i would like to know the hidden side slip that my instruments can not detect.
Unless you have a vane (or the poor man's alternative - a yaw string) you will only be able to make some nominal and approximate inferences regarding sideslip - significant sideslip is easy - but when you get to small angles, pilot assessment is going to tend towards imagination.
The
Concorde folk, on the other hand, had it all laid out before them ...