What is the optimal height and depth for a hood fan?
This is going to be dominated by ergonomics.
The perfect fan for exhaust isn't so perfect if you're always banging your head on it, or can't see in the pan. Some unusual devices are rather tall and wouldn't even fit in your 18&quot; (I can't strain jelly on the worktop because of the cupboards so do that on the cold stove).
In catering, where kitchen air quality is a concern, the fan hoods are normally high, well over head height for the tallest users, but powerful.
The stuff you want to get rid of, whether steam, oil aerosol, or smells, tends to be carried upwards by convection, which gives a push to complement the fan's pull. You also have to consider the source of replacement air - if the house was sealed completely tight there wouldn't be one and the fan would be largely useless.  Airflow from the rest of the house into the kitchen to replaced the exhausted air can be effective in controlling the flow of smells, despite not increasing or even decreasing (for the same total inlet size) the amount of airflow.