How do I know if I need a sub woofer?

It can be difficult. You don't know what you are missing if you can't hear it.

I had a nice pair of ADS L-810II speakers that I purchased new in the late 70's. They were a "full range" speaker and really nice example for that era, still in use by my little brother. With my present, way short of state of the art system, I am frequently shocked by low frequency information that I never knew existed.

I presently have a pair of KEF R3 Meta bookshelf speakers with dual HSU subs. Those subs are essentially flat to around 20hz. I hear (and feel) low frequency music that just was never there before, even on decent headphones,

A subwoofer's job isn't only shoringup bass. 

Room bass management of nodes and anti nodes because... Physics of sound vant be circumvented is why one needs a subwoofer or two.

Has nothing to do with playing low alone even though that is a key objective

Depends on what your listening objectives are.  Home theater- subs can come in handy.  Mostly 2-channel music, you would be better served by using speakers that can supply ample bass bandwidth.  

The sad reality is that unless you have full range speakers (usually very large $) AND sufficient current (not just watts) to drive them you need subs.  Sigh.