Modeling LLSC

1: EMA HIRF Background (IEL)
2: HIRF Certification Requirements
3: Methods of Modeling Cable Harnesses For LLSC Evaluation

3.1 Canonical Aircraft Model

3.1.1 Figure of Merit
3.1.2 Broadband Source

3.2 Single Cable Investigations

3.2.1 Source Angle of Incidence and Probe Location
3.2.2 Cable Resistance
3.2.3 Cable Diameter
3.2.4 Number of Harnesses

3.3 Multi-Conductor Investigations

3.3.1 Baseline Model
3.3.2 Single Wire and Multi-Conductor Harness
3.3.3 Cable Packing Variations
3.3.4 Cable Branching
3.3.5 Cable “Micro-Branching”
3.3.6 Skin Depth Effects
3.3.7 Combinations of Features

3.4 Summary and Conclusions

4: Methods of Modeling Aircraft for LLSF Evaluation

Chapter 3: Methods of Modeling Cable Harnesses For LLSC Evaluation

In a typical aircraft, hundreds of harnesses are routed throughout, only a fraction of which are typically modeled due to computing resource limitations.  This means that in order to obtain representative coupling levels, some simplifications in the model must be made, e.g., routing a single cable along the path where there are many, omitting cable branches which are not critical, etc.  These simplifications are quite reasonable for coupling predictions at low frequencies (e.g., lightning), and the predictions match measured results nicely. [1,2]

A problem with the above technique for modeling LLSC arises at HIRF frequencies.  It leads to predicting cable coupling levels sometimes higher than those for the real aircraft, as well as very strong cable resonances, which are in some cases two or three orders of magnitude higher than what is typically seen in measurements.  In this work, we investigate cable properties which must be considered in modeling in order to reduce coupling level predictions to more realistic levels, specifically at resonant frequencies.

A 3D canonical aircraft model with a cable harness was created in order to perform parameter studies for including various harness features and complexities. EMA3D V4 integrated with MHARNESS was used to perform the simulations.  Harness bundle currents were calculated in the time domain, after which the transfer function responses in the frequency range of 1 – 400 MHz were determined.  The purpose of this investigation is to determine harness parameters that most significantly affect how electromagnetic fields couple to wire harnesses, and to develop a technique for validating FDTD models in order to predict low level swept current (LLSC) values for certification testing.

Cable harness parameters being investigated in this chapter are as follows:

• Single straight cable:
  • Source angle of incidence (AOI) and probe location
  • Cable resistance
  • Cable diameter
  • Number of harnesses
• Multi-conductor harness:
  • Straight uniformly packed harness
  • Cable packing variations
  • Cable branching
  • Small differences in cable individual conductor lengths and paths (micro-branching)
  • Skin effects
  • Combinations of above features

3.1        Canonical Aircraft Model

The canonical aircraft consists of a 20 m long, 2.2 m² fuselage shown in Fig. 3.1(a). The outer skin is a carbon fiber reinforced plastic (CFRP) type material, with a thickness of 8 mm and a conductivity of 10⁴ S/m.  The apertures in the fuselage consist of a cockpit window opening (3.2 m² total area) and seven cabin window openings on each side (0.25 m² each).  There are four baffles and a bulkhead with the same CFRP material in the interior, as shown in Fig. 3.1(b).  A metal cable tray spans the length of the fuselage and is centered on the fuselage floor.  Several different cable configurations were used during the parameter investigation, and the specific layout will be described within each subsection.  All cables were positioned at a height of 1 FDTD cell (10 cm) above the cable tray.  Bundle currents were probed at location 1 in Fig. 3.1(b) unless specified otherwise.

Figure 3.1 Canonical fuselage model shown with CFRP baffles (orange), HIRF cable tray (blue), and cable spanning from nose to tail (green).

3.1.1        Figure of Merit

We constructed a numerical model with a multi-conductor harness without an overbraid, representing a bundle of twisted shielded pairs (TSP).  The cable is strongly coupled to the aircraft EM environment.  A figure of merit for HIRF LLSC certification is an enveloped bundle current transfer function, enveloped over the resonance peaks of the transfer function response [3].  This means that bulk current on a cable bundle is measured at some location near a box, normalized to the incident electric field amplitude to obtain the transfer function, then enveloped.  As we use a FDTD code for this investigation, the bulk bundle currents are first calculated in the time domain, then Fourier transformed to the frequency domain and normalized to the incident electric field.  The transfer functions and their resonance peaks will then be compared for various simulations.

3.1.2        Broadband Source

A broadband Gaussian plane wave electric field source shown in Fig. 3.2 was used for external excitation. For the single cable investigations, the AOI was varied, but for the multi-conductor harness the AOI was fixed at 90° (broadside), with horizontal polarization (see Fig. 3.1(a)). The source covers a frequency range from 1 – 400 MHz.

Figure 3.2 Gaussian pulse source in time domain (left) and its frequency content (right), used as plane wave excitation for all simulations.

3.2        Single Cable Investigations

3.2.1         Source Angle of Incidence and Probe Location

For the first category of simulations, the cable used was a single wire spanning the length of the vehicle as shown in Fig. 3.3.  The diameter of the cable was 4 mm with the resistance of 35 mΩ/m, which is similar to the shield of an AWG 22 TSP type cable.  The single cable terminates directly to the metal HIRF tray at the nose and tail of the fuselage, emulating a real life shielded cable with the shield grounded at both ends.

Figure 3.3 Three current probes were used to measure cable currents: 1 in the cockpit 0.5 m from the nose, 2 in the cabin near the windows and 3 in the empennage 1.5 m from the tail.

The incidence angle of the of the source plane wave varied from 180° (from the top), to 135°, to 90° (broadside) for the first series of simulations, as shown in Fig. 3.4.  The cable current was recorded at three locations along the length, indicated in Fig. 3.3, where location 1 is 0.5 m from the nose in the cockpit region, location 2 is in the cabin region taken at the fourth window, and location 3 is in the empennage 1.5 m from the tail.

Figure 3.4 Three angles of incidence used to simulate canonical fuselage model

The results for the AOI and probe location simulations are presented in Figs. 3.5-3.7.  In the figures on the left are the time domain results, next to the transfer functions in the frequency domain.  While the plane wave source is a Gaussian waveform with full width at half-max (FWHM) of approximately 6 ns, the currents induced on the cable oscillate for at least 200 ms before ringing down enough to take a Fourier Transform.  This is due to the cable being connected to the metal tray in a short circuit at both ends. The ohmic losses are low due to the very low cable resistance (35 mΩ/m x 20 m), with radiation resistance being the only other loss mechanism.  The first 400 ns of the current waveforms are shown in the insets of Figs. 3.5-3.7.  This long ring-down time also gives rise to sharp resonances in the frequency domain.

The top down AOI produced the largest cable currents at all three probe positions, followed by the 135° AOI and then the broadside AOI.  It is evident in the transfer function plots that the top down AOI typically produces cable currents that are 2-10 dB larger than the broadside AOI at frequencies up to 100 MHz.  The first vehicle resonance is the half wavelength resonance, which occurs at 7.5 MHz for this model.

The plot in Fig. 3.8 compares the three different probe positions for the broadside AOI.  The three different probe positions indicate that the coupled currents can differ significantly for the different regions of the aircraft.  The first and second vehicle resonances are captured by all three probe locations with similar magnitudes, but above 20 MHz, the peak transfer function response for all three probe locations occur at different frequencies.  The harness responses above 20 MHz vary significantly between the three fuselage regions implying that structural geometry greatly affects the fields that drive the harnesses in the different regions.

Figure 3.5 Time domain (a) and transfer function (b) results for the three AOIs at probe location 1.

Figure 3.6 Time domain (a) and transfer function (b) results for the three AOIs at probe location 2.

Figure 3.7 Time domain (a) and transfer function (b) results for the three AOIs at probe location 3.

Figure 3.8 Time domain (a) and transfer function (b) results for the three probe positions with the broadside AOI.

For all remaining simulations, the broadside AOI with horizontal polarization was used, as this orientation is typical in LLSC measurements.  The cable current comparisons are made at probe location 1 only.

3.2.2        Cable Resistance

Material properties, specifically the resistance of a cable or harness, play a significant role in the coupling characteristics in a HIRF environment.  For the investigation of resistance effects, the same single wire shown in Figure 3.3 was used with a diameter of 4 mm.  The resistances were varied as follows:

• 1 mΩ/m
• 10 mΩ/m
• 35 mΩ/m
• 100 mΩ/m

The resistance variation results are presented in Figs. 3.9 and 3.10.  The resistance of a cable has a significant effect on the amount of time needed for energy to dissipate from that cable. The loss mechanism associated with the ring down time is ohmic loss in the cable.  Higher resistances have higher ohmic losses and therefore faster decay times. The time domain peak current values differ by only 2 dB between all cable resistances, but the transfer function magnitudes can differ by as much as 30 dB.  The largest magnitude current couples to the 1 mΩ/m cable, having a peak value of – 6 dB (500 mA/V/m), and that cable rings down at around 2 ms.  In contrast, the 100 mΩ/m cable couples a maximum of -32 dB (25 mA/V/m) and has 100 times faster ring down time.

Figure 3.9 Time domain (a) and transfer function (b) plots comparing resistance effects on single cables.

Figure 3.10 Zoomed in transfer function plot with comparing resistance effects on single cables.

3.2.3        Cable Diameter

The simulations of varying cable diameters from 4 mm to 38 mm indicated that the diameter has a very small effect on the coupling characteristics in the HIRF environment.  Here, the resistance was held constant at 35 mΩ/m for each cable, and the results were nearly identical.

3.2.4        Number of Harnesses

It is common that multiple harnesses are routed alongside each other as the wiring is placed within an aircraft.  The effect of routing multiple harnesses together was investigated in the canonical model by simulating harness configurations with 3 and 7 parallel segments as shown in Fig. 3.11.  All of the harnesses were 4 mm in diameter with a resistance of 35 mΩ/m. The harnesses were spaced 1 mesh cell (10 cm) from each other, with 1 harness on each side of the original harness for the 3 harness case.  For the 7 harness configuration, 3 harnesses were included symmetrically on each side of the original harness.

Figure 3.11 The metal HIRF tray (blue) is shown with the appropriate number of harnesses (green) used for the 1, 3 and 7 harness configurations.

The results for the center cable of the multiple harness configurations are compared to the single harness configuration in Figs. 3.12 – 3.13.  As more harnesses are added on each side the center harness becomes more shielded.  The center harness in the 3-harness configuration experiences a 10% drop in peak transfer function response from the single harness case.   For the 7-harness configuration, an even larger amount of shielding is provided from the outer harnesses resulting in a 25-50% drop in transfer function magnitudes.

A comparison was made between several of the cables in the 7-harness configuration to determine how position affects the response of a particular harness.  The four cables that were compared are shown in Fig. 3.14 as Cables 1, 2, 4 and 6. Cable 1 is the center cable and the cable numbers increase as they move outward with Cable 6 being the outermost cable.

Figure 3.12 Time domain (a) and transfer function (b) plots comparing multiple harness configurations.

Figure 3.13 Zoomed in transfer function plot with comparing multiple harness configurations.

The results comparing cable positioning are shown in Figs. 3.15 and 3.16. Each cable dissipates energy at about the same rate, fully decaying by 200 μs.  The transfer function magnitudes are largest for the outer Cable 6 and decrease as the position moves inward with Cable 1 having the smallest response.  The peak transfer function magnitude for Cable 6 was -23 dB (70 mA/V/m) while the peak response for Cable 1 was -27 dB (45 mA/V/m), but at most frequencies the outer cables provide more than 6 dB of shielding for Cable 1.

Figure 3.14 Cable numbering within the 7 harness configuration.  Cable 1 is at the center and cable 6 is the outermost cable.

Figure 3.15 Time domain (a) and transfer function (b) plots comparing the harness currents within the 7 harness configuration.

Figure 3.16 Zoomed in transfer function plot with comparing harness currents within the 7 harness configuration.

3.3        Multi-Conductor Investigations

Actual harnesses within aircraft are likely to have very complex packing schemes that are random and vary over the entire length of the harness.  This type of complexity and randomness is very difficult to model numerically.  A statistical analysis covering a large range of possibilities could provide an adequate prediction of coupling behavior, but this approach is not practical for the analysis of a typical aircraft containing tens to hundreds of harnesses throughout the entire vehicle. The following simulations attempt to separate and quantify the coupling effects associated with some complex features of actual cable harnesses within aircraft.

All of the remaining simulations use a different type of cable than has been used thus far.  The previous simulations all used a single wire, whereas the remaining simulations take advantage of the MHARNESS capabilities to explore some characteristics of multi-conductor harnesses.

3.3.1        Baseline Model

The baseline harness consists of 19 individual cables (conductors) arranged in a closely packed hexagonal order, shown in Fig. 3.17.  All conductors in the bundle are 3 mm in diameter, and have individual resistances of 35 mΩ/m.  These values are similar to the shield of an AWG 22 TSP type cable.  The overall diameter of the cable bundle is about 18 mm at its largest section. All 19 conductors within the baseline harness maintain their position throughout the entire 20 m length of the harness.  This is referred to here as the uniformly packed harness.  All comparisons will be made to this baseline model.

Figure 3.17 Cross section view of the baseline harness, with each conductor numbered.

3.3.2        Single Wire and Multi-Conductor Harness

A comparison of the single wire and multi-conductor cables with the same diameter and bulk resistance was performed.  Because in this case all of the conductors are terminated at the nose and the tail similarly, the bulk resistance of the baseline harness is the parallel resistance of the 19 conductors (R_total = 1.84 mΩ/m).  The results for the baseline harness were compared with a single wire cable with a diameter of 18 mm and a resistance of 1.84 mΩ/m.

Compared results are shown in Fig. 3.18.  The two different techniques for modeling cables produce nearly identical time domain and transfer function results.  This indicates that a single cable can accurately represent a particular harness of uniformly packed multi-conductors, so long as each harness has the same diameter and bulk resistance.  However, typical multi-conductor harnesses will have branches where some of the conductors separate from the main branch to connect to some electronic device.  Furthermore, the multi-conductor harnesses will not typically have a uniformly packed arrangement over the entire length of the cable.  They will likely have a random organization that continually varies over the length of the harness.

Figure 3.18(b) shows that the peak transfer function response is -6 dB (500 mA/V/m) for both the single wire cable and a multi-conductor harness.  The decay time of the waveform in Fig. 3.18(a), defined as the time it takes for the energy on the harness bundle to dissipate completely (time it takes for the waveform to ring down), is 1.5 ms.  These values will serve as the basis for comparison for the remaining multi-conductor simulations.

Figure 3.18 Time domain results (a) and transfer functions (b) comparing a single conductor with a multi-conductor harness. The inset in (a) shows first 1 ms of the time-domain waveform.

3.3.3        Cable Packing Variations

Harnesses that contain many individual cables are unlikely to maintain the same uniform packing scheme over the entire length of the harness. Instead, the cables will likely twist, rotate and weave with respect to the other cables in a highly randomized fashion.  It would be very difficult to replicate the randomized organization of individual conductors for an entire set of aircraft harnesses.  This investigation merely aims to understand how rotating a set of the cables could affect the coupling response.

The effect of cable rotations has been approached in a limited manner using two different techniques.  One technique, abrupt triangular rotation, switches the position of six cables within the 19 conductor bundle every few meters, but maintains the hexagonal packing scheme throughout the length of the harness.  The second rotation method moves the same six conductors in small increments along a set triangular path.  A full description of the rotation techniques is provided below in their respective subsection.

3.3.3.1       Abrupt Triangular Rotation

The abrupt rotation technique is such that cables 1, 2, 3, 9, 10 and 11 in Fig. 3.17 exchange positions with each other in a clockwise manner.  These six cables change positions every 3 m, but the overall hexagonal packing scheme and the position of the other cables does not change.  This rotation technique is depicted for the first six segments in Fig. 3.19. The last segment, segment 7, is just a repeat of the original packing scheme of segment 1.

The results for the abrupt triangular rotation technique are shown in Fig. 3.20.  The time domain waveform shows that the rotation of cables changes the bulk response of the harness as compared with the baseline harness (see Fig. 3.18 for comparison).  The waveform in Fig. 3.20 decays more uniformly and the current has completely dissipated by about 500 μs, nearly three times as fast as the baseline harness.  The peak transfer function response has dropped to -18 dB (126 mA/V/m), a 12 dB drop from the baseline harness.

Figure 3.19 Abrupt triangular rotation technique.

Figure 3.20 Time-domain (a) and transfer function (b) results for the abrupt triangular rotation technique.

3.3.3.2       Gradual Triangular Rotation

The gradual triangular rotation technique depicted in Fig. 3.21 moves the same cables as the abrupt technique, but only in small increments every 20 cm along the length of the harness.  Since the packing scheme is altered every 20 cm, 200 total segments were used to comprise the full 20 m harness.

The overall hexagonal packing scheme is not maintained as the six cables rotate, but all of the other cables still remain in their original positions.  The six cables being rotated underwent one complete twist over the course of the 20 m harness length.

The results for the gradual triangular rotation technique are shown in Fig. 3.22.  The time domain waveform again decays more uniformly than the baseline model, and the current has completely dissipated by approximately 300 μs, more than five times faster than the baseline.  The peak transfer function response has dropped to -23 dB (63 mA/V/m), a 16 dB drop from the baseline harness.

Figure 3.21 Gradual triangular rotation technique.

Figure 3.22 Time-domain (a) and transfer function (b) results for the gradual triangular rotation technique.

3.3.4        Cable Branching

Harnesses in an aircraft are likely to have at least one branch where some of the conductors will break away from the main multi-conductor branch to connect to an electronic device.  The branching of conductors introduces a mechanism by which energy can be transferred to some of the inner and middle ring conductors of the cable bundle.  Each conductor in the harness will likely be exposed to the external field as an outer ring conductor for at least one segment of the harness.

The geometry setup for the branching simulation is shown in Fig. 3.23.  Although it is not likely a harness will branch as many times and places as the harness explored here, the extreme effect of branching is worthwhile to investigate.  The metallic cable tray was given branches that travel to the sides of the fuselage so that the branched cables can terminate to the metal ground plane.  The harness starts with the same 19 conductor hexagonally packed scheme that was used previously.  This is the first segment of the harness that terminates at the nose of the canonical fuselage.

Branches were created every 2 m, starting at a location 1 m from the nose, that alternate in direction, port and starboard, all the way to a location 1 m from the tail.  The first 8 branches all have 2 conductors, and the last 2 branches have 1 conductor each.  This leaves 1 conductor in the main branch, which terminates at the tail.  The cable numbers were branched from the main harness in descending order starting with cable 19.  Therefore branch 1 contains cables 18 and 19; branch 2 contains cables 16 and 17, etc.

The bundle current results for the branched cable simulation are shown in Fig. 3.24.  Notice the significant difference in the uniform decay shape and decay time that the bundle current displays in the time domain plot of Fig. 3.24.  Whereas the baseline harness has a peak time-domain current value of 60 μA, same as a branched harness, it takes over 1.5 ms for the current to dissipate from the harness.  The branched harness dissipates nearly all of its energy by 100 μs, fifteen times faster than the baseline.  The peak transfer function response has dropped to nearly -25 dB (56 mA/V/m), a 19 dB effect.  Furthermore, the first vehicle resonance and the other resonances below 30 MHz have been largely destroyed.  Adding branches allows cable currents to dissipate more quickly by breaking up the lower frequency resonances and distributing the currents out more evenly to all of the individual conductors.  Thus cable branching is important to the mode destruction that a particular harness may experience, as well as proper resonance damping.

Figure 3.23 Branched harness configuration.

Figure 3.24 Time-domain (a) and transfer function (b) results for a branched  harness.

3.3.5        Cable “Micro-Branching”

In real aircraft individual cables sometimes break out of the bundle to connect to different electronics in the same general location.  We call these small differences in individual cable lengths and paths “micro-branching”.  Here, simulations use the same 19 conductor harness with a total of 8 branches, but all of the branches were created at the tail end of the canonical model as shown in Fig. 3.25.  Each branch is spaced 20 cm (2 cells) apart and contains 2 cables.  The first branch contains cables 18 and 19, the second branch contains cables 16 and 17, and the remaining branches contain the other cables in descending order.  The last segment of the harness that terminates to the tail contains cables 1, 2 and 3.

The bundle current results for this simulation are presented in Fig. 3.26.  The peak time domain current of 50 μA and uniform decay time of ~200 μs are similar to the standard branched configuration.  The peak transfer function response has dropped to -26 dB (50 mA/V/m), a 20 dB effect compared with the baseline.  Resonant mode destruction can be attributed to the micro-branched configuration, but not in exactly the same manner as for the standard branched case.  The micro-branched harness still has three significant resonances below 30 MHz whereas the standard branched harness does not.

Figure 3.25 Micro-branched harness configuration.

Figure 3.26 Time-domain (a) and transfer function (b) results for a micro-branched harness.

3.3.6        Skin Depth Effects

The individual cable shields have a frequency dependent resistance due to skin effect.  The MHARNESS solver used for this particular parameter investigation did not have frequency dependent skin depth capability at the time (which was developed later for combination of features investigations).  In order to sample the effect of frequency dependence on cable shields, the shield resistance was altered to explore skin effect at only one frequency, 100 MHz, which yields 350 mΩ/m for each of the 19 cables.  Increasing the resistance of the cable shield affects the response behaviour at all frequencies, but since we are only focusing on the effects at one frequency, 100 MHz, only the results near that frequency will be discussed.

From Fig. 3.18(b), the transfer function response at 100 MHz is 28.2 mA/V/m.  From Fig. 3.27, which shows the time domain current and transfer function of a harness which includes skin effect, the transfer function response at the same frequency was reduced to 14 mA/V/m, a 6 dB drop.

Figure 3.27 Time-domain (a) and transfer function (b) results for a harness with adjusted resistance.

3.3.7        Combinations of Features

3.3.7.1       Standard and Micro-Branching

The standard plus micro-branching simulations used a 19 conductor harness with a total of 4 standard branches, with 3 micro-branches at the end of each standard branch and tail end connection, as depicted in Fig. 3.28.  There are 16 total micro-branches, three of which contain 2 cables and the remaining 13 that have a single cable.  The cables were peeled off of the main branch in descending order as was done for the previous branching cases.

The results are presented in Fig. 3.29.  The peak time domain current response was 60 μA, and a uniform waveform decay shape with a time of ~100 μs are similar to the standard branched configuration.  The transfer function plot indicates a peak magnitude response of -36 dB (16 mA/V/m), which is lower than either the standard or micro-branched configurations alone.  This suggests that if harnesses have separate breakouts to connect with electronics boxes, or if small branches exist at the end of a larger branch, these small sections are important to coupling behavior.

Figure 3.28 A combination of standard branching and micro-branching.

Figure 3.29 Time-domain (a) and transfer function (b) results for a harness that includes standard branching and micro-branching features.

3.3.7.2       Other Combinations

Other combinations include micro-branching and abrupt position adjustment, standard branching and skin effect (now fully implemented into MHARNESS), micro-branching and skin effect, and finally standard branching, micro-branching, and skin effect. A summary of features and their effects is presented in Table 3.1.

Table 3.1 Summary of Modeled Cable Features and Results

3.4        Summary and Conclusions

Canonical models were used to investigate factors that contribute to the coupling response of cable harnesses in an aircraft exposed to a HIRF environment.  The primary modeling aspects include accurate surrounding geometry, accurate material properties for the surrounding vehicle and harness contents, and proper routing and branching of all harnesses.

Once the harness coupling field is accurately obtained, the most significant harness parameter is the ability of the external field to couple to all cables in the bundle.  If the harness remains uniformly packed over its entire length and contains no branches or rotations, some of the conductors remain shielded by the outer ring of cables, and current does not spread evenly to all conductors.  It takes a relatively long time for energy to dissipate from this type of harness, and the transfer function coupling level can be as high as 500 mA/V/m. Note that the ARP 5583 [3] certification document has generic transfer functions whose values do not exceed 2.5 mA/V/m.

It is apparent that both forms of branching modeled here significantly reduce harness coupling magnitudes and energy dissipation times.  Branching exposes the inner most cables to the exterior field at some point and also destroys some of the modal frequencies. The most accurate representation, one that matches the actual harness routing of the vehicle, should generate the most representative results.

The second technique for spreading current to all conductors is to rotate the position of some of the cables within a bundle.  It did not seem to matter significantly if the cables were rotated abruptly or gradually, as both methods reduced the peak transfer function amplitude by 12-18 dB, a significant albeit smaller effect than branching.

The biggest reduction in coupling levels was observed when branching and skins effects were applied. This reduced the coupling levels from a single cable bundle by 38 dB to 6 mA/V/m.  While this value is still higher than the ARP 5583 generic transfer function level, one can imagine a further reduction in coupling when the aircraft is filled with absorbing materials such as seats, bulkheads, etc. This is explored further in Chapters 5 and 6.

Although actual cables in harnesses are likely to rotate, the authors believe representative harness coupling can be achieved without rotations and it would be far more efficient to exclude the rotating  technique from the numerical model.  More important to the coupling response is including the correct number of harness conductors along with the proper routing and branches, as well as filling aircraft with appropriate absorbing materials.  It may also be possible to come up with some average reduction factor from cable rotations based on the number of conductors in a given harness bundle, however this technique would require further investigation.

In addition to the different types of branching, skin depth effects reduce the coupling levels significantly.  A frequency dependent skin depth algorithm has already been implemented into the MHARNESS code.  Thus with a combination of techniques investigated in this work, the correlation between predicted coupling levels in a canonical model and measured aircraft coupling levels has been drastically improved.