This article first appeared in Spanish on 20/2/2020.
This revised English version first appeared as a guest publication on Scottish Watches on 2/3/2020.
Today, I want to present a prized piece within my collection: the Longines Lindbergh Hour Angle, specifically the limited edition brought out to commemorate the 90th anniversary of the first transatlantic solo flight, successfully completed when Charles Lindbergh landed in Paris on May 21, 1927.
I usually prefer to look into the background of a watch and then examine the piece itself. In this case, however, I think it more logical to do the opposite, as this watch has an unusual complication: the ability to calculate the hour angle and, thus, longitude. It goes without saying that the explanation of this function is quite complex…
In addition, we have to acknowledge the plain fact that, firstly radio beacon triangulation, then inertial navigation systems, and most recently GPS, have rendered totally obsolete the functionality for which this watch was designed. Its value, therefore, lies in what it represents in historical terms. It is a unique watch with a unique complication designed by someone who achieved a unique aviation feat.
At Baselworld 2017, as is the custom, various anniversaries within the sector were commemorated. Amongst these was the 90th anniversary of Charles Lindbergh’s historic transatlantic solo flight in the “Spirit of St. Louis”, which was timed by Longines (33 hours, 30 minutes, 29.8 seconds, if you’re interested). To celebrate this occasion, the brand launched a 90-piece limited edition of the Lindbergh Hour Angle. Without further ado, I present the watch in the following carousel of images.
This version is faithful to the original 1931 watch in certain aspects. The design of the dial and bezel, which we will explain later, follows the original. So does the size of the watch, at 47.5 mm in diameter, without the crown. This onion-type crown is also faithful to the original, in both shape and size. However, there are important differences. The silver and black finish of the dial, the polished hands, and the black PVD bezel are new features. So is the titanium case, which obviously helps lighten the weight of a piece of this scale. Finally, the limited edition relinquished the “hunter” style case-back cover. Below we show the 90th anniversary piece and the non-limited version together to illustrate clearly these differences.
Apart from the reduced legibility of the new design, what purists criticised most when this variation was launched was the change to the case back of the watch (i.e., the loss of the hunter cover). They missed the engraving that was on the interior of the hunter cover, even though there is an equivalent engraving on the case back of the limited edition. They also criticised the fact that it was now impossible to see the caliber (this is an unusually large watch with an unusually large caliber; the hunter cover allowed watch aficionados to experience this ‘element of surprise’). Eliminating the hunter cover obviously reduced the height of the watch, and also its weight. Perhaps it was not possible, or practical, to add this mechanism to a small production run of the titanium cases.
In this image you can see the tradicional protective hunter-style caseback.
While the following image shows the caseback of the 90th anniversary limited edition.
Before I explain the operation of the hour angle complication, I want to review other features of the watch, in addition to relating my experience of it.
As a commemorative piece, the watch is presented very carefully. It comes in a large outer cardboard box that protects the beautiful wooden box inside. This second box has a leather clasp; inside is an engraved plate commemorating the anniversary, the watch documentation, a replica map and an extension strap to allow the watch to be worn over a flying jacket. A nice gesture, albeit a useless one in this day and age.
The watch incorporates a modern automatic caliber, the L699, based on the ETA A07-111, which in turn is based on the ETA-7750. This movement has a diameter of 36.6 mm, 24 jewels and vibrates at 28,800 bph. It has a power reserve of 46 hours. The crystal is sapphire with an anti-reflective coating on the inside. Its bezel is bi-directional, appropriate for its function. The watch is only water resistant up to 3 ATM, in other words, you must be careful and avoid wetting it.
The case measures 25 mm between the lugs. This causes problems with finding alternative straps. The original strap is very good quality, in a slightly odd brown colour, but it has a very nice texture and is very supple. I usually replace the straps on my watches to preserve the originals; in this case, I had to order a custom hand-made strap of high-quality grey leather from Zaid Made.
If I am totally honest, I don’t wear the watch often. Although my 17.5 cm wrist can handle the size, there is no denying it is a very large piece. In addition, legibility is clearly a problem on sunny days, of which Mallorca, where I spend long periods, has many. And most importantly, this is a collector’s item and I treat it as such.
Having said all that, the titanium case makes the watch surprisingly light for its size, and the width of the strap and curved lugs make it very comfortable to wear. The problem is finding the occasion to wear it, as I tend to treat it so carefully whenever I do.
Explaining The Fundamentals
In this section I propose to explain the theory behind the watch’s complication. Essentially, it enables the wearer to determine the longitude of their position, which requires certain knowledge of celestial navigation. For the nerdier among you, I have provided further references in the footer…
The predecessor of the Lindbergh Hour Angle is known as the Weens Second-Setting Watch, designed by Captain Philip Van Horn Weems, an officer of the US Navy and a pioneer of modern navigation. Its purpose was to correct for the difference between the indicated seconds on the watch and the actual time, received via radio signals. A few seconds here or there are not important in everyday life, but when navigating over long distances, these inaccuracies can introduce significant errors and lead to danger. Its main component is a rotating central ring, which allows a kind of hacking whilst the clock is running. In 1929, Captain Weems, alongside Wittnauer (essentially Longines US at the time), developed this piece, which is still marketed, as shown in the following image. The inner ring is rotated by pulling out the crown to the first position.
One of the great lessons learned by Lindbergh during his transatlantic voyage in 1927 was the need to determine his position the minimum number of times and as accurately as possible. There is a famous mantra among pilots: “aviate, navigate, communicate”, which establishes the clear order of priorities in flight. The first is, always, flying the plane; navigation, especially if you are flying alone, is a distraction. With this in mind, Lindbergh got to work to improve the design of the Weens watch and presented Longines with a draft drawing, which was turned into reality in 1931.
Thus, the Lindbergh Hour Angle was born, a watch able to determine longitude based on the hour angle difference between the user’s position and Greenwich. In order to do this, three things are required. First, the watch must be set to display GMT, which is transmitted via radio. Second, a nautical almanac is required to establish the Equation of Time (see the next paragraph) adjustment on the date on which the measurement is taken. Third, an understanding of the relationship between time and longitude is needed. Basically, each hour difference between Greenwich Mean Time and local time corresponds to 15 °, as 15 ° multiplied by 24 hours is the 360-degree circumference of the planet. This means that every four minutes represents one degree of longitude. In turn, 60 seconds represents 15 minutes of arc.
The watch also allows for the necessary adjustments arising from the Equation of Time, i.e., the difference between solar real time and what we call “mean time”, or the 24 hours into which, by convention, we have divided days. These differences arise from the orbit of the planet not being a perfect circle. This affects the speed of orbit around the Sun (if not, the Earth would go out of orbit, which would not be a good thing). The second factor is the movement of the Sun within the galaxy itself, which from our perspective is influenced by the inclination of the Earth’s axis. Because of all this, there are only four solar days in the year that last exactly 24 hours; all the other solar days have a different duration, from 16 minutes, 25 seconds less up to 14 minutes, 15 seconds more. (1)
Although some high-end watches incorporate an Equation of Time complication, it is usual practice to look up the differences between civil time and solar time in nautical almanacs, regular publications containing astronomical information used in navigation. The first is from 1702, published in France and known as the Connaissance Des Temps. In Great Britain, the Nautical Almanac has been published annually by HM Nautical Almanac Office, ever since the first edition in 1767. In Spain, the Naval Observatory in San Fernando, Cadiz, began publishing its Nautical Almanac in 1792. From 1911, following an astronomical ephemerides conference held in Paris, it was agreed that the calculations were to be shared among the observatories in Berlin, Greenwich, Paris, San Fernando and Washington, an international system of cooperation which remains in force. (2)
In 2017, Longines posted a video, briefly explaining how to use the watch. The video is attached below.
Below I include a series of images with the key stages taken from the video. Further below, I attempt to determine the longitude of my position using my watch, which is quite difficult because of my proximity to the Greenwich Meridian.
The first step involves the use of a sextant to determine latitude. This step in itself is complex, requiring knowledge of celestial navigation and how to use the instrument. Furthermore, once the Sun’s height is recorded, alongside an exact time for the measurement, the recorded measurement needs to be corrected to allow for several factors (instrument error, the position of the observer, atmospheric refraction, etc.), with the aid of tables.
Assuming we know our latitude, the next step is to determine the hour angle of solar noon at Greenwich. We know when civil noon occurs as we can synchronise the watch via radio signal (in 1931, at least; now we can also just look at our phones). The bezel of the Lindbergh Hour Angle can be rotated to reflect any necessary Equation of Time adjustment for the date of the measurement, as indicated in the nautical almanac, and the hour angle can thereafter be read off the watch.
Now let’s work out a specific example.
Let’s assume that at my location (on February 19, 2020) the latitude was 39.8 ° N. Note that this is not the true latitude, as you would be able to pinpoint my house… However, in terms of longitude, which is what concerns us today, I promise to be more precise.
The almanac shows that the adjustment of the Equation of Time is 13 minutes and 51 seconds at noon on this date. This basically tells us that on February 19, 2020, solar noon in Greenwich occurred at 12:14 GMT.
With this information, the bezel is rotated 14 minutes to the left until the number 15 (remember the 15 º per hour) on the bezel coincides with the number 46 marker on the minute rail track. From here we can directly read the hour angle. The hour hand (at 12:00 GMT) points to the number 180 under the number XII hour marker. We can use 180 º or 0 °. For East longitude choose 0 º. For West longitude choose 180 º. The minute hand points to 3 º and 30 ‘ on the bezel. In principle, the hour angle is the sum of both, i.e., 3 º 30 ‘ 0 “.
We can fine tune this further. Returning to the almanac, the correct offset of the bezel should have been 13 minutes and 51 seconds, not 14 minutes, although in practice achieving such precision on the watch is impossible. It is best to go for round numbers, and then adjust for any missing or excess seconds. Since we know we turned the bezel too far, we can subtract 9/60 (0.15) of the rotation of the earth that occurs in a minute, which is equivalent to the aforementioned 15 minutes of arc, resulting in 2 minutes and 15 seconds that we need to subtract.
It is also possible to determine this visually using the Hour Angle watch. With the crown in the first position, the inner ring can be rotated so that the 60-seconds marker is aligned with the 9-minute marker on the minute rail track. It is advisable to imagine the seconds hand extending through these two points towards the bezel. The difference between the bezel marker at XII and that at the 9-minute marker is 2 ° 15 ‘. However, we are now dealing with a per-degree scale, so this represents a scaled 2 ‘ 15 “. Alternatively, we can simply read this from the minutes of arc scale that is contained within the rotating inner ring, where each four seconds represents a minute of arc. The 9 happens to be one-quarter of the way between the 2 and 3 markers, i.e., it is at 2 ‘ 15 “.
Following this adjustment for seconds, we can obtain an even more accurate measurement of the hour angle at Greenwich at solar noon, which in this case is 3 ° 27 ‘ 45 “.
All this can be determined even when the watch indicates a different time. All we need to do is shift the bezel to the offset indicated by the almanac and picture the hands at the XII position.
The next step is to determine solar noon at my location. In my case it happens earlier than at Greenwich because I am in Mallorca and therefore East of the Greenwich Meridian. The Sun will be at its highest point (solar noon) earlier at my location than at Greenwich. If I had been in the middle of the Atlantic Ocean, this would obviously happen later, although the technique used would be the same.
Using a sextant, it is possible to determine GMT solar noon at my location. If I don’t happen to be enjoying myself on a boat, the sextant can still be used on land to determine the maximum height by using any horizontal object as a reference point. The height measurement would be inaccurate, but what interests us here is timing the event. There is also a much more rudimentary way to go about this, what I would call the Bear Grylls’ way. You can observe the shadow of an object (a stick positioned vertically, for example) and determine when it is at its shortest, which should occur when the Sun is at its highest point of the day. You need to note the time when this happens. In practice, you need to take several measurements and the time when they occur, and extrapolate to find the right answer. For example, a way of achieving this is to mark the boundary of the shadow on a piece of paper at set time intervals. This would give us a curve; our objective is to identify the shortest shadow indicated by this curve, and when this occurs.
In my case, the minimum shadow occurred yesterday at about 12:02 GMT; an hour more in local time. Happily, it was earlier than at the Greenwich Meridian, as predicted. All’s right with the world, as the poet once said.
As we are trying to determine solar noon it is not necessary to adjust for the Equation of Time at this stage. Therefore, we simply return the bezel to its original position and read off it. The hour hand indicates 0 ° (or 180 °, whatever convention we have chosen) and the minute hand points to the 30 ‘ bezel marker, i.e., the hour angle at solar noon at my location is therefore 0 ° 30 ‘ 0 “. If I were able to determine the time of solar noon at my location more accurately, i.e., including seconds, I could refine this hour angle further. This measurement can be taken at any longitude. The only important thing is that the watch must be set for GMT at solar noon.
Once we have both hour angles, we simply need to subtract the hour angle of the solar noon that occurs first, from the hour angle of the one that occurs later, and in this case we obtain a difference of -2 ° 57 ‘ 45 “, or in other words 2.9625 ° E. If we were West of the Greenwich Meridian, solar noon would happen later and the subtraction would yield a positive figure, indicating West longitude.
There is another way to calculate longitude that is easier but considerably less accurate. We would simply subtract 12:02 (the estimated solar noon at my location) from 12:14, the indicated solar noon at Greenwich, according to the nautical almanac. The result is 00:12, a fifth of an hour, which you will recall represents 15 ° of rotation of the Earth. 15 ° divided by 5 gives 3 °. Since our solar noon is earlier than the one at Greenwich, we know that these are degrees East longitude.
My location has an actual longitude of 2.9125 ° E. Therefore, the calculation error is 0.05 °. At this latitude, this represents about 2 nautical miles (4 km, roughly).
It is also noteworthy that the solar noon at my location on February 19, 2020 happened exactly at 13:02:06 local time, according to the solar calendar that you can find via this link. This deviation of six seconds relative to the time that I used in my calculations represents an inaccuracy of 1 ‘ 30 ” of error (0.025 °). Had I been able to determine the time of the solar noon with this level of precision, I would have estimated the longitude of my location to be 2.9375 ° E, a point that is a mere 2 km away from my actual location. I trust that you can appreciate that flying over the vast Atlantic Ocean a 2 km margin of error represents an excellent degree of situational awareness.
In short, no matter how outdated this method is, it is clear the watch fulfils the objective that it was designed for: easily and accurately determining the longitude of one’s position at solar noon.
In this post I have not addressed the history of the watch, which has gone through many editions as well as various case sizes. The following link from Your Watch Hub presents a very detailed account of this history, which I cannot improve upon, so I refer you to this page if you want to investigate further.
The facts are what they are and, nowadays, GPS and other electronic navigation aids make celestial navigation techniques unnecessary. In addition, computers, tablets, mobile phones and calculators can determine, on the fly and in a very short time, the position of the stars. Therefore, I would even speculate that the days are numbered for the paper versions of nautical almanacs, an outcome that would be logical, but in my view, quite sad.
Despite the great historical interest that this piece evokes, due to who designed it, and the unique functionality that it offers, this watch no longer has any practical application. Its value, therefore, is as a museum piece. I appreciate it precisely because of what it represents. As a collector of aviation-related watches, the Lindbergh Hour Angle will always occupy an important place in my watch box.
1 The following in-the-sky.org link contains the most complete description that I have found about the Equation of Time, which also happens to be written in plain language.
2 Source: https://en.wikipedia.org/wiki/Nautical_almanac
A nautical almanac is a publication describing the positions of a selection of celestial bodies for the purpose of enabling navigators to use celestial navigation to determine the position of their ship while at sea. The almanac specifies for each whole hour of the year the position on the Earth’s surface (in declination and Greenwich hour angle) at which the Sun, Moon, planets and first point of Aries is directly overhead. The positions of 57 selected stars are specified relative to the first point of Aries.
Well done Adam!
Yo también te quiero. 🙂