Olaf One-Brow
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How deep would subs need to be in order to communicate effectively with satellites?
Depends on what you're using to communicate with. VLF signals will only go down about 20m in water, so you're sub's downlink needs to be pretty damn close to the surface to receive signals from a VLF array. Any they can't transmit signals back due to size limitations.
I mean, good luck putting this on a submarine.
Rather then surface to near surface waters to receive signals, submarines will float a cable to that depth instead.
You generally aren't going to launch expendables, like a buoy (this one is an emergency beacon).
For UHF, those will penetrate greater distances and rather then VLF, UHF is generally used by satellites to communicate with submarines. Being hyper directional, only the recipient of the communications is going to receive it, so these types of satellite comms are very secure as well. Also they're encrypted.
ELF will go down hundreds of meters, but their arrays are massive and their wavelength 1/4 the diameter of Earth.
But how long is a typical radio buoy cable?
Could be meters. Could be kilometers. Same with your towed sonar cable.
How deep would subs need to be in order to communicate effectively with satellites? And does the transmission capabilities (in the required frequencies) exist with our present or future sats?
The SSIXS satellite system used by the USN is for communications with all USN assets, submarines included.
Currently a mix of FLTSATCOM
UFO
And their replacement MUOS are forming the USN's communications capability.
If India can talk to its ships, it can talk to its submarines using the same assets. VLF and UHF are still used, but ELF arrays are large and largely obsolete.