RDF Analysis, page 4
The Bearings

Bearing reports and signal descriptions from source documents are presented and analyzed here, in chronological order.

the analysis of each bearing includes a table showing, for each potential signal source, the times of sunrise and sunset, the bearing – and its reciprocal – of the source from the DF site, the mean SNR for a signal from the source, and the probability that the SNR would exceed the reception threshold.

Most official messages and reports cited in this paper used Greenwich Civil Time (GCT), designated by the “Z” time zone and now known as Greenwich Mean Time (GMT), but some used Honolulu Standard Time (HST), which was 10.5 hours behind GCT. Both notations are retained in this paper, with each instance of HST time and date accompanied by the corresponding Z time and date to avoid confusion, since some events occurred on different HST and Z dates depending on the event time. For example, 4 PM (1600) HST on July 4 was 0230Z on July 5.

Bearing 1: 1512Z July 4, Mokapu Point
Honolulu radio station KGMB (1320 kHz) made a series of broadcasts to Earhart, beginning at 2000 HST July 3 (0630Z July 4) and continuing at intervals of about 15 minutes for several hours,48 requesting that she indicate her general location by sending a combination of dashes from a list of options provided in the broadcasts. At 1512Z July 4 (0442 HST July 4), Mokapu obtained a bearing of 175 degrees on a signal presumably on 3105 kHz. this signal is not mentioned in the Mokapu supervisor’s post-search report49 but was reported by the operator in charge at the Midway site,50 who wrote:
At 1512 GCT, a very faint broad signal apparently a phone was heard here but again was far too weak to take a bearing. Wake reported unheard while Mokapu reported taking a bearing on it which might be 175 approximately.
Table 4 shows the source data for this signal. The “SSS” entries for sunset and sunrise at Billings signify that the site, being on the East Siberian Sea above the Arctic Circle, was continuously in daylight.

Table 4: Signal Data for Bearing 1

Source
Sun
Set
Z
Sun
Rise
Z
Source
Brg
Recip
Brg
Mokapu
Sunset:0518Z
Sunrise: 1555Z
Bearing: 175
SNR
dB
Prob
Quarry Heights
2341
1104
086
266
-181
1.1E-155
Melbourne
0712
2136
222
042
0
Navarin Mys
0945
1430
346
166
-11
2.6E-09
Stalino
2136
0134
349
169
-129
8.2E-79
Gardner Island
0538
1747
214
034
20
9.2E-03
Oust-Kiakhta
1307
2051
320
140
-10
1.1E-09
San Diego acft
0300
1245
064
244
-5
3.3E-08
Los Angeles acft
0309
1245
061
241
-3
1.2E-07
San Francisco acft
0335
1253
054
234
0
1.7E-06
Seattle acft
0408
1219
039
219
-2
1.3E-07
Billings
SSS
SSS
349
169
-28
1.5E-13

Analysis

Click on the map to open a much larger version in a new window.
  1. Bearing Map 1The fact that this bearing was known to Midway but is not in the Mokapu report suggests that the Mokapu DF operator mentioned it on the inter-site radio circuit during the event, but the bearing was subsequently deemed by the Mokapu supervisor to be too unreliable for serious consideration.
  2. The signal bearing passes near the Cook Islands and the Society Islands, but there were no known sources of signals on 3105 kHz in that area.
  3. The possibility that this was an erroneous bearing on a signal from the Itasca can be ruled out because the ship did not transmit51 on either 3105 kHz or 6210 kHz between 0645Z and 2100Z.
  4. The Quarry Heights site can be ruled out because of bearing incompatibility – it was in a bearing sector unaffected by terrain – and because the reception probability was so low as to be virtually zero.
  5. The Melbourne broadcast station harmonic could not be heard at Mokapu, as shown in Table 3.
  6. The reciprocal bearing of Navarin Mys, 166 degrees, was near the reported signal bearing, but the reception probability was about 4 million times lower than that for a signal from Gardner Island.
  7. Although the Stalino broadcast station harmonic could theoretically be heard at Mokapu, and the reciprocal bearing of Stalino, 169 degrees, was near the reported signal bearing, the reception probability was so low as to be virtually zero. Furthermore, as stated earlier, it is highly doubtful that the Soviet government would have permitted significant harmonic radiation.
  8. The reciprocal bearing of Oust-Kiakhta, 140 degrees, was 30 degrees off the reported signal bearing, and the reception probability was about 8 million times lower than that for a signal from Gardner Island.
  9. West coast aircraft can be ruled out because of bearing incompatibility, since the entire west coast was in a DF site sector unaffected by terrain.
  10. The reciprocal bearing of Billings, 169 degrees, was close to the reported signal bearing, but the reception probability was about 6 million times less than the probability for a signal from Gardner Island.
  11. The reception probabilities strongly suggest that Gardner Island was the most likely source. But the computed vertical arrival angle for a signal from Gardner was 12.5 degrees, which argues against terrain effects sufficient to account for the 39-degree difference between the reported signal bearing and the bearing of Gardner. Notwithstanding the probability argument in favor of Gardner, the possibility, however remote, that one of the Soviet stations near the reciprocal bearing was the source, cannot be ruled out on the basis of the available evidence.
Bearing 2: 1523Z to 1530Z, July 4 Mokapu Point
The Mokapu supervisor’s post-search report52 states:
Carrier again heard on 3105 – rough bearing only possible due to weakness and swinging of signals. Get bearing from Mokapu of approximately 213 degrees. Advised Coast Guard.
Mr. G. W. Angus, the PAA Pacific Division Communication Superintendent, was at Midway when this bearing was taken, and later stated in his post-search report:53
On Sunday morning about 5:30 a.m., local time at Mokapu, Mr. Paulson stated he heard signals in the vicinity of 3105 KC, although the frequency could not be accurately determined and on which he obtained an approximate bearing of 210 degrees. the signals Mr. Paulson heard were, undoubtedly, carrier signals modulated with voice although he could not understand the voice part of it. Although it is true several of the domestic lines use frequencies close to 3105 KC, it is doubtful if these signals would have carried to Honolulu at this particular time of day, the time then being 8:00 a. m., Pacific Standard Time. Usually at this time, stations on the West Coast have changed to day frequencies. I believe the signals heard by Mr. Paulson were from the Itasca. this information was passed on to the Coast Guard at Honolulu for whatever it was worth and we continued to listen to the two frequencies used by the plane.

Table 5: Signal Data for Bearing 2

Source
Sun
Set
Z
Sun
Rise
Z
Source
Brg
Recip
Brg
Mokapu
Sunset: 0518Z
Sunrise: 1555Z
Sig Brng: 213
SNR
Prob
Quarry Heights
2341
1104
086
266
-181
1.1E-155
Melbourne
0712
2136
222
042
–-
0
Navarin Mys
0945
1430
346
166
-11
2.6E-09
Stalino
2136
0134
349
169
-129
8.2E-79
Gardner Island
0538
1747
214
034
20
9.2E-03
Oust-Kiakhta
1307
2051
320
140
-10
1.1E-09
San Diego acft
0300
1245
064
244
-5
3.3E-08
Los Angeles acft
0309
1245
061
241
-3
1.2E-07
San Francisco acft
0335
1253
054
234
0
1.7E-06
Seattle acft
0408
1219
039
219
-2
1.3E-07
Billings
SSS
SSS
349
169
-28
1.5E-13

Analysis

Click on the map to open a much larger version in a new window.
  1. Bearing 2The bearing of 213 degrees reported by the Mokapu supervisor passes within 30 nmi southeast of Gardner Island. This bearing, evidently based on direct analysis of the DF operator’s readings, is considered more accurate than the value cited by Angus.
  2. The elevation angle for a signal from Gardner at this time was 12 degrees, well above the terrain masking limit.
  3. The time cited by Angus, 0530 HST July 4 (1600Z July 4), appears to be when Paulson mentioned the bearing on the inter-site circuit, rather than when he took the bearing (1523Z to 1530Z).
  4. The bearing of the Itasca54at this time was 229.6 degrees, but the Itasca could not have been the source of this signal since the ship55 did not transmit on 3105 kHz between 0645Z and 2100Z.
  5. Other than Gardner Island, the only potential source near the reported bearing was AM broadcast station 3AR in Melbourne, which could not be heard at Mokapu.
  6. Angus’ comment about signals from west coast aircraft –
    … it is doubtful if these signals would have carried to Honolulu at this particular time of day, the time then being 8:00 a.m., Pacific Standard Time. Usually at this time, stations on the West Coast have changed to day frequencies.
    – indicates that the DF system was bi-directional, hence the possibility of a reciprocal bearing must be considered. He was correct about commercial aircraft changing to day frequencies, but he failed to consider general aviation aircraft, for which 3105 was the designated calling frequency.
  7. The signal was heard approximately 3 hours after sunrise on the west coast, and about 30 minutes before sunrise at Mokapu. Hence nearly the entire propagation path was in daylight, and conditions at 3105 kHz were deteriorating. In contrast, the path from Gardner Island to Mokapu was still in darkness.
  8. The reciprocal of the reported signal bearing was 033 degrees. The Seattle area, bearing 039 degrees, was the only source area close to the reciprocal bearing. The reception probability for a signal from Seattle was very low, but that value takes on added significance when compared to the probability for a signal from Gardner. The ratio of the two probabilities shows that a signal from Gardner was 71,000 times more likely to have been heard at Mokapu than a signal from the Seattle area.
  9. Although not conclusive, the available evidence strongly suggests that Gardner Island was the most likely source of the signal.
Bearing 3: 0630Z July 5, Mokapu Point
On the evening of Sunday, July 4, KGMB (1320 kHz) conducted its second night of broadcasts, beginning at 8 PM (2000) HST (0630Z July 5), with instructions56 for Earhart to turn on her transmitter for one minute for tuning purposes, then to send 4 long dashes, then wait for an acknowledgment by KGMB 15 minutes later.

Mokapu obtained a bearing of approximately 215 degrees on a carrier signal at 3105 kHz immediately following the KGMB broadcast. The post-search report57 by K. C. Ambler, the Mokapu supervisor, described the signal as

… close to 3105 but signals so weak that it was impossible to obtain even a fair check. Average seems to be around 215 degrees – very doubtful bearing.
He further stated that although the KGMB broadcast was repeated at half hour intervals during the evening, no further signals were heard that appeared to correlate with the broadcasts. But he did mention that at 1225Z the same day, Wake obtained an approximate bearing of 144 degrees, which seemed
… to tie in fairly well with our two bearings of 213 and 215.
The Wake bearing is discussed later in this paper.

Mr. Angus, the Pacific Division Communication Superintendent, stated in his report:58

Arriving at Mokapu Sunday, I spent most of Sunday night at the radio station and we set up a watch on 3105 KC at the DF and the receiving station. At 7:30 p.m. local Honolulu time, the broadcast station KGMB arranged a special broadcast to the plane on their broadcast frequency, requesting the plane to transmit four long dashes on 3105 KC if they heard KGMB plane. broadcast. Immediately after the broadcast, Mr. Ambler and myself both distinctly heard four dashes on 3105 KC. We are certain of the frequency because the Coast Guard Cutter, Itasca, had previously set their transmitter on this frequency in an effort to contact the Shortly before, we had taken bearings on the Itasca on this frequency, obtaining an approximate bearing of 210 degrees. Upon hearing the four dashes mentioned above, we immediately called KGMB by phone and asked them to repeat the test. This was done and immediately after the second test, we again heard the same signals except at this time, only two dashes were received and the second dash trailed off to a weak signal as though the power supply on the transmitter had failed. Nothing was heard thereafter although a continuous watch was maintained on this frequency all night. During the time these dashes were heard, it was possible to obtain an approximate bearing of 213 degrees from Mokapu.

Table 6: Signal Data for Bearing 3

Source
Sun
Set
Z
Sun
Rise
Z
Source
Brg
Recip
Brg
Mokapu
Sunset: 0518Z
Sunrise: 1555Z
Sig Brng: 213
SNR
Prob
Quarry Heights
2341
1104
086
266
-36
1.4E-09
Melbourne
0712
2136
222
042
–-
0
Navarin Mys
0945
1430
346
166
-9
1.9E-12
Stalino
2136
0134
349
169
-300
0
Gardner Island
0538
1747
214
034
27
2.1E-02
Oust-Kiakhta
1307
2051
320
140
-114
7.1E-117
San Diego acft
0300
1245
064
244
15
1.4E-02
Los Angeles acft
0309
1245
061
241
16
1.7E-02
San Francisco acft
0335
1253
054
234
18
2.3E-04
Seattle acft
0408
1219
039
219
22
1.9E-02
Billings
SSS
SSS
349
169
-23
3.0E-20

Analysis

Click on the map to open a much larger version in a new window.
  1. Bearing 3The timing of this signal relative to the broadcast strongly suggests it was a response to the broadcast.
  2. The bearing line passes approximately 30 nmi southeast of Gardner Island.
  3. Angus had the event time wrong. The KGMB request for dashes was sent at 8:00 p.m. (2000) HST, not 7:30 p.m . At 6:30 p.m. (1830) HST (0500Z), and again at 7:30 p.m. (1930) HST (0600Z), KGMB broadcast59
    Calling Earhart plane. Every effort being made to locate you. This station will call at 0630 GCT at which time please reply on 3105 kilocycles. Listen on 1320 as all communications originate here.
    At 8 p.m. (2000) HST (0630Z), KGMB broadcast60
    To the Earhart plane. We are using every means to establish communication with you. If you hear this broadcast please come in on 3105 kilocycles. Use key if possible, otherwise voice. If you hear this broadcast turn your carrier signal on one minute so we can tune you in, then turn your carrier signal on and off four times. Then listen for our acknowledgment [sic].
  4. Angus’ statement
    Shortly before, we had taken bearings on the Itasca on this frequency, obtaining an approximate bearing of 210 degrees
    is not consistent with known facts. The Mokapu supervisor’s report61 states that the DF watch on 3105 kHz started at 0600Z on July 5, and that the bearing of 215 degrees was obtained at 0630Z. Thus the “shortly before” bearing must have been taken between 0600Z and 0630Z. But the Itasca did not transmit62 on 3105 kHz between 0330Z and 0730Z. Hence, the Itasca could not have been the signal source for the bearing cited by Angus, although the ship was near the bearing line. The bearing of the Itasca63 during the 24 hours preceding the 0630Z KGMB broadcast varied between 227 degrees and 230 degrees.
  5. The “shortly before” bearing cited by Angus may have been taken on a signal misidentified as being from the Itasca. This would be consistent with a premature Earhart response to the 0600Z KGMB broadcast alerting her that a 0630Z broadcast would request her to reply at that time. The fact that Ambler did not mention this bearing in his report may indicate that he considered it too indefinite for serious consideration.
  6. The only land source near the signal bearing, other than Gardner Island, was AM broadcast station 3AR in Melbourne, the 3100 kHz harmonic of which could not be heard at Mokapu. But even if 3AR could be heard, and even assuming the station staff heard the KGMB broadcast, it is inconceivable that 3AR would send dashes in response.
  7. The elevation angle for a signal from Gardner at this time was approximately 2 degrees, which was below the Koolau ridge line elevation angle, and could explain the signal weakness and hence the difficulty in getting the bearing.
  8. The fact that this signal appears to have been a response to KGMB raises the question of whether it could have originated on the west coast. A station responding to KGMB would first have to hear the broadcast. The KGMB signal was strong enough on the west coast to be heard if there was no interference. However, there were two 24-hour stations on 1320 kHz: KID in Idaho Falls, Idaho, and KGHF in Pueblo, Colorado. The interference by those stations was evaluated using the LFMF model, and the results are shown in Table 7.
  9. Table 7: Interference With West Coast Reception of KGMB

    Station
    Seattle
    San Francisco
    Los Angeles
    San Diego
    KGMB, Honolulu, 1320 kHz 1000 w
    Distance, nmi
    2332
    2079
    2214
    2267
    Ground wave field strength, dBuv
    -148.1
    -104.8
    -117.3
    -120.0
    Skywave field strength, dBuv
    16.6
    20.5
    19.9
    19.7
    KID, Idaho Falls, 1320 kHz 500 w
    Distance, nmi
    414
    785
    909
    969
    Ground wave field strength, dBuv
    -35.5
    -92.3
    -121.5
    -130.7
    Skywave field strength, dBuv
    32.5
    26.0
    24.5
    23.7
    Skywave interference ratio, dB
    15.9
    5.5
    4.6
    4.0
    KGHF, Pueblo, CO, 1320 kHz 500 w
    Distance, nmi
    959
    840
    713
    693
    Groundwave field strength, dBuv
    -131.6
    -102.2
    -86.8
    -78.1
    Skywave field strength, dBuv
    22.4
    27.3
    30.3
    30.9
    Skywave interference ratio, dB
    5.8
    6.8
    10.4
    11.2
    Combined interference ratio
    dB
    16.9
    8.7
    11.4
    11.9
    Numerical
    49.3
    7.5
    13.7
    15.5

    Since the background noise level at a given location was common to signals from KGMB, KID, and KGHF, the interference level can be determined by considering the field strength, in dB above one microvolt , arriving from each station. The table shows that the KGMB ground wave signal was far too weak to have been heard on the west coast, whereas the skywave signal was strong enough for reception. A similar situation existed for the signals from KID and KGHF. The skywave interference ratio for KID and KGHF at each of the four west coast areas is the difference, in dB, between the field strength from each station and the field strength from KGMB. Since the KID and KGHF signals could be heard simultaneously anywhere on the west coast, the combined interference must be considered. The combined interference ratio is the square root of the sum of the squared individual skywave interference ratios. The results, in dB and numerical form, are shown in the bottom row of the table. The maximum combined interference was 49.3 times the KGMB signal strength, at Seattle, and the minimum was 7.5 times the KGMB signal strength, at San Francisco, showing that the interference from KID and KGHF prevented reception of the KGMB signal anywhere on the west coast. Therefore, the signal heard at Mokapu could not have been a response to the KGMB broadcast by a station on the west coast.

  10. Ruling out the Itasca, 3AR in Melbourne, and west coast stations as sources of a signal responding to the KGMB broadcast leaves only one plausible possibility, i.e., a voice-capable transmitter on 3105 kHz on the bearing of Gardner Island. KHAQQ on the Earhart aircraft is the only known source fitting that description.

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