Why is the DC-9-80 ("MD-80") prohibited from taking off with a flap setting between 13 and 15 degrees? A bit of digging into the 7Z9363 accident investigation has brought up some interesting information regarding the DC-9-80 (&quot;MD-80&quot;)'s flap system:

Flaps may be positioned in any of the six permanent detents in a 0 to 40-degree range by movement of the Flap/Slat Handle. The authorized flap settings for takeoff in the MD-83 were 4, 6, 11, 15, 17, 20, and 24.73 A “Flap T.O. Sel Wheel” on the center pedestal would allow the pilot to further position the flaps from the position selected by the Flap/Slat Handle position anywhere in the 0- to 13- and 15- to 24-degree range.74 This was used to set the final takeoff flap setting, as determined
by the runway analysis review for the airport/runway.
[...]

[...]
74The Ameristar Air Cargo MD-83 COM, Limitations, page 1-24, stated “Flaps (AFM): Do not use flap settings between 13 and 15 degrees.” [Operations Group Chairman's Factual Report, NTSB docket DCA17FA076, page 32, my emphasis.]

and

4.1.3.1 Flaps
4.1.3.1.1 System Description
The aircraft has an inboard and an outboard flap on each wing. The flaps are mechanically controlled and hydraulically actuated. The crew moves the flap lever to the appropriate detent depending on the flight condition (i.e. take-off, landing). The flap lever has fixed detents at UP, 0, 11, 15, 28, and 40. The lever can also be positioned in one-degree increments for takeoff settings using the Dial-A-Flap from 0 to 24, except for a small do-not-use range at 14. Through a series of cables and pulleys, control valves are exercised and provide hydraulic pressure to the flap actuators to extend or retract the flaps. [Systems Group Chairman's Factual Report, NTSB docket DCA17FA076, page 59, section headings bolded in original, other emphasis mine.]

Reinforcing this prohibition, the DC-9-80's takeoff-flap selector wheel has a yellow &quot;DO NOT USE&quot; label covering the space between the 13-degree and 15-degree markings:

(Image originally by the National Transportation Safety Board [it's on page 32];1 cropped and red-ovalled by me.)
Why does the DC-9-80's flap system come with a prohibition against using flap settings between 13 and 15 degrees for takeoff?

1: The underlying photograph was taken by NTSB personnel, and the red arrow was added by the NTSB to point out the selector wheel in question.
When the FLAP/SLAT handle is in the 0° to 13° range, the slats are in the mid-sealed position. The slats will be in the extended position whenever the FLAP/SLAT is in the 15° to 40° range. The range between 13° and 15° is the DO NOT USE range.[1]

Given the above and the analogue nature of the input (dial-a-flap), between 13 and 15° the slats are very likely not to settle on a position.

(...) with the flaps flap/slat control lever in the cockpit below flaps 14°, the slats extend to their intermediate position (MID); and with flap/slat control lever positions above flaps 14°, the slats are fully extended (EXT).[2]

In other words:
$$0° \le \text{slat}_1 \lt 14°$$
$$14° \lt \text{slat}_2$$
What happens at 14°? Simply &quot;Do Not Use&quot;. The slat is both alive and dead.
Chronology of Douglas / McDonnell Douglas flaps/slats for context:




EIS Year
Plane
T.O. Flaps
Slats




1959
DC-8
fixed detents
slots (with an O);[a] doors opened when flaps extended


1965
DC-9-10
fixed detents
no slats


1967
Rest of the Original DC-9 Family
fixed detents
manual slats; separate lever


1971
DC-10
dial-a-flap (patent)
manual slats; separate lever


1980
MD-80
dial-a-flap
automatic flap-based three-position[b] slats (leading to the switch point at 14°)


1990
MD-11
dial-a-flap
automatic slats having only one extension position; slats stow button


1995
MD-90
dial-a-flap
same as MD-80


1999
717 (MD-95)
dial-a-flap
automatic slats having only one extension position




a: the DC-8 slots failed to produce the desired pitch-down on the DC-9 during development; tests revealed it was due to the lack of engine pylons; further experiments led to the invention of mini-pylons – the vortilons[4]
b: counting the retracted position
How can the narrow-body MD-80 be compared to the much larger tri-jet MD-11? The underlying high-lift system is practically unchanged since the 60s:

The DC-10 models utilize the DC-9 high-lift technology, and the MD-11, being a derivative of the DC-10, is very similar to it. (...) All its airplanes today, the MD-80s, MD-90s, and MD-11s are derivatives of the DC-9 and DC-10 airplanes, and they use their almost-30-year-old high-lift system technology with few changes.[3]


1: MD-80 FCOM
2: Report A-032/2008 – Accident involving a McDonnell Douglas DC-9-82 (MD-82) aircraft
3: Peter, K. C. &quot;High-Lift systems on commercial subsonic airliners.&quot; NASA Contractor Rept 4746 (1996).
4: Shevell, Richard S. &quot;Aerodynamic anomalies-Can CFD prevent or correct them?.&quot; Journal of Aircraft 23.8 (1986): 641-649.