C-172 N (?) circa mid-70s... the POH expressly states slips with 30 degrees flaps is prohibited. I don't have it in front of me, but I think it can be found in the EMERGENCY section.
No, it doesn't. The old owners handbooks did say "prohibited" in early models, but by the early 1970s the caution was relaxed to "avoid", and even that has now been dropped:
1966 C-172G Owner's Manual, page 2-10:
"Slips are prohibited in full flap approaches because of a downward pitch encountered under certain conditions of airspeed and sideslip angle."
1972 C-172L Owner's Manual, page 2-15:
"Slips should be avoided with flap settings greater than 30° due to a downward pitch encountered under certain combinations of airspeed, side slip angle, and center of gravity loadings."
1977 C-172N Pilots Operating Handbook, page 4-19:
"Steep slips should be avoided with flap settings greater than 20° due to a slight tendency for the elevator to oscillate under certain combinations of airspeed, sideslip angle, and center of gravity loadings."
2007 C-172S Pilots Information Manual, page 4-43:
"Steep slips with flap settings greater than 20° can cause a slight tendency for the elevator to oscillate under certain combinations of airspeed, sideslip angle, and center of gravity loadings."
As I said in
Post #14 above, the "pitch-down" and "oscillation" were two different aerodynamic phenomena. The larger dorsal of the 1972 C-172L apparently solved the "pitch-down" and the remaining "oscillation" is barely noticeable and completely harmless.
Importantly, those old pre-1979 owners handbooks do not have force of law; look to the
Type Certificate Data Sheet for the actual, current limitations. The TCDS is revised from time to time, and there is no
prohibition against slips with flaps in the current TCDS. The only versions still required to carry an "
avoid slips with flaps" placard are the Models 172 through 172F (1956-65).