What exactly is the 'relaxed geometry' of a touring bike? And what specific numbers should I look at, and what do the numbers mean, to find this relaxed geometry?
Simple words for a simple mind please.
Compared to a race bike, the steering has more stability, esp when the bike is heavily loaded. This is a combination of head-tube angle and fork trail (how far the front wheel is offset from the steering axis)
As usual there is more to it. The head-tube angle determines the sensitivity of the bike to changes in trail. You can get graphs of HT angle vs trail with the steering characteristics and applications identified. I can't supply a ref for this yet...
The rear triangle is longer i.e. longer wheelbase, so more of the load falls within the wheelbase. You can load up a bike with weight hanging outside the wheelbase but the bike rapidly becomes tail heavy. Some people regard wheelbase as an input to the specifications ( I want a wheelbase of Xcm) but really it is an outcome of the design process.
Sometimes the seat-tube angle is more sloped back , but this is really down to individual shape of the rider and is not that significant to the stability. Modern seatposts come in sufficient variety to set the saddle in any reasonable position fore-aft.
When specifying bikes to a custom builder it is usual to say what you want it for, how much load you will carry and what size/shape you are and leave the exact geometry to his/her experience.
A useful reference is
Lots of touring bike wisdom at