#### JSS

• 676
• Math is math!
##### Re: Around-the-World Sailing Races?
« Reply #20 on: May 18, 2020, 04:16:22 PM »
Yes, indeed you would end up back at the pole on a FE with your proposed trip, BUT the flaw in that is that you have not made an equilateral triangle on your flat earth since the equator part of the trip is a curved line, a radius around the North Pole.  The math would then fail.  On a globe my route from pole to equator and back to the pole is a perfectly fine 90-90-90 equilateral spherical triangle.  Yours is a pie wedge.

And so far, no one has answered why celestial navigation, based on spherical trigonometry, works if the earth is truly flat.  Plus the matching issue as to why sea captains don’t believe in a flat earth.
Everything above our heads appears as if it is in a cylinder.

That is how objects would appear above an x/y coordinate system.

You don't need spherical trigonometry to negotiate an ocean trip.

That's just nonsense.

A sextant uses the angle of celestial objects to the horizon in a formula to plot it onto a sphere, and they have been used for centuries and been proven accurate. It matches up perfectly with GPS coordinates as stated before, they are both commonly used together even now.

Can you please explain the math behind your cylindrical x/y coordinate system? How do you use that to navigate? Thanks.

#### totallackey

##### Re: Around-the-World Sailing Races?
« Reply #21 on: May 18, 2020, 04:17:44 PM »
Yes, indeed you would end up back at the pole on a FE with your proposed trip, BUT the flaw in that is that you have not made an equilateral triangle on your flat earth since the equator part of the trip is a curved line, a radius around the North Pole.  The math would then fail.  On a globe my route from pole to equator and back to the pole is a perfectly fine 90-90-90 equilateral spherical triangle.  Yours is a pie wedge.

And so far, no one has answered why celestial navigation, based on spherical trigonometry, works if the earth is truly flat.  Plus the matching issue as to why sea captains don’t believe in a flat earth.
Everything above our heads appears as if it is in a cylinder.

That is how objects would appear above an x/y coordinate system.

You don't need spherical trigonometry to negotiate an ocean trip.

That's just nonsense.

A sextant uses the angle of celestial objects to the horizon in a formula to plot it onto a sphere, and they have been used for centuries and been proven accurate. It matches up perfectly with GPS coordinates as stated before, they are both commonly used together even now.

Can you please explain the math behind your cylindrical x/y coordinate system? How do you use that to navigate? Thanks.
A sextant is not used to plot things onto a sphere.

Where did you get that from?

They do not carry globes on ships.

They carry flat charts.

#### JSS

• 676
• Math is math!
##### Re: Around-the-World Sailing Races?
« Reply #22 on: May 18, 2020, 04:32:09 PM »
A sextant uses the angle of celestial objects to the horizon in a formula to plot it onto a sphere, and they have been used for centuries and been proven accurate. It matches up perfectly with GPS coordinates as stated before, they are both commonly used together even now.

Can you please explain the math behind your cylindrical x/y coordinate system? How do you use that to navigate? Thanks.
A sextant is not used to plot things onto a sphere.

Where did you get that from?

They do not carry globes on ships.

They carry flat charts.

Sextants do indeed plot onto a sphere. I got that from the manual of the sextant I own, plus every article describing how they work on the internet.

Part 2 - Applying Spherical Trigonometry. In this section the two formulas of spherical trigonometry that are needed to solve the celestial navigation problem will be derived.  Recall from Part 1 that a great circle is any circle on the surface of a sphere whose center is also the center of the sphere. The angle of intersection of two arcs of great circles is defined as the angle formed by the tangents to these arcs at their point of intersection.

Page 33 of this document has some images explaining how to use a sextants measurements to plot onto a sphere - https://pbps.org/docs/Celestial%20Navigation%20Book.pdf

Yes, ships don't carry 100's of huge globes with them because there isn't room for them. Flat maps take up much less space and are easier to draw and measure on.

#### somerled

• 319
##### Re: Around-the-World Sailing Races?
« Reply #23 on: May 18, 2020, 05:54:03 PM »
Okay, I gave the illustration of an equilateral triangle on a sphere with three 90 degree angles to contrast to the standard flat equilateral triangle of three 60 degree angles just to illustrate the difference and to make sure readers knew what I was talking about.  Never-the-less spherical trig is indeed different than flat trig, and celestial navigation is based on spherical trig.  It uses spherical trig to calculate the angles relative to where a celestial body is directly over the surface of the earth at the time you are taking the sight.  (In other words the place you would be if the celestial body you are using was straight up over your head.) If that were the case all the time then celestial would be absurdly easy. Since the celestial object (sun, moon stars, planets) is almost never directly over your head, you use a sextant to measure the angle that object appears above the horizon.  Celestial then uses that angle with spherical trig to determine your "line of position".  (It's a movie myth that a single sextant sight gives you an "X marks the spot" position.  Except for the famous "noon sight" you get a short line that you are somewhere on that line.  There are other ways to then upscale that to a more precise position.).  And in reality nobody does the math themselves.  You use either books of detailed tables or later computer/calculators to do that math.  BUT the reality is that the system is indeed based on spherical trig, not flat trig.  The respondent's statement that you don't need spherical trig to navigate, that it's "nonsense" is simply not true for celestial navigation.  it is true for navigating on a chart, within sight of land, to work out your bearing to a lighthouse for example.  Flat trig works fine for that, because the distances involved are so short that the "needed correction" for being on the surface of a sphere is trivial.  It's the same reason you can use a flat paper chart to navigate along the coast.  Technically that flat chart is slightly "wrong" since you cannot accurately depict a sphere on a flat paper, but again for the distances involved the "error" is trivial.  But out on the open ocean, trying to determine your position is an entirely different matter.  Prior to GPS, you needed celestial navigation to do that. And without the spherical trig behind celestial, it would fail. And it doesn't fail - it works.  It's worked for hundreds of years.  If the earth was flat, then the math for celestial would be standard flat trig, but it's not.  There would be no need to calculate spherical triangles to determine your position since you are on a alleged flat surface.  This is a simple non-disputable fact.

I feel I speak with some degree of real-world expertise about celestial navigation.  Anybody out there who has used celestial who disagrees with me?

Celestial navigation has been carried out for thousands of years. Mankind knows the celestial sphere rotates overhead and has always used this for navigation .The stars rise and set , and all reach zenith which has always given a good approximation of longitude .

The spherical calculations are pointless as shown , none of what you say points to earth being a globe .

A trip from N pole to the equator and back after travelling a quarter of the equators length is not a short journey so how can you say it only works on short trips?

#### GreatATuin

• 235
• It's turtles all the way down
##### Re: Around-the-World Sailing Races?
« Reply #24 on: May 18, 2020, 09:36:41 PM »
Yes, indeed you would end up back at the pole on a FE with your proposed trip, BUT the flaw in that is that you have not made an equilateral triangle on your flat earth since the equator part of the trip is a curved line, a radius around the North Pole.  The math would then fail.  On a globe my route from pole to equator and back to the pole is a perfectly fine 90-90-90 equilateral spherical triangle.  Yours is a pie wedge.

And so far, no one has answered why celestial navigation, based on spherical trigonometry, works if the earth is truly flat.  Plus the matching issue as to why sea captains don’t believe in a flat earth.
Everything above our heads appears as if it is in a cylinder.

Only if you consider the southern hemisphere doesn't exist.
Nearly all flat earthers agree the earth is not a globe.

#### somerled

• 319
##### Re: Around-the-World Sailing Races?
« Reply #25 on: May 18, 2020, 09:39:42 PM »
It doesn't.

#### GreatATuin

• 235
• It's turtles all the way down
##### Re: Around-the-World Sailing Races?
« Reply #26 on: May 18, 2020, 09:48:33 PM »
It doesn't.

Very clever.

Why is there "another cylinder" south of the Equator?

Anyway, what's so special about the Equator on a flat Earth? What's so special about the tropics on a flat Earth?
Nearly all flat earthers agree the earth is not a globe.

#### somerled

• 319
##### Re: Around-the-World Sailing Races?
« Reply #27 on: May 19, 2020, 06:46:46 AM »
Not clever . It's a statement of the bleedin obvious.

The tropics mark the Northern and Southernmost limits of the sun's journey as it orbits around the plane . The equator is the midpoint on it's journey .

The globe model has the tropics at 66.6 degrees from the poles and the polar circles at 66.6 degrees from the equator . The apparent cause is the tilt of the earths axis being 23.4 degrees - which is 66.6 degrees if you take the angle from the horizontal.
And earth scoots around the sun at an average distance of 93,000,000 miles and completes it orbit in 365.25 days (hence our need for  leap years) which gives a velocity of 66,600 mph.
Interesting that.

#### totallackey

##### Re: Around-the-World Sailing Races?
« Reply #28 on: May 19, 2020, 11:32:50 AM »
Sextants do indeed plot onto a sphere. I got that from the manual of the sextant I own, plus every article describing how they work on the internet.

Part 2 - Applying Spherical Trigonometry. In this section the two formulas of spherical trigonometry that are needed to solve the celestial navigation problem will be derived.  Recall from Part 1 that a great circle is any circle on the surface of a sphere whose center is also the center of the sphere. The angle of intersection of two arcs of great circles is defined as the angle formed by the tangents to these arcs at their point of intersection.

Page 33 of this document has some images explaining how to use a sextants measurements to plot onto a sphere - https://pbps.org/docs/Celestial%20Navigation%20Book.pdf

Yes, ships don't carry 100's of huge globes with them because there isn't room for them. Flat maps take up much less space and are easier to draw and measure on.

"I know I claimed that sextants plot on a sphere; because, while I do understand ships do not carry around a globe for the purpose of drawing lines on it (...they carry perfectly flat charts where they end up plotting what they derive from the sextant, just like you wrote totallackey!), I gonna stick with what the writing says because it fits my narrative. Real life experience be damned."

But thanks for admitting what I wrote was true.

There is hope for you yet.

#### JSS

• 676
• Math is math!
##### Re: Around-the-World Sailing Races?
« Reply #29 on: May 19, 2020, 12:36:29 PM »
Sextants do indeed plot onto a sphere. I got that from the manual of the sextant I own, plus every article describing how they work on the internet.

Part 2 - Applying Spherical Trigonometry. In this section the two formulas of spherical trigonometry that are needed to solve the celestial navigation problem will be derived.  Recall from Part 1 that a great circle is any circle on the surface of a sphere whose center is also the center of the sphere. The angle of intersection of two arcs of great circles is defined as the angle formed by the tangents to these arcs at their point of intersection.

Page 33 of this document has some images explaining how to use a sextants measurements to plot onto a sphere - https://pbps.org/docs/Celestial%20Navigation%20Book.pdf

Yes, ships don't carry 100's of huge globes with them because there isn't room for them. Flat maps take up much less space and are easier to draw and measure on.

"I know I claimed that sextants plot on a sphere; because, while I do understand ships do not carry around a globe for the purpose of drawing lines on it (...they carry perfectly flat charts where they end up plotting what they derive from the sextant, just like you wrote totallackey!), I gonna stick with what the writing says because it fits my narrative. Real life experience be damned."

But thanks for admitting what I wrote was true.

There is hope for you yet.

You claimed sextants don't plot onto a sphere, I showed that yes, the math indeed takes a sextants measurements and plots it onto a sphere. This is a simple fact, the math is very clear.

Putting words in my mouth doesn't prove otherwise, it's rude and doesn't contribute to the discussion, so please stop doing that.

Can you show me what math you think sextants use that don't require spherical mapping and calculations?

#### totallackey

##### Re: Around-the-World Sailing Races?
« Reply #30 on: May 19, 2020, 12:58:23 PM »
You claimed sextants don't plot onto a sphere, I showed that yes, the math indeed takes a sextants measurements and plots it onto a sphere. This is a simple fact, the math is very clear.
You showed that math doesn't actually plot things on a sphere.

You admitted the plotting is circumscribed on flat charts found on ships.

That too is a simple fact.
Putting words in my mouth doesn't prove otherwise, it's rude and doesn't contribute to the discussion, so please stop doing that.
I objectively paraphrased what you wrote.

Nothing wrong with that at all.
Can you show me what math you think sextants use that don't require spherical mapping and calculations?
Obviously none of the math is based on spherical mapping and calculations because the plotting is done on a flat chart.

#### JSS

• 676
• Math is math!
##### Re: Around-the-World Sailing Races?
« Reply #31 on: May 19, 2020, 01:40:48 PM »
You claimed sextants don't plot onto a sphere, I showed that yes, the math indeed takes a sextants measurements and plots it onto a sphere. This is a simple fact, the math is very clear.
You showed that math doesn't actually plot things on a sphere.

Please show where I showed math that doesn't plot data onto a sphere for a sextant.  I'll quote myself earlier, saying the opposite.

Part 2 - Applying Spherical Trigonometry. In this section the two formulas of spherical trigonometry that are needed to solve the celestial navigation problem will be derived.  Recall from Part 1 that a great circle is any circle on the surface of a sphere whose center is also the center of the sphere. The angle of intersection of two arcs of great circles is defined as the angle formed by the tangents to these arcs at their point of intersection.

Obviously none of the math is based on spherical mapping and calculations because the plotting is done on a flat chart.

If I draw a picture of you on paper does it mean you are flat?

#### totallackey

##### Re: Around-the-World Sailing Races?
« Reply #32 on: May 19, 2020, 01:54:10 PM »
You claimed sextants don't plot onto a sphere, I showed that yes, the math indeed takes a sextants measurements and plots it onto a sphere. This is a simple fact, the math is very clear.
You showed that math doesn't actually plot things on a sphere.

Please show where I showed math that doesn't plot data onto a sphere for a sextant.  I'll quote myself earlier, saying the opposite.
You stated quite succinctly that ships do not carry spheres for charting.

You stated they carry flat charts and maps.

You wrote it, I didn't.

Why would you ask me to show you something you wrote?

If I draw a picture of you on paper does it mean you are flat?
You and I both know that I am not flat.

The reason we know this is simple.

Simply by standing in the same room, you can see that.

No such luck with the supposed globe.

#### somerled

• 319
##### Re: Around-the-World Sailing Races?
« Reply #33 on: May 19, 2020, 01:56:17 PM »
The use of a sextant isn't a complicated matter JSS .

Sextants measure angles up to 60 degrees . Used at sea to measure the angle between the horizon and whichever celestial body you want to use for navigation .

On land you you would set up a sextant to measure the angle between the horizontal , found by plumb line and set square , and which ever body . You don't use a plumb bob at sea because it would be difficult to set .

If you want to measure an angle greater than 60 degrees you use a quadrant .

If you want to plot your results onto a globe you would apply spherical trig .

It's just a device for measuring angles between points and says nothing about the earth being a sphere .

#### JSS

• 676
• Math is math!
##### Re: Around-the-World Sailing Races?
« Reply #34 on: May 19, 2020, 02:02:18 PM »
The use of a sextant isn't a complicated matter JSS .

Sextants measure angles up to 60 degrees . Used at sea to measure the angle between the horizon and whichever celestial body you want to use for navigation .

On land you you would set up a sextant to measure the angle between the horizontal , found by plumb line and set square , and which ever body . You don't use a plumb bob at sea because it would be difficult to set .

If you want to measure an angle greater than 60 degrees you use a quadrant .

If you want to plot your results onto a globe you would apply spherical trig .

It's just a device for measuring angles between points and says nothing about the earth being a sphere .

If plotting your position has nothing to do with spheres then why use spherical trig?

#### somerled

• 319
##### Re: Around-the-World Sailing Races?
« Reply #35 on: May 19, 2020, 02:06:13 PM »
To map your findings onto a sphere .

#### JSS

• 676
• Math is math!
##### Re: Around-the-World Sailing Races?
« Reply #36 on: May 19, 2020, 02:06:47 PM »
You claimed sextants don't plot onto a sphere, I showed that yes, the math indeed takes a sextants measurements and plots it onto a sphere. This is a simple fact, the math is very clear.
You showed that math doesn't actually plot things on a sphere.

Please show where I showed math that doesn't plot data onto a sphere for a sextant.  I'll quote myself earlier, saying the opposite.
You stated quite succinctly that ships do not carry spheres for charting.

You stated they carry flat charts and maps.

You wrote it, I didn't.

I think I see what you mean now.  You are claiming that because I said ships don't carry globes, the math for sextants doesn't use spherical geometry?

That is deeply flawed logic.  What ships carry has nothing to do with math for calculating a position with a sextant.

The math for sextants uses spherical calculations, I've shown you this several times. Sextants plot onto a sphere. What you do with that data later doesn't change the math.

#### JSS

• 676
• Math is math!
##### Re: Around-the-World Sailing Races?
« Reply #37 on: May 19, 2020, 02:08:40 PM »
To map your findings onto a sphere .

Exactly.  You take a reading of an angle with a sextant. You then use math to plot this onto a sphere to find your position.

If you try and map the angle directly it to a plane, it doesn't work.

Thus, the shape of the earth is a sphere.

#### totallackey

##### Re: Around-the-World Sailing Races?
« Reply #38 on: May 19, 2020, 03:11:26 PM »
To map your findings onto a sphere .

Exactly.  You take a reading of an angle with a sextant. You then use math to plot this onto a sphere to find your position.

If you try and map the angle directly it to a plane, it doesn't work.

Thus, the shape of the earth is a sphere.

You wrote earlier that the angles are plotted onto flat charts.

Even my great uncle, who used a sextant in WWII in the Pacific Theater, showed me a sextant and showed me to use it.

He drew all the angles on a lfat piece of paper.

He didn't use a sphere.

#### JSS

• 676
• Math is math!
##### Re: Around-the-World Sailing Races?
« Reply #39 on: May 19, 2020, 03:19:58 PM »
To map your findings onto a sphere .

Exactly.  You take a reading of an angle with a sextant. You then use math to plot this onto a sphere to find your position.

If you try and map the angle directly it to a plane, it doesn't work.

Thus, the shape of the earth is a sphere.

You wrote earlier that the angles are plotted onto flat charts.

Even my great uncle, who used a sextant in WWII in the Pacific Theater, showed me a sextant and showed me to use it.

He drew all the angles on a lfat piece of paper.

He didn't use a sphere.

I think you are getting confused about what plot onto a sphere means.  Let me try and be more precise in my wording.

You use a sextant to measure the angles of the heavenly bodies you are measuring.

You take these angles and use a formula to mathematically transform them into a set of spherical co-ordinates.

You can then take these spherical co-ordinates and use a pen to draw them onto a physical map, or a globe, or any other surface you can reach.