Weighted squat vs Body Weight Single legged squat
Summary
The load on single leg from body weight single legged squates will be the same as weighted squates if the weight in the latter is equal to the weight of the person!
Calculation
Assume the mass of a person is $M$ and the weight of their both legs is $x M$. Then, if the person does squates with weight $W$, then the weight on single leg will be $(W + (1-x) M)/2$.
If the person does sigle leg body weight squates, then the weight on single leg will be $(1- x/2) M$. Equating these two to find the value of $W$, we get
\[\begin{align} \frac{W + (1-x)M}{2} &= (1 - x/2) M \\ \implies W + (1-x)M &= (2 - x) M \\ \implies W &= M \end{align}\]Surprisingly, the final result does not even depend upon the value of $x$. Neat!
Visualization
Clone a person A. Let us name the clone B. Make B stand on shoulder’s of A and let A do a squat. Then, the load on one leg of A is equal to half of A’s upper body, half of B’s upper body and one of B’s legs.
Let A do single legged body-weight squat. Weight of A’s single leg is half of A’s upper body + the other half + weight of his single leg.
The result does not depend upon the weight of legs and upper body in question.
Comments
- Single leg squates can also be great for stability and put less load on spine.
- Single leg squates appears safer from injuries and does not require equipments.
- Weighted squates can be great to train the spine for load and core strengthening.