I did this thought experiment a year or two ago and thought I'd run it by y'all. I was thinking about aircraft rudders and the "natural" semi-coordinated behavior in which some airplanes fly. If you're straight and level and stand on the rudder pedal, most GA airplanes will drop a wing. I attribute this to the rudder being above the center of mass of the airplane. Mooneys, with their backwards tail, I assume have that rudder shape as to have more rudder authority in slower flight and high angles of attack. Also, while I've never spun a Mooney and don't intend to, what I've read states you should be abrupt and violent with your control inputs in a Mooney to stop a spin. My thoughts on this are that abrupt control movement would add some inertia into stopping rotation. I've read the rear-swept rudder of the C172 was a marketing design choice, because jets had swept wings and control surfaces.

Acrobatic airplanes have rudders that increase in size near the bottom. I assume this reduces drag and saves the design compromises that would have to be made for ground clearance to have it balanced from top to bottom, and such designs prevent the behavior I mentioned at the beginning of the post.

There are several reasons for the unlimited aerobatic aircraft having the rudder area as close to the longitudinal axis as possible - it reduces the bending moment on the vertical stabilizer spar, it reduces the rolling moment the rudder induces around the longitudinal axis while increases the yawing moment around the vertical axis, and it puts more rudder area into the propwash for better control during very low speed/high power manuvers such as torque rolls etc.

Likewise, there are several reasons an aircraft will drop a wing when the rudder is stepped on.   Stepping on the left rudder pedal, for example, yaws the aircraft to the left.  For a brief amount of time, the right wing is accelerated through the air, producing slightly more lift while the left wing produces slightly less lift as it's relative airspeed decreases slightly.   More lift on the right and less on the left results in a left rolling tendency.   Dihedral will increase this effect, and is why R/C models with only rudder but no ailerons can still turn quite effectively.   If the wing is swept, this adds yet another aspect - rolls can be done very effectively using rudder alone in some swept wing aircraft.

Interesting, in aircraft like the one you pictured, the rudder has little or no roll coupling - it mostly just points the nose left or right.   That's due to a number of factors, including a mid-wing design, rudder area mostly centered around the longitudinal axis, no dihedral, symmetrical airfoil, and probably several other things I either don't remember or am ignorant of.

The "wing drop" is actually due to the differential lift between the wings when not flying directly into the relative wind.  It is not based on size/shape/placement of the rudder.

What is done on acrobatic aircraft to help counter this? Or is it something the pilots do?

When I've talked about my understanding of what causes stall/spin accidents, the effect you mention is how I describe them. The bottom wing stalls because of the differential lift as well as potential "shadowing" from the fuselage. The forward CG pulls the nose down. The wing that isn't stalled accelerates faster and away you go, and, for that reason, I always think of slips whether it's in a turn or straight or to the side as "top rudder"; the thought being that if I were to stall for whatever reason -- wind shear, indication error (I almost always crosscheck with GPS on approach), et cetera, it might buy me a split second to unload the wing. In extreme cases, can you stop a snap roll once its begun?

ETA: Per @ChiefPilot 's post regarding swept wing aircraft, that makes a lot of sense. You apply rudder and now the swept wing becomes more like a straight wing and increases lift further, while the other drops even more out of the way.

The dihedral effect (not dihedral angle of the wing) is the result of many design factors and not the result of any single one.  

Depending on the airplane's purpose in life, some positive dihedral effect (roll away from the wind, ie. Roll left when the airflow is coming from the right side of the aircraft) is generally desirable.  

The explanations many people use to explain dihedral effect are gross simplifications.  You can have positive or negative dihedral effect with both low and high wing mountings and with both positive and negative wing dihedral angles.

According to the book “Those Remarkable Mooneys” the tail is on backwards to squeeze more speed out of the airplane.  Al also thought the forward sweep of the rudder would remain effective deeper into a stall than a traditional tail design.  Roy Lopresti seemed to agree.

Incorrect.

The rolling moment associated with the the rudder is absolutely affected by how far the geometric center of the rudder is from the  longitudinal axis of the aircraft.

I didn't say anything about the size of the rolling moment.

Sorry.  I read "wing drop" to be rolling about the longitudinal axis.

Interesting discussion here.
Aircraft design is the epitome of trade-offs, balancing performance vs stability.
My senior design project involved design/build/fly where high lift/aircraft weight determined success. If the design was based purely on performance, it was destined to crash (didn't have big $ for computer assisted control). The most fun I had in college (access to a wind tunnel any time I wanted it helped).

Rudder makes the nose go left or right.

My ole granny called the rudder a tail flipper. When I took her flying on windy days she would get scared when we hit air pockets and I would do my best footwork on the tail flipper to keep the ball in the middle so granny wouldn’t blow beans.

Back during the revolution when I was try to gain enough college crediks to get myownself inducted into USAF UPT I once found myself intoxicated on tequila spirits during participation in collegiate intramural drinking competitions.

As a result of these activities I subsequently, only once, found myself in close proximity to a full figured coed that demonstrated to me the real world importance of grasping the significance of rolling moment.  If she had possessed much more of a rolling moment factor I might have suffocated.

She was built somewhat like an F-4 and every time I banked the KC-97L I was reminded of her rolling moment.  



Political correctness has made it harder and harder to explain moments of rolling.

I once flew an experimental tailless airplane.

It had spoilers on the outboard sides of the vertical fins at the wingtips. It was different. I don’t know how I did without fly by wire.

Those seem quite popular around here.