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If the constraints at the bottom of the squat are:
then there are an infinite number of shank/knee angle combinations that satisfy this constraint. As a coach, and lifter, how does one decide which knee angle is best?
I understand that as the knee angle becomes more acute, the hamstring tension reduces (bad thing), and that if you open up the knee angle too much, then you reach the limit of how acute the hip angle can be to keep the bar over midfoot (i.e. you can't go below a hip angle of 0 degrees).
The question is this: How do you judge the correct combination of knee and shank angle? Is the "knees slightly over toes" the heuristic here?
You judge the back angle, not the knee/shank angle. The correct back angle places the hips in the best position to drive the back/barbell upward using the most muscle mass. The resulting knee angle is a side-effect of this back/hips position, because the squat is not a "legs" exercise. This usually places the knees in the vicinity of the toes, either just forward or behind them, with some room for variation, shins not vertical, and is why the squat is the most difficult of the lifts to coach.
The NSCA recommends weight-bearing exercises that load the axial skeleton through the spine and hips to provide an osteogenic stimulus for those with osteopenia/osteoporosis. I know this may seem like a stupid question, but if the Low Bar Back Squatter has to fight shear instead of compression, can it still cause Skeletal Loading/Bone Density Enhancements through the hip and spine? Or will there only be skeletal loading around the scapula and the thoracic spine, due to the weight going straight down? And we all know shear wouldn't necessarily occur if the muscles responsible for maintaining those interverterbral relationships are contracting.
Are you seriously asking if the spine is still under load at the bottom of the squat? Like if the spine wasn't there, the squat could be performed anyway? How much sense does this make? Moment is the force distributed along the spine in any position that is not vertical. There are moment forces on the spine in an Olympic squat and a low-bar squat, the difference is one of degree. Moment is a shear force, i.e. a composition of compression and tension along the segment that would produce shearing strain if it were sufficient to deform the material. As such, a portion of the moment force is compression, and the response of the tissue to this compression component is densification, since that is how bone responds to compressive strain. The compressive component can be calculated with trig, but not by me -- I'm just the qualitative guy. Be ye not insulted when I remind you that taking the bar out of the rack and into the rack produces a more pure compressive stress that would indeed cause the adaptation even if the squat itself somehow stopped being partially compressive during the rep.
And in addition to racking and unracking, there is the standing upright that serves as the starting point for each rep. At this time you are taking a deep breath and setting your valsalva. I find this duration to be approximately as long as the rep itself, save for rep 5 of set 3 perhaps.
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