# How ascending airplanes debunk the globe – Part 2

In my last post about how an ascending plane debunks the globe, I wrote that the GE folks will use the argument that the plane is tracking with the curve therefore, curvature is of no consequence.

Even though I have the mathematical proof of this impossibility, I was challenged anyway.  It seems the only way to provide definitive proof, is to show that the rate of climb, the climb angle and the speed of the aircraft make it impossible for it to track with the curvature.

As the aircraft ascends, it does so at a specific angle and speed.   Knowing these values, we can map the actual path of the aircraft as it ascends.  For the aircraft to track with curvature, it would need a much smaller climb angle since the curvature alone provides 4.37 miles of altitude.

It must also be noted that commercial aircraft like 747s gain altitude by aiming the nose upward and gaining lift through forward motion; they do not act like balloons and float upward.  When the aircraft starts to take-off it angles the nose upward and ascends away from the ground.  In order for the aircraft to track with the curvature it would have to stay perpendicular to the axis of the earth.  As the distance from the starting point increases, the smaller the climb angle would need to be.

The final altitude is 6.62 miles which leaves 2.25 miles that the aircraft would need to climb.  To calculate the necessary angle we would take the inverse TAN of 2.25 miles / 185.97 miles.

2.25 miles / 185.97 miles = .012 miles

TAN -1 (.012 miles) = 0.69°

This means that the average angle over the entire ascent would have to be 0.69°.  Unfortunately for GE folks, this is not what happens in the real world.  During take off most 747 aircraft use a climb rate of about 12° but reduce that by about 0.5° every minute or so.  There is obviously variability based upon certain conditions but this is sufficient for this case.  By recording the level on a flight to France I can confirm this reality with going into speculative territory.

I can say for certain that the pitch of the aircraft for the first 12 minutes was between 4-12° and the final 13 minutes ranged between 1-3° making an average of 0.69° impossible.

At the end of the day for an aircraft to ascend on a curved surface while tracking with that curve, it must be perpendicular to the axis of the earth and ascend like a balloon.

# How the climb rate of an airplane debunks the globe

I have watched and read FlatEarth (“FE”) content that talks about the issue with flight paths, times and other anomalies that are difficult or impossible on a GlobeEarth (“GE”).  However, many GE folks tend to write-off these anomalies by evoking gravity.  Though the gravity excuse can be rebuked, it gives the GE folks a free pass.  This pass is about to be taken away.

My previous work on curvature calculations has given me the idea to track the flight path of a 747-200 class aircraft during the ascent phase of the journey.  On a recent trip to France I recorded the angle of ascent using a bubble level and screen capture software.  This allowed me to compare (in real-time) the ascent angle over time with the flight data from Flight Aware.  The majority of the ascent was between 1-3°.  It lost about 1° of angle every minute.  During the initial take off the angle was much higher at around 12° but it quickly reduced to 2° in about 12 minutes. The final 13 minutes was at a nominal angle of 1°.  A quick calculation shows that TAN(2°) x 185 miles (6.46 miles) is close to the 6.62 miles achieved after 25 minutes.  In other words, the bubble level and the recorded values from flight aware seem to correlate.

If you have an account at flight aware, you can take a look at the actual flight taken.  I will add the data tables here for those who don’t wish to create an account.

The purpose of this post is to show that if there is curvature to the earth, the climb rate over time and the curvature of the earth must place any average international flight at more than double the recorded cruising altitude. This is because the amount of curvature during the ascent phase of the example flight below would be approximately 4.37 miles even without adding any climb at all.

All of the data is publicly available and anyone can do the same calculations I’m going to do.  In fact, any international flight can be used for this experiment.

If you take a look at this graph:

you can see the ascent is in the first 25 minutes and 25 seconds of the flight (01:59:02 – 02:24:27).  You can compare this to the table data below:

An examination of this data eliminates a potential objection by GE folks that plane is flying with the curvature of the earth since the plane cannot be tracking with the curvature and ascending at the same time.  By it’s very definition, the plane is moving away from the ground (ascending), not tracking with it as it should during cruising altitude.  This might seem obvious to most logically minded folks but we are dealing with hardened attitudes that will use any argument, no matter how illogical, to avoid the conclusions reached here.

Since the plane is ascending, and if we are living on a ball, we must take into account the ascending and curvature rates at the same time.  There is no getting away from this.  This also destroys the idea that gravity keeps the plane moving along the curve, since if this was the case, a plane could never ascend at all.  The ascent angle over time is the key.

For example, if a plane took off and ascended at a nominal climbing rate of 1 meter / hour at an average speed of 450 miles / hour, it would reach a cruising altitude of 4.7 miles in 26 minutes.  If it continued at this rate for 52 minutes (or an additional 26 minutes), it would be at a cruising altitude of 19.8 miles.  The plane can ascend because it’s under it’s own power.  It has already overcome the force of gravity or it would fall to the ground.  But I digress….

Using a real example, if we include curvature into the calculation with the recorded climb rate, the plane should reach a cruising altitude of 35,000 feet (or 6.62 miles) in approximately 13 minutes.  This was calculated using 51 specific data points.  Each point contains time, latitude, longitude, course, direction, kts (knots), km/h, meters, climb rate and reporting facility.  By calculating the speed by the time interval, I can calculate the total distance travelled during each time interval.

The first 12 data points are ignored for distance travelled since the plane took off in a westerly direction and then turned around to a northeast direction.  We still need to include the altitude reach during this time frame which is approximately 1.26 miles.  This altitude was reached at 2:02:17 pm.

To accurately calculate the distance travelled, I had to measure the time difference between each data point (between 15-60 seconds) and multiply by the speed of the plane at that interval.  This eliminated the use of an average speed which would most likely be used as an additional rebuttal against this proposal.

If you examine the table below, you can see each time interval along with the height and curvature reached.

The 7 columns of the far right show the curvature that would occur over the distance travelled.  The distance travelled was calculated by converting the speed to nautical miles/min (i.e 281 kts / 60 min = 4.68 nm/min).

I then divided the time frame for each data point by 60 seconds to get the fraction of a minute that the plane travelled during that time frame (ie. 25 seconds / 60 seconds = .41 min)

Once I had that value, I was able to multiply that by the plane’s current speed to get the distance travelled (i.e. 4.68 nm/min × .41 min = 1.95 nm).  I then converted the value from nautical miles to miles (i.e. 1.95 nm × 1.15 = 2.24 miles).

Once I had the distance at each interval I could calculate the amount of curvature in feet.  Whew !!!

Since curvature is accumulative, the total arc distance from the starting point to the specific time frame must be included not just the distance travelled in that particular time frame.

I finally converted the last 21 data points into miles of curvature.  Since the plane was already 1.26 miles in altitude when it started heading northeast, I had to add that value to the curvature accumulated from 02:02:17 pm onward.  I calculated both the altitude of the plane without curvature and one with curvature.

As you can see from the table, the cruising altitude should have been reached at approximately the 13 minute mark.  Since the plane does not stop ascending at the 13 minute mark but continues for an additional 12 minutes, we are left with the inescapable conclusion that there is no curvature.

I’ve included a link to a post that calculates the distance covered during take off and the time taken to reach cruising altitude for comparison purposes.

https://aviation.stackexchange.com/questions/14357/how-long-after-takeoff-for-a-boeing-747-400-to-reach-cruise-speed