[NOTE: this was dashed off as a comment response in a thread elsewhere, and requires/assumes a lot of prior knowledge and training on how to safely perform each of the exercises mentioned, as well as how to build progression towards the explosive speed and strength goals.]
Sport specificity is an important thing to keep in mind as you program your workouts. In our case, what do we need for better swordfighting performance?
Squats are a foundation of lower body strength. But we need the glutes and hams to fire explosively. So, sprint drills are good. But we fight to maneuver for position, not sprinting in a long, straight line. So we need constant start/stop sprints in different directions. Thus, our squats should be preparing us for football style cone drills and/or (my favorite) 1m/3m suicide sprints.
On the suicide sprints, I like to drop to a sprinting position, but with palms on the floor, elbows flexed, so I can explosively push-up to launch headlong into the next sprint, take 1-3 strides, turn immediately to drop into the starting position facing the opposite direction and using the opposite leg, and repeat. Based on our fencing strip floor, we do 60m total with 28 turn-and-drop changes. Really vital to keep good alignment on the ankles and knees on every turn, plus get low with the sprint lunge squat in order to minimize back strain and keep the back straight (lumbar focus).
That in turn requires a lot of joint stabilization strength, so balancing on bosu balls, simply balancing with a slightly flexed knee on the ball of one foot on the floor, one-legged calf raises, etc.
Then we need good core strength to protect our spine, maintain good balance and structure, and to explosively fire obliquely. Most people think in terms of abs and rotating at the waist. However, the torso has both anterior and posterior muscle chains that run vertically. The lumbar muscles along the back (by the spine) keep your posture upright, preventing you from dropping headfirst into the opponent's strikes when you rapidly change from forward to backward motion. Do reverse leg lifts and supermans. You'll also need good muscles back there to kick off a strong rising short edge strike (e.g. from albers or dente di zhenghiare).
A lot of the power for an accurate, clean, nearly vertical zornhau or any other overhand strike comes from the abs firing, contracting as when doing crunches. But overhand strikes are a full body motion, so pull-ups are really one of the best exercises you can possibly do. And ultimately, not just any pull-ups, but explosive clapping pull-ups (from the hang at 90% extension, pull up and launch up off the bar just a few inches to clap the hands, then catch the bar on your way down; don't hyperextend any joints in doing so -- ability to do about 50-60 pull-ups in sets of 10-20 roughly correlates to being able to do 5-15 clapping pull-ups in sets of 5). Also, pull-ups with knees together, tucking opposite right knee up to left elbow and vice versa really help work the obliques for the fastest, most powerful oberhau.
Putting it all together, box jumps are a brutal full-body exercise when done with full range of motion from a chair-sit squat, throwing the mass of the upper body upward into the launch, the sharp knee tuck to the chest, and the landing in a chair-sit squat on the balls of the feet. Your glutes, hams, calves, abs, and lower back all really work for this one, esp as you work towards anything over 36" tall. But the coordination of explosive strength makes for powerful drives from a crouched position.
GI Jane style burpees are also good, esp if done in highly focused concentration mode nonstop. From the push-up, explosively push (as if for a clapping push-up) to tuck the knees under. This puts you into the chair-sit squat, from which you IMMEDIATELY launch up for the pull-up bar -- no pause to spot the bar. So you have to spot the bar for your hands WHILE DRIVING UP INTO THE AIR, practicing your hand-eye coordination under fairly quick time pressure. Snatch the bar, do the pull-up. On the way down, release and fall, landing on the balls of your feet and IMMEDIATELY tuck into the chair-sit squat as you continue falling. Fall as if you're going to faceplant on the ground, but catch yourself with your hands in the push-up plank position, shooting your feet behind you. Help protect the shoulders by making sure you do it as a military press, which engages the lats and more core muscles to help support the shoulders -- winging them out puts a LOT of leverage strain on the shoulder joint alone, upon impact.
Slow, safe GI Janes with time for spotting the bar and the landing-to-plank are about 4 seconds per full rep. Done with dynamic spotting and no pauses, about 2.5-3 seconds per full rep. Closer to 2 seconds when actively propelling yourself down off the bar, but I was never able to reliably or consistently maintain that pace.
For extra extra bonus points, do a full muscle-up by launching more powerfully up to snatch the bar and smoothly launch with the pull-up into the muscle-up. Don't lose momentum during the pull-up by pausing in the hang before kipping into the muscle-up.
Overhead presses are very useful. In our case, we need light to medium weights, pressing dumbbells overhead in an over/under grip configuration, i.e. pressing the sword into ochs. But we need slow medium weight for strength and stability of the joints especially the shoulder, and then we need to build up fast, eventually explosive presses with lighter weights b/c the upper hanger needs to be sharp and fast -- especially if you prefer to fight from the nach, counterattacking with a sharp, slinging strike that rolls from the cover. So throwing an 8-lb medicine ball overhead and lightly bouncing it off a high wall in front of you is good.
And finally, wrist and elbow strengthening and stretching are important for range of motion and protecting these weakest, smallest joints from injury. Sort-of military presses (push-ups with elbows no farther than 45 degrees from the ribs) done as knuckle push-ups (or use parallette bars or dumbbells) helps with straight wrist stabilization as well as building stabilization strength for the shoulders. Also, use lighter dumbbells to rotate and flex the wrists; be sure to steadily work on the typically much weaker extensor muscles on the outside of the forearm with a palm-down dumbbell wrist curl.
- 10 mins: squats to box jumps
- 10 mins: pull-ups/push-ups alternating, or burpees
- 10 mins: overhead presses
- 10 mins: wrist/arm dumbbell strengthening (good set for resting if done as part of a superset)
- 7 mins: 6x60m with 20 direction changes, suicide sprints at 45 sec/sprint
The 4x10 minute sections can obviously be rotated as 3-5 supersets, instead of doing each one as a solid block of 3-5 sets of the same exercise.
Be careful training up for this, as the complete 50-minute workout done at full-tilt with box jumps, GI Jane burpees, presses, wrists/arms, and capping off with suicide sprints can make you easily puke. The GI Jane burpees and suicides in particular will wipe out your immediate intramuscular glycogen reserves b/c they're designed to be HIIT exercises.
I especially have to emphasize the importance of going slowly to build up good form and strength in the tendons and stabilizers through many many MANY slow to medium reps. Otherwise you will strain, pull, and inflame numerous muscles and joints, which will only set back your training goals by weeks to months each time.
Most people take 2-3 months just to get up to each full HIIT exercise at a slow pace, and then easily 6-12 months to be able to do all of them in one session. The suicides alone take about 4-6 months to reach and sustain the 45-sec lap time if you start from a base of no exercise.