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Conversion of g acceleration into "body weight"

  1. Jul 28, 2015 #1
    Hi guys,

    I have a table with vertical peak acceleration values [g] and I want to find out a formula that convert the [g] values into ground reaction forces in units of body weight (BW). I think Newton´s 2nd law (F = m x a) may help but I am stuck on finding a generic relationship (problem is that I do not have the body mass values...)

    Example: peak acceleration of a walking person is 2 "g". How much is it in terms of body weights?

    Activity [g] [Body weight]
    -----------------------------------------------------------
    Walking 2 ????
    Jumping 5 ????


    Thank you!

    tjvv
     
    Last edited: Jul 28, 2015
  2. jcsd
  3. Jul 28, 2015 #2

    A.T.

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    Coordinate acceleration (CA) relative to ground, or proper acceleration (PA) that an accelerometer measures?

    You mean the vertical ground reaction force (VGRF) needed to achieve that vertical acceleration?

    VGRF[BW] = PA[g] = CA+1[g]
     
  4. Jul 28, 2015 #3

    Andrew Mason

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    Body weight is a force so to express body weight in terms of acceleration you would have to multiply by the body's mass.

    g = 9.8 m/sec2. The body weight of a person of mass M (in kg) is Mg =9.8M Newtons.

    So a person walking horizontally and accelerating horizontally at 2g = 19.6 m/sec2 would have to exert a force of 2Mg = 19.6M Newtons, where M=mass of the person.

    AM
     
    Last edited: Jul 28, 2015
  5. Jul 28, 2015 #4
    I mean proper acceleration (PA) that an accelerometer measures.

    Yes, when I mean bodyweight it is the vertical ground reaction force.

    Since it is a force we can put in newton´s 2nd law (F=m * a):

    F = [(m * acceleration measured) / (m * earth acceleration)] + 1 //+1 is to consider only linear acceleration (excluding earth gravity)
    BW = [acceleration measured / earth gravity] +1

    So in the example from the table above:

    BW = [2 / 10] +1 //considering gravity as 10m/s2 to simplify
    BW = 0.2 +1
    BW = 1.2 which means the force of walking would be 1.2 times the body weight of a person

    General formula would be this: BW = [acceleration measured / earth gravity] +1

    Is this correct?
     
  6. Jul 28, 2015 #5

    A.T.

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    If "acceleration measured" is proper acceleration then you don't need that "+1". See my formula in post #2.
     
  7. Jul 28, 2015 #6
    Hi AT,

    sorry I meant Coordinate acceleration (CA) relative to ground (since it excludes the earth gravity).

    So from your formula it means that to convert a G force into BW it is just sum the measured g force with earth´s gravity?
    Example:
    BW = CA+1[g]
    BW = 2 + 1
    BW = 3 (getting the initial table example, would mean that the force acting when people is walking would be 3 times person´s body weight)

    Can you please confirm?

    Thanks
     
  8. Jul 28, 2015 #7

    A.T.

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    To accelerate your center of mass at 2g upwards, relative to the ground, you have to apply 3 times your body weight to the ground. But you don't have such high accelerations during walking.
     
  9. Jul 29, 2015 #8

    Andrew Mason

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    Just to add to what AT has said, if you think of the acceleration provided by a 100 m. sprinter running the 100 m. dash in 10.4 seconds and taking 1 second to get up to a speed of 10 m/sec, the acceleration is only 1 g. I think that is pretty close to the maximum horizontal human acceleration you are going to see.

    AM
     
  10. Jul 29, 2015 #9

    A.T.

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    He is asking about vertical accelerations, which can be higher for a fraction of a second during landing impact (jumping, running fast). But during normal walking the vertical ground reaction doesn't go much beyond 1 body weight, so the vertical acceleration is a small fraction of 1g.
     
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