Appendix

 

The opportunity to prepare for the Canada Wide Science Fair allowed the researcher some time for afterthoughts and further introspection into her results.  The question was posed:

 

Is there a quantitative relationship between the load position and the relative magnitude of the counterbalancing forces?

 

With reference to the force diagram previously referenced (Foerster and Miller, 2006), it is observed that the vector established by the load connecting to the shoulder joint is the hypotenuse of a right angle triangle with the vertical side always equivalent to the vertical weight .   The horizontal side to the triangle is the horizontal component of force that causes the load to pull the shoulder back.  The counterbalancing force required to stabilize the load is the opposite force equal in magnitude.  This right angle triangle changes in shape as the load is varied in position but the vertical component is always the same.  The horizontal component equalled to the counterbalancing force also changes and does so in agreement with what was observed in the experiments.  This is illustrated in figure A1.

                                                                                            VERTICAL FORCE, V (ie., Weight)                          X
The following relationship exists:  HORIZONTAL FORCE, H  =  ---------------------------------------     =     V   x   -----                                                                                                                             tan (Ǿ )                                               Y

                                   where Ǿ = angle bisected by the horizontal and the vector from shoulder to load

                                                      Y
                                                tan Ǿ = -----
                                                               X

With the vertical weight vector fixed, the horizontal vector that represents the counterbalancing force changes as the angle Ǿ changes.  In the diagram below, it is clear that the H force in position C is much larger than the H force in position B.  The H force in position A and D is the same because their corresponding Ǿ are very close.
    Figure A1: Force Vector Diagram of Loads in Various Positions within a BackPack

 

Using an Excel spreadsheet, the analysis below took the 12" x 16" metal grid and at each intersection point calculated the (X/Y) ratio.  These calculations are presented in the spreadsheet shown in figure A2.  The x and y component represents the distance from the horizontal and vertical distance from the shoulder joint.

The (X/Y) ratio represents the scale factor that the horizontal counterbalancing force is greater than the vertical force, being the weight.  The observations from experiment 1 that the counterbalancing force increases as the load heads in the direction of the red arrow shown below, is validated.  Even the normalized force ratios are somewhat substantiated.

The 45 degree bisector is the dividing line which dictates if the load feels "heavier" or "lighter".  Above the line, the counterbalancing force is greater than the weight of the load.  Below the line, the force is less.

The blue arrow shows where counterbalancing force sensitivity to load position increases.  In regions of high sensitivity, small changes in load position causes substantial relative changes to the counterbalancing force.

 
    Figure A2: Spatial Distribution of Horizontal / Vertical Force Ratio over Backpack

 
The H / V Force Ratio spatial distribution over the regions of the backpack is best viewed as a 3-D surface graph and a topography map.  The latter are generated with the help of Microsoft Excel's graphing features.  It better illustrates the regions of high counterbalancing forces.  These are shown in figures A3 and A4.  The red arrow is the dividing line below which the counterbalancing force is greater than the vertical weight of the load.
    Figure A3: 3-D Representation of H / V Force Ratio over the Regions of the BackPack

 
    Figure A4: Topography Map of the H / V Force Ratio over the Regions of the BackPack

 
One of the experiments involved re-distributing some of the weight from a backpack position to a frontpack worn in conjunction with the backpack..  The force vector analysis below shows the effects of reducing the counterbalancing forces by doing just that.

 

 

 

 
    Figure A5: A Force Vector Illustration of Redistribution of Loads with a FRONTPACK