae (hip flexors and internal rotators)
- Trunk rotates to the left using the obliquus internus abdominis (internal obliques) on the same side and the obliquus externus adbominis (external obliques) on the opposite/right side
- Right hip extends using the right gluteus maximus
- Right foot pushes into the ground and ankle dorsi flexes (straightens) using the both the soleus and gastrocnemius (together they are the calf), but to a larger extent the gastrocnemius as it is more explosive and has more FT fibers (fast twitch)
- Right knee flexes using the semitendinosus, semimembranosus and biceps femoris (hamstring mucles)
- Left foot pushes into the ground and ankle dorsi flexes (straightens) using the the soleus and gastrocnemius (calf)
- Momentum is carried turning the body and pivoting the left foot
- Trunk lateral flexes on the right side, raising your pelvis/hip up using the quadratus lomborum and to some extent the obliques on the right side
- Right knee extends using the vastus lateralis, rectus femoris, vastus medialis and vastus intermedius (better known as the quadriceps, quad or front thigh muscle)
- Left hip extends fully using the left gluteus maximus while stabilising with the gluteus medius and other pelvis/hip stabilisers
- Left knee extends using the quadriceps and stabilising with co-contraction of the hamstrings
- Shin hits
So to summarize, we have the core bracers, the obliques, hip flexors, the glutes, the quadriceps and the calfs. I'm sure upper body and arm swing matters a lot for velocity as well, but I can't be arsed to analyse that right now.
Obviously nothing trumps technique work, but if you already do S&C and would like some sports specific for kicking velocity I'd suggest:
DISCLAIMER: I would never have someone do this without having good quality of movement, and a good fundamental strength base. Eccentric, slow and controlled strenght training should be a requirement to prevent injury and increase tissue strength. Doesn't have to be extensive, but consistent. Both bilateral and single leg exercises are good.
Anyway-
Triple extension exercises (extends the hip, knee and ankles in one exercise):
Bilateral (both feet at the same time):
- CMJ/Counter Movement Jumps - soft landing
- Powercleans/clean - technique training with low weight initially
- Squat Jumps
- Weighted Squat Jumps (about 20-40% of 1RM)
- Depth Jumps - minimum ground contact
Unilateral (single legged):
- Single Leg Jumps from a single leg deadlift start position - soft landing
- Skip variations (A, B and perhaps C skip)
- Sprinting
- Boundings
Obviously you can't do all of them at once. Just pick one or two to use in a power session, and switch them up, or feel which you prefer. Keep it all
few reps, few sets with these. There's no set in stone way to do it, but velocity is about
maximal effort with rest inbetween. Something like 2-3 sets with 5-8 reps would be sensible, or simply feel when you start to slow down and stop. Use good rest between sets. Get the feel for the exercises for a few sessions before you use max effort. Try to get as much air time on the jumps and perhaps use visual or mental cues.
I highly suggest implementing A (and perhaps B) skips. It's a track and field exercise and it's great. You have triple extension, and you have a single leg element. It has good carryover. Start with walking A skips, learn the technique, and go fast when you get the hang of it. You can switch in the air when you get good as well. These you can do for a few more reps than the rest.
Trunk exercises:
- Med ball slams to the side/rotational into wall - all about explosiveness, doesn't have to be too heavy
- Med ball slams into the ground
- Resisted hip turns - You can use bands here - explosiveness is key again
- Fun: Wood chopping variations, baseball, golf
BONUS: Search for some hip and trunk rotation mobility drills and use dynamic warmups regularly
