If I disoriented you beyond doubt, so that you didnt know your location on earth, and if I dropped you in some ocean;
1... could you determine your approximate location, say within a few hundred miles, given a raft full of non-electronic navigation equipment and publications?
Gentlemen, hope you can help me in this little "predicament."
At first , a few general terms:
1. Apparent time is a measure of the sun' true position. To get Greenwich apparent time at any instant we just convert GHA of the sun into time (hh/min/ec)., We need apparent time to find when the sun will be on the observer's meridian. Local apparent noone, when the observations for latitude are made. We know that it is different for each meridian, and unless two places are on the same meridian- apparent time is different.
2. On the Mercator chart every parallel is expanded in the ration of the secant of its latitude.
To avoid local distortion every meridian of a Mercator chart must also be expaned in the vicinity of each parallel by multiplying it by the secantr of the latitude of the parallel.
My question:
When the vessel is located above let's say 50 deg Lat. and we are trying to find LAN the natural curvature of meridians would make GHA slightly shorter than Mercator chart projections ( straight, parallel lines). And it means LAN calculated would be different from LAN real , considering expansion ratio of scant of the latitude. And it means the moment we are catching the sun in a sextant is not exactly the time the sun is in Zenith. Difference should not be significant, but I just want your expert opinion about it.
Greetings, gentlemen. I found a couple of interesting old books which, considering lockdowns and general inability to cross a street without damn mask, may help to develop not very useful skills. But a lot of people have used them for sure. One of them Mathematics for navigators by Delwyn Hyatt. Yes, 1944. Of course it is kind of obsolete. But please consider the fact it was taught during WWII to officers who would serve in the real situations, not in a front of a simulator. In many cases its methods are kinda "not straight forward" to say least. But some are really good. For instance, Adding and subtracting figures from left to right, they way we write them. I tried it and after several attempts found out that it is much faster than traditional ones. Also, havesine and other formulas presented in quite different, again, not easy for me to understand, wording and form. Anyway, real navy folks really used it. So, as a due respect tio their work, let's try to understand their daily routines doing it. Not easy, my opinion.
Another one, Navigation and NAutical Astronomy, by Dutton, 1943. Again, thyere are a lot of info, which probably none of us would ever use, but there are also a lot of proves and explanations, which we take for granted without even thinking where did it come from. Moder editions of Dutton don't have some of it. I consider it as of a hystorical value.
I am always fascinated by the old methods of navigation, when Energizer' Bunny wasn't even conceived yet. No batteries, cloudy skies, rolling horizon and wet and misery all around. And they did it. Years ago we were taught to use sliding rules. It gives you anything, up to 3 decimal. Recently saw it in the antique shop for $271. And only then I realized how ancient am I.
I've been playing around trying to learn the old compass rose. I found out a few things and developed some memory aids. Drawing my own compass helped tremendously. See attachment. You will note the intersecting archs around the perimeter of the compass - these are drawn to divide the circle into points.
Here are a few more memory aids.
The 4 large points contain a single letter, N, S, E, W (cardinal points)
The 4 secondary points contain two letters combining the cardinal points. NE, SE, SW, NW
The 8 smaller tertiary points have 3 letters combining the cardinal and secondary points. NNE, ENE, ESE, SSE, SSW, WSW, WNW, NNW.
The 16 smallest points all contain the word BY: North By East, NEBN, NEBE, EBN... etc. These refer to the cardinal and secondary points only - the tertiary points are not used in reference to "by" points.
A cardinal letter always follows the word BY - South West by West... etc. There is no such heading as North by North West or South West by West South West. Also I don't think there is such a heading as North by West and a quarter North... THAT point, rather, might be given as North and three quarters West.
Just playing with a quadrant at a time lessens the confusion. For example, just practice with the North East quadrant first and discover how it makes sense. The others follow the same pattern.
Draw your own rose with paper and a draftsman compass, you can't do that with a circle of 360 degress ... try drawing half of 45 and you'll get a headache; dividing a sector into 90 equal parts is no picknic. The old compass rose has a total of 32 points with the addition of quarter marks. very easy to make.
If the captain ordered North and a quarter East the helmsman would stear to the first tickmark to the right of North. If North East and a half North was ordered the wheelman steared to the second mark to the left of NE... etc. I was too lazy to draw every quarter mark.
Next time you're bored give the old compass points a try... you'll soon realize it has some merit over the 360 degree system.... Who needs 360 degrees anyway. You'll just wear yourself and the stearing gear out trying to keep that precise. Might as well make the compass 720 degrees... lol.
I own some pocket compasses that only show tick marks at 5 degree intervals - thats only 72 compass points. Might as well have printed the old rose and made orienteering some fun.
The really interesting thing here is that after a while you won't need written point letters to tell you what point you're looking at. As long as you know which large point is North you'll know the others, and North may be identified with color rather than a letter from the alphabet. I bet that even before you begin studying the old compass points you could close your eyes and from the very start imagine 8 of them; North, North East, East, South East, South, South West, West, North West. That's already a fourth of the points. Think a bit harder and imagine the points between these such as North North East... etc. That's half the points.
Admittedly, the toughest points for me to learn were the BY points such as North by East, but adding a little relative bearing grease to my brain quickly put those points in order.
The quarter marks were almost a no-brainer. Just remember that the BY points have no quarter.
Have fun and keep at it - that's how tradition survives modernity.
Just finishing making some dividers out of old brass flat stock I've had for 10 years.
I hand sawed the brass into long wedges, used a small file to get it in shape, used some old aviation hardware with a plastic washer between the wedges, and presto... damn near perfect dividers - they work great.
Generally store bought brass dividers come in 7 and 8 inch lengths. I couldn't decide which I might want so I made mine 7.5 inches.
Just goes to show a navigator doesnt need to spend gobs of cash to have some tools.
Next - maybe a plotting triangle from old plastic.
BTW - the photo shows where I live in relation to the last great sea battle of ww2. The upper divider point is on my house. The lower divider length shows the southern route the Japanese navy used to attack the America forces at Leyte. The pencil is on the Surigao straights where the battle took place. The Surigao southern entrance is 88 nm from my house. Japanese lost and the surviving ships went back the same way they came.
Leyte is where general MacArthur returned to the Philippines.
My island is where Magellan was killed... lots of history here.
I took 3 AH sightings and averaged them. Learning to average hexadecimal was a bit tricky, but I found that making the hours of time or sextant altitude equal helps.
For example:
83 10.7 = 82 70.7 - adding 1 degree to min.
82 33.7 = 82 33.7
82 05.0 = 82 05.0
So 82 is the obvious average for degrees and what remains is to average the minutes: 109.4 ÷ 3 = 36.5
Averaging time was a bit more difficult :
06 22 30 = 06 22 30
06 24 12 = 06 22 132 - adding 2 min to seconds
06 25 26 = 06 22 206 - adding 3 min to seconds
so, 368 ÷ 3 = 122.7. Move 120 seconds back to minutes with a remainder of 2.7 seconds: 06 24 03. (My watch was 7 sec fast so actual time is on the first post line above)
Of course one could change each shot to a decimal value, add together, divide by 3, then change back to the hexadecimal, but that takes a calculater and lots of button pushing, given your calculator has a button to do this.
I'd be interested to learn how you swabbies average shots. I tried 4 or 5 different ways to average shots all resulting in different values. The way I've shown works best for me and put my LOP right on my position. See LOP 3 on the worksheet.
The arithmetic mean works great if the shots are spaced near equally: (a+b+c)÷3= mean average. Simple.
But if shots are delayed due to clouds or such a better solution might be the geometric mean: a×b×c =d then take the cubed root of d. If you have 5 shots then multiply and take the 5th root... etc. If a data set has flyers that skew the average -such as in the set 2.4, 2.3, 2.6, 2.1, 2.2, 2.4, 2.3, 7.5, 5.2 - You can see that the 7.5 and 5.2 will skew the average of two somethings out of proportion. The geometric method helps reduce the skew to something more reasonable.
Without the big numbers - 2.4+2.3+2.6+2.1+2.2+2.4+2.3 = 16.3, 16.3÷7=2.33
_________________________ - 2.4×2.3×2.6×2.1×2.2×2.4×2.3 = 366, 7th root of 366 = 2.32
I'm not sure how many here remember the slide rule (SR). if you were in high school in the 60s then you would probably have some experience.
I went to HS in the 70s and never heard of the SR. Only 10 years ago did I discover them as a source of enjoyment. it feels pretty cool to know how to use some of the scales, and the more I use them the more I like SRs. Just yesterday I bought a full sized 10in SR used from a guy in manila. My new toy will be here in 2 days. Up until now I've been using a 5in model. I can hardly wait.
Anyway, a couple years ago I found this PDF book about how to use SRs for marine and aviation problems; from simple time, speed, distance calculations to cargo handling and trim. I wrote about it here at the time. However, maybe some of you missed that post. Just goes to show I'm still excited about the subject.
I'm thinking some of you might like to review the book, a free download, and discover how fascinating and ingenuous the SR really is. You don't need to have the same one they use in their example; any SR with similar basic scales will do.
I was playing with some math today figuring out the best way to use my E6-B flight computer for marine applications. Somehow my mind went to log lines and sand timers.
I got the idea that with todays watches, all of which incorporate a second hand, working a log contrary to the old way, which took counting knots to determine speed after a certain time, typically 28 or 30 seconds, a predetermined length of log line might easily be timed to determine speed.
The following is a list reflecting time in seconds vs speed in knots for a log line extending 60ft:
So you take a fishing line 60 feet long on a cuban rig fishing spool. Attach a log device to throw into the water which pulls the line. Throw the log into the sea and start your timer. When the line pulls taught stop the timer. Determine your speed over the water using the chart above. If the spool is held any more than 4 or 5 feet off the water accuracy may suffer. With high cockpits a longer line would be better; just refigure the knots vs time table.
The math is thus:
1knot = 6076ft ÷ 3600s = 1.6878ft/s
You could have a log line 6076 feet long and spool it off for 3600 seconds which would tell you your speed is 1 knot. But there's a better, faster way.
60ft of line ÷ multiples of 1.6878 gives time in seconds
Ex:
60 ÷ 1.6878 = 35.5s for 1 knot
60 ÷ (2 × 1.6878) = 17.8s for 2 knots ... etc.
You can help me out here and let me know if I got the figures wrong. Any length of line would do beyond a certain minimum. I took 60 because in an emergency 10 arms spread would about equal 60ft. You can kinda sense here that line length doesnt get critical until you reach the higher speeds.
Have fun and give it a try next time you're out on the lake and dont forget to tell us what happened.
Its 22 14 00 gmt dec 27. That's 06 23 00 local. I was up before nautical twilight to shoot venus, spica, and perhaps regulus, but there was complete overcast. Now that rainy season is over we're getting all the rain we missed during rainy season. Let's hope the rest of the day isn't as frustrating... Maybe I'm getting too old for this business. Naw. You're only too old if you can't see the sun through the sextant. I have a hankerin to go to sea... anyone wanna go? Who's gotta boat I can borrow?
Cheers
PS 21 09 00 now and still overcast... just not my day for CN. I wonder if at sea how long I could go without a fix before I'd get nervous. I suppose that might depend on how close I thought I was to some obstruction - like a continent.
"The reason why the haversine function has come out of fashion is that with the help of calculators and computers it’s easy enough to work out the distance straight from formula (2). That’s why you don’t find a haversine button on your average calculator. "
Here is a quote from another pub describing haversine as it relates to the Gunter versed sine line :
"The scale title V * S means versed sines, but it does not reflect our current versine which equals (1 -cosine). It actually represents, in modern terminology, the logarithm of (1 -haversine), or 1/2 (1 + cosine). The haversine function (half-versed-sine) was introduced for computational reasons in the formula that calculates the angular distance between two arbitrary points on the globe. This formula could be calculated between the NUM, the SIN and the V * S scales on the Gunter rule."
So that's pretty much why we have haversine tables. If you've never used the haversine table give it a try... you'll get a good feel for what our forefather navigators went through to chart their ships. Where once about every navigator knew the meaning of haversine, now you can consider yourself a member of a select few who still do :)
