Balancing Cards

Take a full suit of 13 cards. Each card weighs as many ounces as its value. Aces weigh 1 ounce, Jacks weigh 11, Queens weigh 12, and Kings weigh 13 ounces. Take four bars of length 4 inches and create a mobile with the cards. You can tie to each bar in 5 places (at locations 0, 1, 2, 3, and 4 inches.) You can only tie once to each location. On the lowest bar, tie 4 cards, and one string up to the next bar. On the other three bars, tie 3 cards, one string down to the previous bar, and one string up to the next (the top bar has one string up to the ceiling.) All bars balance. Assume the weight of the bars and strings are negligible. Try to find solutions for which the center of mass is as high as possible and as low as possible.

Source: Original.

Solutions were received from Jozef Hanenberg, L. Maia, David Madfes, Steign Kistemaker, and Bernie Erickson.  The highest center of mass found was 57/182 above the center.  The lowest was 11/182 below the center.  Some examples are below.
From David Madfes: 
Solution with lowest center of mass I can find:
Assuming string has a length of 1, center of mass is
11/182 below the center of the center string

K Q A ^ V
    T 7 2 ^ V
       4 8 3 ^ V
             5 J ^ 9 6

Solution with highest center of mass I can find:
Center of mass is 33/182 above the center of the center string

7 K Q ^ V
   2  J  9 ^ V
     4  3  6 ^ V
             T A ^ 5 8
From Bernie Ericson:

A good puzzle.  Lot’s of fiddling around.  Not sure how center of mass works but here are a few possible solutions:

 Two with high centers [Center of mass is 53/182 above center.]: 

11         9          10         up        down 

13         12         up        down    2 

8          7          up        down    4 

5          3          up        1          6 

Replace the top row with 10 11 9 and it has the same center of mass, I think.
 

Two with Low Centers [Center of mass is 11/182 below center.]:

12         13         2          up        down

11         6          1          up        down 

7          4          3          up        down 

8          9          up        5          10

  

13         11         3          up        down 

12         4          2          up        down 

5          8          1          up        down 

7          10         up        9          6 

 This was a lot of fun.  It is a surprise to me that 11 12 and 13 must be high up to give it a low center of mass.

From L. Maia: 
  High center of mass: [Center of mass is 57/182 above center.]
    First solution:
      1    7-13-12-U-D
      2       3-9-10-U-D
      3           11-6-U-D-8
      4              2-5-U-1-4
    Second solution:
      1    7-13-12-U-D
      2       3-9-10-U-D
      3           11-8-U-6-D
      4                2-5-U-1-4
  Low center of mass: [Center of mass is 11/182 below center.]
    First solution:
      1    12-13-2-U-D
      2       11-6-1-U-D
      3          7-4-3-U-D
      4              8-9-U-5-10
    Second solution:
      1    13-11-3-U-D
      2       12-4-2-U-D
      3          5-8-1-U-D
      4             7-10-U-6-9
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