that the balloon fabric and miscellaneous will not weigh more than 150% of the gross weight of 500 ft. of 1-1/2-inch-diameter copper rods. To maximize the strength of the composite umbilical, 10 strands per cable (positive and negative) would be used. The wire would be A.W.G. 0000 gage, hard-drawn copper wire (0.460 inch diameter), rated for 325 amps per strand. Thus, the over-all ratings would be 3250 amps [36]. Since as shown below, 27100 amps are to be carried, which is not necessarily a problem, because they are bare wires in open air. The tensile strength of 0000 hard-drawn copper wire is 49000 psi. Therefore, the dual cable system could support 163000 pounds. This means that each 500 ft. section (which weighs 6407 lbs) will support it’s own weight, plus 24 additional sections. Drag on balloon airfoils contiguous with umbilical “Beanstalk” umbilicals clearly would need to be mounted in relatively wind-free areas. To maximize independence from unavoidable wind forces, balloon vertical-lift must be maximized, while balloon (lateral) drag must be minimized. Pressure maximum windspeed of 68.18 mph (= 100 ft/s), and a 12%-thick (vertical-balloon) airfoil section, the drag of each 500 ft umbilical-balloon section will be given by [37]: where: Let the horizontal cross-sectional area of the balloon (upended) “wing” sections be 500 ft2, (yielding net vertical lift of bottom-most and each additional balloon, respectively, of 17400 lb). Then approximately for 12%-thick bottom-most balloon wing, the chord is 73 ft and the (maximum) thickness is 9 ft. Balloon “wing” sections will need to grow proportionally in volume, as one moves toward the top of the Beanstalk (so that each supports 17400 lb). Also, above the altitude of most winds, linear sections should grow more circular in cross-section. Estimating the drag force at or near sea level for 12%-thick, smooth wing section, the drag coefficient may be assumed about CD = 0.004 [38]. Drag, in pounds, under all the above conditions, on the sea-level, vertical balloon wing (low-drag) section (where S = 73ftx9ft = 657 ft2) will be » 31 lbs. Higher wind speeds dramatically increase drag. For example, at 200 ft/s (136 mph), drag ~ 125 lbs. Similarly, extreme increase in drag coefficient (as by damage to or distortion of balloon wings) could inordinately increase drag. Generally, increased drag evidently will be experienced as increased tension force in the (copper) umbilical cables. However, at 163000 lb maximum permissible tensile load for each balloon supported segment, it is difficult to conceive of natural circumstances imposing excessive tensile stress.
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