Navigators and Napiers Rules

Hello, I'm new here so this may have been discussed before.

No Flat Earther at all could be a ship (or plane) navigator.  The various equations that have been worked out to calculate the course and distance between two points on the earths surface show that the earth is curved. 
If you google Napiers Rules, you'll come up with a complex bit of maths based on spherical trigonometry that can calculate (among other things) the course to steer, and distance between, any two points on the earths surface.  These formulae work because the earth is curved.  Now, ignoring the proof of the equations as evidence entirely, these equations are much more complex than pretending the earth is flat and using plane trigonometry; no time pressed navigator (of which I am one) would bother using Napiers rules unless there was a damned good reason.  Seriously, if you're planning a 3000 mile voyage, you want the maths to be as simple as possible; bear in mind too that many merchant ship's officers a couple of hundred years ago would have finished school at 12 or younger.  I have a degree and find Napiers Rules (whilst not impenetrable) a bit of a hassle.  We bother using them because pretending the earth is flat leads to massive inaccuracies.  Travelling any distance over a few miles on the pretence of a flat earty means that you'll find yourself somewhere other than you planned on being.  Like on a massive rock with a hole in your ship and several dead sailors.

Napiers rules were come up with a very long time before any space programme was even envisaged, so don't be starting any conspiracy theories.  This isn't about NASA or even the US; when Napiers rules came out the British Empire was the pre-eminent power.  And the British Empire's space program at the time consisted of a nutcase, a firework and a bar of soap.

I await an intelligent response...

Hypothetically: If the earth was spherical - don't you think it would be more likely that the navigators had look up tables in books... I don't think the average person right now at age 12 knows trigonometry very well.. and certainly wouldn't remember it after a few years at sea....

The look up books/maps are probably faked...

You should design a challenge where navigation with methods that imply a spherical Earth is put to the test. Preferably they should be inexpensive, based on widely available information and with no requirements that make the test exclusive to a small group.

I have already proposed experiments based on Google maps, where somebody just needs to travel a few miles with any car and do some maths, and experiments based on navigation by stars, that only need a small telescope with a good mount, preferably equatorial.

Flat earthers cannot spin that kind of experiments and can only ignore them. On the other hand they are thrilled with mental experiments that require trips to Antarctica, to outer space, around the world, anything that few people can do, so they are "in the conspiracy".

Why don't you post this test then?

Why don't you post this test then?

Lets start with this one:

Lots of things do not work when even the most basic navigation methods are attempted on a flat Earth:

• To measure latitude, any visible star's position moves South one degree for every 60 nautical miles your position moves North. And this is true for all the stars, not just those close to your zenith.
• At a latitude of 45 degrees North there is a difference of 35% between the FE's length of a degree of longitude and that of RE. You don't even have to go south of the Equator to find big discrepancies.
• Every distance of a few kilometers is easy to calculate according to the Round Earth model using the data available in Google Earth. Anyone can measure distances close to their own homes with the odometer of their cars and compare them with what Google Earth says, and see that the discrepancies seen in North-South trips is the same as in East-West trips.
• Latitude measurements are routinely done with stars that are in any place of the sky, not just near the zenith. On a flat Earth this would not be possible.

There is no way somebody who has navigated using sextants, star maps and chronometers can think that the Earth is flat.

The look up books/maps are probably faked...

How do you come to that conclusion?

Quote from: Johannes Kepler on November 05, 2008, 06:56:05 AM

Why don't you post this test then?

A simple test would be to try an observe Polaris from Sydney Australia. It should be about 21^o according to FE calculations. If it's not observed then FE Theory is rubbished. I'm sure others will post other tests.

Better yet, from any place in the world, measure the altitude from the horizon of Polaris. If you do not see it,  because you live in the Southern Hemisphere, chose any star that is more or less north of the zenith. Move 60 nautical miles north and measure the altitude from the horizon again. If the Earth is spherical, this test will succeed, whatever the starting location, and whatever the star you choose. If the Earth is flat, the sum of all the inconsistencies seen by different people in different places will not only destroy the RET, but will give Robosteve what he needs to finally give us the maths for bendy light.

PS. If you cannot travel the 60 nautical miles in less than an hour or so, you should do the second measurement the next day, at the same time as the first.

Correct me if I am wrong, but if you are at a high enough altitude, you might be able to see Polaris from slightly below the equator.  That test should be done as close to sea level as possible.  No standing on top of the Andes.

Correct me if I am wrong, but if you are at a high enough altitude, you might be able to see Polaris from slightly below the equator.  That test should be done as close to sea level as possible.  No standing on top of the Andes.

You are right, but the angle you are talking about is minuscule. And, anyhow, Polaris makes the test much more convenient, but any star will do. If you use Polaris,  you do not have to worry about the time you spend traveling the 60 nautical miles; that is the only reason to prefer it.

Changing your altitude above sea level does not affect the test, since our hills are microscopic compared with the diameter of Earth.

Hypothetically: If the earth was spherical - don't you think it would be more likely that the navigators had look up tables in books... I don't think the average person right now at age 12 knows trigonometry very well.. and certainly wouldn't remember it after a few years at sea....

The look up books/maps are probably faked...

Yes, there are some look up tables, but not for round earth spherical Trigonometry (Napiers rules).  The look up tables refer to fudged maths which assume a flat earth; the spherical earth bit relies on equations.  Thus if the tables were faked, then the flat earth bit would be the one shot down.  Flat earth calculations can only be used up to a point, as I said, past that you end up in a very different position to the one you intended.  Flat earth calculations are so damned simple that no navigator would bother using the more complex spherical earth ones if he didn't have to. 

I can say the above with confidence because I am a ships navigator...

In the UK, 12 year olds are doing trigonometry (albeit not spherical trigonometry) at school, so they're probably better at it than you.  And that's not a dig at you, I mean that unpractised skills fade over time.  These twelve year olds would remember it better after a few years at sea as they'd use it frequently.  I know I do.

Right, to make a few points I heard about in other posts.  Firstly, no you cannot see Polaris in the Southern Hemisphere; one more against a flat earth.  I lived in Australia for a year, and have spent a good few months of every year since south of the equator. As a navigator I spend a large amount of time looking up at the sky for stars, so I'd notice if you could.  In fact, being in the northern hemisphere means we can work out our latitide very quickly by using Polaris; if we could do so in the Southern Hemisphere we would.  So no polaris in SH.  In the same vein, you cannot see the southern cross in the northen hemisphere.  Furthermore, as has been suggested, being on a hill would make very little difference to what stars you can see.  Navigators take the height of the observer into account, but only because we try to work out our position to within metres.  In the grand scheme of things, being on a hill makes not the blindest bit of difference.

Firstly, no you cannot see Polaris in the Southern Hemisphere; one more against a flat earth.  I lived in Australia for a year, and have spent a good few months of every year since south of the equator. As a navigator I spend a large amount of time looking up at the sky for stars, so I'd notice if you could.

Can you prove that Polaris is never visible from the southern hemiplane, or is it possible that you were just unlucky enough to always be in a location from which you could not see it while in the southern latitudes?

In the northern hemisphere we notice that Polaris is fixed in the sky.  There is no observational evidence that it moves.  Taking that into consideration, if it is not visible from the southern hemisphere at any point in time it should never be visible because it never moves from earths perspective.

In the northern hemisphere we notice that Polaris is fixed in the sky.  There is no observational evidence that it moves.

I can confirm through observations that Polaris (North Star) does "wobble" within a degree of true north when observed using a compass.

I wish you REers would stop contradicting each other. It would make debating with you a lot easier.

Quote from: ragnarr on November 06, 2008, 04:39:23 AM

In the northern hemisphere we notice that Polaris is fixed in the sky.  There is no observational evidence that it moves.

Quote from: Rig Navigator on June 24, 2008, 03:55:08 AM

I can confirm through observations that Polaris (North Star) does "wobble" within a degree of true north when observed using a compass.

I wish you REers would stop contradicting each other. It would make debating with you a lot easier.

Maybe Ragnarr never observed it with a compass. And I'm sure that he will accept Rig Navigator's explanation because it is more accurate and scientific.
Stop holding on to nothing, and answer to Goldstein.

You are right.  After looking it up and reading a bit it does wobble a little, I was unaware of that.

From Wikipedia: http://en.wikipedia.org/wiki/Polaris#Pole_Star

Polaris is 0.7? away from the pole of rotation (1.4 times the Moon disc) and hence revolves around the pole in a small circle 1?? in diameter.  Only twice during every sidereal day does Polaris accurately define the true north azimuth; the rest of the time it is only an approximation and must be corrected using tables or a rough rule of thumb.

Also interesting, Polaris will not always be our north pole star because the axis of the earths rotation itself does slowly wobble.  Though it takes almost 26k years to do so.  Very cool.

Quote from: ragnarr on November 06, 2008, 04:39:23 AM

In the northern hemisphere we notice that Polaris is fixed in the sky.  There is no observational evidence that it moves.

Quote from: Rig Navigator on June 24, 2008, 03:55:08 AM

I can confirm through observations that Polaris (North Star) does "wobble" within a degree of true north when observed using a compass.

I wish you REers would stop contradicting each other. It would make debating with you a lot easier.

In science there is always an expected range and an expected accuracy for every result, whether it is for an observation or an experiment. It is acceptable to say something is "fixed" if the degree of movement is small enough to be irrelevant. This is one such case.

The case where these discrepancies are not acceptable is with the "bendy light" hypothesis. Just one example: current scientific knowledge (what you call RET) predicts that anywhere in the world except very close to the poles, during an Equinox, the sun will rise at an azimuth of 270 degrees and set at an azimuth of 90 degrees. You can give yourself a few degrees to account for errors in measurement. If FET is right, the azimuth of the place where the Sun rises is significantly more than 270 degrees, and it is significantly less than 90 degrees during sunset.

For example, in the USA, the sunset will be at an azimuth of less than 70 degrees. That is very easy to measure by anyone, with little more than a good compass.

And this is true, with or without "bendy light".

Why don't you post this test then?

Wanted simple experiments? Check the previous post.

Can you prove that Polaris is never visible from the southern hemiplane, or is it possible that you were just unlucky enough to always be in a location from which you could not see it while in the southern latitudes?

Lets look at this.

From the calculations done (and since the results were not disputed despite the ample opportunities we can assume that you agree with them, but feel free to correct that if you do disagree with them), if the Earth is Flat, then from the Southern Hemisphere/plane Polaris should be approximately around 21 degrees from true horizon (the true horizon is the horizon you would see from sea level and with no obstructions to block your line of sight like mountains and such) plus or minus 1 degree (to account for the slight wobble).

At this height, Polaris should easily be seen from many places on the Southern Hemisphere/plane. And further more, since it doesn't move much, it should easily be seen and located.

However, as an amateur astronomer in the southern hemisphere/plane (among other things) I have never seen Polaris. There have been many events in the Northern Hemisphere/plane sky that I would have really liked to see, but was not able to due to this same problem.

In fact, here is a challenge:

In the Northern Hemisphere/plane align your camera with a compass to point due north (it won't be exactly on the rotational north, but you will still get the effect) and angled slightly upwards and take normal photo and a time lapse photo of the sky.

Then take a nice holiday to somewhere in the Southern Hemisphere/plane and do the same experiment. Take a normal photo and a time lapse photo of the sky with the camera pointed due north and at the same elevation. Also take a set with the corrected angles (simple geometry will give you the needed angles) for the distance you ahve travelled south so you are supposedly pointing at the same patch of sky (however, this will only be the same patch of sky if the Flat Earth is correct).

If you are extremely paranoid about conspiracies, then use an old optical (non digital) camera and process the photos yourself (if you know how or get someone you trust to do so).

There is no explanation that I have heard that will explain these photos.

If Flat Earth is correct, then you will see the same (or at least recognisably similar) images in the photos as the point of the experiment is to try and take photos of the same part of the sky in a FE). However, in RE the images will be vastly different because if Round Earth is correct, you would actually be looking at a completely different part of the sky (hence why it will be completely different).

I wish you REers would stop contradicting each other. It would make debating with you a lot easier.

Interesting that the same request could be made of FEers. 

Does the Earth look flat or does light bend making it look curved?  That one hasn't been answered with consistency.

Hypothetically: If the earth was spherical - don't you think it would be more likely that the navigators had look up tables in books...

It depends on what is being calculated.  There are a lot of things where it is easier to look it up in a table because of the fact that if you were going to calculate everything, there would be multiple references to multiple sources.  For many things, one table can sum up that variables with a single reference.

I don't think the average person right now at age 12 knows trigonometry very well.. and certainly wouldn't remember it after a few years at sea....

Like anything, if you use it every day, it is easy to remember.  I know specialists that can remember lots of strange equations and can often calculate them in their head because they get used daily.

I can rattle off the spherical trig formula for calculating the azimuth to a celestial body because I have to use it daily.  Many people can still remember the trig functions (SOHCAHTOA anyone?) that they learned years, and sometimes decades ago, even when they don't use it daily.

The look up books/maps are probably faked...

No, the books and charts are real and match what is observed when you get to a location.  That is better than any of the FE charts that I have seen.  Of course, as Tom will tell us, there is no "real FE map" because of the lack of research into the matter.

I have been thinking a bit more about navigating on a FE as compared to a RE and I think there is actually a definite proof here that we can not be living on a FE. The problem lies with the East/West directions.

East/West is defined as being at 90 degrees (right angle/perpendicular) to the North South direction. If you take a compass bearing to North, then from this bearing travel due East as compared to the starting point for some distance, then at this new point take another compass bearing of North and then travel due West as compared to this second point the same distance again.

Now on a RE model, this set of movements will mean that you end up at the same place. However, on a FE this would not be the case (as shown in this image):



If you were to take constant readings on the compass as you travelled, then you would walk around in the circle, but because in this example you only take two compass readings (one at the start and one at the second point) and always travel at right angles to this reading, then you end up in a different place to where you started.

This is because of the difference between Euclidean and Non-Euclidean geometry. Euclidean geometry only works if the surface you are on is flat, where as Non-Euclidean geometry can work in the surface is not flat (eg: Round).

Now it would be possible to make a compass where the East/West direction where curved on the compass itself (because the compass makers could be in on the conspiracy), but the angle that the East/West was on the compass would be specific to the distance from the Hub. Thus to crack the conspiracy, all you would have to do is take a comps that work near the Hub/North Pole and use it further away form it. Or, make your own compass (by magnetising a needle for instance), and marking off the perpendicular angle yourself.

This means that Navigating on a Flat Earth would lead you to a different position than you would if the Earth was round.

This experiment is easy to try, cheap to implement, is not fooled by bendy light or other optical illusions, and gives a definite difference between a Round Earth and a Flat Earth. As the components needed to perform this experiment are capable of being made by virtually anyone, it also avoids any chance that members of a conspiracy could construct the devices to give false readings to trick you.

After browsing these board for a few days, I have a basic understanding of the objections against the various experiments that have been proposed. This one, however, bypasses all these objections that I have read and is simple enough that anybody on these boards could perform it (which is one of the objections that has been put forward to many experiments, namely that they are too complex or are too expensive to perform.

I have been thinking a bit more about navigating on a FE as compared to a RE and I think there is actually a definite proof here that we can not be living on a FE. The problem lies with the East/West directions.

East/West is defined as being at 90 degrees (right angle/perpendicular) to the North South direction. If you take a compass bearing to North, then from this bearing travel due East as compared to the starting point for some distance, then at this new point take another compass bearing of North and then travel due West as compared to this second point the same distance again.

This works the same in FE and RE models.  Because the compass you are steering with is pointing North, the course of East or West would be 90? relative to North.

Now on a RE model, this set of movements will mean that you end up at the same place. However, on a FE this would not be the case (as shown in this image):

The course that you have drawn (assuming a polar projection) is south of west, not a true westerly course.

If you were to take constant readings on the compass as you travelled, then you would walk around in the circle, but because in this example you only take two compass readings (one at the start and one at the second point) and always travel at right angles to this reading, then you end up in a different place to where you started.

This is the reason that the shortest distance on a globe is a curve, if you steer a constant course, you end up moving in an arc.

This means that Navigating on a Flat Earth would lead you to a different position than you would if the Earth was round.

The difference isn't in the compass itself, the difference is in the courses and distances that would be steered.  On a FE model of the Earth, for travel in the southern hemisphere you would go closer to the equator while in the RE model, you steer closer to the pole.

This experiment is easy to try, cheap to implement, is not fooled by bendy light or other optical illusions, and gives a definite difference between a Round Earth and a Flat Earth. As the components needed to perform this experiment are capable of being made by virtually anyone, it also avoids any chance that members of a conspiracy could construct the devices to give false readings to trick you.

Navigation and celestial mechanics are some of the largest obstacles for the FE model.

After browsing these board for a few days, I have a basic understanding of the objections against the various experiments that have been proposed. This one, however, bypasses all these objections that I have read and is simple enough that anybody on these boards could perform it (which is one of the objections that has been put forward to many experiments, namely that they are too complex or are too expensive to perform.

As has been pointed out, FE advocates have a tendency to ignore evidence that doesn't support their worldview.  Observations of the azimuth of sunrise, which are different that those predicted by the FE model, and observations of navigation in the southern hemisphere are either ignored, or called lies.

This works the same in FE and RE models.  Because the compass you are steering with is pointing North, the course of East or West would be 90? relative to North.

Yes. The point I was making is that there is a difference between using this system to navigate on a round Earth or a Flat Earth gives different results.

The course that you have drawn (assuming a polar projection) is south of west, not a true westerly course.

That wasn't supposed to a pic of a round earth, but of a flat earth. So it si not a polar projection, but an overhead image of a flat earth.

This is the reason that the shortest distance on a globe is a curve, if you steer a constant course, you end up moving in an arc.

Specifically called a geodesic, which under Non-Euclidean geometry is equivalent to a Straight line in Euclidean geometry.

The difference isn't in the compass itself, the difference is in the courses and distances that would be steered.  On a FE model of the Earth, for travel in the southern hemisphere you would go closer to the equator while in the RE model, you steer closer to the pole.

This is the question that needs to be addressed by the FEers, that if there is such an easy way to show that you are on a Flat Earth or a Round Earth, then how can they support their claims of a Conspiracy, and that the Earth is indeed flat as anyone with a Magnet, A Car and a spare weekend could easily do this and break the conspiracy and prove that the Earth is indeed Flat. But perhaps it is the fear that they will not get the result predicted by a Flat Earth and instead get the result predicted by a Round Earth.