What is the reasoning behind the "don't slip with flpas extended" placard? Nobody could ever explain why it is so.
Bp244
I can give you real information on this. As a bit of background, I used to work for Cessna. I started as a mechanic in Experimental on the single-engine restart airplanes, and I ended as a production test pilot.
The reason for the placard has to do with the FAA's rules for computing unusable fuel! When they calculate the unusable fuel number to be published in the POH, there is a specific flight profile that includes uncoordinated flight. The "downhill" wing in a slip is going to naturally slope the fuel in the tank away from the fuel pick-up.
I didn't do this procedure myself, but my second-hand understanding is that the test pilot using a particular tank flies the airplane coordinated for 30 seconds then uncoordinated for 30 seconds. This pattern is alternated until the engine coughs due to fuel starvation caused by the fuel not getting picked up. Naturally not much fuel is in the tank to start with to reduce the test time. At the first sign of engine hesitation, the other fuel tank is selected to preserve the quantity of the tank being tested. When the airplane returns, all of the fuel is drained out of the tested tank and measured. From this the unusable fuel is calculated.
The use of flaps aggravates the slope of the slip which would then increase the amount of unusable fuel that would have to be published. Of course, increased unusable fuel is undesirable as it increases the basic empty weight and decreases range, etc.
When the 172R/S were first made with the standard instrument panel, the "Avoid Slips..." placard was on the panel. When Cessna went to the G1000, of course a whole new instrument panel was designed. I noticed the lack of the placard, and looked up the engineering drawing. That's been a few years ago. What was it, 2005 when Cessna introduced the G1000 172? As I recall, I ran into a mystery. The placard was shown in the Illustrated Parts Catalog, but not on the actual engineering drawing -- or maybe it was the other way around. I tried to raise the attention of the powers that be, but no one cared. At the time, it was more obvious because Cessna was still producing the traditional 6-pack panel and what was then the optional G1000. The exact same airframe, wing, tank, and flight controls -- just different instrumentation. The traditional panel had the placard, and the glass didn't -- being produced on the same line at the same time.
The only justification that I've ever figured is the G1000 inclinometer is quite different in response than the traditional ball in the turn indicator. That's just a guess.
Bottom line is the placard had nothing to do with stress on the airframe. If your tanks are more than a 1/4 full (my estimate, no official insight here), slip with flaps to your hearts content. If you're low on gas....an extended slip might get your engine to stop for fuel starvation
if you have the fuel selector on the "downhill" tank. And at the speed slips are typically done the prop will most likely not keep windmilling. That could be exciting. Most 172 pilots use the "both" fuel position, and then it would be a non issue.