# Thread: Quarter Squats can't improve athletic performance

1. Starting Strength Coach
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Originally Posted by tzanghi
My point is this: At any given instant, if you only know the velocity of the bar and the weight of the bar, you cannot determine the force being applied to the bar(If you think this is wrong, use v=1m/s and w=1lb and prove us wrong; find out the force). Since you don't know anything about the current force on the bar given only velocity and mass, the velocity of the bar at the point of amoritization of a full squat is worthless by itself and is not the reason that the full squat is better for VJ.

I don't know what else to say except to challenge all of you who think that force can be determined by velocity to do so given the velocity and weight above. Prove me wrong if I am wrong.
Here's the thing: in the context of the discussion, that is not all you know. You also know that at some point prior to your hypothetical point in time, the bar speed was zero. And you know (approximately) the distance between this point and the point that a VJ amortization phase that we're interested in. Therefore, average acceleration can be looked at and a judgement made as to how much force was applied. To whit, the faster the bar is moving, then the more force was applied to it. Since the distance between these two points actually varies only a couple of inches between individuals, assumptions can be made as to who applied the most total force to the bar.

But you are correct, given ONLY velocity, it is impossible to determine the amount and duration of force applied to an object. Your point would have been far clearer had you stated this plainly right at the beginning.

As you said:

Originally Posted by tzanghi
I may have done a poor job of explaining it so far, so I'll try to do better.
The problem for the last two pages was that your explanation was not clear and cogent as Strato's was. It was open to a vast array of misinterpretation as to both your explanation of the physics and your (eventual) point.

In any event, as stated above, your eventual point that you wanted to make is right in its minutia, but slightly wrong in the context of the overall discussion.

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Best bet might be to find a way to increase gravity and jump a lot in that environment.
How is this much different than doing jump squats (COM change notwithstanding)?

Originally Posted by tzanghi
Most of the things you say are well tied in with my point(and 100% accurate), but that's not exactly my point.

My point is this: At any given instant, if you only know the velocity of the bar and the weight of the bar, you cannot determine the force being applied to the bar(If you think this is wrong, use v=1m/s and w=1lb and prove us wrong; find out the force). Since you don't know anything about the current force on the bar given only velocity and mass, the velocity of the bar at the point of amortization of a full squat is worthless by itself and is not the reason that the full squat is better for VJ.

I don't know what else to say except to challenge all of you who think that force can be determined by velocity to do so given the velocity and weight above. Prove me wrong if I am wrong.
But in the case of a full squat versus a quarter squat we *do* have more information than just velocity and mass; we know the maximal distance over which force could have been applied (the human body being a set of levers with fixed lengths).

Let's assume:
.a constant net force produced by the lifter from the bottom of each squat
.that a quarter squat covers distance k0, and the full squat k1, k1>k0.
.a bar weight of 100kg
.at the point of measurement the bar is moving at v=1m/s (your mixing of m/s and lbs above almost gave me an aneurysm, btw .
.that position 0 will be the bottom of each squat, and velocity at this point is 0m/s.
.the time it takes the quarter squat to happen is t0 and the full squat is t1, with initial time measure as 0 from the bottom of each squat.

The change in the bar's kinetic energy is, in both cases, 50J; since force is constant, we get for the quarter squat:
integral(0,k0) F ds = 50J
This yields:
F*k0 = 50J, so F = 50/k0 N

The change in the bar's momentum in both cases is 100Ns; since we know the force, the impulse for the quarter squat is:
integral(0,t0) F dt = 100Ns
integral(0,t0) 50/k0 dt = 100Ns
so:
50t0/k0 = 100Ns
t0 = 2*k0 sec
By construction, then, t1 = 2*k1 sec

Now we know everything. Since F = 50/k0 for the quarter squat:
.acceleration = 1/(2k0)
.velocity = t/(2k0) (note, plug-in 2k0 for the time yields velocity = 1m/s)
.position = t^2/(4k0)

Moreover, note that F = 50/k0 for the quarter squat, and F = 50/k1 for the full squat. Since k1>k0, this means that the quarter squat takes more force to achieve the same velocity as the full squat for a given load under conditions of constant force.

Here's a picture for the case where k0=1 and k1=2 (so the full squat moves twice the distance as the quarter squat)
http://i47.tinypic.com/mmbjma.png

Now, of course, the picture gets more complicated for non-constant force. But this does raise the question of whether the improvement in mechanics that the quarter squat affords give it the extra force production it needs to trump the full squat in cases where velocity at the top matters.

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You just need two velocities at different positions.

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Originally Posted by Steve in ATL
Here's the thing: in the context of the discussion, that is not all you know. You also know that at some point prior to your hypothetical point in time, the bar speed was zero. And you know (approximately) the distance between this point and the point that a VJ amortization phase that we're interested in. Therefore, average acceleration can be looked at and a judgement made as to how much force was applied. To whit, the faster the bar is moving, then the more force was applied to it. Since the distance between these two points actually varies only a couple of inches between individuals, assumptions can be made as to who applied the most total force to the bar.

But you are correct, given ONLY velocity, it is impossible to determine the amount and duration of force applied to an object. Your point would have been far clearer had you stated this plainly right at the beginning.

As you said:

The problem for the last two pages was that your explanation was not clear and cogent as Strato's was. It was open to a vast array of misinterpretation as to both your explanation of the physics and your (eventual) point.

In any event, as stated above, your eventual point that you wanted to make is right in its minutia, but slightly wrong in the context of the overall discussion.
You make excellent points, however I was only referring to the force being applied to the bar at the amoritization point. Surely, you can figure out the total force that was applied if you know the distance from the bottom of the squat to the amoritization point. The OP said that the full squat is better because of the high velocity at the amoritization point during a full squat, which involves nothing regarding the force applied prior to the amoritization force other than the mere fact that the force has caused the bar to achieve a given velocity. If this was his way of stating that the force applied before the amoritization point in a full squat is what makes the full squat better for VJ, then he may be right, but he was horribly unclear in saying so.

Also, I would like to state that my piecemeal explanations may have been poor, but this was largely due to irrelevant and confounding questions that had no bearing on the point. I had to explain why things that had nothing to do with my point(e.g., that a person with a bar on a scale would not weigh 0 lbs). When I was asked a large number of questions, I could not always stick to my point because I had to address other objections.

Originally Posted by RRod
How is this much different than doing jump squats (COM change notwithstanding)?

But in the case of a full squat versus a quarter squat we *do* have more information than just velocity and mass; we know the maximal distance over which force could have been applied (the human body being a set of levers with fixed lengths).

Let's assume:
.a constant net force produced by the lifter from the bottom of each squat
.that a quarter squat covers distance k0, and the full squat k1, k1>k0.
.a bar weight of 100kg
.at the point of measurement the bar is moving at v=1m/s (your mixing of m/s and lbs above almost gave me an aneurysm, btw .
.that position 0 will be the bottom of each squat, and velocity at this point is 0m/s.
.the time it takes the quarter squat to happen is t0 and the full squat is t1, with initial time measure as 0 from the bottom of each squat.

The change in the bar's kinetic energy is, in both cases, 50J; since force is constant, we get for the quarter squat:
integral(0,k0) F ds = 50J
This yields:
F*k0 = 50J, so F = 50/k0 N

The change in the bar's momentum in both cases is 100Ns; since we know the force, the impulse for the quarter squat is:
integral(0,t0) F dt = 100Ns
integral(0,t0) 50/k0 dt = 100Ns
so:
50t0/k0 = 100Ns
t0 = 2*k0 sec
By construction, then, t1 = 2*k1 sec

Now we know everything. Since F = 50/k0 for the quarter squat:
.acceleration = 1/(2k0)
.velocity = t/(2k0) (note, plug-in 2k0 for the time yields velocity = 1m/s)
.position = t^2/(4k0)

Moreover, note that F = 50/k0 for the quarter squat, and F = 50/k1 for the full squat. Since k1>k0, this means that the quarter squat takes more force to achieve the same velocity as the full squat for a given load under conditions of constant force.

Here's a picture for the case where k0=1 and k1=2 (so the full squat moves twice the distance as the quarter squat)
http://i47.tinypic.com/mmbjma.png

Now, of course, the picture gets more complicated for non-constant force. But this does raise the question of whether the improvement in mechanics that the quarter squat affords give it the extra force production it needs to trump the full squat in cases where velocity at the top matters.
Again, I was only talking about the force being applied to the bar at the amoritization point. My point is not that you cannot determine the force before that point, but that at that single point you do not know the force being applied at that point.

5. SMC
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Originally Posted by tzanghi
You make excellent points, however I was only referring to the force being applied to the bar at the amoritization point. Surely, you can figure out the total force that was applied if you know the distance from the bottom of the squat to the amoritization point. The OP said that the full squat is better because of the high velocity at the amoritization point during a full squat, which involves nothing regarding the force applied prior to the amoritization force other than the mere fact that the force has caused the bar to achieve a given velocity. If this was his way of stating that the force applied before the amoritization point in a full squat is what makes the full squat better for VJ, then he may be right, but he was horribly unclear in saying so.

Also, I would like to state that my piecemeal explanations may have been poor, but this was largely due to irrelevant and confounding questions that had no bearing on the point. I had to explain why things that had nothing to do with my point(e.g., that a person with a bar on a scale would not weigh 0 lbs). When I was asked a large number of questions, I could not always stick to my point because I had to address other objections.

Again, I was only talking about the force being applied to the bar at the amoritization point. My point is not that you cannot determine the force before that point, but that at that single point you do not know the force being applied at that point.
Can you determine the velocity just before and just after the amoritization point?

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Originally Posted by SMC
Can you determine the velocity just before and just after the amoritization point?
If you have the acceleration or force, you could, but I didn't provide those in my hypothetical. I didn't include them because the OP only referenced the velocity at the amoritization point as the reason full squats were better for VJ, and not force or acceleration.

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What is the point of this thread? What are you trying to prove professors? I ask because it's way over my head.

8. SMC
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Originally Posted by tzanghi
If you have the acceleration or force, you could, but I didn't provide those in my hypothetical. I didn't include them because the OP only referenced the velocity at the amoritization point as the reason full squats were better for VJ, and not force or acceleration.
Not what I was getting at.

It was sort of a rhetorical question. Yes, in the very specific situation you lay out, where you ONLY know ONE velocity at ONE given time, you cannot determine the force. But as someone mentioned, this not going to be the case in an actual situation.

If you have a clock or stopwatch and a meter stick(or some scale for measurement), you can figure out the position vs time right? Such as where the bar is before, during, and after the amoritization point relative to time

If you can figure out the position and time points around around and including the amoritization point, you can find the velocity just before, and just after, and even right at

If you can find the velocity just before, during, and after the amoritzation point, you can find the acceleration before, during, and after. It might not be perfectly accurate, but it'll be pretty close if you take smaller changes in time. In fact this will be MORE accurate than starting with the acceleration or force and then finding the velocity at a given time(since such a process would be missing the initial velocity in whatever time period you're looking at as well as fail to take into account changing acceleration)

This will give us the instantaneous acceleration (from which force can be solved for) AT the point of amoritzation

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Just do the Fucking experiment. Measure your vertical and go do a bunch of quarter squats and remeasure.

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Originally Posted by SMC
Not what I was getting at.

It was sort of a rhetorical question. Yes, in the very specific situation you lay out, where you ONLY know ONE velocity at ONE given time, you cannot determine the force. But as someone mentioned, this not going to be the case in an actual situation.
I was only addressing the OP's claim that the higher velocity at the amoritization point is the reason the full squat is better. This is the very specific situation I lay out because it's addressing a very specific situation the OP argued for, that's all.