Radio Communication Delay Experiment

Hi all, I thought of a potentially low budget test that should provide convincing results for the curvature, or lack thereof, of the Earth.

Two "balloons" can be released from two different locations on Earth - say, for example, two different US states. These balloons should have radio communication with each other, and can ping one another (measure the delay time in a round trip message) to get their relative distance apart. Now the balloons start pinging each other, and then each one is released at the same time. Assume they float directly upward.

Then:

FET predicts the balloons will stay the same distance apart.
RET predicts the balloons will get farther apart as they climb higher.

If, say, the balloons start at opposite coasts of the US, then by the time they are only a half-mile above ground, the radio delay time will already be well over one microsecond, which should be easily measurable by electronics (especially if we can do multiple trials).

Cons:
We need the balloons to fly relatively straight upwards. Any engineers know how to do that? I suppose multiple trials would help lessen the error from random drift of the balloons due to our lovely Earth's weather.
Also, the types of electronics needed are ready available, and don't sound very expensive to me - but they might be expensive, because I simply don't know the price. The cost might turn out to be very high, at least for anyone here.

Hi all, I thought of a potentially low budget test that should provide convincing results for the curvature, or lack thereof, of the Earth.

Two "balloons" can be released from two different locations on Earth - say, for example, two different US states. These balloons should have radio communication with each other, and can ping one another (measure the delay time in a round trip message) to get their relative distance apart. Now the balloons start pinging each other, and then each one is released at the same time. Assume they float directly upward.

Then:

FET predicts the balloons will stay the same distance apart.
RET predicts the balloons will get farther apart as they climb higher.

If, say, the balloons start at opposite coasts of the US, then by the time they are only a half-mile above ground, the radio delay time will already be well over one microsecond, which should be easily measurable by electronics (especially if we can do multiple trials).

Cons:
We need the balloons to fly relatively straight upwards. Any engineers know how to do that? I suppose multiple trials would help lessen the error from random drift of the balloons due to our lovely Earth's weather.
Also, the types of electronics needed are ready available, and don't sound very expensive to me - but they might be expensive, because I simply don't know the price. The cost might turn out to be very high, at least for anyone here.

Save yourself the bother, go ask an astronomer.....or anyone with some sense....it's a sphere! .......and it's not hot news, nor a secret, it's been know about for hundreds of years......no balloons required.

FET predicts the balloons will stay the same distance apart.
RET predicts the balloons will get farther apart as they climb higher.

I thought I already explained the problem with this to you.
The difference is tiny compared to the distance and there will be too many complicating factors that will create far too much error. That includes things like water droplets in the air scattering the radiation or delaying its transmission, and the local direction of gravity not actually pointing to the centre of Earth making it impossible to go straight up unless you use something like GPS to determine position.

If, say, the balloons start at opposite coasts of the US, then by the time they are only a half-mile above ground, the radio delay time will already be well over one microsecond, which should be easily measurable by electronics (especially if we can do multiple trials).

There is also the issue of needing them to be able to start pinging each other, which if you are doing it over the US is a distance of 4000 km. That is quite considerable compared to the size of Earth.
Do you know how high they would need to be to begin with?

Well, assuming my math is right, assuming Earth's radius to be 6371 km, and assuming they start 4000 km apart, they would each need to start at an altitude of 327.35 km.
As a comparison, the ISS is currently cruising at an altitude of roughly 400 km.
So you need your balloons to start in space, and then move away.

To get a better idea of a possible result, lets start them 1 km off the ground.
This has them starting at a distance (measured along an arc on the surface of Earth below them) of 225.7461721 km, with an angle subtended at the centre of Earth of roughly 2 degrees.
Also, the straight line distance between the 2 will be slightly longer, at 225.7697943 km.

Now, for any given h, you can find the distance between them:
sin(t/2)=(d/2)/(h+R), so d=2*(h+R)*sin(t/2), which can be separated to:2*h*sin(t/2)+2*R*sin(t/2)
And we can now use this form to easily find the change:
dd/dh=2*sin(t/2) or dd=2*sin(t/2)*dh.
So if you increase h by 1 km, you will increase d by 2*sin(t/2).
2*sin(t/2), at least in this case, is 0.035431543.
The speed of light is 299792.458 km/s.

That means for each km you go up, the delay is increased by roughly 0.1 microsecond.

That, along with all the errors involved, will make it almost impossible (if not actually impossible) to measure.

We need the balloons to fly relatively straight upwards. Any engineers know how to do that? I suppose multiple trials would help lessen the error from random drift of the balloons due to our lovely Earth's weather.

Use GPS to accurately determine the position and correct for any variations.

Also, the types of electronics needed are ready available, and don't sound very expensive to me - but they might be expensive, because I simply don't know the price. The cost might turn out to be very high, at least for anyone here.

A bigger issue may be the license requirements for using such a powerful EM pulse to measure the distance.

JackBlack, that was a very thorough and thought out reply. Thank you.

Quote from: tomato on June 01, 2017, 06:03:50 AM

FET predicts the balloons will stay the same distance apart.
RET predicts the balloons will get farther apart as they climb higher.

I thought I already explained the problem with this to you.

Me? Not me.

Quote from: tomato on June 01, 2017, 06:03:50 AM

If, say, the balloons start at opposite coasts of the US, then by the time they are only a half-mile above ground, the radio delay time will already be well over one microsecond, which should be easily measurable by electronics (especially if we can do multiple trials).

There is also the issue of needing them to be able to start pinging each other, which if you are doing it over the US is a distance of 4000 km. That is quite considerable compared to the size of Earth.
Do you know how high they would need to be to begin with?

Well, assuming my math is right, assuming Earth's radius to be 6371 km, and assuming they start 4000 km apart, they would each need to start at an altitude of 327.35 km.
As a comparison, the ISS is currently cruising at an altitude of roughly 400 km.
So you need your balloons to start in space, and then move away.

Welp, I forgot about that. Oops.
Strangely enough I get 311.4 km, rather than 327, but either way, yes, that kind of puts the noose around the neck for this experiment.

To get a better idea of a possible result, lets start them 1 km off the ground.
This has them starting at a distance (measured along an arc on the surface of Earth below them) of 225.7461721 km, with an angle subtended at the centre of Earth of roughly 2 degrees.

3.5 degrees (but like it matters).

Also, the straight line distance between the 2 will be slightly longer, at 225.7697943 km.

Now, for any given h, you can find the distance between them:
sin(t/2)=(d/2)/(h+R), so d=2*(h+R)*sin(t/2), which can be separated to:2*h*sin(t/2)+2*R*sin(t/2)
And we can now use this form to easily find the change:
dd/dh=2*sin(t/2) or dd=2*sin(t/2)*dh.
So if you increase h by 1 km, you will increase d by 2*sin(t/2).
2*sin(t/2), at least in this case, is 0.035431543.
The speed of light is 299792.458 km/s.

That means for each km you go up, the delay is increased by roughly 0.1 microsecond.

That, along with all the errors involved, will make it almost impossible (if not actually impossible) to measure.

Quote from: tomato on June 01, 2017, 06:03:50 AM

We need the balloons to fly relatively straight upwards. Any engineers know how to do that? I suppose multiple trials would help lessen the error from random drift of the balloons due to our lovely Earth's weather.

Use GPS to accurately determine the position and correct for any variations.

Quote from: tomato on June 01, 2017, 06:03:50 AM

Also, the types of electronics needed are ready available, and don't sound very expensive to me - but they might be expensive, because I simply don't know the price. The cost might turn out to be very high, at least for anyone here.

A bigger issue may be the license requirements for using such a powerful EM pulse to measure the distance.

I agree with all your numbers here. And I never even considered regulations or licensing. GPS is another thing I didn't consider - you've brought up a lot of things I didn't think about.

So finding adequate radio equipment is not practical, let alone starting your balloons in space... thanks for setting this straight, though. I appreciate the reply.

Me? Not me.

My bad. I know someone suggested something akin to this not too long ago.

Welp, I forgot about that. Oops.
Strangely enough I get 311.4 km, rather than 327, but either way, yes, that kind of puts the noose around the neck for this experiment.

It varies depending upon how you do it. You can either use arc length along earth, the tangent to Earth, use trig properly or use simplified formulas.
When you are just dealing with small distances they all work fine and give pretty much the same result.
But when you go to massive distances, like thousands of km, the approximations start to fail.

I agree with all your numbers here. And I never even considered regulations or licensing. GPS is another thing I didn't consider - you've brought up a lot of things I didn't think about.

So finding adequate radio equipment is not practical, let alone starting your balloons in space... thanks for setting this straight, though. I appreciate the reply.

Your welcome. Always happy to help. Even if that "help" is explaining that something wont work or may get you in serious trouble.
Better finding out now than when you have already bought the stuff.