[UKönig]

I have read that over the course of the war, the Germans tried several different things to improve the low U-boat visibility problem.
As you sit so low in the water your range is limited to the horizon, or roughly 16km from surface level. Which is a laughably small area when compared to the total size of the Atlantic and the places that a convoy can hide.
Radar was intended to give the crew visibility beyond the level of the horizon. Also in response to the allied improvements to convoy defense. With radar, theoretically, you could spot the ships electronically and plot your intercept course without having to get close enough to risk detection by any escorts who may be on sweep patrol.
But it was unreliable. The field of micro electronics had be largely overlooked in Germany, while the allies put it to great effect. The Germans were always playing 'catch up' in the arms race. All these measures were done to extend the life of the U-boats currently in service, when they should have just built a better boat. Essentially they were fixing all the wrong problems.
The early sets were big bulky things rigidly attached the the structure of the conning tower. But the search area is still too small. What like, +-15 degrees on each side of 0. In order to scan a full circle, you'd have to sail the boat around the same. A time consuming process under normal conditions, impossible to perform during battle. Later sets, equipped with rotating antennas solved some of these problems, but it was still a crapshoot.
At other times, they resorted to strapping a luckless bosun into a chair and strapped said chair to the periscope mast, in an attempt to get more visual range. And the Bachstelze or 'water-wagtail'. A sort of kite/gyrocopter towed behind the surfaced uboat, with a man with binoculars to scan, up in the air. The main drawback to these is that crash diving is not possible without sacrificing the crewman in question. These alternate methods of extending u-boat visibility only met with minor success and were not done on more than 2 or 3 occasions. The cons simply outweighed the pros. Fortunately, they stayed with the electronic detection method.