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Q & A: Legs supporting weight while walking

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Most recent answer: 02/16/2011
Q:
Do our legs really support 3 times our body weight when we walk? If not, what is the weight our legs support when we walk?
- Qi Han and Wu Fan
A:

While walking, the maximum force on your legs exceeds the weight they normally support by quite a bit, although the exact factor depends on how you walk.

If when you walk, you don�t bounce up and down (this is not how people usually walk, but it is easier to think about), and each foot is in contact with the ground 50% of the time, the maximum weight on the legs will be about twice what they usually support, because only one leg is holding you up at a time and the weight is not shared. When a foot is lifted off of the ground, it supports no weight.

If you bounce up and down a bit when you walk, the legs must supply the force needed to do that. This force depends on if the bouncing is jerky or smooth, and is probably best measured with pressure-sensing devices in the shoes. If you don�t bend your knees when walking, you will send pounding shocks up your legs and back when they hit the ground.

Still, while walking, my guess is that the maximum force is only three times the usual weight they support (half of the body weight per leg -- it�s shared between two legs) and not three times the total body weight. The time-average weight supported by both legs is just the total body weight.

When you run, the fraction of the time the feet are in contact with the ground decreases. In Olympic walking, the rules are that the athlete must not leave the ground at any time. This means that before one foot can be picked up, the other foot must be on the ground, making for a fraction of ground time for each foot greater than 50%, but as close to that as the walker can manage. When running, both feet leave the ground at times, and there is more bouncing, and thus more pounding force on the legs.

Tom


(published on 10/22/2007)

Follow-Up #1: acceleration on landing from jump

Q:
How do you calculate how many times body weight is impacted through the body when stepping off a 2 or 4 meter high wall, landing on the feet and bending the legs as usual to absorb the impact? (I'm not to concerned about precision just estimated) Thanks
- Kevin Webster (age 33)
Catterick, North Yorkshire, England
A:
This is a fun question. Call the height you jump from h, the gravitational acceleration g. Then your velocity when you land is v=sqrt(2gh). (Air friction should be unimportant from these heights.) Now you have to decelerate back to v=0 in distance L, the length of flexing you get from bending your knees. So the acceleration (assuming it's uniform) is v2/2L= gh/L, a nice simple result. If you can flex about 0.25m (about my number in creaky old age) , and you jump from 2m, the acceleration is 8g. In no acceleration, you feel a body-weight force from 1g. So the force you feel here is about 9 times what you usually feel from body weight. From 4m, it would be 16+1=17 times body weight.

Mike W.

(published on 02/11/2011)

Follow-Up #2: kinematic equations

Q:
That answer is exactly what I was looking for. Could you recommend a cited reference for this calculation as I would like to use it in a dissertation Many Thanks
- Kevin W (age 33)
Catterick
A:
Hi Kevin- The basic equations relating acceleration, distance, time, mass, and force can be found in any introductory physics text. Here's a link to the first one that happened to cross my mind:

BTW, I just measured how much my knees flex. As an average-size person, kind of creaky, I was able to flex about 0.23 m. So I've altered the calculations above to use 0.25m rather than 0.5m as the flexing distance.

Mike W.

(published on 02/16/2011)

Follow-up on this answer.