New Clocks to Keep Time for Galileo If you want to know precisely where you are, get an accurate clock. This was true in the seventeenth century, when sailors struggled to find a way of measuring longitude at sea. And it’s equally true now, even though satellites have taken over from sextants, the Sun and fixed stars as the navigation aids of choice. Seventeenth century navigators could tell local time from the position of the Sun, but to determine their longitude, they needed also to know the time at a fixed reference point, i.e. Greenwich, the location of the prime meridian. This is because local time moves forward or backward by one hour for every 15 degrees longitude one travels. The clocks available at the time were notoriously inaccurate at sea and the problem was solved only when John Harrison, a joiner from England, built a seaworthy clock that kept time to within about 1 second per day, equivalent to a positioning accuracy of about 500 metres. His clocks, which took him all his life to build, can still be seen at the Royal Observatory, Greenwich. Next Generation Clocks The clocks that will mark time for the next generation of navigation satellites will look very different from Harrison’s elegant timepieces. Based on atomic frequency standards, they are under development for Europe’s Galileo satellite navigation system at the Observatoire de Neuchatel and Temex Neuchatel Time, both located in the centre of the Swiss clock industry. These clocks are being designed to a standard that seventeenth century sailors would find impossible to comprehend. They will keep time to within a few hundred millionths of a second per day.

IN THIS ISSUE From Time to Time Albuquerque Annual Meeting Annual Meeting Awards Departments: From the ION President: Exciting Times Congressional Fellow Report: Working in the "War Room" Portney’s Corner: Mayday... Mayday! From the ION Historian: Navigation and Sociology GNSS Around the Globe: News in Brief, Section News, Launches, and more Calendar

Why, you may ask, would anyone want to keep time so closely? The answer has to do with the speed of light. Nowadays, you can determine your position on the Earth’s surface by measuring the time taken for a signal broadcast by a navigation satellite to reach you. As signals travel at the speed of light, this means measuring tiny fractions of a second very accurately. And to do that, you need to know precisely when the signal left the satellite and precisely when it arrived at your receiver. “In navigation, clocks are the driving factor for determining positions accurately. With an accuracy of better than one billionth of a second in one hour, the clocks on the Galileo satellites will allow you to resolve your position anywhere on the Earth’s surface to within 45 cm,” says Franco Emma, the clock expert and navigation engineer at ESTEC, ESA’s technical centre in the Netherlands.

Two Technologies—One Principle
Each of the 30 satellites in the Galileo system will have two clocks on board; one based on the rubidium atomic frequency standard and the other using a passive hydrogen maser. Both clocks use different technologies, but make use of the same principle—if you force an atom to jump from one particular energy state to another, it will radiate a microwave signal at an extremely stable characteristic frequency.

This frequency is around 6GHz for the rubidium clock and around 1.4GHz for the hydrogen clock. “We will use the clock frequency as a very stable reference by which other units can generate the accurate signals that the satellites will broadcast,” says Emma. The broadcast signals will also provide a reference by which the less stable clocks in user’s receivers can continuously reset their time.

ESA chose the rubidium and hydrogen maser clocks because they are very stable over a few hours and their technology can fly onboard the Galileo satellites. If they were left to run indefinitely, though, their accuracy would drift, so they need to be synchronised regularly with a network of even more stable ground-based reference clocks.

Galileo System Time
These will include clocks based on the caesium frequency standard, which show far better long-term stability than either rubidium or hydrogen maser clocks. The caesium frequency standard is based on atomic transitions in the caesium atom and is the standard on which universal time is based. “The clocks on the ground will also generate what we are calling Galileo System Time,” says Emma. The clocks that will fly on the satellites are the first of their type to be developed and built in Europe. “Similar clocks are available in the US and in Russia (e.g., those flown on the GPS and GLONASS satellites), but we believe that we need to have an independent capability,” states Emma. The passive hydrogen maser clock will actually be the first one of its type ever to fly. It is being built by the Observatoire de Neuchatel in cooperation with Officine Galileo of Italy, the former being responsible for the overall development and in particular for the so-called physics package, and the latter being in charge of the electronics. A similar arrangement applies for the rubidium clock, with Temex Neuchatel Time assuming overall responsibility and Astrium, Germany contributing the electronics. The rubidium clock should be ready for qualification by the end of 2001, by which time an engineering model of the hydrogen maser should be available. Both clocks will really show their capabilities in 2004, when the first Galileo satellites go on trial.

GPS Augmentations Fare Well in Congress

Congress gave the GPS Augmentation program most of the funding that it requested for Fiscal Year 2002 (FY02), which starts Oct.1 but still has issues to clarify before the end of this year’s session. The House version of the bill (H.R. 2299) passed on June 26, following subcommittee and committee markups on June 11 and 20. The committee recommended full funding for WAAS at $75.9 million and LAAS at $42.45 million. It hopes to accelerate the implementation of LAAS. However, the committee zeroed out funding for NDGPS.

The Senate version (S. 1178) passed the committee on July 12. It also fully funds WAAS. Noting the Independent Review Board’s finding that WAAS is a sound and valuable concept, the committee earmarked $5 million to increase the number of non-precision GPS instrument approaches and to develop GPS routes to supplement the current airway route system. The committee encourages FAA to “aggressively pursue resolution of the integrity challenges facing the program and to expeditiously seek certification of procedures consistent with the current program decision altitudes.” The committee earmarked another $10 million for the development of standards and procedures, including surveys. “In addition, should this program continue to experience the programmatic slippages that have plagued it since its inception, the Committee would look favorably on a reprogramming to commit additional resources to this immediately beneficial activity.”

The Senate committee funded LAAS at $44.12 million, $10 million more than requested. The increase is for certification support and additional implementation activities. The committee recommendation includes funds to resolve the integrity issue. The committee fully funded NDGPS at $6 million through the Federal Highway Administration. NDGPS was previously funded through FAA.

From the ION President: Exciting Times in the Field of Navigation Ronald R. Hatch

Thank you for the opportunity to serve as the president of The Institute of Navigation. Karen Van Dyke set a high standard. I will do my best to follow her example. I am pleased to report that the Institute remains in excellent health. The National Office staff does an admirable job administering the day-to-day operations of the ION. We have excellent leadership in the organization. If you have not yet explored the ION Web site and the services now offered—it is time to do so.

These are exciting times in the field of navigation. The GPS system is at the beginning of a planned major improvement. We are already enjoying the improved accuracy that has resulted from the removal of the (Selective Availability) dithering of the satellite clocks. Plans for the European Galileo system are proceeding rapidly. The FAA’s WAAS system now seems to be on track to not only improve accuracy but to dramatically improve the integrity of GPS. Japan’s MSAS and Europe’s EGNOS promise to extend the accuracy and integrity of WAAS into Asia and Europe. GPS receivers continue to decrease in cost and the application areas continue to expand. If the ION continues to provide a forum for reporting these developments in our quality conferences, our continued health would seem to be assured.

The June annual meeting was indeed a quality conference. Dan Crouch, the general chair, and Dr. Chris Bartone, the program chair are to be commended for organizing an excellent and well attended conference. The upcoming ION GPS 2001 Conference promises to be the best conference yet. Larry Hothem, general chair, and Dr. Gerard Lachapelle, program chair, report that over 500 abstracts were submitted for presentation. In an attempt to accommodate as many presentations as possible, they have gone to three full days with six parallel tracks of presentations. Our thanks to the many who have volunteered to assist in organizing and running this conference.

In addition to the many volunteers who help organize and run the conferences, the ION is blessed by very capable members who have been elected to serve on the Council or been appointed to serve as chair of Standing or Ad Hoc Committees. During the GPS 2001 Conference, the Council will be voting upon a reorganization designed to improve the continuity of leadership and balance the regional representation. Rather than the current three regional divisions, it is proposed that only two divisions exist, an East and a West division. It is proposed that the two council members lost by this reorganization be replaced by having two representatives at large from each division and that they be elected to staggered two-year terms.

While thanking the many who have volunteered to serve the ION in various capacities, we would be remiss not to mention the many who also serve in the local sections. It is pleasing to see the local sections increase in number and in activity. They provide a strong base for the national organization to draw upon. ION section activities are highlighted in this newsletter. Finally, the ION is pleased to welcome our second congressional fellow, Dr. Clark Cohen. Phil Ward will be completing his term as our first congressional fellow and I am sure offering valuable advice and assistance to Dr. Cohen as he begins his term.

I look forward to this next year and to seeing many of you in Salt Lake.

Regards,

The Purpose of The ION The Institute of Navigation, founded in 1945, is a non-profit professional society dedicated to the advancement of the art and science of navigation. It serves a diverse community including those interested in air, space, marine, land navigation and position determination. Although basically a national organization, its membership is worldwide, and it is affiliated with the International Association of the Institutes of Navigation. 2000-01 National Executive Committee President: Mr. Ron Hatch Executive Vice President: Dr. Rudy Kalafus Treasurer: Mr. Larry Hothem Eastern Region Vice President: Ms. Sally Frodge Central Region Vice President: Maj. John Raquet Western Region Vice President: Dr. A.J. Van Dierendonck Immediate Past President: Ms. Karen Van Dyke How to Reach The ION Telephone: 703-683-7101 Facsimile: 703-683-7105 Web site: http://www.ion.org E-mail: membership@ion.org ION National Office Staff Director of Operations: Lisa Beaty Technical Director: Carl Andren Office Manager: Jennifer Murphy-Smith Assistant to the Technical Director: Miriam Lewis Meeting Services/Author Liaison: Connie Mayes Member Services/Registrar: Wendy Hickman Graphic Design/Editor: Paula Danko Information Manager: Rick Buongiovanni

From the ION Congressional Fellow: The War Room Phil Ward

It is hard to believe that my tenure as a congressional fellow is at the halfway point. My one sentence summary of this assignment is: “This is a once-in-a-lifetime most enjoyable learning experience!” Since the ION has extended my tenure until March 2001, I expect that my overall experience will change in substance, but my summary opinion will remain the same.

Mission Impossible… But Survivable
My day–to-day mission primarily involves the Senate Armed Services Committee (SASC). When a hearing is scheduled for the SASC or for any of Sen. Inhofe’s three SASC subcommittees (Readiness, AirLand and Strategic), the staff in the “war room” (our office nickname) researches the subject material and prepares an opening statement and questions for Sen. Inhofe. There has been as many as four hearings a week for several weeks in a row! The hearings usually last all morning or all afternoon and are occasionally continued at a later date. We make every effort to get the prepared material ready and provide a briefing as early as possible, but it is not uncommon that this all takes place while escorting the senator to the hearing room. There, you sit directly behind your member and when that member turns toward you, you hope and pray you know the answer to the question about to be asked. Contrary to reports I have heard from some congressional fellows that they seldom see their member, I meet with Sen. Inhofe on a regular basis. James M. Inhofe is not only a great senator who happens to be a strong supporter of our military (including GPS); he is also a man of high integrity and tireless energy. The state of Oklahoma should be proud!

Let’s See, What Exactly Did I Come Here to Do?
Because of the fast pace, long hours and ever changing agenda, it is difficult to remain focused on my goal to benefit the Global Positioning System (GPS) satellite navigation program in some legislative manner. GPS is my professional area of expertise (to which I will return as a Consultant when my tenure as a Science Fellow ends). I have already been involved to some extent with the Ultra Wide Band (UWB) spectrum issue by attending a couple of meetings at the invitation of the Institute for Defense Analysis (IDA). Prior professional contacts at IDA and the Department of Transportation (DOT) have provided me an abundance of relevant material on the UWB subject. This fits well with a forthcoming SASC Readiness Subcommittee hearing on “Spectrum Encroachment” that is in the planning stage, but not yet scheduled. Everyone in the “war room” knows that DoD spectrum issues are in my domain, so I will be in the driver’s seat when it happens. Recently, I attended a 3-day CIA-sponsored seminar in Reston, Va., on the new Chinese BeiDou satellite navigation system, which is identical to (or should I say a “Chinese Copy” of) the U.S. Geostar system that went bankrupt in the late 1980s. I have also attended a three-day top secret meeting on Electronic Support (Navwar) for GPS at the Aerospace Building in Chantilly, Va. As a follow-up to this meeting, I am coordinating a briefing to Rep. Joseph R. Pitts (R-Pa.) on the Navwar program. I believe this will lead to several additional meetings with interested members of both the Senate and House on the subject of Navwar. I have Sen. Inhofe’s attention on the Navwar subject because GPS jamming is a very real vulnerability to this excellent DoD asset and countermeasures are not being adequately funded.

What Does a Congressional Fellow Do?
In addition to my SASC related work, there are many other tasks that cross my desk daily. When the senator is scheduled for an interview on “Crossfire” or similar TV program, if the subject is related to his SASC affiliation, then the “war room” prepares “talking points” on the subject matter. Sen. Inhofe’s staff answers all correspondence including e-mail with an official signed letter from his office. This amounts to more than 400 letters a month. I have written a few responses to letters requiring a “scientific” input and some that just landed on my desk. If the chief of staff or the legislative assistant or the military legislative assistant tasks you to work a problem that requires persistence, you take it on with a smile and, most of the time, it is very enjoyable, especially the people you meet in the name of your member. Naturally, there are constituent phone calls that must be fielded and I get my fair share of these. In the course of these duties, some of which are not scientific, I have interacted with staff members of numerous senators and members of the House, the Congressional Research Service, the Justice Department, and every branch of the service in the Pentagon, with numerous high-ranking as well as ordinary citizen constituents from Oklahoma, and the list goes on. On behalf of our ION D.C. chapter, I volunteered to reserve a reception room at the Russell Senate Office Building (RSOB), where I work, for a meeting on Wednesday, Aug. 15, and made arrangements with the Senate Restaurants Special Events Services to serve light refreshments. Sen. Inhofe was kind enough to make arrangements for a special after-hours tour of our nation’s Capitol with the director of Capitol Guided Tours, Mr. Ted Daniel. All the attendees had the opportunity to take the short ride on the Senate subway between the RSOB and the Capitol!

All Work And No Play? No Way!
There are many enjoyable perks that come with the territory. The AAAS provided an excellent two-week orientation in September 2000, and hosts numerous seminars and social functions for the AAAS fellows. The AAAS fellows, in addition to being talented and well educated, are also a very close-knit and social group of scientists and engineers. But there is more. My wife, Nancy, and I have attended two embassy receptions, one hosted by Sweden and the other by Estonia. Very fancy! We have also been guests at social and professional (lobby) receptions and other forms of evening entertainment related to my affiliation with Sen. Inhofe’s staff. General Dynamics invited me on a Gulfstream IV Executive Jet round trip flight from Washington Reagan to their manufacturing facility in Savannah, Ga. Naturally, there are special agendas for the member’s staff to see and hear at these functions. If I had the stamina and time, I am sure I could find a technical seminar or reception (or both) at noon or evening nearly every workday. There is an unbelievable amount of social and professional activity in Washington, D.C.

Gracias Amigos!
I continue to be very grateful to the AAAS and to the ION Council for their support of the congressional fellowship program. It is truly a unique opportunity in a dimension of life and professionalism that I would not otherwise experience. With the recent change in the Senate majority from Republican to Democrat, I am now privileged to switch from offense to defense, all without changing members or without my member changing Parties. Again, a once in a lifetime experience! I am looking forward to meeting and helping other congressional fellows get well placed. I have already met with our second ION fellow, Dr. Clark Cohen, on two occasions here in DC. I am in a position to help him find a place on the Hill by opening some doors from “the inside” following the forthcoming September orientation provided by the AAAS. With special permission from the Congressional Fellow Committee, Clark will be our first “September start” fellow, so we will overlap six months on the Hill. He is an outstanding selection!

I Have Already Made a Difference
As it has turned out, Sen. Inhofe and his staff very much like the idea of always having an AAAS congressional fellow in addition to always having a military congressional fellow from the Pentagon. In fact, they have expressed their desire for a science fellow interested in supporting his environmental as well as transportation policy areas. I am pleased to say that I am not only the first congressional fellow for the ION, but I am also the first science and technology fellow to ever work for this office.

From Time to Time

By Bill Klepczynski, Ed Powers, Rob Douglas and Pat Fenton

Historically, navigation systems have depended on time. This was clearly demonstrated by the sailing of Harrison’s chronometer on HMS Deptford in 1761, to prove that the instrument allowed navigators for the first time to determine longitude accurately and reliably. Because of this relationship between navigation and time, the time-keeping community has always had a keen interest in the use of navigation systems for the distribution of time. Even today, the heart of the GPS rests on a highly evolved clock technology. Unlike navigators, who need four GPS satellites by which to determine their position, timekeepers, who know their position, need only one satellite to determine time. Observations of a single satellite also allow timekeepers to remotely synchronize clocks around the world.

This article summarizes the result of a recent study, which showed that the GPS Wide Area Augmentation System (WAAS), once fully operational, should provide a very stable, continuously available timing signal. It should also allow the development of more economical timing systems utilizing its signals, the almost instantaneous detection of any pathological behavior in a system providing time, and an extremely robust check for many timed systems. The WAAS is one of the most recent developments in the evolution of navigation systems. While it is similar to other differential GPS systems in concept, the WAAS gives the Federal Aviation Administration (FAA) and air navigation a significantly higher level of performance than other differential GPS (DGPS) systems. Because of the augmentation methods utilized by the WAAS, it provides not only improved accuracy, but also increased availability, integrity, and continuity of service. It does this by continually monitoring GPS transmissions from WAAS Reference Stations (WRSs) and by transmitting an augmented message from several geostationary communications satellites (GEOs). The WAAS is currently in its early stages of development. Current studies on the use of WAAS for time transfer and time distribution indicate that it is already at the level of the GPS Precise Positioning System (PPS). We can reasonably expect improved levels of precision and accuracy as the system matures.

Time and the WAAS
Figure 1 schematically depicts the WAAS process, as it will be once fully implemented. The basic unit is the WAAS Reference Equipment (WRE), consisting of a cesium beam frequency standard, a 12-channel, dual-frequency WAAS-GPS receiver, and a wide- and a narrow-band GPS receiver. Each WRE continuously tracks as many GPS satellites and GEOs as it is able to acquire.

Each WRS contains three identical WREs. This redundancy ensures that each WRS will continue to provide data to its WMS in the event that one of the WREs fails. Each WRS, in turn, transmits the data it obtains to two WAAS Master Stations (WMS), which form the WAAS navigation message and WAAS Network Time (WNT). The message contains information on satellite orbits, the current state of the ionosphere, timing information, and system health. Each WMS passes the navigation message to each of, initially, two Geostationary Uplink Stations (GUSs), which upload it to the two Phase 1 GEOs which then transmit it to the user.

Once per second, all WRSs transmit all their data to all WMSs, which then perform the functions of correction processing, satellite orbit determination, integrity determination, verification, validation, and WAAS message generation, and transmit a formatted 250-bit WAAS message to all GUSs.

WNT Time Scale
In order for the WAAS signal to supplement the GPS navigation signals, the GEOs must synchronize their transmissions with those from the GPS satellites. In other words, WAAS must be on GPS time. The reference for the WAAS is called WAAS Network Time (WNT). Measurements from all WREs at all WRSs are sent to each WMS. The corrections processor at each WMS employs a WNT algorithm to compute a potentially independent WNT time scale from the data received from the WRSs. All “good clocks” contribute to the WRE measurements that a WMS corrections processor receives and uses to form the WNT time scale. This time scale is then steered to GPS time with the same algorithm. Ground Uplink Stations (GUS) will each have a cesium clock, slaved to WNT. Once per day, the WMS will issue commands to steer the GUS clock in order to reduce any offset it may have from GPS time. The GUS clock controls the synchronization of the WAAS navigation message from the GEO.

WAAS Time Distribution
As a secondary mission, the WAAS provides coordinated universal time (UTC). To this purpose, the WAAS compares WNT, which is synchronized to GPS time, with the UTC provided by the U.S. Naval Observatory (USNO), and transmits the offsets as part of the WAAS navigation message.

Status of WAAS Time-keeping
Data collection commenced at USNO on October 6, 1999. Every 15 seconds, GPS and Atlantic Ocean Region-West (AOR-W) WAAS GEO satellites make pseudorange and carrier-phase measurements. All of the broadcast data from the satellites are now collected for postprocessing.

Time Transfer Capabilities
Figure 2 illustrates the computed difference between USNO and GPS system time. We included this difference as a common denominator benchmark process. Most GPS timing receivers today use this observable to provide time reference information. Note that selective availability (SA) caused most of the 43-nanosecond standard deviation. On May 1, 2000, the U.S. Department of Defense (DoD) turned off this intentional degradation and performance has since substantially improved.

These results, at this early stage in the development of the WAAS, indicate the future promise of this technique for time transfer and time distribution.

Future Potential of SBAS
The WAAS will contribute to the timing infrastructure of the U.S. by providing time within the National Airspace System (NAS) for the recording of all events. It will also provide a very stable timing signal for the timekeeping community. Because the source remains at the same approximate point in the sky, a high-gain antenna can provide a very good signal to the stationary user. The offset of WNT from UTC will be transmitted within the WAAS navigation message. The signal will be available continuously.

Such a signal provides some unusual capabilities for the timekeeping community. It should allow the development of more economical timing systems utilizing its signals. Cheaper crystals can now be used in systems that rely on atomic standards as their flywheel while they continuously integrate GPS time or UTC using only one geostationary satellite. A user will be able to instantly detect any pathological behavior in a system providing time by comparing signals with another visible GEO. With GPS, one has to wait to see whether the transients are due to anomalous clock behavior in a satellite. The WAAS, on the other hand, provides an immediate redundancy check to anyone who is within the footprint of its two transmitting geostationary satellites. This can be used as an extremely robust check for many timed systems.

—W.J. Klepczynski, GPS TAC/WAAS Team (and 730); Ed Powers, United States Naval Observatory; Rob Douglas, National Research Council of Canada; Pat Fenton, NovAtel WAAS Master Stations

57th Annual Meeting Report

June 2001, Albuquerque, New Mexico

Attendance at the ION 57th Annual Meeting and CIGTF 20th Biennial Guidance Test Symposium in June neared the 350 mark. More than 120 technical papers were on the program at the three-day meeting held at the Crowne Plaza Pyramid Hotel in Albuquerque, New Mexico, June 11–13.

The technical program was highlighted by both a plenary session that provided up-to-date perspectives on GPS Utilization, Modernization and Galileo, as well as two well attended classified sessions on GPS Jamming/Vulnerability, Antijam and Emerging technologies.

Dan Crouch, USAF/TER was general chair, and Dr. Chris Bartone, Ohio University, served as program chair. Many thanks to all those who volunteered their time and talents to help make this meeting a success.

Annual Awards

Presented at ION 57th Annual Meeting

Portney's Corner: Mayday ... Mayday! Courtesy of Litton Guidance and Control

“Mayday, Mayday … ”
This message of a pilot in distress on radio three days before Christmas 1978, is heard by Auckland ATC. The saga of how Jay Prochnow was finally located by the innovative navigational techniques of Captain Gordon Vette, aided by Malcolm Forsyth, both of Air New Zealand, Auckland ATC, Norfolk Island, and the crew of the Royal New Zealand Air Force (RNZAF) Orion is made into a Brain Game. The Penrod, a towed oil rig with running lights, served as a beacon that enabled Captain Vette to rendezvous with Jay Prochnow.

The Sun reached its highest ascension December 21, 1978, at the winter solstice (summer in the Southern Hemisphere) and the very next day Jay Prochnow (a former U.S. Navy pilot), piloting a Cessna 188 AgWagon, found himself lost. He was ferrying the Cessna from Pago Pago to Norfolk Island. With a failed ADF and an overdue ETA, he was deeply worried.

Prochnow began an expanding square pattern hoping to find Norfolk Island before the fuel ran out. Captain Gordon Vette in command of an Air New Zealand DC-10 (equipped with three inertial navigation systems), believed to be near the Cessna, was enlisted by Auckland ATC to help locate the lost Cessna. Vette, a qualified navigator, contacted Prochnow and asked him to head toward the Sun and to report his magnetic heading. Prochnow pointed the Cessna to magnetic heading 274 degrees as Vette steered his DC-10 toward the Sun and read his magnetic heading as 270 degrees. Next, Vette instructed Prochnow to determine the elevation angle of the Sun above the horizon using his partially outstretched arm and fingers as a sextant. Prochnow established the elevation of the Sun as four fingers as Vette measured the elevation of the Sun as two fingers. Vette estimated the Cessna was about 240–250 nmi from the DC-10 (each finger was slightly more than 2 degrees with each degree worth 60 nmi). Vette was then able to get within VHF boxing range of Prochnow in 7 or 8 minutes. Prochnow was directed to fly east toward the DC-10. The Sun began to set. Norfolk Island and Prochnow were both instructed to note the time that the upper limb of the Sun sank below the horizon. With this information, the results of VHF radio reception (contact/loss) and the time of sunset comparison observed at Norfolk Island and the Cessna, the Cessna’s position was determined to be within 290 miles of its destination. Rendezvous over a towed ocean rig refined the position and Prochnow was directed to a heading to intercept Norfolk Island.

We may conclude that the Cessna was at which location?
A. Northeast of the DC-10 initially and located by using sunset tables adjusted for altitude and VHF reception.
B. Southeast of the DC-10 initially and located by using sunset tables unadjusted for altitude and VHF reception.
C. Southwest of the DC-10 initially and located by using sunset tables adjusted for altitude and VHF reception
D. Northwest of the DC-10 initially and located by using sunset and declination tables adjusted for altitude and VHF reception

In constructing this ponderable, certain liberties were taken regarding details of air-to-ground-to-air coordination. However, the concepts of location finding portrayed are based on the valid techniques employed by the DC-10, Norfolk Island, Aukland ATC, and the Cessna. Space limitations prevent including all the details of the crisis confronted by Prochnow and all the refinements employed in the search in this article. Since the heading of the Cessna to the Sun was 274°, it was greater than the 270° heading to the DC-10, as shown in Figure 21. Since the elevation angle of the Sun measured by Prochnow was higher than that established by Vette, the Cessna was closer to the Sun or west of the DC-10, as shown in Figure 22. Thus, the Cessna was southwest of the DC-10. Using the Communication Link Vette recognized that the VHF communication link could be exploited to locate the Cessna. He requested that the Cessna orbit as he raced through the VHF range circle which had a radius of about 200 nmi, as depicted in Figure 23. A map of the region, courses, and events is depicted in Figure 24. Captain Vette reasoned that if he marked the points at which he established and lost contact with the Cessna, he could find the location of the Cessna. He knew the diameter of the VHF range circle was 400 nmi. He flew his DC-10 along track 1-2, as depicted in Figure 25. He acquired VHF contract at point 1 and lost VHF contact from the Cessna at point 2 (marking the point), at which time he turned 90° left and began his aural box pattern. After flying on this new leg for a reasonable period, he turned 90° left for a short period followed by another 90° turn to the left and at point 3 he regained VHF contact with the Cessna (as he marked his map). He continued through point 4 where he lost VHF contact with the Cessna. Using the intersection of the perpendicular bisectors to the two chords flown within the VHF range circle, Captain Vette established the center and the location of the Cessna. The Cessna, however, was not immediately found. Earlier, the DC-10 had dumped to leave a trail which was not seen by Prochnow. Captain Vette recognized that one can determine the difference of longitude between Norfolk Island and the Cessna by noting the GMT of sunset at the two locations. Norfolk’s local time was 1900 for this event. The Cessna’s time was reduced to sea level (as Prochnow would see sunset later owing to his altitude and his eastward displacement from Norfolk Island). The difference between the times in GMT for sunset at the two observations was 22.5 minutes which corre-sponds to 5.6° longitude (a degree is equal to 4 minutes in time). Norfolk’s coordinates were latitude 30°S, longitude 168°E. This would place the Cessna at longitude of 173.6°E, 291 nmi east of Norfolk (5.6° x 60 nmi/deg x cos 30°). Prochnow was directed to fly northwest during this interlude as he was regarded as being southeast of Norfolk Island. A RNZAF Orion was dispatched to help find the Cessna which had been airborne for 20. 5 hours and now had minimum fuel remaining. Continued plotting by the navigators showed that the Cessna was approximately at 30°S, 171°E. Prochnow soon saw a light on the water’s surface. Prochnow found an oil rig under tow whose coordinates (31°S, 170° 21’E) were relayed to the DC-10 and enabled a rendezvous with the Cessna. The Cessna was less than 150 nmi from Norfolk and was given a steering direction by Vette of 294° magnetic heading to Norfolk Island. The Cessna landed safely after being airborne 23 hours and 5 minutes arriving at close to midnight 8 hours beyond its 1600 ETA. Prochnow had stretched the Cessna’s 22 hours of fuel by 5 percent through cruise control. Sources of Error Aural Boxing. Aural boxing depends on continuous transmission on VHF, otherwise a silence can be construed as loss of contact. To be accurate the acquisition and loss of Prochnow’s VHF transmissions would have to be accurately noted. There could be timing errors in this procedure in noting these events (30 seconds error in the same direction on each end contributes to 10 nmi error at 600 knots groundspeed).

Sunset observation.
Accurate determination of longitude by observing time of sunset requires knowledge of latitude. By observing sunset and noting the time in GMT one may determine longitude by assuming a latitude of the site.

The Local Mean Time of sunset changes 13 min/5°latitude in this region of 30° latitude. Therefore, an error or 1° latitude contributes to 2.6 minutes in time error, which is 2.6 min x 1°/4 min or 0.65° of longitude uncertainty or 0.65° x 60 nmi/° xcos 30° or 0.65x60x0.866=33.8 nmi error in longitude, which demonstrates that determining longitude by assuming a latitude is very sensitive to the latitude assumption.

Afterword
Captain Vette dumped fuel when he thought he was within visual contact of the Cessna. He believes that the Cessna’s opaque canopy prevented Prochnow from sighting the DC-10. Vette concluded that his dump position was behind the Cessna as verified from his inertial navigation coordinates and an HF line of position.

Pondering Portney's Ponderables

A Letter to the Editor

Editor’s note: The following response was prepared by Joe Portney to address comments received by Mr. Portney and the Institute of Navigation from Dr. Fiona Vincent of the University of St. Andrews and from Dr. John Ponsby of the UK.

In late May, I received a shorter derivation for deriving latitude for the one-body fix from Dr. Fiona Vincent of the University of St. Andrews. She had seen the puzzle prior to its publication in the ION Newsletter Spring 2001.

Her derivation (using simplified notation) followed ours to: cos (h) dh/dt = -cos(L) cos (d) sin (t) and then went directly to the Astronomical Triangle II ending with cos (L) = dh/dt csc (Zn). We congratulate her for the shorter solution. Unfortunately, it was too late to include in the ION newsletter. We show it here ( simplified notation):

from
cos(h) dh/dt = - cos(L) cos(d) sin(t)

apply the sine rule directly to “the” astronomical triangle (triangle II):
sin(t) / sin(90-h) = sin(Zn) / sin(90-d)
so sin(t) cos(d) = sin(Zn) cos(h)

Substituting the RHS of this equation for the terms on the LHS, into the equation above, gives:
cos(h) dh/dt = - cos(L) sin(Zn) cos(h)
so dh/dt = - cos(L) sin(Zn)
or cos(L) = - dh/dt cosec(Zn)

We are indebted to Dr. John Ponsonby for this contribution. (Joe Portney’s response is in italics.) Dr. John Ponsonby found that Figure 1 in the Lost Sub puzzle in the Spring issue of the ION Newsletter (Vol. 11.1) was in error in that arc ZQ’ was not 90° as implied: the sum of arcs (90°-h) + (h). This is true as the Arc ZQ’ spans a distance greater than arc PnQ’ (=90°) and less than arc QQ’ (=180°) since Z is shown to be on the 180° meridian and Q’ to be on the Greenwich meridian. The remedy is to portray the astronomical triangle with either of its two meridian arcs or both moved inward as seen in the revised Figure 1 furnished by the author or as Dr. Vincent did go directly to triangle II (deleting lower triangle I). Dr. Ponsonby also noted that the derivation incorrectly referred to triangle PnQ’m as triangle I. Furthermore, he noted that the law of cosines were erroneously type set. This error resulted from an undetected wrap around of two equations and the omission of the word therefore between the two equations. The equations, with type set error corrected, should read as follows:

cos (90°- h) = cos (90°- L) cos (90°- d) + sin (90°- L) sin (90°- d) cos ( t)
therefore
sin (h) = sin (L) sin (d) + cos (L) cos (d) cos (t)

In the last equation on page 15, he further noted the = symbol should have been a +. This was owing to a type set error where the shift key was not activated for the plus/= key.

Dr. Ponsonby noted that the cosine function cannot decide the sign of the latitude. But the navigator clearly knows the hemisphere in which he is and the answers to select from are all in the northern hemisphere.

We shared Dr. Vincent’s shorter derivation With Dr. Ponsonby
Dr. Ponsonby rightly pointed out that the lower triangle could be eliminated from the derivation and provided his own solution based on the upper triangle (triangle II) arriving at the same cos (L) = dh/dt csc (Zn) and ending with Longitude l = sin -1 [ cos (h) sin ( Zn ) sec (d) ] + GHA sun .

Here we have assumed that the quantities dL/dt & dd/dt (in the intervening steps of the derivation) are negligible though of course the sun for certain and the sub in all likelihood are moving in declination/latitude. The declination of stars changes negligibly on the order of an arcminute per year. The declination of the Sun during the equinoxes changes at the rate of an arcminute per hour hardly a reason for concern and at the solstices there is no change. Motion of the observer corrections in latitude can be made if movement is significant.

The observer can measure dh/dt by timing how long it takes the sun to set, from first contact with the horizon to final extinction. He can also measure Zn, though he needs it rather accurately. He had better have a good compass or be able to use the pole star. Given these two observed quantities he can use cos (L) = -dh/dt.cosec(Zn) to obtain his latitude L.

Inertialy stabilized quality bearings (within arcminutes) obtained from the body are required to achieve reasonable accuracy. In this puzzle, the observer knows that the Sun sets due west (within arcminutes) as it is on the equinox.

When the sun is setting h=0 degree nominally, though in reality there should perhaps be a correction for refraction (the apparent sun disappears later than the true sun) so cos(h)=1. He knows the true time of course, so his almanac gives him the GHAsun and the declination of the sun d. Using these he can evaluate l =sin -1 [cos(h).sin(Zn)/cos(d)] +GHAsun to obtain his longitude l. Here we note the elapsed time of the transit of the Sun’s disk through the horizon: measured from the moment the lower limb of the Sun touches the horizon until the upper limb disappears below the horizon. The refraction correction is for the same elevation value of 0°, the contact elevation of either limb with the horizon, and therefore is self canceling. In solving for longitude based on sunset, the practice in emergency navigation is to compare the GMT at local observation of sunset for the same tabulated latitude to the GMT at sunset on the Greenwich meridian (found in almanacs). The difference in times noted multiplied by 15° / hr yields longitude.

Joe Portney’s Added Note
The configuration of the astronomical triangle for the unique case of the lost sub during Sunset on the equinox is shown in Figure 2. Both the declination of the Sun and its elevation are 0º. Visualize the submarine projected to its zenith Z, its horizon would be contained in its tangential plane projected downward perpendicular to the plane passing through ZMO (where O is the center of the celestial sphere) and intercepting QQ’ at M.

From the ION Historian The Shape of the Earth: Part 1

Perhaps the most fundamental concept of terrestrial navigation and its sister science, geodesy, is the knowledge of the shape of the Earth. Man’s quest for its quantification is a continuing saga of fitful steps. This article, and its sequel, documents some of the major events and contributors, and also some of the backward steps.

The first person recorded as saying the Earth is spherical was the Greek philosopher Pythagoras, who lived in the 6th century B.C. Although he realized the importance of mathematics in describing the universe (the famous Pythagorean Theorem is attributed to him), Pythagoras was not a rigorous scientist. He supported his statement that the Earth is spherical with the semi-mystical reason that the sphere is the “perfect shape,” and that the Earth must therefore be spherical.

Aristotle’s Theories
The philosopher-scientist Aristotle, who lived in the 4th century BC, was the first to give reasons why the Earth is spherical. He supported his statement that the Earth is spherical with three pieces of directly observed evidence.

1. Matter is drawn to the center of the Earth by gravity. This tends to compress the Earth into a spherical shape. (This is the weakest of Aristotle’s arguments; rock is stiff, and is able to resist the tendency to be compressed into a sphere.)

2. As you move from north to south, new constellations are seen rising above the southern horizon. For instance, the Southern Cross is invisible from far northern latitudes because it is hidden by the outward bulge of the spherical Earth. (The Southern Cross appears on the flag of the southern country of Australia.)

The Big Dipper is similarly hidden from far southern latitudes. (The Big Dipper appears on the flag of the northern state of Alaska.) (This is a stronger argument, but still only proves that the Earth is curved in the north-south direction, not in the east-west direction.)

3. During a lunar eclipse, the Earth’s shadow on the Moon is always round. The only object whose shadow is always circular — no matter what its orientation — is a sphere. (This is the strongest of Aristotle’s arguments.)

During the Middle Ages, Aristotle was the standard scientific authority in the Christian and Muslim worlds. Literate individuals (who were, of course, a minority at the time) believed Aristotle’s statement that the world is spherical. The Divine Comedy, for instance, written by Dante in 1300 A.D., makes the basic assumption that the Earth is a sphere—an assumption that Dante shared with all his readers. Not only did ancient and medieval astronomers know the shape of the Earth (starting with Aristotle around 350 B.C.), they also knew the approximate size of the Earth (starting with Eratosthenes around 200 B.C.).

The Assumptions of Eratosthenes
Eratosthenes was the head librarian at the famous Library of Alexandria. He was able to determine the size of the Earth without ever having to leave the city of Alexandria (in northern Egypt). Eratosthenes read, in one of the many scrolls contained in the Library of Alexandria, that at noon on June 22 (the time of the Summer solstice), in the town of Syene, the Sun is at the zenith, directly overhead. (Syene is the modern city of Aswan, located south of Alexandria on the banks of the Nile.)

The next time June 22 rolled around, Eratosthenes stepped outside, and determined that the Sun was NOT directly overhead as seen from Alexandria, but was 7.2 degrees south of the zenith (the point directly overhead). Eratosthenes was able to use these observations to determine the size of the Earth, but only if he made a few assumptions first: The Earth is spherical—this had been known since Aristotle had figured it out a century and a half earlier. The Sun is very far away, compared to the size of the Earth—this implies that a ray of sunlight striking Alexandria and a ray of sunlight striking Syene are essentially parallel. Alexandria is due north of Syene — this isn’t exactly true, but it only introduces a minor error into the result.

Using his observations and assumptions, Eratosthenes made the diagram shown. A ray of sunlight strikes Syene perpendicular to the ground. A parallel ray of sunlight strikes Alexandria at an angle of 7.2 degrees from the perpendicular. The laws of geometry (as compiled by Euclid, a century before the time of Eratosthenes) tell us that the angle from Alexandria to the center of Earth to Syene must also be 7.2 degrees.

Eratosthenes said at this point, “Seen from the center of the Earth, Alexandria and Syene are 7.2 degrees apart; that’s 1/50 of a complete circle. The distance between Alexandria and Syene, as measured on the surface of the Earth, must then be 1/50 of the complete distance around the Earth.” To find the circumference of the Earth, Eratosthenes simply had to find the distance between Alexandria and Syene and multiply it by 50. The road from Alexandria to Syene was a well-traveled trade route, and the Alexandria-Syene distance was well known: The distance from Alexandria to Syene is 5000 stades. The circumference of the Earth is 50 x 5000 = 250,000 stades.

Olympic vs. Egyptian Stade
The stade was a common unit of length in the ancient world. Unfortunately, the length of the stade varied from place to place. The most commonly used value was the Olympic stade of 0.185 kilometers (corresponding to the length of the foot races run at the ancient Olympic games).

If Eratosthenes used the Olympic stade, he found a value for the circumference of 46,250 kilometers (15 percent longer than the true value of 40,000 kilometers). However, since he was in Egypt, he might have been using the Egyptian stade of 0.157 kilometers. This would have given a value for the circumference of 39,300 kilometers, only 2 percent smaller than the true value. No matter which stade Eratosthenes was using, he came remarkably close to the truth.

The Alexandria Library contained all important ancient works. Its destruction in the fire in the third century A.D. resulted in backwards steps in man’s knowledge of the shape of the earth. At the end of the Middle Ages, most advanced thinkers, including explorers like Chistopher Columbus, rejected flat Earth theories and accepted the Earth’s shape as spherical. The interesting part about the Christopher Columbus saga is not that Columbus was right about the shape of the Earth, but that he was wrong about its size. Eratosthenes was lucky to get the size of the Earth so accurately—the errors in his measurements just happened to cancel each other out. Other astronomers, after Eratosthenes, made similar calculations with similar data and got values as small as 30,000 kilometers or so and as large as 50,000 kilometers. Columbus wanted to sell people on the idea that the journey westward from Europe to Asia was a short one. Thus, from all the values published for the circumference of the Earth, he picked the smallest one: 30,000 kilometers. A small Earth means a short journey. From all the values published for the distance eastward from Europe to Asia, he picked the largest one. A long journey eastward means a short journey westward. Columbus was basically picking and choosing from the available numbers to support his preconceived notions. The end result: Columbus computed the distance westward from the Canary Islands (his jumping- off point) to Japan as being only 4000 kilometers. The actual value is 20,000 kilometers. What saved Columbus from becoming fish food is that the Bahamas are about 4000 kilometers west of the Canaries. Columbus had convinced himself that Asia was only 4000 kilometers west of the Canariesthus, when he discovered land in that position, he stubbornly clung to his belief that he had landed on islands lying just off the coast of Asia, even during his three subsequent journeys to the New World.
Happy Columbus Day!

—Most of this article was excerpted from a lecture of Professor Barbara Lyden of Ohio State University. See the next newsletter for Part 2 of The Shape of the Earth.

NEW ENGLAND SECTION
The New England Section held its twenty-first meeting at the Volpe National Transportation Systems Center, Kendall Square, Cambridge, Mass. A presentation on “Planned GPS Civil Signals and Their Benefit to the Civil Community” was given by Dr. A.J. Van Dierendonck of AJ Systems. The presentation detailed how the new civil signals will greatly benefit the diverse civil community and how the new receivers using the new signals will perform significantly better.

WASHINGTON, D.C. SECTION
ION Congressional Fellow Phil Ward arranged for the Washington, D.C. Section to hold its business meeting and reception in the Russell Senate Office Building. The meeting, held August 15, 2001, included a special private tour of the nation’s Capitol.

Cadets Honored

New ION Congressional Fellow Named

New Corporate Members _____________________ The ION extends a warm welcome to the following new Corporate Members: Fastrax Ltd., Vanta Finlandia Korea First Microwave Co., Ltd., Seoul, Korea Loran Support Unit, Wildwood, N.J. Sigtec Navigation Pty Ltd., Australia Skyguide (Swiss Air Navigation Services), Zurich, Switzerland

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