Height is only one factor. There are many factors for using a sat system with an external antenna, including antenna type, placement on the airframe, cable type, length, termination quality, and so on. Cabling is especially important. What kind of system are you using? Is it Iridium based, or Globalstar, or another type?

I second this. I also work in the industry and people generally don't know that not only do you have to be outside, but you have to have a clear line of sight to the sky and not be near obstructions like buildings. Also, the higher off the ground you are, or the higher the elevation, the better. Even in the best conditions, the call quality can vary as a satellite goes over the horizon and passes your call to another satellite. Also, satellite calls are very expensive, and the hand held units, although getting smaller (like the Iridium 9555 handset), are still bigger than a large cell phone.

...some explosives inside an annoying crying baby, then they'd ban them.

to know that most people don't base their beliefs on facts. Like there is no evidience for Jesus outside of the Bible.