This paper is provided as technical background for the signals analysis discussions presented elsewhere on this topic.

Computer modeling was used in the analysis of known and potential radio signals from NR16020. Computer modeling is a powerful tool, but it is not a panacea. A computer model uses a combination of internal mathematical algorithms and user-supplied data to approximate reality. A model’s mathematical algorithms are parametric representations of the underlying phenomena or processes being studied. The user-supplied data provides the specific values, or ranges of values, to be used by the model's algorithms. The quality of a model’s output depends upon the validity of its algorithms and the degree of uncertainty inherent in the user inputs. We believe that the models used are the best available for the purposes of this analysis. As for the user inputs, it should be noted that uncertainty is an abundant commodity in the Earhart saga. While no computer model can compensate for uncertainties in the input data, the user can do so by establishing conservative upper and lower bounds which can reasonably be expected to contain the true value of each parameter of interest, and then making model runs for the bounding values. This approach, which was used in this analysis, produces useful results without masking the uncertainty in the input data. This approach has the additional benefit of facilitating follow-on analysis in the event that new information is discovered which reduces the uncertainty of previously used input data.

The analysis focused on three key unknowns regarding the disappearance of Amelia Earhart and Fred Noonan: (1) their closest point of approach to Howland Island; (2) the reason for the Itasca’s failure to hear any further signals from NR16020 on July 2nd following Earhart’s 2013 GMT message stating "We are on the line 157-337. Will repeat message. We will repeat this on 6210 KCs . . . "; and (3) whether NR16020 originated any of the reported post-loss radio signals.

The Models

Two models, ICEPAC and NEC4WIN95, were used in the analysis.

ICEPAC

ICEPAC^[1] is the Ionospheric Communications Enhanced Profile Analysis and Circuit prediction program, developed by the Department of Commerce Institute for Telecommunications Science (ITS) at Boulder, Colorado. ICEPAC is a direct descendant of the Ionospheric Communications Analysis Program (IONCAP) and is a product of nearly 60 years of research, by ITS and its predecessors in the U.S. Department of Commerce, in collecting ionospheric data and developing methods for using those data in predicting and analyzing the performance of high-frequency (HF) communications systems which depend on ionospheric propagation. ICEPAC runs with the Windows 98 operating system.

ICEPAC computes HF system performance over a specified path, using a combination of user inputs and the contents of internal data base files. User inputs are: year, month, and day; the hours within the specified day, and the radio frequencies, for which performance results are desired; sunspot number ^[2]; the geographic coordinates of the transmitter and the receiver; the transmitting and receiving antennas to be used; the input power supplied to the transmitting antenna; and the level of man-made noise at the receiving site. The internal data base files contain: (1) statistical parameters of the time-dependent variations of the ionosphere ^[3] and of atmospheric noise; and (2) the characteristics of commonly used antennas in terms of antenna gain in one-degree increments of azimuth and elevation, relative to an isotropic ^[4] antenna.

For each run, ICEPAC gives the great circle azimuth and distance from the transmitter to the receiver, and the reciprocal azimuth from the receiver to the transmitter. Additionally, for each user-specified combination of time of interest and frequency, ICEPAC computes 22 parameter values, any subset of which can be selected for display in a variety of graphic and tabular formats. Signal-to-Noise Ratio (SNR) at the receiver site is the principal ICEPAC output used in this analysis. ICEPAC gives SNR in terms of the median ^[5], 10th-percentile ^[6], and 90th percentile ^[7] values, to quantify the range of statistical uncertainty due to random variations in the ionosphere and in atmospheric noise. Lucas and Haydon ^[8] provide a detailed mathematical treatment of the methods used in ICEPAC to model those variations.

NEC4WIN95

The ICEPAC internal antenna characteristics data base file does not include an antenna similar to that on NR16020 ^[9]. A model of the NR16020 antenna was created using NEC4WIN95, a Windows 95/98 implementation ^[10] of the Numerical Electromagnetic Code (NEC) ^[11]. The antenna’s radiation gain characteristics were generated for both Earhart frequencies (3105 kHz and 6210 kHz) and were transferred into the ICEPAC antenna database.

The radiation gain pattern of the antenna at both frequencies, viewed from above, is omni-directional when the takeoff angle ^[12] is greater than 60 degrees. When the takeoff angle is less than 60 degrees, the gain pattern of the antenna takes on a “figure-8” shape with two identical lobes, each approximately 80 degrees wide, centered on a common axis oriented 030 / 210 degrees relative to the heading of the aircraft.

The “waist” of the “figure-8” pattern is perpendicular to the main lobe axis of the pattern, and has a “pinch,” or gain reduction, which varies with frequency and the takeoff angle.

At 3105 kHz, the gain reduction on the “waist” axis for a takeoff angle of 1 degree is 19 dB relative to the main lobe gain. The gain reduction decreases smoothly as the takeoff angle increases, reaching 5 dB at 32 degrees, and tapering smoothly from that value to 0 dB at 60 degrees.

At 6210 kHz, the gain reduction on the “waist” axis is 4 dB for a 1-degree takeoff angle. The gain reduction increases to 7 dB at 10 degrees, and then decreases smoothly to 0 dB at 60 degrees.

The model was validated as described later in this appendix.

Technical Background, Methods and Assumptions

Assumptions have been made to facilitate the signals analysis in cases where required documented information is not available. Each assumption has been developed so that it conservatively bounds the true parameter value for which it is a proxy. Assumptions are described at the points where they are introduced into the analysis. The methods used in the signals analysis are not dependent upon the nature of any of the assumptions that were used. Hence, if documented information becomes available to replace any assumption(s), only the affected computed results will change.

Signals and Noise

General

This section presents background material and derivations pertinent to assessing signal reception criteria. Since signal-to-noise ratio (SNR) is the principal ICEPAC output used in the signals analysis, the following discussion is provided as background for the signals analysis discussions in this volume.

A radio signal arriving at a receiver is accompanied by a noise ^[13] background which is a combination of man-made noise and atmospheric noise. The noise power against which the received signal power competes in the receiver is proportional to the receiver’s bandwidth. It is the signal-to-noise ratio, SNR, which determines whether the signal can be detected, and whether its information content can be extracted. For the purposes of this analysis, it is assumed that all radio receivers had a noise bandwidth of 5,000 Hz.

Typical sources of man-made noise are high-voltage power lines, aircraft and automotive ignition systems, electrical machinery, and electrical appliances. Atmospheric noise, or static, can be divided into two general types ^[14]: (1) intermittent high-intensity impulses caused by local thunderstorms, and (2) a steady rattling or crackling caused by distant thunderstorms.

High frequency static is subject to the same propagation factors that govern radio signals, hence distant static sources can interfere with radio signals ^[15]. Earhart’s entire flight was over an ocean area known as the Tropical Western Pacific Warm Pool ^[16], a region characterized by frequent thunderstorms. Therefore, it is no surprise that radio operators on the Itasca and elsewhere often referred to static in their radio signal logs.

SNR Considerations for Amplitude Modulated Signals

The radio transmitter in NR16020 ^[17] was configured to transmit double-sideband amplitude modulated (AM) voice radio signals. A double sideband AM signal consists of a carrier frequency and two sidebands. The sideband spectra extend from the carrier frequency plus and minus the lowest modulating voice frequency used (around 200 Hz for basic communications) out to the carrier frequency plus and minus the highest modulating voice frequency used (about 3000 Hz for basic communications). If the carrier signal is fully (100%) modulated, two thirds of the total radiated power is in the carrier (which carries no intelligence) and one third is divided equally between the two sidebands, each of which carries identical intelligence and 16.67% of the total signal power. The signal is demodulated at the receiver, and the intelligence is recovered, by rectifying the signal in one sideband and converting the amplitude variations to frequency variations which are heard as audio signals at the output of the receiver. The SNR at the receiver input is the ratio of total incoming signal power to total incoming noise power. But since the recovered intelligence is carried by only 16.67% of the total incoming signal power, there is a 7.78 dB loss of SNR due to demodulation.

Everette has reported results of experiments ^[18] showing that the modulation circuitry used in Earhart’s transmitter was capable of only 80% modulation. Since the amount of signal power in the sidebands is proportional to the square of the modulation percentage, ^[19] 80% modulation means that only 21.3% of Earhart’s total radiated signal was in the sidebands, and 10.7% of the total signal was recovered in demodulation. This represents a 9.7 dB loss in SNR, rather than the 7.78 dB loss in the case of a 100% modulated signal.

The audio signal heard by the operator is the output of the demodulation process. If the receiver input SNR equals the demodulation loss, then the post-demodulation audio signal will be just equal to the background noise level, giving an audio SNR of 0 dB. The operator would be able to detect the presence of such a signal, but would not be able to recognize any of the sideband information. Hamsher ^[20] states that a 6 dB audio SNR is required for 90% intelligibility of unrelated words, which he describes as "just usable" quality for operator-to-operator communications. Using Hamsher’s criterion, a 15.7 dB receiver input SNR is required for "just usable" signal quality. For the purposes of this analysis, the receiver input SNR threshold for barely detecting the presence of a voice signal was set at 9.7 dB, and the threshold for "just usable" signal quality was set at 15.7 dB.

SNR Considerations for Continuous Wave Signals

During the post-loss search phase, some radio messages were sent requesting Earhart to “send dashes.” If Earhart complied with any of those requests, she would have been operating her transmitter in the continuous wave (CW), or telegraphy mode, by keying the microphone without speaking into it. Intelligence is transmitted in CW mode by turning the transmitter’s carrier wave on and off to form short pulses (dots) and somewhat longer pulses (dashes) which, when sent in appropriate sequences, represent symbols such as letters and numbers.

CW signals have the important advantage of being usable in atmospheric noise conditions that would mask AM voice signals. This advantage stems from the fact that a CW signal has no sidebands and all of the transmitted intelligence is contained in the carrier signal, which also contains all of the transmitted power. Consequently, a CW signal does not experience the demodulation loss in SNR incurred by an AM signal. Hamsher ^[21] states that a CW signal is usable with a receiver input SNR of -7 dB. Hence, the detection and readability threshold for a CW signal is 16.7 dB below the threshold for barely detecting the presence an AM voice signal.

It seems clear that the radio operators who asked Earhart to send dashes were well aware of the SNR advantage of a CW signal over an AM signal. Given the noisy AM signal environment that was mentioned so frequently in the radio logs, and in view of the urgent need to find some indication that Earhart was alive, it was quite logical to ask her to send dashes.

The SNR advantage of a CW signal over an AM signal was factored into the analysis of whether potential responses to the requests for dashes were from Earhart.

Validating the NR16020 Antenna Model

The NR16020 antenna model was validated by using it in ICEPAC calculations of signal strength for the in-flight radio signals received from NR16020 on July 2nd, at 0718, 1415, 1515, 1623, 1744, and 1815 (all times GMT) and comparing the results with the signal quality observations reported by Chater^[22] and others.^[23] The details of the content and circumstances of the July 2nd messages are presented in The Final Flight, and will not be repeated here. In what follows, the term “the model” refers to the combination of the ICEPAC model and the NR16020 antenna model.

The model reported SNR values consistent with the qualitative observations recorded by Chater and others, indicating that the NR16020 antenna model was acceptably accurate, thus justifying its use in ICEPAC for the remainder of the signals analysis.

Chater

According to Chater, Earhart’s 0718 GMT position report on 6210 kHz was a “very strong” signal and that her signals were getting stronger. The 0718 GMT position report put NR16020 about 770 nautical miles from Lae, but we don’t know whether NR16020 was actually there at that time. The reported position could have been as much as an hour old, in which case NR16020 was at least 100 nautical miles beyond the reported position. Both position possibilities were examined in model runs, and in both cases the model correctly reported the “very strong” signal that Chater observed on 6210 kHz. For the case where NR16020 was 770 miles from Lae, the median SNR was 15 dB, and the 90th percentile SNR was 24 dB. This means that for the case where NR16020 was 100 miles further East, the median SNR was 13 dB and the 90th percentile SNR was 22 dB. The model also reported, for both distance cases at 0718 GMT and later, that the median SNR on 3105 kHz was about 20 dB below the threshold for signal detection, which agrees with Chater’s observation that no further signals were heard because Earhart shifted frequencies at sunset.

The Other Signals

Since we don’t know NR16020’s actual positions at the times the signals at 1415 GMT, 1515 GMT, 1623 GMT, 1744 GMT, and 1815 GMT were sent on 3105 kHz, estimated positions were derived for use in the model.

The 1912 GMT signal, in which Earhart said “We must be on you but cannot see you, but gas is running low. Been unable to reach you by radio. We are flying at a thousand feet,” was taken as the starting point for deriving the estimated positions. It was assumed that Noonan was able to determine when NR16020 reached the 157E/ 337E degree line of position (LOP) through Howland Island, but not where it was along the LOP. Given that NR16020 was on the LOP at 1912 GMT, the distance to the Howland LOP at any prior time can be calculated from ground speed and the elapsed time to 1912 GMT. Unfortunately, we don’t know the plane’s actual ground speed at any time during the flight. But it is possible to establish bounds on the LOP-distances by defining bounds on the plane’s ground speed. For this analysis, it was assumed that the plane’s minimum and maximum ground speeds during the approach to Howland were 100 knots (corresponding to a head wind component of 30 knots) and 130 knots (corresponding to a head wind component of zero knots), respectively. Note that for a fixed time of arrival at the LOP, the plane’s distance from the LOP at any given time is proportional to ground speed.

The resultant LOP-distance estimates in nautical miles are listed here in the form: GMT (minimum, maximum): 1415 (495, 646), 1515 (395, 515), 1623 (282, 368), 1744 (147, 191), and 1815 (95, 124).

Each distance pair was transformed to a corresponding pair of latitude / longitude positions on the planned track to Howland, so that each position was a point on a circle centered at Howland, with radius equal to the position’s distance from Howland. A cross-track navigation error would displace each affected position along a line parallel to the LOP, thus preserving the distance to the LOP. But cross-track displacements less than 200 miles would not change the radial distance to Howland enough to cause a significant difference in radio signal path loss.

These geographic position pairs were used in the model for the respective signal cases and the resultant SNR values were found to be consistent with the radio signal descriptions in the Itasca’s radio log. At 1415 GMT, the estimated distance was between 495 and 646 miles and, the Itasca’s radio log describes the signal as "Heard but unreadable thru static." This log entry suggests a signal barely above the detection threshold. At 495 miles, the model reported a median SNR of -3 dB, and a 90th percentile level of 6 dB. At 646 miles, the median SNR was -7 dB and the 90th percentile level was 3 dB. In both cases, the SNR was consistent with a detectable but unreadable signal being present less than 10 percent of the time.

At 1515 GMT, the estimated distance was between 395 and 515 miles and the Itasca’s radio log states “Earhart heard - says she will listen on 3105 on hour and half hour.” That the operator was able to understand the content of the message suggests that the SNR was somewhat above the signal detection threshold. At 395 miles, the model reported a median SNR of 2 dB, and a 90th percentile level of 12 dB. At 515 miles, the median SNR was -2 dB, and the 90th percentile level was 8 dB. In both cases, the SNR was consistent with a readable signal being present less than 10 percent of the time.

At 1623 GMT, the estimated distance was between 282 and 368 miles. One Itasca radio operator logged “Heard Earhart (Part cloudy).” At 1625 GMT, a second Itasca operator logged “...Earhart broke in on fone 3105 / nw ??? unreadable.” Both log entries suggest a signal that was fading in and out, with varying degrees of readability. At 282 miles, the model reported a median SNR of 8 dB and a 90th percentile level of 19 dB. These values indicate that the SNR was above the 10 dB detection threshold, with varying degrees of signal readability, about 40% of the time. At 368 miles, the median SNR was 5 dB and the 90th percentile level was 16 dB. These values indicate that the SNR was above the detection th% of the time. Both cases are consistent with a signal that faded in and out with varying degrees of variability.

At 1744 GMT, the estimated distance was between 147 and 191 miles, and the Itasca’s radio log states “Wants bearing on 3105 // on hour // will whistle in microphone about two hundred miles out // Approximate // Whistling // Now.” This entry clearly is a paraphrased condensation of the actual signal, and suggests that the signal was sufficiently readable for the operator to glean its essential meaning. At 147 miles, the model reported a median SNR of 13 dB and a 90th percentile level of 26 dB. These values indicate that the SNR was above the 10 dB detection threshold about 60% of the time, and was above the 16 dB 90% intelligibility level about 40% of the time. At 191 miles, the median SNR was 11 dB, and the 90th percentile level was 24 dB. These values indicate that the SNR was above the detection threshold about 50% of the time, and was above the 90% intelligibility level about 30% of the time. Both cases are consistent with the conditions suggested by the log entry. It is interesting to note that the 200-mile estimate is close to the upper bound of the LOP-distance estimate.

At 1815 GMT, the estimated distance was between 95 and 124 miles, and the ship’s radio log states “Please take bearing on us and report in half hour - - I will make noise in mike - abt 100 miles out.” It is not clear whether Earhart said she was about 100 miles out or whether the operator estimated the distance, but the estimate is within the LOP-distance bounds. Shortly before this signal, at 1812 GMT, another operator logged “Earhart on the air now, with reception fairly clear.” These two separate log entries, taken together, suggest a somewhat stronger signal than had been heard previously. At 95 miles, the model reported a median SNR of 15 dB, and a 90th percentile level of 28 dB. These values indicate that the SNR was above the 10 dB detection threshold about 70% of the time, and was above 90% intelligibility level about 50% of the time. At 124 miles, the median SNR was 14 dB, and the 90th percentile level was 27 dB. These values indicate conditions virtually identical to those for the 95-mile case. Both cases are consistent with a clear and readable signal being present at least 50% of the time.

At 1912 GMT, the ship’s radio log states that Earhart’s signal strength is S-5, i.e., very strong. The model reported a median SNR of 19 dB and a 90th percentile level of 32 dB, values which are consistent with a very strong signal.

Time of Arrival at the Howland LOP

This section presents the rationale for assuming that Earhart arrived at the 157E/337E LOP through Howland Island at 1912 GMT.

First, it should be noted that although a line has no width when defined as a mathematical entity, a navigational line of position does have width due to the inherent uncertainty in measuring the altitude of the celestial body upon which the LOP is based. In air navigation using a bubble sextant, an error of 5 to 10 miles is considered normal for favorable conditions. ^[24] Consequently, an air navigation LOP is a swath with a potential width of 10 miles or more. In this analysis, the term “on the LOP” will be understood to mean “in the swath centered on the nominal LOP.”

A literal reading of the initial phrase “We must be on you . . .” in Earhart’s 1912 GMT signal reveals that she thought she was at the Itasca’s position, and therefore on the Howland LOP, at 1912. There is no reason to doubt that she was on or close to the Howland LOP at that time. Noonan had ample time since his sunrise at approximately 1752, to take sun sights and calculate distance to the Howland LOP, as well as his ground speed and time of arrival at the LOP, well before getting there. The bearing request in Earhart’s 1815 GMT signal can be explained by the fact that Noonan’s sun lines were parallel to the Howland LOP and thus could not show where his ground track would intercept that LOP.

The question is whether Earhart arrived at the Howland LOP at 1912 GMT and made a contemporaneous report, or whether she arrived at some earlier time and delayed reporting that fact.

The early-arrival hypothesis has crucial defects that render it untenable: First, there is no evidence of early arrival at the Howland LOP. Second, the hypothesis assumes that Earhart delayed reporting the most important event in the flight up to that point. Failure to find the Itasca where and when expected obviously had potentially fatal consequences, and there is no apparent logical reason for delay in reporting. Conformance to the communication schedule cannot be invoked to explain the reporting delay, since Earhart’s 1744 GMT signal was one minute early, her 1623 GMT signal was 8 minutes late, and her 1912 GMT signal was 3 minutes early. Clearly, she was not conforming to the schedule. In particular, if she had conformed to the schedule, she would have sent her report at 1915 GMT, instead of at 1912 GMT.

In contrast, there is a simple hypothesis that logically explains the timing of the 1912 GMT signal and the absence of a 1915 GMT signal: (1) Noonan calculated that NR16020 would arrive within sight of the Itasca at 1912 GMT; (2) NR16020 reached the Howland LOP at 1912 GMT, but the Itasca was nowhere in sight and Earhart immediately sent her signal to that effect; and (3) Earhart skipped the scheduled 1915 GMT signal because there had been no new developments since 1912 GMT. This hypothesis is supported by the fact that the average ground speed required to travel the 2238 nautical mile rhumb distance from Lae to Howland in 19.2 hours was 116.6 knots, which is consistent with the available data on flight winds along the route. Because of its simplicity and completeness, and since there is no evidence of early arrival at the Howland LOP, this hypothesis was adopted as the basis for the analysis.

Power Input to the NR16020 Antenna

ICEPAC requires the user to specify each transmitter antenna’s power input. Since we know that Earhart’s transmitter was capable of delivering 50 watts of power, it might seem that 50 watts should be specified as the antenna input power. But that is not the case.

ICEPAC assumes that the every transmitting antenna radiates all of the input power supplied by the transmitter. That is a reasonable assumption for the antennas in ICEPAC’s internal antenna data base file, because all of those antennas are types which have inherently high radiating efficiency. But such is not the case for the dorsal vee antenna on NR16020. Radiating efficiency can be defined ^[25] as the ratio of the radiated power to the input power of an antenna. An antenna can be considered as an equivalent circuit consisting of two resistances in series, the radiation resistance and the loss resistance. Power radiated from the antenna can be considered as being dissipated by the radiation resistance. Any input power not radiated from the antenna can be considered as being dissipated in the loss resistance, and appears chiefly in the form of heat in the antenna wire. In terms of these two resistances, antenna radiating efficiency is the ratio of the radiation resistance to the sum of radiation resistance and loss resistance.

For antennas typically used in commercial shortwave applications, or for amateur radio applications, the radiation resistance is much greater than the loss resistance, and the radiating efficiency is near 100%. However, that is not the case for aircraft wire antennas such as that on NR16020.

In 1938, Haller ^[26] made in-flight measurements of the radiation resistance of various wire antenna configurations on metal-skinned military aircraft. One of the aircraft used was a low-wing attack aircraft with overall dimensions similar to those of NR16020. And one of the antennas tested on this aircraft was a vee-antenna with dimensions comparable to those of the NR16020 antenna, with an offset feed point on the starboard leg of the antenna, similar to that on NR16020. Haller measured the radiation resistance of this antenna as 1.4 ohms at 3105 kHz and 5.0 ohms at 6210 kHz. Haller’s values were used in for the NR16020 antenna in this analysis.

Given the estimated radiation resistance of the NR16020 antenna, it remained to find the loss resistance of the antenna at the two frequencies of interest and to compute the radiation efficiency. Haller reported that the antennas he tested were constructed from #18 copperclad steel wire. But we have no information about the size or composition of the wire used in the NR16020 antenna. Therefore it was decided to give NR16020 the benefit of the doubt by assuming that its antenna was made from #12 CopperWeld ^[27] wire, which has a substantially lower loss resistance than #18. Using the formulas in Terman,^[28] the loss resistance was found to be 1.01 ohms at 3105 kHz and 1.29 ohms at 6210 kHz. The resultant radiation efficiencies were found to be approximately 59% at 3105 kHz, and 80% at 6210 kHz, yielding effective antenna input power levels of 30 watts at 3105 kHz, and 40 watts at 6210 kHz, for use in ICEPAC.

For comparison, if it had been assumed that the NR16020 antenna was constructed of #18 copperclad wire as Haller used, the antenna’s radiation efficiencies would have been 34.1% at 3105 kHz and 56.2% at 6210 kHz, yielding equivalent antenna input power levels of 17.05 watts and 28.1 watts, respectively.

It is interesting to consider the effective radiated power from the NR16020 antenna used in this analysis.

At 3105 kHz, the radiated power is 0.3 watts at takeoff angles less than 15 degrees, with a smooth nonlinear taper up to 6 watts at takeoff angles above 80 degrees. Perpendicular to the main-lobe axis, the radiated power is 0.003 watts at takeoff angles less than 5 degrees, tapering up to 6 watts for takeoff angles greater than 75 degrees.

At 6210 kHz, the radiated power is 0.2 watts at takeoff angles less than 5 degrees, with a smooth nonlinear taper up to 40 watts at takeoff angles greater than 80 degrees. Perpendicular to the main-lobe axis, the radiated power is 0.06 watts at takeoff angles less than 5 degrees and 40 watts at takeoff angles greater than 80 degrees.

Comparing these two power profiles shows that the NR16020 antenna radiated a much stronger signal at 6210 kHz than at 3105 kHz, at all but the lowest takeoff angles.

NR16020 Antenna Loading Coil and Feed Line Loss Assumptions

For two reasons, it was assumed that there was no transmitter output power loss in either the antenna loading coil or the antenna feed line of the NR16020 antenna.

First, there is some evidence that a radio technician ^[29] may have made undocumented modifications to the antenna loading coil during repairs to NR16020 following the takeoff accident at Luke Field, Hawaii, in March 1937. And it is unclear whether the original loading coil or a homemade replacement fabricated by the aforementioned technician was in use when Earhart departed Miami on the Eastbound circumnavigation attempt. Neither do we know how efficiently the installed loading coil coupled the transmitter to the dorsal antenna which was modified during repairs to NR16020. Therefore, we have no basis for estimating how much transmitter power was dissipated in the loading coil. Accordingly, it was assumed that there was no power loss in the loading coil.

Second, as to the antenna feedline, it has been shown ^[30] that a single-wire feedline of the type used on NR16020, can be as efficient as a balanced two-wire transmission line if the antenna feed point is selected to minimize or eliminate standing waves on the feedline. But we have no information on how the attachment point on the antenna was selected when the NR16020 antenna was lengthened,^[31] or to what extent the selected attachment point optimized the impedance of the feedline. Therefore, there is no basis for estimating feed line loss, and it was assumed that the feedline was loss-free.

These assumptions give the NR16020 antenna the benefit of the doubt, and can be revisited if definitive information about either the loading coil or the feedline is discovered.

Antennas at Other Locations

No information is available about the antenna types or configurations used at any of the other locations, including the Itasca. Therefore, in all ICEPAC runs, it was assumed that the receiving or transmitting antenna at each location was a generic type with a gain of 3 dB in the direction of NR16020 at all times.

Man-Made Noise Levels at Receiving Sites

For all ICEPAC runs, the man-made noise level at each receiving site was set to the “quiet rural” level. This is the quietest of the four available settings for ICEPAC. The ICEPAC technical documentation defines a “quiet rural” area as one that is “well-removed from all populated areas and chosen to be as free as possible of man-made noise.”

This definition obviously is a good fit for locations such as Wake Island, Midway Island, and Tutuila. But it also applies well to shipboard environments, such as the Coast Guard cutter Itasca and HMS Achilles. Warships and Coast Guard cutters of the 1930’s were constructed of steel. Their electrical machinery was enclosed in steel compartments (rooms) which shielded them from noise-sensitive equipment such as radio receivers, and the entire ship’s hull was grounded by the sea water in which it floated.

As for Honolulu and San Francisco, it might appear that they were anything but “quiet rural” locations. But closer inspection reveals that the antennas in those localities probably were in very quiet locations. The Navy radio receiving station at Wailupe, Hawaii, was located near the Southeast tip of the island of Oahu, between Diamond Head and Koko Head, in an area that was well-removed from downtown Honolulu. Similarly, the Pan American Airways radio station on Oahu was situated at Mokapu Point, on the east coast of Oahu, well away from Honolulu.

The San Francisco Coast Guard radio station receiving site used during the Earhart search was located at Fort Funston ^[32] which is bounded by the Pacific Ocean on the west and the Olympic Country Club on the east and south. The area north of Fort Funston is a park.

The airport at Lae, Papua New Guinea, was assumed to be well-removed from municipal or industrial noise sources.

Nauru Island, although clearly a remote location, was involved in phosphate mining and presumably had a significant amount of operating machinery. But it is not known whether that machinery was powered by steam, diesel, or electricity. It was assumed for this analysis that Nauru was an electrically quiet locale.

The Radio Riddle

The Radio Riddle comprises two questions: (1) What was Earhart’s closest point of approach (CPA) to Howland Island? and (2) Why was 2013 GMT the last time that the Itasca heard a radio signal from Earhart on July 2nd?

Answers were derived by analyzing the median and 90th percentile SNR for NR16020 signals on 3105 kHz and 6210 kHz, at hourly intervals from 1900 GMT through 2300 GMT, versus distance in 50-mile increments along the 157E/ 337E LOP through Howland Island. The results, obtained from 70 computer model runs, are shown in Table A1 and are applicable in both directions along the LOP. Distances greater than 350 nmi were not considered, since the distance from Howland to Gardner Island is 353 nmi.

TABLE A1

Each column in the table represents a one-hour interval centered at the time in the column heading, to conform to the time resolution used by ICEPAC. For example, the values in the 1900 GMT column apply to the time interval from 1830 GMT to 1930 GMT. Since sunrise at Howland Island was at 1746 GMT, the time scale of the data in the table begins about 45 minutes after sunrise.

The intensity of solar radiation received by the ionosphere varies with the Sun’s angular altitude above the horizon. This process is of particular importance to the D-layer, the ionosphere layer closest to the surface of the earth, and which is a major factor in attenuation of daytime signals at lower HF frequencies such as the 3105 kHz signal used by Earhart. The D-layer exists during daylight hours, starting to form at sunrise, reaching maximum density near midday, and dissipating after sunset. Attenuation in the D-layer, as well as the other ionospheric layers, depends largely upon distance traveled in the layer before the signal is refracted back to earth. D-layer attenuation of signals at 3105 kHz is much greater than at 6210 kHz, which is why 3105 kHz was considered a “night” frequency and 6210 kHz was considered a “day” frequency.

The signal energy reaching a receiver antenna via an ionospheric path leaves the transmitter antenna at an elevation angle (the takeoff angle, or TOA), which varies inversely with distance from the transmitter to the receiver. The TOA approaches 90 degrees at distances on the order of a few miles, and 1 degree or less at long distances. Low-TOA daytime signals at Earhart’s frequencies propagate almost exclusively in the D-layer during refraction, and are attenuated accordingly. Signals with greater TOAs penetrate the D-layer and are refracted by higher layers in the ionosphere. Those signals penetrate the D-layer twice, going up and coming down. The two-way D-layer attenuation combined with the attenuation experienced in the upper layers approximates that of low-TOA signals in the D-layer alone.

With this background, it is easy to see the signal attenuation pattern depicted by the data in Table A1 and to derive answers to the Radio Riddle questions.

Earhart’s estimated CPA to Howland Island is derived as follows:

1). Note that the Itasca’s radio log described Earhart’s 1912 GMT signal strength as “S-5,” which indicates a very strong signal. Since a 16 dB SNR provides 90% intelligibility for a voice signal, an “S-5” signal implies a median SNR greater than 16 dB.

2). The estimated CPA is found by searching down the “1900 GMT” column of Table A1 to find the lowest median SNR greater than 16 dB at 3105 kHz, and extract the corresponding distance from the “Dist” column. The threshold SNR value occurs between the tabulated values for distances of 50 and 100 miles, but the 50-mile distance increment is too large for reliable interpolation. So intermediate values at 10-mile increments were computed and tabulated in Table A2, showing that 17 dB is the lowest median SNR greater than 16 dB. There are two 17-dB entries because ICEPAC rounds median SNR to the nearest integer value. Therefore, the 80-mile entry is the threshold value and the CPA is estimated to be a maximum of 80 miles. The minimum value of CPA cannot be estimated from signal strength because the SNR increases with decreasing distance from the Itasca.

TABLE A2

An answer to the question of why the Itasca didn’t hear any radio signals from Earhart after 2013 GMT can be derived as follows:

1). Note that Earhart had been flying at 1,000 feet since 1912 at the latest, having descended from 10,000 feet to get below the clouds in order to look for Howland Island. And having descended to 1,000 feet, she was essentially trapped there because climbing to a higher altitude would have required increased fuel consumption that she could ill afford. But the air density at 1,000 feet is approximately 31% greater than at 10,000 feet,^[33] and Earhart could not maintain 130 knots airspeed unless she increased power to compensate for the increased air density, which would have increased fuel flow thus reducing the flying time remaining in which to find land. If altitude is changed without changing the level-flight power setting, level-flight airspeed at the final altitude is equal to the airspeed at the initial altitude multiplied by the square root of the ratio of the air densities ^[34] at the initial and final altitudes. Therefore, Earhart’s airspeed at 1,000 feet in a standard atmosphere would have been approximately 113 knots. But since standard atmosphere conditions do not apply at the equator, and since we don’t know the actual values of air temperature, pressure, and humidity in which she was flying, we are unable to calculate her actual airspeed at 1,000 feet. However, we do know that Earhart had the option of increasing power setting to maintain 130 knots airspeed, or of retaining her at-altitude power setting and flying at a reduced airspeed at 1,000 feet. For this analysis, it is assumed that if Earhart did not change power settings, her airspeed at 1,000 feet was 115 knots. It is further assumed that there was no headwind component along the Howland LOP. Therefore, this analysis assumes that Earhart’s ground speed on the LOP was bounded by a minimum of 115 knots and a maximum of 130 knots.

2). Note the 2013 GMT entry in the Itasca’s rough radio log, which states in relevant part: “KHAQQ to Itasca we are on the line 157-337. Will repeat message. We will repeat this on 6210 KCs wait, 3105/A3 S5 (?/KHAQQ xmision we are running on line . . ..” The Itasca responded to Earhart at 2014 GMT, asking her to remain on 3105 kHz because they did not hear her on 6210 kHz. The Itasca received no response to this signal.

3). Note that the question mark in the 2013 GMT log entry indicates uncertainty about what was said in the parenthetical phrase, suggesting that the SNR was below the 100% intelligibility level, and thus somewhat below that implied by the “S5” estimate of signal strength. This suggests that the signal was sent from a distance consistent with an SNR of at least 16 dB.

4). Note that Table A1 shows 200 miles as the maximum distance from which the 2013 GMT signal could have been sent. At that distance, the 90th percentile SNR was 13 dB, indicating a signal that was readable less than 10% of the time. Given this maximum distance, a ground speed of 115 knots along the LOP since 1912 GMT implies that Earhart’s maximum distance from Howland at 1912 GMT was 83 miles. A ground speed of 130 knots implies that her distance from Howland at 1912 GMT was not more than 68 miles. It is interesting to compare these distance limits with the 80-mile maximum CPA value derived from the SNR of the 1912 GMT signal.

5). Note that at 2115 GMT, Earhart’s next scheduled transmission time, signals on 3105 kHz were unreadable beyond 100 miles, and were unreadable at any distance after the 2100 hour. Therefore, 2013 GMT was the last time at which the Itasca could have heard a signal from Earhart on 3105 kHz.

6). Note that signals on 6210 kHz were readable anywhere between Howland and Gardner during the 1900, 2000, and 2100 hours, up to 250 miles during the 2200 hour, and up to 200 miles during the 2300 hour. Thus if Earhart had shifted to 6210 kHz, her 2115 GMT signal would have been heard by the Itasca. But when would she have reached the 250-mile reception limit for her 2215 GMT signal? If her actual CPA distance at 1912 GMT was 10 miles (and assuming that she didn’t see the Itasca), she would have reached the 250-mile limit by 2117 GMT if she continued along the LOP at 115 knots after 2013 GMT. If her 1912 GMT CPA was 80 miles, she would have reached the 250-mile limit by 2041 GMT at 115 knots. Therefore, Earhart would have reached the 250-mile limit no later than 2117 at a ground speed of 115 knots, and would have reached the limit earlier at any higher ground speed. Consequently, she was beyond the maximum range for communication with the Itasca by 2215 GMT.

7). It can be concluded from steps 1 through 6 above that the Itasca heard no signals from Earhart after 2013 GMT because: (a) she did not transmit on 6210 kHz following her 2013 GMT signal; (b) she was too far away at 2115 GMT for her signal to be heard on 3105 kHz; and (c) she was too far from Itasca at 2215 GMT for her signal to be heard on either frequency. It also can be concluded that Earhart could have reached Gardner between 2134 GMT and 2211 GMT at 115 knots ground speed. So the possibility of safe arrival at Gardner cannot be ruled out on the basis of these findings. On the other hand, these findings do not rule out the possibility that Earhart simply stopped transmitting after 2013 GMT, or that she encountered a sudden catastrophic event causing loss of the aircraft before she could send another signal.

Post-Loss Signals

The TIGHAR research data base contains many known post-loss signals that were thought by observers at the time to possibly have originated from NR16020. Many are weak carrier signals with no modulation and no accompanying identifying characteristics other than frequency. A few signals, however, are well-documented and 4 such cases were selected for analysis in this edition. A volunteer TIGHAR Team is working on assessing and cataloging the remaining signals to identify candidates for future detailed analysis.

The 4 cases analyzed are:

1). The Nauru intercept on July 3rd (GMT).

2). The HMS Achilles intercept on July 3rd (GMT).

3). Responses to the Honolulu radio station KGMB broadcast on July 5th (GMT).

4). The “281” message intercepted in Honolulu on July 5th (GMT).

The details of each case are discussed in Section V. B of the main text and are not repeated here except where essential to this analysis.

In each case, the hypothesis “The signal of interest could have originated from NR16020 on Gardner Island” was tested on the basis of the SNR computed by the model. Since the Itasca departed the vicinity of Howland Island late on the 2nd to search for Earhart, the Itasca’s actual position, taken from the ship’s deck log, was used in calculating SNR when a question arose as to whether the Itasca could have heard a signal from Earhart.

Given a successful landing on Gardner Island, NR16020’s final heading determined the orientation of the dorsal antenna’s gain pattern, thus affecting the SNR at the intercepting site. The maximum SNR occurred if the intercepting site’s azimuth was within the antenna’s main lobe, and the minimum occurred if the main lobe axis was orthogonal to the intercepting site’s azimuth. The hypothesis is rejected if the maximum SNR is too low to support signal reception. The hypothesis is accepted if the maximum SNR supports reception, and is strengthened if both the maximum and the minimum SNR support reception.

Acceptance of the hypothesis supports, but does not prove, the theory that Earhart and Noonan reached Gardner. Such a proof would require showing that the signal could not have originated from any other place, a task which is beyond the scope of this edition. A method for generating such proof via computer modeling is being developed by TIGHAR researchers, and is expected to be available during 2001.

The Nauru Intercept

At 1030 GMT on July 3rd , Itasca intercepted a message^[35] from KPH (Radiomarine Corporation of America, at Bolinas, CA to Coast Guard radio San Francisco, reporting the following message from Nauru and requesting that it be relayed to Itasca: “Voice heard fairly strong signals strength to S3 0843 0854 GMT 48.31 meters speech not interpreted owing bad modulation or speaker shouting into microphone but voice similar to that emitted from plane in flight last night with exception no hum of plane in back ground.” 48.31 meters is the wavelength corresponding to a frequency of 6210 kHz. At 1200 GMT on July 3rd, a message was sent from Sydney, Australia, presumably by the U.S. Consulate, to the Secretary of State^[36] in Washington, relaying information from Amalgamated Wireless that Nauru radio had sent the following message to Bolinas radio:

At 6:31, 6:43, and 6:54 PM Sydney time today on 48.31 meters, fairly strong signals, speech not intelligible, no hum of airplane in background but voice similar to that emitted from plane in flight last night between 4:30 and 9:30 PM. Message from plane when at least 60 miles south of Nauru received 8:30 PM Sydney time July 2nd saying "a ship in sight ahead". Since identified as steamer Myrtle Bank which arrived Nauru daybreak today. Reported no contact between Itasca and Nauru radio. Continuous watch being maintained by Nauru radio.

The three times given in the message for hearing the "fairly strong" signals correspond to 0831 GMT, 0843 GMT, and 0854 GMT. The times given for signal intercepts the previous night correspond to the interval between 0630 GMT and 1130 GMT. The time given for the “ship sighted” signal corresponds to 1030 GMT.

These two messages illustrate the problems inherent in the relatively crude methods of radio communication used in connection with the Earhart flight and post-loss search. Messages were sent in Morse Code and message drafters typically tried to use the fewest possible words. The results were often vague or misleading, producing the sort of confusion known in military circles as the “fog of war.” The messages above provide a good example of the “fog” that permeated the Earhart episode. Both messages purport to describe the same report from Nauru to Bolinas Radio, but neither includes all of the information in the report. Only a reader privy to both messages would have the full context.

The maximum SNR at Nauru had a median value of 7 dB and a 90th percentile value of 16 dB. The minimum SNR had a median value of 4 dB and a 90th percentile value of 13 dB. So, in either case, the 90th percentile level is consistent with the Nauru operator’s characterization of the signals as “fairly strong.”

The hypothesis “The signal of interest could have originated from Gardner Island” cannot be rejected on the basis of these results. Therefore we conclude that the signal heard by Nauru could have originated from NR16020 at Gardner Island. This conclusion is strengthened by the Nauru operator’s observation that the voice heard in the signals was similar to that heard from Earhart during the previous night, and by the fact that the speech was unintelligible due to “bad modulation or speaker shouting into microphone,” which is consistent with the modulation problem on 6210 kHz cited by the radio technician who had worked on Earhart’s radio at Lae.

The HMS Achilles Intercept

On July 3rd, while about 900 nautical miles East-Southeast of Gardner Island, the British cruiser HMS Achilles intercepted an exchange of signals on 3105 kHz, between 0600 GMT and 0620 GMT, in which Achilles heard an unknown station request another unknown station to send dashes, and then heard dashes. Achilles also heard the call letters KHAQQ mentioned.

The question is whether the dashes heard by the Achilles could have originated from NR16020 on Gardner Island. Since dashes are essentially CW signals, the criteria for usability of a CW signal were applied in testing the hypothesis that the dashes heard by Achilles originated from NR16020 on Gardner Island.

The maximum SNR at the Achilles had a median value of -6 dB and a 90th percentile value of 5 dB. The minimum SNR had a median value of -24 dB and a 90th percentile value of -19 dB.

The hypothesis “The signal of interest could have originated from Gardner Island” cannot be rejected on the basis of these results alone, since the maximum SNR supports CW reception.

However, it is instructive to consider the SNR at the Itasca, which had requested Earhart to “send dashes on 3105 kHz . . .” the request that Achilles heard . At the time Achilles heard the dashes, the maximum SNR for a signal from Gardner Island to the Itasca had a median value of 10 dB and a 90th percentile value of 24 dB. The minimum SNR had a median value of 7 dB and a 90th percentile value of 21 dB. In either case, the SNR to the Itasca would be very strong and the Itasca would have heard dashes if sent by Earhart. Since the Itasca did not hear dashes, we can conclude that the dashes heard by HMS Achilles were not sent from Gardner Island, and we can reject the hypothesis.

Responses to The KGMB Broadcast

On July 5th at 0630 GMT, Honolulu radio station KGMB broadcast a request for Earhart to respond on 3105 kHz with dashes. The Pan American Airways (PAA) station at Mokapu Point, a few miles East of Honolulu, reported hearing four distinct dashes on 3105 kHz immediately following the broadcast.

At the time PAA heard the dashes, the maximum SNR at Mokapu Point for a signal from NR16020 at Gardner island had a median value of -21 dB and a 90th percentile value of -9 dB. The minimum SNR had a median value of -39 dB and a 90th percentile value of -27 dB. Therefore, we conclude that the dashes heard by PAA could not have originated from NR16020 at Gardner Island and we reject the hypothesis.

But the Naval Radio Station at Tutuila, about 620 nautical miles South Southeast of Gardner Island, reported hearing “Four series of dashes” between 0700 and 0704 GMT, and “Four series of dashes” between 0714 and 0716 GMT, and “Eight series of dashes four of which were very strong . Voice indicated but not distinguishable. All on 3105“ between 0727 and 0731 GMT. It is not clear whether Tutuila literally meant to say, for example, “. . . 4 series of dashes” , or whether “. . . series of 4 dashes” was meant. But it is clear that Tutuila heard several series of dashes.

At the time of these intercepts, the maximum SNR at Tutuila for a signal from NR16020 on Gardner Island had a median value of 3 dB and a 90th percentile value of 14 dB. The minimum SNR had a median value of 0 dB and a 90th percentile value of 11 dB. Based on these values, we conclude that the dashes heard by Tutuila could have originated from NR16020 on Gardner Island regardless of the aircraft’s heading.

Therefore, it appears that the signals heard by PAA at Mokapu Point either were spurious or were a hoax.

The “281” Message Intercept

The “281” message was a CW signal heard by three radio operators at the Naval Radio Station at Wailupe, East of Honolulu, between 1130 GMT and 1230 GMT on July 5th.

The maximum SNR for a CW signal from NR16020 on Gardner Island to Wailupe during that period had a median value of -33 dB and a 90th percentile value of -24 dB. The minimum SNR had a median value of -52 dB and a 90th percentile value of -63 dB. Clearly, such a signal was far below the threshold for either detection or usability, and the hypothesis is rejected. The signal heard at Wailupe could not have originated at Gardner Island.

Summary

This analysis has shown that the signals intercepted by HMS Achilles on July 3rd , and the “281” message intercepted by Navy Radio Wailupe on July 5th, could not have originated from Gardner Island.

But this analysis also has shown that the signal heard at Nauru Island on July 3rd and the signals heard by Navy Radio Tutuila on July 5th, could have originated from NR16020 at Gardner Island.

Therefore, the possibility that Earhart successfully landed on Gardner Island cannot be ruled out by these results.