In my logic: Flaps extended will cause a greater Angle of Attack, to maintain Straight and Level Flight, AoA will be reduced, due to the increased "Surface", this allows to fly at lower Angle of Attack, tis means lower induced Drag causing downwash to decrease? However why does this result in an increased Tail Down Force and how does the downwash of the wing affect the tail force?
What happens to aerofoil downwash with Flaps extended vs retracted and how does it affect the Tail down force?
$\begingroup$ See last paragraph of my answer-- the nuance here is, we have to consider whether the question is about what happens to the tail downforce upon flap deployment if the tail configuration (including elevator position) remains exactly the same, or what has happened to the tail downforce after flap deployment after the aircraft has been re-trimmed to hold some given parameter constant (such as airspeed) -- or both. $\endgroup$– quiet flyerJan 29 at 20:00
A flap works increasing camber, angle of attack and surface of the airfoil.
Anyway, in order to compare the change of the aerodynamic characteristics in respect to the basis airfoil, everything is packed inside the relevant coefficients: if before deploying the flaps the wing has a NACA 65012 airfoil, an AoA of 2° and a surface of 100m², after the deployment of the flaps the wing still has a NACA 65012 airfoil, an AoA of 2° and a surface of 100m². Anyway $C_l$, $Cd$ and $C_m$ they all have changed and, in particular, they all have increased, as visible in the following pictures taken from this report:
Here we see the trends of $C_l$, $Cd$ and $C_m$ for several flap angles. The black line is the one for the basis airfoil. The plot for $C_l$ is shifted upward toward higher lift; the plot for $Cd$ is also shifted upward toward higher drag; and the plot for $C_m$ becomes more and more negative i.e. more and more pitch nose-down.
why does this result in an increased Tail Down Force?
In order to compensated for the:
- lift increment $\rightarrow$ speed and AoA are decreased;
- drag increment $\rightarrow$ thrust is increased, albeit the previous decrement in speed and AoA partially offset this;
- higher nose-down pitch $\rightarrow$ tail downforce is increased.
Plus, flaps are deployed slowly and in steps.
Downwash is proportional to lift which, in turn, equals weight. Not changing the weight during the deployment of the flaps, downwash doesn't change too, at least globally: there's a local increase of lift (and therefore downwash) on the flapped surfaces of the wing and a local decrease on the non-flapped surfaces, but globally it remains the same.
how does the downwash of the wing affect the tail force?
If the higher downwash shed from the flapped surfaces impinges on the horizontal tailplane, its AoA has to be adjusted not only to compensate for the higher wing's $C_m$ but also for the changed local airflow. Note that these two effects are one the opposite of the other.
In the specific case of radio-controlled model gliders with the wings mounted at about the same level as the horizontal tail, I've found the following:
Deploying flaps that only cover the inboard portions of the wing, i.e. the portions of the wing in front of the horizontal tail, causes the aircraft to pitch up to a higher angle-of-attack. If the aircraft was initially trimmed to fly near best-glide or min-sink speed, then after flaps are deployed, a nose-down stick (elevator) input may need to be maintained to prevent the aircraft from stalling, unless the aircraft is re-trimmed.
Deploying flaps that cover the entire wingspan causes the aircraft to pitch down to a lower angle-of-attack and gain airspeed, at least in cases where the wingspan is large compared to the span of the horizontal tail, unless a nose-up stick (elevator) input is maintained, or the aircraft is re-trimmed.
With a high-wing full-scale airplane such as a Cessna 152 or Cessna 172, lowering the flaps (which only cover the inboard portions of the wing) cause the aircraft to pitch up to a higher angle-of-attack and a lower airspeed, especially at high power settings. If the aircraft was initially trimmed to fly near best-glide or min-sink speed, then after flaps are deployed, a nose-down stick (elevator) input may need to be maintained to prevent the aircraft from stalling, unless the aircraft is re-trimmed, especially at high power settings. In this case, it's clear that the flaps are creating a stronger downwash over the horizontal tail, especially at high power settings, which more than offsets the increased nose-down pitching moment associated with increasing the camber of the wing.
So in all these cases we have a "balancing act"-- increasing the camber of the wing causes the wing to create a stronger nose-down pitching moment, but also increases the downwash over the tail, which creates a nose-up pitching moment. The "balance" tends to be tipped toward the former factor if the span of the tail is small compared to the span of the portion of the wing covered by the flaps. However a strong propwash tends to tip the balance toward the latter factor, if the flapped portion of the wing and the horizontal tail are both in the propwash.
If you are asking about the tail downforce after the aircraft is re-trimmed as needed to maintain the original airspeed, then you can be sure that the tail downforce is increased (or tail upforce is decreased) after the flaps are deployed, regardless of any other factors. This is due to the way that the wing's pitching coefficient and pitching moment increase when the camber of the wing is increased. But since the tail often lies in the downwash of the flapped portion of the wing, this simple observation alone isn't sufficient to tell us whether the elevator would have to be re-positioned higher, or lower, or neither, to deliver the appropriate increase in tail downforce (or decrease in tail upforce).
$\begingroup$ Not really a complete answer but still intended to convey some relevant useful info-- $\endgroup$ Jan 29 at 19:52