Help with (fictional) celestial navigation

[skipmac]

Originally Posted by Wotname

In theory, 2 LOPs give two possible fixes, usually a thousand plus miles apart;
In practice, you can usually eliminate one possible position as it will some considerable distant from your DR position.
3 LOPs give only one possible solution.

[skipmac]

HI Chris,

A couple of points for you.

First there is a thing called an artificial horizon which you can rig at home. Forget the exact method but it involved a mirror and a pan of water if I recall. Also, the purpose of the horizon is to establish a point of measurement. In airplanes they use a sextant with a leveling bubble (kind of like in carpenter's level) which keeps the sextant horizontal and allows you to measure the angle to the star. I feel certain that the helmets worn by your characters would have a way to establish level.

One trick to get a more accurate fix, especially if for some reason your star shots may be randomly off is to take a series of shots, measuring the angle (which changes over time as the Earth or Mars rotates) and the time of each shot. You can then take the series of shots and plot them on a graph. They should form a straight line. Any points far from the line you throw out and then draw a line around the middle of the points. Take a point off the line and it will be the most accurate.

Originally Posted by ceswiedler

Wow! Thanks, everyone.

I think Wotname and others confirmed what I was thinking: that if you sight 3+ stars "perfectly", then you would get a single point, but if you mess anything up, you get a polygon with 3+ sides. So an inexperienced navigator could get a position with a relatively large margin of error.

If that's even more-or-less true, then I'm happy. This isn't a book about navigation (or even sailing) and so I mostly just don't want to describe the process completely inaccurately.

One thing I didn't realize is that you have to be able to see the horizon, though of course that makes sense. Fortunately, this is science fiction. If you're interested, here's the situation in more detail:

Two kids living on Mars ~100 years in the future steal a rover and run away. A solar flare destroys all of the GPS satellites, leaving them with no way to navigate. One of the kids has a decent amount of training, and has been taught how to sight stars. I'm handwaving the measurement stuff with sci-fi magic: for example I'm saying that gizmos in their helmet will help them measure the angles of stars, and it's easy enough to say that they can do this without actually seeing the horizon.

Now, obviously you could ask why their suit computers are good at measuring the angles of stars but leave the rest of the process and most of the math up to the kids. To that, all I can say is that the story demands it: it can't be impossible, and it can't be easy. If you see something that's fundamentally wrong with what I'm describing, please let me know, but if it's just hard-to-believe-if-you-know-a-lot-about-navigation, then I'm going to have to let it pass unless we can figure out another way to achieve the same end in the story.

One other thing I'd like is to have them come up with some way of improving their largish-polygon plot. Something like sighting one of the moons of Mars (which was suggested in The Martian by Andy Weir if you've read that). I'd like it to be a eureka kind of moment--"hey, we can do XXX and get a more accurate location!" So if anyone has a suggestion along those lines, I'd love to hear it.

Thanks again for letting me hijack your forum for my completely-non-sailing-related question.

chris

[El Pinguino]

Originally Posted by ceswiedler

One other thing I'd like is to have them come up with some way of improving their largish-polygon plot. Something like sighting one of the moons of Mars (which was suggested in The Martian by Andy Weir if you've read that). I'd like it to be a eureka kind of moment--"hey, we can do XXX and get a more accurate location!" So if anyone has a suggestion along those lines, I'd love to hear it.

If they had taken morning stars and had obtained a big cocked hat they could then get venus on the meridian mid morning, notice their mistake and then re-work their stars.

[/QUOTE]Thanks again for letting me hijack your forum for my completely-non-sailing-related question.
chris[/QUOTE]


I think it was a very sailing related question.

[rhubstuff]

It might take some convincing to suggest that two guys living 100 years from now don't have access to software that was developed 30+ years ago. I have a Sharp PC1270 calculator built in 1991 that computes all celestial problems given only altitude, azimuth, and time, for any celestial body, forever. And you don't even have to know the name of the body. Just shoot and compute. I'd suggest the OP establish contact with someone experienced with celestial to review the appropriate portion of the text before publishing. The subject is complicated enough to make errors of fact very easily.

[skipmac]

Originally Posted by rhubstuff

It might take some convincing to suggest that two guys living 100 years from now don't have access to software that was developed 30+ years ago. I have a Sharp PC1270 calculator built in 1991 that computes all celestial problems given only altitude, azimuth, and time, for any celestial body, forever. And you don't even have to know the name of the body. Just shoot and compute. I'd suggest the OP establish contact with someone experienced with celestial to review the appropriate portion of the text before publishing. The subject is complicated enough to make errors of fact very easily.

Ah but by that time celestial navigation and all associated technology would be totally obsolete so who would have such antiquated software.

After all, how many 5 1/4" disk drives do you have around to run programs on old floppy disks?

[El Pinguino]

Originally Posted by rhubstuff

I have a Sharp PC1270 calculator built in 1991 that computes all celestial problems given only altitude, azimuth, and time, for any celestial body, forever. And you don't even have to know the name of the body. Just shoot and compute.

I had a sharp PC-1248 which ran a Mike Harris program... took it out of chart table drawer last year... ded...changed battery...still ded.... was cutting edge in its day...

[El Pinguino]

also with that program ( written in basic ) you had to update the variables for the ephemeris annualy... the P, Q and R ones... I only have them up to 2010 although I imagine they are available somewhere 'out there'..

[Wotname]

Chris, for the record, if you end up introducing the term DR into the story, the normally accepted short form is "ded recckoning" rather than "dead reckoning" even though it is pronouned as "dead". The long form is deduced reckoning.

Apologies to those who use "dead reckoning"

[Wotname]

Originally Posted by El Pinguino

I had a sharp PC-1248 which ran a Mike Harris program... took it out of chart table drawer last year... ded...changed battery...still ded.... was cutting edge in its day...

I feel for your loss, mine did the same so I tossed it into the bin - sad day

[FamilyVan]

Originally Posted by skipmac

I saw your reference but I don't think dead reckoning relates to the point I was trying to explain to the OP that is, the circular LOP on the globe is very large and the actual navigation takes place on a chart showing a small area and a very small section of that circle. In practical use that is a straight line. I just thought that someone completely unfamiliar with celestial navigation might be confused by the several posts that referred to the circular line of position.

Also, when you mention dead reckoning you say that is how to resolve which of the two points of intersection of the two LOPs will be your correct position. First, since the two points of intersection of LOPs in celestial are generally hundreds if not thousands of miles apart, if you aren't certain which one is correct you would have to be pretty lost. Plus, if your actual position is 100 miles away from your celestial then you are not doing very well with the celestial. It has been 35 years but as I recall the worst I got even in very rough seas and poor observation conditions was 12-15 mile box.

Second, dead reckoning is navigating from a known point using course, speed and adjustments for current, leeway, etc to deduce your current position. If you don't know where you are to start with from celestial or some other method then dead reckoning won't find you.

Not sure why you are picking my post apart. Its been nearly 20 years since I studied nautical science, the guy asked a question I noticed nobody had answered him, so I gave him the best answer I could so his thread didn't get buried. I'm pretty sure every thing I said was technically correct, except for misspelling of ded reckoning (thank you for pointing that out Wotname).

Sent from my SGH-I547C using Cruisers Sailing Forum mobile app

[rhubstuff]

It has, of course, occurred to most of us that celestial navigation on Mars would require a completely different set of ephemeris data, and different Prime Meridian, time system, etc. Plus the fact that Mars has no water, so the horizon would be cratered and mountainous, and height of eye indeterminable. Without accurate HE and a good horizon, celestial navigation is impossible. (OK, an artificial horizon could work.) But how would you compute the Equation of Time or LMT, even if you had a Martian Almanac? And you'd need to find the body's GHA and declination, and then sight reduction tables. (You could use basic spherical trig, I guess...). But there is no coordinate system in place...no equator, no Prime meridian. There can be roughly 40 steps in a typical sight reduction. Most of them would be different on Mars than on Earth, and no such computations have ever been done.

[budm303]

[QUOTE=ceswiedler;1804619]Wow! Thanks, everyone.

"Two kids living on Mars ~100 years in the future steal a rover and run away. A solar flare destroys all of the GPS satellites, leaving them with no way to navigate. One of the kids has a decent amount of training, and has been taught how to sight stars. I'm handwaving the measurement stuff with sci-fi magic: for example I'm saying that gizmos in their helmet will help them measure the angles of stars, and it's easy enough to say that they can do this without actually seeing the horizon.

If you see something that's fundamentally wrong with what I'm describing, please let me know, but if it's just hard-to-believe-if-you-know-a-lot-about-navigation, then I'm going to have to let it pass unless we can figure out another way to achieve the same end in the story."

~100 on Mars: a "helmet" celestial device may probably only require the user to look at a star to establish a time-space continuum, as with current F-35 units. Suit computers? Probably not necessary. Human bodies adapt very quickly to harsh conditions ... you're advancing five generations ... low oxygen enhancement likely (e.g., Andes residents). Sci-fi futures fantasies are based on historical data colored by imagination.

[skipmac]

Originally Posted by Wotname

Chris, for the record, if you end up introducing the term DR into the story, the normally accepted short form is "ded recckoning" rather than "dead reckoning" even though it is pronouned as "dead". The long form is deduced reckoning.

Apologies to those who use "dead reckoning"

Absolutely correct that the term derived from deduced reckoning, however it seems like "dead" has become the accepted spelling instead of the more relevant "ded".

I just went back to see if my memory had failed on this and all the references I checked: Chapmans, Wikipedia , Encyclopedia Britannica and a couple of old navigation books including Mary Blewitt all spelled it "dead".

I just checked an old book I had found on Gutenburg, The Sailor's Wordbook written by a British Admiral and published in 1867 which also spells it "dead reckoning".

CORRECTION.

After reading The Sailor's Dictionary I did a little google research and found an article refuting the origin of the term from deduced which is what I had always thought. However there was no alternate theory on the origin of the term offered only a claim that "dead" had been the spelling since the 1700s.

So a mystery. What is the origin of the term dead reckoning?

[jheldatksuedu]

Concerning accuracy, an experienced celestial navigator under somewhat good conditions should be able to get his position within a small number of miles, close enough that when he nears land he should be able to avoid disasters and can eventually see something on the horizon and figure out how to get to port safely. Dead reckoning will carry him through the bad observational times as best as it can. Most travel before gps was done with the time of sun rise or sunset, and a noon sun sight, advancing the lines of position (using his boat speed and direction, water current guesses and time since his last position) to get a fix. Dead reckoning is used with the speed direction and time on cloudy days. It involves accurate time, a clock more than anything. A short wave radio can get you accurate time at sea to set the clock, or more normally keep track of it's error. A minute of time error is roughly 15 miles, so seconds are important, that's roughly how far you can see on the horizon. A minute of arc error (60 minutes in a degree) is roughly a mile, so angles are important too.

[Chuck Hawley]

Here's my two cents:

In 1980, I sailed to Hawaii in a small boat during the summer, and you end up sailing "under" the sun on the way there (your latitude crosses underneath the sun's position on the earth's surface.) So I had to learn to use HO 249 and the stars mid ocean. About 1000 miles from land, with a good DR, I cracked open the sight reduction tables and found the three stars that were recommended. I ended up with a very right "cocked hat" that was almost exactly 60nm south of my DR position. I waited until the next night to take another round of sites, but the result was the same: 60nm south. I was really creeped out, to be at sea, sailing towards an island chain, without knowing if I should trust my sun lines or star fix.

The answer became clearer later that night. The star to the south of me turned out to be a planet which was brighter than the navigational star, so it showed up earlier in the twilight. And, wait for it, it was one degree lower in the sky, so my position was one degree further south.

I think this might be a good way to have several days of confusing information for the navigator, but a relatively simple answer.

Cheers, and good luck with the book. Let me know if you need a technical consultant!

Chuck Hawley