Ways to contact an Arduino from 100km away or more

I'm not very educated on telemetry besides a few pirate radio stations I've made in the past with a friend but I'm very new to Arduino telemetry. Recently I got interested in more advanced rocket flight computers but my main concern is the telemetry. You may know a rocket reaches very large distances but I'm having trouble with figuring out how I can communicate with the Arduino. I've made a few APCP rocket motors before in the past and curently I've been designing LOX engines at a small scale, my APCP rockets have only reached a max of 56,000 m high but as you start to advance to larger distances aerodynamic forces act on the rocket greatly, especially when reaching max Q. I need to be able to gather information from the rocket to see the areas where rocket struggles in so intern I can improve but in my case that becomes a challenge when the only info I get from a rocket that blows up mid-air is a flash and pieces of shrapnel I find laying around. I would like to be able to communicate to it from at least 100,000m away mostly just to gather information and I don't need to be able to send commands although it would be nice if I could. Any suggestions or strategies I could use to accomplish my goal?

LoRaWAN can communicate great distances with clear line of site and use very little power. However, the amount of data you can send is really small. On paper, you can get 10Km+ with favorable environmental factors (the world record stands at over 700km for LoRaWAN - I personally have managed 6km in semi-urban environments before).

Presumably if your rocket explodes, you will lose the arduino board too?

I can see two ways of working this. You either use a LoRa (or Sigfox, but you have to pay a subscription for that but it does come with a receiver network and all the backhaul already dealt with) chip, and send very small packets of sensor data (you are going to have to really streamline your sensor data).

OR

You use sigfox as a locator (LoRa isn’t feasible to do this with, unless you can get base stations put around the area and get it talking to a load of base stations you can’t triangulate though you could use a GPS shield I guess, but sigfox already has base stations dotted around and triangulation works, you can buy off the shelf Sigfox locator beacons with GPS on board), and have the rocket jetison your board and have the board saving to an SD card for better resolution data. You then just go find the board after it has been thrown off.

Both methods are difficult though…

Connect to a mobile phone network?
Install a GPRS/3G/4G/5G module (whatever available) on the Arduino side and have it call home over the Internet.

LoRa will do this easily.

During some testing I did in 2015;

http://www.southgatearc.org/news/2015/january/lora_low_cost_long_distance_telemetry.htm#.WxJSu4rTXcs

So 105km @ 13.7kbits @ 5mW.

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srnet:
LoRa will do this easily.

During some testing I did in 2015;

http://www.southgatearc.org/news/2015/january/lora_low_cost_long_distance_telemetry.htm#.WxJSu4rTXcs

So 105km @ 13.7kbits @ 5mW.

Depends of course on the payload... if he wants second by second real-time telemetry of heading, bearing, acceleration, speed, X Y and Z inertia, position, air temperature, engine temperature, altitude... it's going to be difficult.

One possible issue with a rocket however is the rate of change of doppler shift, this could be a problem close in, but should reduce as the rocket moves away.

Didn't think of that, could be be a factor!

srnet:
One possible issue with a rocket however is the rate of change of doppler shift, this could be a problem close in, but should reduce as the rocket moves away.

Another factor to take in account is the that as the rocket increases altitude the atmosphere takes much less of an effect on electromagnetic waves and is much less susceptible to refraction or absorption, from this we can conclude that it would increase the range of the device and has more range vertically (the thickest parts of the atmosphere are the stratosphere reaching a height of 50,000m high which would have the largest effect) than horizontally where atmospheric distortion has much more of an effect on the electronics.