Earhart Project Research Bulletin #30
March 15, 2001
Harmony and Power:

Could Betty Have Heard Amelia Earhart on a Harmonic?

by Bob Brandenburg
TIGHAR #2286

*Please note that this bulletin has been superseded by the following files:*

Probability Tables


This report presents the results of a computer simulation analysis performed by the author as part of TIGHAR’s assessment of Betty’s report that she heard signals from Amelia Earhart in July 1937, while listening to her father’s shortwave radio at St. Petersburg, Florida.

This analysis is the product of a team effort. Ric Gillespie, TIGHAR’s Executive Director, relayed requests to Betty for additional information as the analysis unfolded. Mike Everette, TIGHAR #2194, provided crucial insights on the design of Amelia’s transmitter and its tendency to produce harmonic radiation. And Harry Poole, TIGHAR #2300, researched property records in St. Petersburg, and took photographs and measurements of Betty’s former house and adjoining property, thus enabling derivation of the geometry of Betty’s receiver antenna.

A previous analysis, performed when Betty’s report was received, addressed the question of whether Betty could have heard Amelia on 3105 kHz (Amelia’s night frequency) or 6210 kHz (her day frequency). The results showed that such reception was impossible. The entire propagation path from Gardner Island to St. Petersburg was in daylight, and the path loss was too high for reception on either frequency. But Betty’s notebook was too credible to be dismissed out of hand, so it was decided to consider alternative explanations. During that process, Mike Everette and the author concurrently, and independently, recognized the possibility that Betty heard Amelia on a harmonic of 3105 kHz or 6210 kHz.

Amelia’s transmitter generated the output, or channel, frequency on 3105 kHz and 6210 kHz by doubling the frequency of an exciter crystal. Hence it was possible for harmonics of the crystal frequencies to appear in the output, along with the channel frequency harmonics normally generated in the transmitter’s final power amplifier. Mike Everette showed that the design of Amelia’s transmitter output and antenna coupling circuits did not have any means of harmonic suppression1 and that consequently, any harmonics present in the transmitter’s output were passed directly to the antenna and could potentially be radiated.

The question of whether any of those harmonics could propagate a detectable signal from Gardner Island to St. Petersburg was the starting point for this analysis.

Computer modeling was used to simulate the propagation conditions for harmonics that could be produced in Amelia’s transmitter, and to compute the probability that the signal-to-noise ratio (SNR) required for reception at Betty’s radio would be available during the period from July 2 through July 9, 1937, between 3 PM and 6 PM, local time in St. Petersburg.
 Computer Models
Two computer models, ICEPAC2 and NEC4WIN95,3 were used in this analysis. Both have been used by the author in previous TIGHAR signal propagation studies.

ICEPAC was used to simulate the propagation conditions and to calculate the probability of achieving the required SNR.

NEC4WIN95 was used to derive the frequency-dependent 3-dimensional gain patterns of Betty’s antenna and Amelia’s antenna (at frequencies above 6210 kHz) for use in ICEPAC, since SNR calculations depend in part upon the gain of the transmitter and receiver antennas at the respective ends of the propagation path. The ICEPAC antenna library already included the gain patterns of Amelia’s antenna at 3105 kHz and 6210 kHz, derived with NEC4WIN95 for use in previous TIGHAR analyses.

 Amelia’s Antenna
The antenna gain in the direction of St. Petersburg, at harmonic frequencies up to 15525 kHz, was approximately half the gain at Amelia’s channel frequencies of 3105 kHz and 6210 kHz. But the gain at harmonics above 15525 kHz was about the same as at the fundamental frequencies. It is interesting to note that Amelia’s antenna was broadly resonant between 15.5 MHz to 24 MHz, which would be conducive to radiation of harmonics in that range.
 Betty’s Antenna
The configuration of Betty’s antenna is shown in Figure 1. The antenna gain pattern had a broad lobe in the direction of Gardner Island, with a gain of 2 dB to 3 dB at harmonic frequencies above 12240 kHz. This antenna had broad resonances at 17 MHz, 23 MHz, and 25 MHz.
 Betty’s Radio
It was important to know the make and model of Betty’s radio, because receiver sensitivity and tuning range are important factors in evaluating whether she could have heard signals on a harmonic. Betty did not recall the make and model of her radio, but she provided information that led to a determination that it probably was a Zenith model 1000Z “Stratosphere.”4 When shown a color photograph of a Zenith 1000Z that had been restored to new condition, Betty positively identified it as the model she had used.

The model 1000Z was sold by Zenith during 1935-1938, and was a very capable radio with extensive shortwave coverage. Approximately 350 sets were produced. The first 100 production units had shortwave coverage up to 64.3 MHz, and the remaining sets had coverage up to 45 MHz. The radio had 25 vacuum tubes, of which 12 were in the audio amplifier section. It had 2 tuned RF amplifier stages and 2 IF amplifier stages with variable bandwidth. This radio clearly had the sensitivity and tuning range needed for receiving signals from Gardner Island.

 Required SNR
The required SNR was set at 3 dB for the purposes of this analysis. This SNR is half the standard 6 dB level specified5 for just-usable operator-to-operator communication, and approximates the marginal conditions described by Betty. She recalls that the signals were “scratchy,” and that she couldn’t always make out complete phrases. She compares the quality of the signals to marginal signals heard on a police scanner, breaking in through the static and then fading out.
 The Probability of Achieving the Required SNR
Signal power and noise power are random variables. Their instantaneous values vary about their median values, in response to random changes in the propagation environment. Since the ratio of two random variables is a random variable, the SNR is a random variable. In an ideal situation, the median SNR is well above the reception threshold, and the random variations are not noticed. But in a marginal situation such as described by Betty, the median SNR is below the reception threshold, and the random variations occasionally raise the instantaneous SNR above the threshold, permitting some words and phrases to be recognized.

The probability of achieving the required SNR or better is computed for a specified percentage of time. The unit of time in this analysis is one hour, and each hour is uniquely defined in terms of year, month, date, time, radio frequency, and propagation conditions. For example, if the percentage of time for the calculation is specified as 5%, then ICEPAC computes the probability that the required SNR will be achieved in 5% of hours with identical conditions. Since any given hour occurs once per day, this is equivalent to the probability that the required SNR will be achieved on 5% of days with identical conditions at the specified hour.

 Identifying Feasible Frequencies
Betty does not remember the frequency on which she was listening, but she does recall that the radio tuning dial pointer was about “an inch or so” to the right of the top of the dial. That location is in the 18 MHz to 25 MHz region on the dial of a Zenith 1000Z. But that information is not sufficient for deciding which frequencies should be tested for reception feasibility.

Feasible frequencies were identified by computing the probability of achieving the required SNR on all harmonics of the crystal frequencies, and harmonics of 3105 kHz and 6210 kHz, up to the maximum usable frequency (approximately 27 MHz) over the propagation path from Gardner Island to St. Petersburg during the periods of interest. Frequencies with zero probability of achieving the required SNR were eliminated. In this procedure, it was assumed that the full rated 50-watt output of Amelia’s transmitter was delivered to the antenna on each harmonic. Although such harmonic power levels could not actually be achieved, since harmonic power varies inversely with the order of the harmonic, this procedure is an effective method of eliminating infeasible frequencies. If reception was not possible on a harmonic frequency at 50 watts, then reception on that frequency would not be possible at any lower power.

This procedure yielded the following feasible frequencies:

15525 kHz 10 x 1552.5 kHz and 5 x 3105 kHz6
17077.5 kHz 11 x 1552.5 kHz
18630 kHz 12 x 1552.5 kHz, 6 x 3105 kHz, and 3 x 6210 kHz
20182.5 kHz 13 x 1552.5 kHz
21735 kHz 14 x 1552.5 kHz and 7 x 3105 kHz
23287.5 kHz 15 x 1552.5 kHz
24840 kHz 16 x 1552.5 kHz, 8 x 3105 kHz, and 4 x 6210 kHz
26392.5 kHz 17 x 1552.5 kHz

The harmonics of 1552.5 kHz (the crystal frequency on the 3105 kHz channel) were removed from this list to simplify the analysis. The even harmonics were superfluous because they occur at lower-order (hence higher-power) harmonics of 3105 kHz or 6210 kHz. The odd harmonics would be irrelevant if Betty could have heard Amelia on any harmonic of 3105 kHz or 6210 kHz. If it turned out that Betty could not have heard Amelia on any harmonic of 3105 kHz or 6210 kHz, then the odd harmonics of 1552.5 kHz could be revisited. As it turned out, it was not necessary to revisit the odd harmonics.

Removing the harmonics of 1552.5 kHz yielded the following list of feasible frequencies:

15525 kHz 5 x 3105 kHz
18630 kHz 6 x 3105 kHz and 3 x 6210 kHz
21735 kHz 7 x 3105 kHz
24840 kHz 8 x 3105 kHz and 4 x 6210 kHz

It is not certain that Amelia adhered to her in-flight day/night frequency plan after arriving at Gardner Island. She could have tried both frequencies, at every transmission opportunity, in the hope of improving her chances of being heard. If Amelia transmitted on 3105 kHz, all four frequencies could be generated as harmonics of 3105 kHz in the transmitter’s final power amplifier. If she transmitted on 6210 kHz, harmonics at 18630 kHz and 24840 kHz could be generated as in the final power amplifier, and the even order harmonics of the crystal frequency could be disregarded. Since Amelia’s actual frequency usage is unknown, all four frequencies were tested.

It is interesting to note that the final four feasible frequencies generally agree with Betty’s recollection of where the tuning pointer was positioned on her radio dial.

 SNR Calculations at the Feasible Frequencies
The probability of achieving the required SNR was computed for each feasible frequency, for each hour, for specified percentages of days with identical conditions at each hour, for five harmonic power levels (the 50-watt level used in the frequency feasibility screening, retained for comparison, and four reduced power levels).

Terman7 gives the output power level of a well-designed harmonic generator, as a percentage of output at the fundamental frequency: 2nd harmonic, 65%; 3rd harmonic, 40%; 4th harmonic, 30%; and 5th harmonic, 25%. The 4 reduced harmonic power levels used in this analysis, and their respective percentages of 50 watts are: 5 watts (10% ), 1 watt (2% ), 0.5 watt (1%) and 0.1 watt (0.2%). These power levels are conservative compared to Terman’s values, and are assumed to represent a reasonable range of harmonic power levels that could be expected at the output of Amelia’s transmitter.

The results show that Betty could have heard Amelia on a harmonic.

The probabilities of achieving the required SNR are given in Tables 1 through 5, and show that hearing Amelia was an unusual, but definitely possible, event. Table 1 shows the probability that the required SNR would occur on 1 day out of 20, or 5% of days. Table 2 shows the probability for 2 days out of 20, or 10% of days, and so on. The reader will note that the probability for a given set of parameters decreases, from table to table, as the percentage of days increases. This trend indicates that the conditions required for Betty to hear Amelia were most likely to occur on 5% of days or less.

The first column in each table shows the date in 1937, the day, and the sunspot number (SSN), an indicator of ionospheric propagation conditions. The second column shows the local zone time in St. Petersburg, corresponding to the time periods described in Betty’s notebook. The third through sixth columns show the probabilities (in percent) of achieving the required SNR at each of the four feasible frequencies, in terms of the transmitter power output to the antenna, in watts. The 50-watt output power level was retained in the tables to serve as a point of reference for the lower power levels, and to provide a scaling reference for interpolating the effects of power levels between 5 watts and 50 watts.

As an example of how to interpret the results, consider the Table 1 entries for 24840 kHz (4 x 6210 kHz) on July 6th during the 1600 hour. For an assumed harmonic power level of 1 watt, there was a 16% probability that the required SNR would occur on 1 day out of 20. On the next day, the probability is 1%. The sunspot number has increased from 108 to 143, indicating a higher degree of ionization in the ionosphere, with correspondingly higher signal absorption losses.

  1. Betty could have heard signals from Amelia at Gardner Island on one or more harmonics, provided that the power level at the output of Amelia’s transmitter was 0.1 watt or higher.
  2. Betty’s recollection of where her radio was tuned, in the general area of 18 MHz to 25 MHz, is consistent with the frequencies on which she could have heard Amelia.
  3. The low probabilities of achieving the required SNR are consistent Betty’s description of the fragmentary signals that she heard.
1 Everette has discussed this topic on the TIGHAR forum.
2 ICEPAC 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.
3 NEC4WIN95 is a widely used commercial model for interactive design and analysis of antennas.
4 Photos and other information are available at www.oldradiozone.com.
5 CCIR Document of the IXth Plenary Assembly, Los Angeles, 1959, vol. VI, Recommendation 161, p. 120, Geneva, 1959
6 The notation “n x frequency” denotes the nth harmonic of the frequency.
7 Terman, F.E. Radio Engineers Handbook, 1st Edition, McGraw-Hill, New York, 1943.

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