Range Hood Window Exhaust

I live in NYC, in a gut-renovated apartment in a pre-war building. In my case, the kitchen had a cooking range and I guess the landlord was perfectly ok with my kitchen accumulating oily vapors on every surface and sending my smoke alarms into a frenzy. Eventually I came across a cheap range hood (how are they so expensive?) and took some cues from the portable air conditioner world to vent the oily vapors outside.

See full build here: https://www.andersknelson.com/blog/?p=1079