[edby]

See below for a plot of flight distances versus flight times.

Methodology:
1. Take airport pairs where there is a direct flight from one airport to the other, and where a flight time is available. 354 pairs in all.

2. Obtain the latitude and longitude of each airport.

3. Use the Haversine formula to determine the distance in km between the airports, using the assumption that the earth is a sphere 6,371km in radius.

4. Plot the distance against the time (see below).

Observations
The distance assumption is clearly based on RE, however the flight time is simply the observed time taken (from published flight times admittedly, but any flat earth observer could easily check these by taking the flights). If the earth is an approximate sphere, we would expect to see a high but not exact correlation between RE distance and time.

The average speed varies between 288 km/h between Paris and Brussels and 939km/h between Jo'burg and Sydney. Generally for shorter times (less than 6 hours) the average speed falls. Hypothesis: this is caused by the time taken to reach maximum speed from zero. One could probably work out an exact relationship, I haven't tried.

[Tom Bishop]

We've discussed this.

How are kilometers gauged on the left hand side in that chart? Spherical coordinate distances from Longitude and Latitude systems? How do you measure that sort of large distance without using the standard Longitude and Latitude system?

That is the matter under question, yet that graph "knows" how many kilometers the planes flew.

That is the matter under question, yet that graph "knows" how many kilometers the planes flew.

No, the airline does.
And they know how long their flights take.
Planes fly at a fairly standard cruising speed and that graph demonstrates that, time and distance largely correlate.
It's almost like they know how far they're flying and how fast and they have a map which works.

Actually I think Tom's problem is the y-axis. This distance depends on spherical assumptions, and I suspect he thinks the logic is somehow circular.

[edby]

It's not the same.

(i) I collected the data myself (ii) there are many more data points (more than 350 in all) (iii) I used the proper formula to compute the RE predicted distance between the locations. The other experimenter used a piece of string and a globe, from memory.

I am now implementing a formula to compute the corresponding FE distance based on the azimuthal equidistant projection. The estimate will vary depending on the map chose, of course.

To avoid all confusion, here is the original graph

[edby]

That is the matter under question, yet that graph "knows" how many kilometers the planes flew.

Yes, because it is worked out using the lat and long of the airport, and a formula which uses RE assumptions. Is that not OK?

[ICanScienceThat]

This is fantastic work. A really nice piece of investigation.

[Tom Bishop]

It's not the same.

(i) I collected the data myself (ii) there are many more data points (more than 350 in all) (iii) I used the proper formula to compute the RE predicted distance between the locations. The other experimenter used a piece of string and a globe, from memory.

If the data is based on the spherical coordinate system of Latitude and Longitude, which you admit is based on the idea that the earth is a sphere, then the results are invalid until you can demonstrate that the system and model is correct.

[ICanScienceThat]

It's not the same.

(i) I collected the data myself (ii) there are many more data points (more than 350 in all) (iii) I used the proper formula to compute the RE predicted distance between the locations. The other experimenter used a piece of string and a globe, from memory.

If the data is based on the spherical coordinate system of Latitude and Longitude, which you admit is based on the idea that the earth is a sphere, then the results are invalid until you can demonstrate that the system and model is correct.

I do not agree with your logic.

This type of experiment does not require that the Earth must be a sphere. Instead, this type of experiment supports the hypothesis that it is. The logic goes like this:
a) If the system and model is correct, this graph will make a straight line.
b) If the graph is NOT a straight line, then the system and model are incorrect.

So we try it out. If the line comes out curvy, we know that the system and model are flawed in some way.
It comes out as a line, so that means we do not have any cause to suspect the model based on this test.

This becomes a little sticky now. This test does not prove the model is correct. What it does is fail to disprove it.

This helps bolster the evidence for the model. As we say, we do not "prove" things in science, but we can "disprove" things.

[Tom Bishop]

The Latitude and Longitude coordinate system does operate under the assumption that the earth is a sphere. Those are spherical coordinates.

If you are comparing spherical coordinates to spherical coordinates, you will get, ...wait for it..., a sphere.

[ICanScienceThat]

The Latitude and Longitude coordinate system does operate under the assumption that the earth is a sphere. Those are spherical coordinates.

If you are comparing spherical coordinates to spherical coordinates, you will get, ...wait for it..., a sphere.

I sometimes wonder whether you read the posts at all, or did you just not understand, or maybe you're deliberately trying to obscure the results?

Let me spell it out
If the relationship between lat/long and distance between points is truly a sphere, then this graph must make a straight line.
If the graph does NOT make a straight line, we will have disproved that spherical relationship.

We did NOT disprove that spherical relationship.

Do you understand?

[edby]

The Latitude and Longitude coordinate system does operate under the assumption that the earth is a sphere. Those are spherical coordinates.

If you are comparing spherical coordinates to spherical coordinates, you will get, ...wait for it..., a sphere.

We are not comparing spherical coordinates to spherical coordinates. We are comparing distances computed from spherical coordinates with flight times. The flight times would be the same whether or not the earth was flat.

[edby]

For comparison, here are the same flight times but now plotted using an estimate of FE distance from the same co-ordinates. The correlation is not so strong. The outliers are caused by southern hemisphere locations, for example Buenos Aires to Auckland (RE distance 10,355km, FE distance 25,006).

[edby]

Here also are RE speeds compared with FE speeds.

Generally for shorter flight times the speeds are lower. My hypothesis is that the plane has to accelerate to full speed then decelerate back to zero again. For short flights, it will never attain full speed. Both models conform to this, however for southern latitudes the FE plane has to fly at much higher speeds to cover the much larger distances, often breaking the sound barrier.

[edit] The highest FE speed was from Perth to Auckland (2,200 km/h), once again an effect of the southerly latitudes.

[Tom Bishop]

What "FE" map are you using? The monopole model is for illustration purposes only and, in fact, was replaced by our predecessor society with a featureless two pole version in the early 1900's after the discovery of the South Pole.

There is no map.

You are going to have to account for all possibilities.

[Tom Bishop]

An interesting quote:

http://www.travelandleisure.com/travel-tips/airlines-airports/why-flights-take-longer

“Surprisingly, flight time is calculated from when the aircraft releases the parking brake (on push back) to when it sets the brake on arrival to the gate,” commercial pilot Chris Cooke told Travel + Leisure. “All that waiting in line during taxi and takeoff counts toward flight time.”

Not surprisingly, saving money is another reason flights take longer today. “Airlines are able to save millions per year by flying slower," reveals a video from Business Insider.

A study which says they are skewing flight times:

https://www.telegraph.co.uk/travel/travel-truths/Are-airlines-exaggerating-flight-times-so-theyre-never-late/

Are you being told the truth about flight times?

Passenger jets have never been more advanced. With Boeing’s 787 Dreamliner, introduced in 2011, leading the charge, and new models like the 737 MAX and the Airbus A320neo following in its wake, the aircraft on which we travel are safer, smoother, quieter and more fuel efficient than ever.

They also appear perfectly capable of flying faster than their predecessors. Just last month the low-cost carrier Norwegian issued a celebratory press release after one of its 787 Dreamliners whizzed from John F. Kennedy International Airport in New York to London Gatwick in five hours and 13 minutes, setting a new transatlantic record for a subsonic plane. That’s three minutes quicker than the previous best time set by British Airways in January 2015.

So why, record-breaking feats notwithstanding, are airlines claiming it takes longer and longer to fly from A to B?

That’s according to research by OAG, the aviation analyst, carried out for Telegraph Travel. It found that over the last couple of decades, despite new technology, scheduled flight times - ie. how long an airline estimates it will take to complete a journey - have actually increased by as much as 50 per cent.

Looking at Europe’s busiest international route, for example - Heathrow to Dublin - it found that in 1996 the vast majority of airlines published a scheduled flight time of between 60 and 74 minutes. Fast forward 22 years and almost all claim the journey takes between 75 and 89 minutes, while a handful bank on 90 minutes or more.

[edby]

This study says that airliners are skewing flight times.

Undoubtedly that is the reason.
Actually I don't think that can be the reason. Some of the discrepancies are very large. Remember that any FE researcher can test these simply by going on the flights, or asking a fellow researcher.

[edby]

You are going to have to account for all possibilities.

I can do the math for pretty much any FE model, if you want to make suggestions.

The problem is that all the maps other than the monopole, you get curved lines of longitude. This would show up pretty quickly in the model.

[Tom Bishop]

I don't know if it is possible to solve all of these problems.

- There is no FE map
- We can't rely on the distances to be accurate because Lat/Lon relies on spherical coordinates
- We can't rely on the flight times to be accurate

On top of all of the above it is also known that on international flights planes regularly use jet streams to quicker get to a destination.

https://books.google.com/books?id=vsodESrwdm4C&lpg=PA183&dq=%22jet%20streams%22%20%22miles%20per%20hour%22&pg=PA183#v=onepage&q&f=true



According to this:

https://books.google.com/books?id=vsodESrwdm4C&lpg=PA183&dq=%22jet%20streams%22%20%22southern%20hemisphere%22%20%22miles%20per%20hour%22&pg=PA183#v=onepage&q=50%20miles%20per%20hour&f=false

"Jet streams are ever-present, relatively narrow, streams of high-speed winds undulating around the Northern and Southern Hemispheres"

There are East and West moving winds in the Southern Hemisphere.

http://thejunkwave.com/what-is-a-gyre/

Look at the South Pacific Gyre:

[Tom Bishop]

It is apparently not uncommon for a plane to fly faster than the speed of sound:

https://www.wired.com/story/norwegian-air-transatlantic-speed-record/

OK, about that "subsonic" bit. You might know that the speed of sound at an altitude of 30,000 to 40,000 feet is roughly 670 mph. But Norwegian’s planes didn't break the sound barrier. Those near-800-mph figures represent ground speed—how fast the aircraft is moving over land. Their air speed, which factors out the 200-mph wind boost, was closer to the 787's standard Mach 0.85. (The older Boeing 747 can cruise at Mach 0.86, but is less efficient than its younger stablemate.) When talking supersonic, and breaking sound barriers, it's all about the speed of the air passing over the wings, which in this case was more like 570 mph.

[BillO]

It's not the same.

(i) I collected the data myself (ii) there are many more data points (more than 350 in all) (iii) I used the proper formula to compute the RE predicted distance between the locations. The other experimenter used a piece of string and a globe, from memory.

If the data is based on the spherical coordinate system of Latitude and Longitude, which you admit is based on the idea that the earth is a sphere, then the results are invalid until you can demonstrate that the system and model is correct.

I have flown from Toronto to Vancouver (3,364km) dozens of times.  Depending on wind conditions it takes from less than 4 3/4 hrs to 5 hrs and change.  That fits with that RE data.  You don't have to have taken all these flights yourself either.  Airlines list their average flight times.  You can just google them.

[edby]

We can't rely on the distances to be accurate because Lat/Lon relies on spherical coordinates

You are still misunderstanding the point of the experiment. The calculation of distance using spherical coordinates relies totally on RE assumptions, correct. It uses the Haversine formula which is or was used frequently in navigation. So we want to test this RE method, by seeing whether it calibrates well to an entirely different method of estimating distance, namely flight times.

There is no FE map

Doesn’t matter. The question is how well the two methods correlate with each other. Is there an FE method of calculating distance between two airports that correlates equally well? Possibly, but I doubt it. The azimuthal projection method works poorly, as shown above.

We can't rely on the flight times to be accurate.
[..]
On top of all of the above it is also known that on international flights planes regularly use jet streams to quicker get to a destination.

Not relevant. Suppose the use of jet streams caused a significant distortion for certain routes. Then this would show up in the correlation chart. There would be significant outliers. But there aren’t, as you can see. You need to explain why the two methods are so highly correlated, not why they might be uncorrelated.

And as Bill points out above, it is open to any FE researcher to check this independently, using the same simple methodology.