Horizontal acceleration of a person

[GingerKhan]

Let's say that an athletic person of average height (1.75 m) and weight (75 kg) is strapped by the feet to a small motorized board. How would one go about calculating the maximum acceleration the person can sustain without falling backwards?

There is no wind and the air density is at sea level.

 

[russ_watters]

The question doesn't really work. If the acceleration starts slow enough, they can just lean forward until they are near horizontal and get crushed by their own weight due to the g-force.

 

[Naty1]

In addition to post#2, the coefficient of fricion between feet and board must in some way be specified...unless that "curl toes and hang ten".

Ginger: maybe you are thinking about tensing muscles to offset the tipping?? That's a really tough question to ask as it's biological and physics...and could depend as well on the length of their feet and the location of their leg with respect to both ends.

 

[meldraft]

If, however you assume foot and the board as a joint (so only rotation), then there is a moment. The axis of rotation is the joint, the distance is the y-coordinate of the center of mass. From Newton's second law:

rxF=rxma => M = mr^2 thetaDoubleDot

How you proceed from this point depends on how you model the problem. You can, for instance, assume that there is a maximum resistance moment from the ground that, when surpassed, will make the object (human) fall.

A more realistic way to model it would be to consider a rectangle with a center of mass. There is a maximum angle after which the rectangle will fall over. You can calculate this angle if you consider a line that originates from the point of rotation (so one corner of the rectangle), and that is perpendicular to your surface. If the center of mass goes beyond this line, the rectangle will fall over.

From Newton's law you have a differential equation of motion for your problem, so you can get the angle as a function of acceleration (angle comes into play from the y-coordinate of the "r" vector).

Depending on the initial conditions, you can derive from that the acceleration that causes you to reach that maximum angle.

 

[Ryan_m_b]

If what you are asking is how much pushing force a human could take before falling over then you would need to find out the strength of all the relevant muscles. As a starting point here is a paper discussing the testing methods for isokinetic testing of the ankle (disclosure: I haven't read more than the abstract).