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to change the impedance of a transmission line significantly you change    the spacing, small hub small hoop = lower impedance higher resonant   frequency, its explained in  the arrl open sleeve article,


your models show that altering the bow changed impedance as expected of a transmission line, less bow higher impedance,


to discover if nec reports that avanti were bsing us over the means to create downtilt in that style antenna i think you may need to find the right size hoop and hub that gives a good match to 50ohm coax when the conductors are parallel to a 1/2wave mast,


since avanti claim a takeoff angle of about 4-5 degrees with the stock setup vs your 9 degrees you may not see the downtilt they claim using parallel conductors.