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So I want to achieve a slim-athletic physique through only doing body-weight exercises.

As I understand it, after you do more than 12-15ish reps of an exercise per set, you're no longer utilising your fast-twitch muscle fibers which are the ones that are more capable of hypertrophy and so you'll mainly be developing endurance with little strength/size improvement (slow-twitch).

I'd like to reach the max amount of the following exercises that will stimulate all possible fast-twitch muscle growth by working out 3 times a week and then maintain it through training once a week (as I run and do BJJ too...).

Wide-grip Pull-ups: 5?x15
Chin-ups: 5?x15
Explosive push-ups: 5?x15
Handstand push-ups: 5?x6 (due to smaller muscles, more challenging)
Jump squats: 5?x15
Deadlift: 5?x12 (60kg barbell...)
Planches: 180 secs

and then I'd do variations on these to hit the muscle groups in different places.

Firstly, does this make sense?

Secondly, how many sets of "up to 12 reps" (using fast-twitch muscle) does it take before you cross over into endurance training? 3? 4? 5?

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Other than working out what is your goal? Why do you want to do these fast twitch exercises? –  DMoore Aug 5 '13 at 16:30
    
Well apart from the goal stated in the first sentence, I'd like to have a decent amount of strength for BJJ. Thanks for the reply. –  Dan Aug 5 '13 at 18:38
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The central idea of explosive training is that is utilizes the anaerobic alactic energy system. This energy system has enough ATP for about 7s of sustained high intensity exercise. This is the system that the fast-twitch muscle fibers use. After 7s, there is not enough ATP for sustaining contraction and the muscle switches to the anaerobic glycolytic (less capable of generating force, and produces lactic acid which inhibits contraction).

To answer your question there are three aspects that have to be taken into consideration

1) Duration of contraction - The contraction should not last longer than 7-10s. That means that you would do about 9-10 jump squats in a set, about 7-8 chin ups etc.; you are constrained by a time limit, not a number of reps.

2) Force of contraction - The force of the contraction has to be as high as possible. The best way to achieve this is to increase the weight which you exercise with. However, since you are doing bodyweight exercises only, the execution is crucial for adaptation to occur, since after a couple of weeks your muscles will get used to the training stimulus and no further increase in strength, hypertrophy or explosiveness will occus. To activate as many motor units as possible (=a greater part of the muscle) you have to perform the exercise as quickly as possible. I.e. try to do as many reps as possible within those 7-10s. Just make sure you use the proper form; don't cheat your way to a higher rep count.

3) Number of sets - When training the anaerobic alactic system you do not have the same adaptation mechanisms as during hypertrophy training. When aiming for bulk, you do 3 sets of 8-12 reps at 4 seconds per rep, totalling a set time of about 40s. However, when training for explosiveness, you do not produce lactic acid, and the muscle does not fatigue as easily, so you have to perform more sets than for hypertrophy. - Firstly because of the lower volume of training; the total number of reps per training is much lower when doing explosive training than for hypertrophy. - Secondly, the muscle hardly fatigues, so theoretically you could perform as many sets as 15-20 or more. In my training (I am a professional sprinter), I usually keep doing sets until my form deteriorates, which usually occurs somewhere around the 7th-9th set depending on the muscle.

So to answer your second question directly, you do not cross over to endurance training by increasing set number, because you actually rest between the sets. You increase the endurance aspect of training by increasing the number of reps within each set. Just make sure you have about 5min of rest between sets so that your ATP has time to replenish.

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okay thanks for the reply. I find when I'm rolling in BJJ, I have plenty of abdominal endurance but I lack explosive strength / strength in general. How am I able to train strength when all bodyweight ab exercises seem to require longer than 7-10s under tension? –  Dan Nov 2 '13 at 11:09
    
That is because of the nature of abdominal contractions. Abdominal muscles do not have a central function in human actions such as throwing, jumping and sprinting. That is, they do not contract in the direction of the movement. They are almost purely stabilizing. Having a strong core with good endurance allows you to transfer forces from your lower body to your upper body efficiently, and vice versa. Increasing explosivenes in the abs does not have that big of an impact on human kinetics. Just think to yourself how often you need to go from full extension to full contraction with the abs... –  Darko Sarovic Nov 2 '13 at 11:23
    
And I suppose the muscle fibres making up the abdominals are mostly slow-twitch? –  Dan Nov 2 '13 at 11:47
    
And you're also saying that the whole 1-5 rep range for strength only works if you're doing it in under 7 seconds? Or does the time limit only apply for "explosive" strength? –  Dan Nov 2 '13 at 15:45
    
Indeed they are. Your only constraint when aiming for an increased speed of contraction is to perform the exercise no longer than 7s. Reps are not important, just a guideline so that you do not have to take the time every time you do an exercise, which can be hard if you do not have someone to help you with the stopwatch. –  Darko Sarovic Nov 3 '13 at 8:03
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If you run and do BJJ and want to increase your strength, particularly your explosive strength, by far your best bet is to start using external resistance tools: dumbbells, barbells, or kettlebells.

The Olympic lifts (the snatch, clean, and jerk, with any of those tools) and their adjuncts (the squat, deadlift, press, push press, and so on) are the best tools for developing strength and explosiveness.

Bodyweight methods for explosiveness include sprints, box jumps, leaps, and clapping push-ups. For general strength using bodyweight, your plan looks fine, though I'd add dips to the pull-ups, push-ups, planches, and handstands.

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