max ebb: star power

How hard could it be? The GPS displays the position, the digital weather files predict the wind and current, and the routing software knows the polars and optimizes the route. So when a friend of a friend asked if I was available to navigate an ocean race on the East Coast, of course I said yes. All I had to do was push the buttons and take the credit. It was a long flight, a long taxi ride, and a long trip in the yacht club launch. It was overcast, raining, and almost dark when we finally found the right boat in the mooring field. "What's with this rain in the summer?" I complained after stowing my gear and introducing myself to the crew. "Don't worry, it's predicted to clear up a day after our start, so we'll have clear skies for star shots," assured the owner and skipper. "And now that you're here, let's get started with the pre-race briefing."

This was the first indication that we were entered in the Celestial Only Division. No GPS, no internet weather, no computer for route optimization. "That’s why we asked you to bring your sextant, Max," explained the skipper as he assembled the crew around the table in the boat's main salon. "We get a big rating credit for entering in the Celestial Division. Yes, we're going to do it the old fashioned way." "All the better," I said with concealed terror. "It's been a long time since I used celestial in anger, but I'm up for it." Fortunately I did have the old sextant with me, but I thought this would be like TransPac, where all they want is a couple of token lines of position in the logbook for show. Now I learned that celestial would be our primary means of finding our position all the way across — and me without so much as a nautical almanac or a copy of H.O. 249.

Our skipper went on to lecture the crew about the boat's safety gear, how we would have our harness tethers clipped in all the time on deck, the watch system, and a hundred other details. Meanwhile, I slid over to the chart table and discreetly turned on the computer. It had a broadband internet connection as long as we were in port. I typed Lee Helm's email address, then the message: "Lee, Max here. It turns out we are entered in the Celestial Division. Do you have a program for sight reduction? Is it small enough to email? Please respond ASAP, much appreciated." The skipper had turned the lecture over to the cook, who was outlining the menu, the operation of the stove, and how galley clean-up would be rotating among the various watch standers.

No response from Lee. She must be offline. Maybe a "tweet" would reach her: "MAYDAY!" I typed. "Entered in Celestial Division. Need sight reduction program!"

Thank Poseidon she was monitoring her portable device, whatever it was. She replied almost immediately:

I'm on campus, will send via remote.

Thank Poseidon again that she had remote access to her computer. And a few minutes later there was an email, with an attachment, in my webmail inbox. But something must have gone wrong — the attachment was only 140 kilobytes, just a fraction of the size of the average digital photo, and certainly not big enough to be an entire celestial navigation software package. I dragged it into a new folder anyway, and clicked on what looked like the executable. The program was up and running instantly, without so much as a hint of an installation wizard to wade through.

Ibreathed a huge sigh of relief. It was the program I had remembered: the old DOS program with a nice, simple command-line interface. And it seemed to be running fine on the ship's hardware. Just in time, too, because right after our cook finished disclosing where all the night watch snacks were stowed, the skipper turned it over to me. "Now Max will say a few words about celestial navigation on this race." I brought up the screen for "dawn, dusk and transit times" to see what sort of objects we would have. Not much Moon — it was preceding the Sun this week, along with most of the other planets. "All the action will be at dawn on this voyage," I said. "As you all probably know, celestial navigation works best when it's dark enough to see the stars and planets, but light enough to see a clear horizon. For a good position

"U get 2 have all the fun."

fix it's useful to observe several different celestial bodies at about the same time. This means I'll have to be up before dawn every morning, when I can get the Moon, Venus and Jupiter. Maybe Mars, too, although I see it's only about two degrees away from Venus so it won't provide any new information." As I spoke, my confidence increased, thanks to this little program. It was making me look smart. "We'll lose the Moon after a day or two," I continued. "So the pre-dawn Venus and Jupiter shots will be important. The Sun will be rising at . . . let's see . . ." Something was wrong. This thing was putting sunrise at 2 a.m. and sunset at 4 in the afternoon. Fortunately, the DOS window with the nav program did not completely cover up the window for incoming messages. U R in EDT zone. GMT-4. Lee.

Of course. Lee had read my mind; I had been subtracting seven instead of four from GMT to get local time. "Sunrise is at 5 in the morning, so the

WWW.NOAA.GOV

Sextants are fancy protractors that measure the angle of celestial bodies above the horizon. Some of them are also collectible antiques.

half hour before sunrise will be the most important part of the navigator's day." I outlined where each of the major planets would be, and explained that sometimes, with a bright Moon, there is enough light to see the horizon and take good star and planet sights all night, but that would not be the case on this trip. Then I demonstrated the program I had just installed, inputting a sample sextant reading, a time, and an approximate position to show how it came back with a precise line of position. And I gave them my one-paragraph explanation of celestial navigation: "At any given time, there's only one spot on earth that is directly under the Sun. If you are at this spot, the Sun appears right overhead, or 90 degrees above the horizon. The computer can calculate, for any second of the year, where that spot is. Same for the Moon, planets and stars.

"The sextant is just a fancy protractor that measures the angle of the Sun above the horizon. If you measured the angle of the Sun above the horizon and found that it was 90 degrees, you would be at that spot directly underneath. "But what if you measured 89 degrees? Then you would be somewhere on a circle one degree away — or a circle with a radius of 60 nautical miles, because a minute of angle on the earth's surface is one nautical mile. If you measured 30 degrees up from the horizon, the circle would have a radius of 60 degrees or 3,600 miles. Now, we can't draw such a big circle on a flat chart, so the computer also gives us instructions for drawing a line that approximates the part of the circle that goes through the part of the ocean we're on." "Ah, so that's how it works," said the watch captain. It was really three paragraphs, but they seemed to get it. "All the rest is details," I added. "There are books of tables to do it without the computer, and to correct for certain errors, but the machine can do it better." "That program will be great to have as a back-up, Max," said the owner. "But you know, to qualify for the Celestial Trophy, we have to submit all our sight reduction calculations by hand." "Uh. . . sure, no problem," I said. Now I was in real trouble. But the topic of discussion moved back to meal planning and how many glasses of wine would be served at dinner. So I was free to sneak back onto the computer for help. "Lee!" I typed. "Thanks much, program runs, but they want hand calcs! Now what do I do?" She answered quickly:

U get 2 have all the fun.

I typed back: "No, really. I didn't bring any sight reduction tables or plotting sheets. HELP!"

No prob. U have calculator with trig? was her next reply. "Yes, we have that," I typed after a panicked search through the contents of the chart table.

Formula:

LHA=arc cos[{sin(Ho)-sin(dec)sin(Lat)}/ {cos(dec)cos(Lat)}]

LHA=long difference btwn U and obsrvd body. Lat=latitude,dec=declination

It wasn't at all clear how I could get a line of position out of that formula. But Lee had only stopped typing because she was at the 140 character limit, and the next tweet explained in more detail. LOP is vertical. Formula gives longitude if U know latitude. Called TIME SIGHT. Use with noon sight 4 running fix. Lee's formula might get us to the finish, but apparently it would not let me take a round of

I didn't bring any sight star shots a good fix to get every reduction tables or plotting morning. I typed sheets. HELP!" back to Lee: "Aren't there some easy formulas that will give me the intercept and azimuth of the line of position, just like the regular sight reduction tables?" Lee had them ready to send: Hc= arc sin[sin(lat)sin(dec)+cos(lat)cos (dec)cos(LHA)] z=arc cos[{sin(dec)-sin(lat)sin(Hc)}/ {cos(Lat)cos(Hc)}] (z=azimuth east or west from N or S, depending)

At least with SIGHT REDUCTION BY H.O. 208 those formulas I five-digit numbers that could get an actual ___ LHA < 90 —> b same sign as Lat, t = LHA date _______ had to be added and line of position. DR is hard part, came another message from Lee. All about crew discitime __________ LHA > 90 —> b opp. sign as Lat, t = 180-LHA ___ d + b < 90 —> add z" ___ d + b > 90 —> subtract Z" GHA or Longitude subtracted by hand. All to save two pounds. By that time, the pline. Crew has 2 pre-race orientation log all speed/course class was almost over. changes. Will send The skipper asked if I spreadsheet 4 add- Longitude or GHA had anything else to ing up lots of small add. legs 2 plot vector "Here's the form we'll sum. be using for sight re-

The spreadsheet Lat L Dec d LHA t duction by hand, no she sent did exactly calculator necessary," that. Entering time, I said, pointing to the course and speed worksheet on the screen for every short leg and holding up the of a watch, it added up all the distances b A C Z' copy this of H.O. 208. "I like method because and courses and the book of tables is gave a single course very small and saves and distance to And, even more plot. useb or d B D Z" weight." "We sure could have ful for working on a used that form last bouncy chart table, year," said the skipper. it also presented the answer in east/ d or b A + B C+ D (-10,000) Z + Z' +/- Z' "The guy who navigated brought a little book like west/north/south that too, but he didn't distances, to make have that form and it it easy to plot on a paper chart without d +b or d-b Hc Z" took him all day just to figure out the instruchaving to measure tions." any angles. "Keeping a good dead But I suspected reckoning plot is going that to compete for to be critical," I lectured. the Celestial Trophy we shouldn't even be seen using a calb, A, C, Z' from Table I, enter with L and t B, D from Table II, enter with d + b (or difference between d and b) "If it stays cloudy, we could go a long time between sights, and the culator, let alone Hc from Table II, work backwards with A + B (used B column) currents are variable, a spreadsheet. I Z" from Table II, work backwards with C + D (use D column) so every time there's searched the chart a change in course or table again — may- speed, it needs to be be there was an H.O. 249 hiding in the I typed back to Lee: logged in. Don't worry about too many back somewhere. No luck. But I did "Have you ever heard of H.O. 208 by entries in the log to plot; I have a program find a small black book titled H.O. no. Dreisonstok? We have a copy of that, but to convert multiple legs into a single vec208, Navigation Tables for Mariners and I can't figure out what it does." tor for the chart." Aviators, by Dreisonstok. It was much Cool! Lee answered. U R saved. 208 is too small to be a book of tables, but I took a look sight reduction inside anyway. logarithmic solution to nav triangle. Will send worksheet with better instructions. "Max," said the owner, putting Every page was full of cryptic tables The attachment with Lee's H.O. 208 his hand on my shoulder, "I can't tell you worksheet arrived a minute later, along how great it is to have a navigator who with another message: comes fully prepared."

Every page was Good luck, gotta run 2 class. Hope its — max ebb full of cryptic tables not 2 cloudy. The real problem = keeping good DR. Here's a link to an old sight reduction of numbers. . . I opened the played the sight attachment and reduction form on disthe program posted in a discussion group on the Marion-Bermuda Race website screen. "What a mess," I thought to (copyright status unknown): http:// of numbers, except for a few pages of myself, looking at all the steps and all racetobermuda.ning.com/forum/topincomprehensible instructions near the the different cases and exceptions that ics/celestial-navigation-software?group back. had to be handled differently, and the Url=gulfstreamstrategy&.