# Equations that define a human fall forward

Ok so what I want to create is a simulation of how the acceleration of a person falling would change according to the person's mass and height. This would then be explored in Matlab.
Therefore, first, I am trying to find out the equations that would relate acceleration motion with mass and height of the individuals. Can anyone share their thoughts on this?

These are the assumptions we should be making (but feel free to change them):
Axes: x, y, z=0
Initially the person would be standing vertically, perpendicular to the floor
They would fall as if they were a stick, without folding (circular trajectory, until impact with the floor)
Frictionless
The feet can be clamped to the floor
The centre of mass is assumed to be at 1/2 the height of the person.

Thanks! xx

## Answers and Replies

berkeman
Mentor
Ok so what I want to create is a simulation of how the acceleration of a person falling would change according to the person's mass and height. This would then be explored in Matlab.
Therefore, first, I am trying to find out the equations that would relate acceleration motion with mass and height of the individuals. Can anyone share their thoughts on this?

These are the assumptions we should be making (but feel free to change them):
Axes: x, y, z=0
Initially the person would be standing vertically, perpendicular to the floor
They would fall as if they were a stick, without folding (circular trajectory, until impact with the floor)
Frictionless
The feet can be clamped to the floor

The centre of mass is assumed to be at 1/2 the height of the person.

Thanks! xx
Welcome to the PF.

You say in your new member introduction thread that you are an engineering student at university. Have you had basic kinematics yet? Have you learned how to draw free body diagrams (FBDs) yet? BTW, the bolded parts of your post are a bit at odds -- you might as well include friction and not worry about actively holding the feet still. For practical friction coefficient values, the feet will stay in place throughout the fall.

CWatters
Science Advisor
Homework Helper
Gold Member
I see a potential problem to think about. If you model the human as a rigid rod it will only start to fall when it is tilted far enough that the centre of gravity is outside of it's footprint. After that point the rate at which it falls depends on how far outboard the centre of mass is. If the initial offset approaches zero then the time it takes to fall becomes very large or infinite. The time is "sensitive" to the initial conditions. A small change in the initial angle will have a big effect on the time taken to fall.