Well, the cadence given in CC is a good standard. But if you want a more precise answer, first realize that it’s actually not about speed, but displacement. By that I mean the particular “path” that your body takes as you move through the range of motion. An obvious change in this displacement would be the difference between regular pull ups and L pull ups. Forcing your legs to stay in the L forces your upper body to engage more effectively.
As far as cadence is concerned, I want you to try something. Hold something in your hand with your palm open. It doesn’t have to be heavy, maybe a water bottle. Now, lift the bottle from a low to a higher position, kind of like a bicep curl, slowly. Then try it quickly. You should notice that, if you do it too quickly, the water bottle will actually bounce out of your hand when you stop. You initially feel it pushing against your hand but eventually your speed overwhelms the resistance and you’re essentially catapulting it instead of lifting it. Now, in contrast, when you do it slowly, you should feel the bottle consistently resisting against your hand. If you feel this particular tension start to ease as you continue moving, change your speed. This experiment, hopefully, will help you understand exactly what you need to be striving for in your movement in order to get the most out of each rep. Because you could easily go at a given cadence and still not get it. Really grind that resistance. Position your body to minimize the effect of your leverage (e.g. do pull ups with your legs straight rather than with your knees bent).
It’s all about optimization, so do what you can and as long as you’re mindful of this, you will have an insight that escapes the majority of trainees (which means more efficient progress).
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