That's interesting. Maybe the loop makes for a more directional radiation pattern, better to penetrate the ocean down to the depths needed to reach a submerged submarine. The HF wire had to be straight, but then they were only making airborne and ground-based contacts.
The loop or tight turns are required to keep the wire vertical - otherwise if they flew straight - the wire would begin to trail behind them and would gradually become straight and level - but then they could not communicate with the sub.
from various source on the internet....Vertical antennas must be used because VLF waves propagate in vertical polarization
and here is a good read...https://fas.org/nuke/guide/usa/c3i/e-6.htm
The improvements probably are why the E6A is now a E6B !
Orbit Improvement Program
The E-6A communications relay mission is accomplished by trailing dual wire antennas while performing a continuous orbit maneuver.
It is essential that the wires obtain as near a vertical attitude as possible for optimum very low frequency connectivity. Currently, there exists orbit control problems and wire/tail contact causing bank-angle restrictions which precludes the E-6A from obtaining optimal wire verticality. Modifications to the avionics systems are required to meet the orbit operational requirements. The E-6A Orbit Improvement Program, which corrects theE-6A deficiency, consists of the installation of autothrottles and software improvements to the Flight Management Computer System (FMCS).
The FMCS will be modified to implement the contractor developed orbit algorithm, with interfaces to the digital autopilot. The system is designed to provide fail-safe capabilities. These modifications will fine tune bank-angle and airspeed inputs enabling the aircraft to fly an orbit which maximizes the verticality of the antennas thus ensuring connectivity to the strategic forces.
An E-6A autothrottle system will be developed based on existing Boeing 737 commercial equipment.
The orbit improvement system does not present any threat shortfalls to the TACAMO mission environment. There are no major cost, schedule, or performance tradeoffs to be performed. A feasibility study for the autothrottle program was previously authorized. Based on preliminary results and background data associated with commercial applications, the orbital improvement control system approach to correcting theE-6A deficiency was the only practical approach. Adaptation of an existing commercial system rather than developing a new system significantly reduces costs without increasing technical risk.
Production was planned for Fiscal Year (FY) 95 through FY 98 with 15 aircraft installations, plus 3 trainers, in addition to a previous engineering and manufacturing development installation for a total of 16 aircraft.
The Orbit Improvement Program will enable the fleet to perform current and projected operational tasking effectively and reliably through the twenty-first century.