# Impact velocity from falling over

While logging into the Straight Dope I saw an ad for some Canadian govt agency stating that a 7 km/hr head impact is all that is required to crack a skull. So I have a question: if someone is doing some mundane thing on a sidewalk or road and they trip and their head hits, what will the impact velocity be? Let’s assume that the person is 5’ 5’’ tall and walking at a speed of 5 km/hr?

Seven kph is two meters per second, approximately the height above ground of an adult head. If it takes one second for your head to reach the pavement from a stumble, that will satisfy the minimum velocity for a skull fracture. An object (say, a head) dropped from a building falls 10 meters in the first second – more than enough to smash it to smithereens. But presumably, a stumbling person executes certain maneuvers that will retard the acceleration of the fall.

Final velocity is √2gd
So, for a 2 metre drop it is √(29.82) = 6.3ms[sup]-1[/sup]. 5.7ms[sup]-1[/sup] for 5.5 feet.
That is a head in free fall. So if your head falls off and onto the ground it will hit at about that speed. (Although the drop is from the bottom of head not the top, so a little less.) If your head remains attached to your body it is a bit messier. But 6ms[sup]-1[/sup] is probably a good limit case.

However it isn’t the speed that matters so much as the change in speed at the end. The distance your head stops over is what will determine how much injury you sustain. Fall onto concrete and the shock is huge, fall onto a newly turned flower bed, and you will simply dust the dirt off yourself and carry on.

I tripped on concrete while walking at a brisk pace. Fortunately my hands kept my head from contact. My hands were very sore (bruised and bloodshot) for three weeks after. Very glad it wasn’t my head that made contact.

During the Turkey Day Race, I tripped while running at racing speed and fell flat on my face. I did not have time to use my hands to deaden the fall. I’ve fallen often while running, but have had times to minimize the impact. This was on a bricked street. I broke my glasses, a tooth, and had swellings on both hands, which even today have not completely subsided. But all soft tissue injuries (other than the tooth). I had numerous cuts on my face, and it was a bloody mess. It looked like someone really socked me. I did not land on the back of my head, but made a face plant.

You also have to worry about the pounds per square inch of the impact. It’s different if you hit something flat or on a corner, or the more pointed part of your head.

And that 6 meters per second equals about 13 miles per hour. That is the speed for which motorcycle helmets are designed – in other words, motorcycle helmets protect your head if you fall down while standing still.