There's a story behind that 178 seconds notion which is told in this article:
Surviving VFR into IMC
VFR into IMC events have a distressingly high fatality rate. Here's why they happen and some strategies for surviving based on research into reports from pilots who successfully handled the challenge.
https://www.avweb.com/flight-safety/technique/surviving-vfr-into-imc/
EXCERPT:
"Perhaps you’ve seen the widely distributed aviation video 178 Seconds to Live. The narrative starts: “The sky is overcast and the visibility poor. That reported five-mile visibility looks more like two and you cannot judge the height of the overcast. . .”
It continues: “. . . You find yourself unconsciously easing back just a bit on the controls to clear those none- too-imaginary towers. With no warning, you are in the soup. . .”
And then, dramatically, “You now have 178 seconds to live!”
Or do you?
As a survivor of a Visual Flight Rules (VFR) into Instrument Meteorological Conditions (IMC) incident that lasted a lot longer than 178 seconds, I often wondered about the veracity of 178 Seconds to Live. It certainly wasn’t true in my case. Where had this video come from? Was it a follow on to those old “scare ‘em straight” propaganda movies they fed us in high school? A post about the video on a social media site mentioned a “study with 20 subjects.”
I started doing research. The oldest reference to the phrase “178 seconds to live” in a VFR into IMC narrative I located was an article with the same title published in the January/February 1993 issue of FAA Aviation News. I then discovered that the “study” was really part of an experiment—the results of which had nothing to do with what eventually became 178 Seconds to Live. And, after the research I conducted into surviving a VFR into IMC encounter, I can’t help but wonder whether teaching that a pilot has but 178 seconds to live has caused fatalities because some who got into what is a frightening situation gave up rather than do what was needed to survive.
In 1954, the University of Illinois published a report entitled The 180—Degree Turn Experiment. The objective of the experiment was to see if 20 non-instrument-rated pilot subjects could be taught a technique for making a 180-degree turn and controlled descent in instrument meteorological conditions. In order to document the progress of the subjects, there had to be a baseline established for the abilities of each at the beginning of the project. Each pilot was evaluated on his or her ability to maintain control of an airplane under simulated instrument conditions. During his or her initial flight, each subject eventually placed the airplane into what the report referred to as “an incipient dangerous attitude.” The minimum time to reach an incipient dangerous attitude was 20 seconds; the maximum time was eight minutes. The average was 178 seconds.
178 seconds was the average of baseline measurements taken for the purpose of evaluating the results of an experiment.
I think it is also important to note that most of the subjects had little or no experience with the type of aircraft used in the experiment, a Beechcraft Bonanza, and that they were flying it with only a bare minimum of instruments—what we would call partial panel.
Over the years, that baseline measurement took on a life of its own. It morphed from being the initial evaluation of a subject’s ability to control a complex aircraft in simulated, partial panel IMC into an urban myth that an unwary pilot can survive for less than three minutes in an inadvertent IMC encounter. Variations of “178 Seconds to Live” have been promoted by the civil aviation authorities of both Canada and Australia.
Are pilots who encounter IMC on a VFR flight doomed as the video claims? Hardly. While they are seriously at risk, a look at the NASA Aviation Safety Reporting System reports finds that pilots can and do survive VFR into IMC encounters ... "