Absolute Simple Proof that the Earth is Round - Taking a Flight

In recent times there has been an increase in the number of people claiming that the earth is flat.

However, what follows is a simple absolute proof that the earth is spherical without needing difficult science or complex maths.
Although this is very simple to demonstrate, to properly verify it one needs to take a flight.

This proof requires making a journey from Sydney, Australia to Johannesburg, South Africa.

First of all, let us look at the journey using the Google Earth application:

Google Earth Sydney to Johannesburg

The line was simply drawn by selecting the two airports and using the ruler, we an see that the straight line distance is 11044Km.

Now let us look for a flight. Qantas airways flies this route and below is a section from their flight booking web page:

Qantas Airways Flight Booking

Notice that the scheduled flight time is 14h05m. In reality it won't be this for various reasons and now there is a very good website[1] that shows all flights and keeps a history of recent flight data, including actual flight time.
Looking again at the Qantas schedule, there is flight QF63 and some flight data from April 2018 is shown below:

FlightRadar24 QF63

What we are interested in is how fast the plane was travelling.
The website shows the distance as 11044Km which agrees with the Google Earth measurement above.
The average flight time is 13h27m so calculating 11044 / 13.45 we get an average speed of 821Kmh.
But something is not quite right here. The Boeing 747 used for this flight typically cruises at 933Kmh,[2] so why the difference?
Below is the flight data for the return flight:

FlightRadar24 QF64

Now the average flight time is only 11h09m so re-calculating we get an average speed of 11044 / 11.15 = 990Kmh.
This is quite a bit faster, and faster than the 747's cruising speed so what is happening?
At these latitudes, there is a prevailing west to east airflow. The same occurs on the northern hemisphere and the author can testify to longer flight times when travelling from Kathmandu, Nepal to Doha, Qatar than when travelling in the opposite direction. These airflows only occur because the earth is spinning.

We can eliminate this air flow by simply taking the average speed to get (821 + 990) / 2 = 906Kmh which is fairly close to the 747's cruise speed, as expected.*
We can calulate the average flight time if there was no wind as (13.45 + 11.15) / 2 = 12.3 hours.

So, the distances, times and speeds approximately agree indicating that this flight is perfectly possible on around earth.**

Now, what happens if we make the same journey on the flat earth?
In the diagram below, which is a scale drawing, n is the North Pole, s is Sydney, j is Johannesburg and r is the rim on the line, longitude 0 (goes through London, UK).

Flat Earth Sydney to Johannesburg.

What we want to do is calculate flat earth distance D between Sydney and Johannesburg and then calculate how fast the plane must travel to cover that distance.

The calculation*** gives D as 23457Km.
Note that this is further than the distance from n to r and can be checked by printing this paper and measuring the two lines.

Using the longest scheduled time (will give the slowest speed) of 14h 05m, the plane needs to travel at an average speed of 23457 / 14.08 = 1666Kmh. This not just a little more than the 747's cruising speed of 933Kmh but 733Kmh more which is clearly impossible. Also this is more than the speed of sound at the cruising altitude and a 747 is not a supersonic aircraft.


There is also a brilliantly clear observation that can be made. Below is the same diagram drawn over the flat earth map:

Flat Earth Sydney to Johannesburg.

Compare the two journeys:
The round earth journey is almost entirely over the sea.
The flat earth journey is over twice as long and about two thirds of it is overland, passing over China, Pakistan, Saudi Arabia and a large part of Africa, crossing the Equator twice.
This can't be emphasised strongly enough, the plane simply does not take this route, not even close.


This can simply checked by merely taking this flight and looking out of the window. If he had the money, the author would happily pay flat earthers to take this trip and and ask flat earthers to explain what they saw. No experiments to set up. No maths needed.
Just eyes to see and a watch to time the journey.

Flat earthers: Please use the eyes that God gave you!

Some Technical Stuff

* This value comes out lower since the journey takes longer due to the extra time needed for take-off and espeially for landing.

** The route shown is the shortest possible distance, being a straight line, but in reality, flight paths, local politics and weather conditions will all cause deviations from the ideal with the distance being longer. With these simple calculations, these factors have not been taken into account but the values, although not exact, are in close agreement.

*** Sydney Airport Latitude -33.9436d, Longitude 151.1842d
Johannesburg Airport Latitude -26.1344d, Longitude 28.2417d

To calculate D we need to us a rule in trigonometry called the cosine rule.[3]
This gives us: D2 = ns2 + nj2 - 2 * ns * ns * cos(t)
On the flat earth and round earth the line nr is 20000Km long and spans 180 degrees of latitude.
ns(Km) = 20000 * ns(deg) / nr = 20000 * (90 + 33.9436) / 180 = 13772Km
nj(Km) = 20000 * nj(deg) / nr = 20000 * (90 + 26.1344) / 180 = 12904Km
t = 151.1842 - 28.2417 = 122.9425 degrees.
So, D2 = 137722 + 129042 - 2 * 13772 * 12904 * cos( 122.9425 )
   = 189667984 + 166513216 - 355427776 * (-0.543797101)
   = 550215218
Taking the square root gives D = 23457Km.

2 Timothy 3:7 always learning and never able to arrive at a knowledge of the truth.
2 Timothy 4:3-4 For the time is coming when people will not endure sound teaching, but having itching ears they will accumulate for themselves teachers to suit their own passions, and will turn away from listening to the truth and wander off into myths.
For comments, questions and suggestions, please contact: Ask me.
23. Apr 2018
[1] https://www.flightradar24.com/
[2] https://en.wikipedia.org/wiki/Boeing_747-400
[3] http://www.cimt.org.uk/projects/mepres/step-up/sect4/index.htm