LoRaWAN: Equal time-on-air for different sized payloads

I guess I have to answer my own question :upside_down_face:

Time-of-air is calculated from the duration of the preamble and the transmitted packet

Screenshot 2021-05-21 at 20.58.30

Both of these durations are based on the symbol period, which is derived from the following equations:

Screenshot 2021-05-21 at 21.01.27

Screenshot 2021-05-21 at 21.01.46

First, the preamble duration is calculated from
Screenshot 2021-05-21 at 21.02.33
where n is the programmed preamble length (8 for EU868)

Next, the payload duration is calculated:

Screenshot 2021-05-21 at 21.04.23

The equation for number of payload symbols creates the staircase increase in total payload/on airtime.

For those who were wondering, these equations are drawn from the SX1276 datasheet (not the lorawan specification document)