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This page is a discussion about the application of multiple catenary curves related to reducing the length of a dipole.

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Catenary DipoleIn addition to the generally known "slow wave" techniques of zig-zag and meander, the studies presented here cover the technique of multiple curves to shorten the arms of a dipole.  This approach is a logical extension of the work on Dipole Sag and the associated development of an antenna model for Catenary Curves.  It was found that if a Catenary dipole was set to sag 35% of the length of a resonant wire, there would be a match for 50 Ohm coaxial cable.  Ease of use set aside, this is a rather large drooping antenna with a broad, higher angle beam.  Why not keep the center feed at the same height as the ends and allow the arms of the dipole to droop but only half as much?  A 2-Droop  4NEC2 Model: Here,  was developed which answers the question:

What happens if both sides of a dipole are drooped?

2-droop dipole 30pct
Figure 1

From Figure 1. The 2-Droop characteristics compared to a 1-Droop catenary dipole are:

Z impedance: 52.7 Ohms vs. 60.4 Ohms
SWR50: 1.06 vs. 1.21
Gain: 6.39 dBi  vs.5.81 dBi
Radiation Efficiency: 71.93%  vs. 76.05%
Resonant Wire Length: 5.08% longer  vs. 1.04%   (Longer than a straight dipole)

Clearly, a 2-Droop dipole is prefered if you accept a longer resonant wire length.

The Far Field Radiation pattern looks very much like that of an ordinary straight dipole.

2-Droop Dipole 31pct Graph 3D
Figure 2
Far Field Radiation Pattern, 2-Droop Dipole at Resonance

Here is a comparison of Figure 2 to a 1-Droop cantenary dipole as in Figure 1:
Angle of maximum radiation (Purple color on 3D view) is 30 up from horizontal vs 40 for the 1-Droop cantenary dipole.
Beam width (at 3dB down) 90 vs 110.
End Null: -3.1 dBi  vs -1.5 dBi                        (Better than the -2.7 dBi of a straight dipole).
Side-to-End Ratio: 9.5 dBi  vs.7.3 dBi            (Close to the 10 dBi of a straight dipole).

To extend this idea of multiple droops, a 4-Droop 4NEC2 Antenna Model: Here,  was developed which answers the question:

What happens if there are two droops
on each side of a dipole?

4-Droop Dipole 30pct
Figure 3

Surprisingly, the answer is "No apparent change". Even though the physical depth of a droop becomes much smaller for the 6-Droop and 8-Droop antenna models, their radiation characteristics turned out to be virtually same. Really unexpected.

Because of this visual commonality of the graphs for each of the 2-,4-,6- and 8-Droop Catenary Dipoles, the graphs were consolidated into the following three figures.

Multi-Droop Catenary SWR Gain
Figure 4

In Figure 4 the Blue line for SWR as before, rises then falls to to a perfect 1:1 match around 0.30-0.32 ratio.
The Red line shows the familiar, unrelenting decrease in dBi Gain for increasing ratios of sag.

Multi-Droop Catenary Eff and Z
Figure 5

Figure 5 confirms that all Multi-Droop configurations have a 50 Ohm impedance around 0.30-0.32 sag ratio (Blue Line) and sag ratio has little effect on % Radiation Efficiency (Red Line).

The single signigficant difference between the 2-,4-,6- and 8-Droop antennas is the length of wire needed.

Multi-droop Catenary Pct-Length Graph
Figure 6

The Cantenary antenna models are based on finding the starting length of wire that, when bent, will resonate the same as a straight wire. As the depth of each droop and the number of droops increase, the % longer lengths of wire needed are summarized in the four curves of Figure 6 above.  For example:  To build a 6-Droop Catenary dipole for the 50 Ohm resonant frequency, you need to start with wire that is 10% Longer than the amount of wire that is resonant as a straight dipole... then divide it into six segments.
In Figure 7, compare the 8-Droop Dipole  Polar Graph and 3D flyover view with Figure 2.  You can see that they are virtually identical indicatiing that the number of droops has no apparent bearing on radiation characteristics.  4NEC2 Antenna Model: Here

8-Droop Dipole 33pct
Figure 7
Far Field Radiation Pattern, 8-Droop Dipole at Resonance

Some practical points for building:  Your target frequency has a bearing on the number of droops to decide upon.  For HF more droops means more work but a more controllable, less wiggly, compact antenna. VHF can get along with 4 or 6 droops.   UHF, attic or wind-free location, 2 or 4 droops could be considered.
Catenary Droop Ratio-Span table
The length of a multi-catenary dipole controls the resonant frequency, so hold the length dimension and open the wire in the center enough to accomodate the coax connector or balun.  Measure and mark the bend points for each droop before bending. Bend both sides of the antenna at the same time for uniformity. It is not at all critical to have sharp well-formed junctions between curves. It is not critical to try to form a catenary curve.  An "S-shape is ok. For tuning, adjust the length of the dipole. 

This approach to shortening and tuning a dipole by multiple droops is an extemely tolerant method.  Any reasonable approximation will work.

Dick Reid, KK4OBI at