Instructions to Modify Excel Spreadsheet for Center of Mass in Backhandspring
Using the picture of the back handspring enter the X, Y coordinates of each segment endpoint into cells
B21, C21 thru cells B32, C32, see the figure below for an example of the X, Y coordinates of the top of
the head and the bottom of the head.
TABLE 12.1
Segment Weight Prediction Equations and Center of Mass Location
Segment
Segment Weight (N)
Head
Trunk
Upper Arm
Forearm
Hand
Thigh
Lower Leg
Foot
0.032 x BW + 18.70
0.532 x BW - 6.93
0.022 x BW + 4.76
0.013 x BW + 2.41
0.005 x BW + 0.75
0.127 x BW - 14.82
0.044 x BW - 1.75
0.009 x BW + 2.48
CM Location (%)
66.3
52.2
50.7
41.7
51.1
39.8
41.3
40.0
Proximal End
Top of Head
1ST Cervical
Shoulder
Elbow
Wrist
Hip
Knee
Ankle
From: Chandler, R. F., C. E. Clauser, et al. (1975). Investigation of Inertial Properties of the Human Body (AMRL-TR-74-137).
Wright-Patterson Air Force Base. Dayton, OH, Aerospace Medical Division NTIS No. AD-A016 485.
Enter Equations to Compute the Segment Weights (Cells F3 thru F10)
Use the equations from Table 12.1 above, for the head segment the weight equation in Cell F3 is:
=(0.032*$L$2)+18.7
To enter the Trunk segment weight in Cell F4, look at the equation in Table 12.1 (p 129) Trunk is 0.532 x
BW - 6.93 enter this equation in cell F4:
=(0.532*$L$2)-6.93
In this analysis we are assuming that the right and left side of the arm and leg segment move
symmetrically. In each case double the weight of the limb segments by multiplying the prediction
equation in Table 12.1 by 2. For the thigh segment Table 12.1 has this weight equation: 0.127 x BW –
14.82. You should enter this in Cell F5 as follows:
=2*((0.127*$L$2)+14.82)
Repeat this for the Lower Legs, Feet, Upper Arms, Forearms and Hands.
Enter the Equations to Compute the X, Y Location of Each Segment’s Center of Mass
Columns G and H compute the X and Y coordinate of each segments center of mass. For the Head
segment enter the following equation in Cell G3 to compute the X coordinate.
=B3+(0.663*(D3-B3))
Place the following equation in cell H3 to compute the Y coordinate of the head segment center of mass:
=C3+(0.663*(E3-C3))
To compute the location of the X coordinate for the trunk look at Table 12.1 on p 129, it indicates that
the trunk CM Location % is 52.2 (or .522) change the formula as follows and enter it in cell G4:
=B4+(0.522*(D4-B4))
Do the same for the Y coordinate of the trunk and place the equation in cell H4:
=C4+(0.522*(E4-C4))
Repeat the above examples to enter the equation to compute the X (column G) and Y (column H)
location of each segments center of mass. Use the CM Location (%) from Table 12.1 to enter the correct
percentage of distance from the proximal end of each segment.
Sum the Torques about the X and Y Axis
To sum up the Torques about the Y axis, enter this equation in cell I12
=sum(I3:I10)
Then sum up the Torques about the X axis, enter this equation in cell J12
=sum(J3:J10)
To find the X and Y location of the body CM we need to divide sum of the torques by the total weight
For X location, enter this equation in cell I14:
=I12/F12
For Y location, enter this equation in cell J14
=J12/F12
Then look at the picture of the back handspring this X, Y location of the center of mass should be logical,
see the figure on the next page.