# At which point in scale reduction do slats and flaps become unnecessary?

Imagine some Fi-156 Storch, and reduce its scale down gradually to 10cm span. Let's assume full scale Fiesler Storch is 100% efficient at, for example, minimizing stall speed.

During this reduction process, if every dimensional element is scaled down perfectly, except airfoil shape, slats airfoil shape, flaps airfoil shape, and slats and flaps relative gap width between them and the wing, how would these (allowed to vary along vertical axis) parameters roughly evolve during scaling down process, so that this aircraft ability to minimize stall speed remains close to 100%? Is there in this case some linear pattern along Reynolds number variation?

• don't forget that the smaller plane would have much, much lower wing loading, which also helps decrease stall speed – Abdullah May 26 at 16:14
• just some math for anyone who can answer: scale:1/143, wing loading: 0.3392kg/m3, wing chord: around 0.013m, weight: 59 newtons. – Abdullah May 26 at 16:24
• the reynolds number will also be 1/143 of the storch at any given speed – Abdullah May 26 at 16:33
• i don't know if i can answer, but i'm trying to help people to. – Abdullah May 26 at 16:34
• @Abdullah many thanks, I feel like this question is broad in the sense that it involves quite a lot of parameters related to at least square cube law, yet I'd like to know if someone could compile some rough big picture of how parts that produce lift would evolve in their vertical axis shape, and if this evolution is linear or filled with gaps and bumps at some thresholds. – qq jkztd May 26 at 16:43

## 1 Answer

Putting slats and flaps on a 10 cm model is extreme, but would add a touch of realism for the serious hobbyist.

At which point in scale do slats and flaps become unnecessary?

We turn to the lift equation:

$$Lift$$ = Air density x Area x Lift Coefficient x Velocity$$^2$$

$$Weight$$= $$Lift$$ for steady state flight so we derive:

$$Weight/Area$$ = Rho x Lift Coefficient x Velocity$$^2$$

In terms of considering the need for slats and flaps, the primary factor is the difference in landing and cruising speed. In an airliner, the difference can be 350 knots! (Maybe a little less, considering Rho at higher altitudes, indicated airspeed). For a Storch, around 60 knots, for a tiny model with light wing loading: maybe 7 knots.

When we compare $$Kinetic$$ $$Energy$$ = 1/2mV$$^2$$, one sees a scaled down model with low airspeed and very little mass makes for a landing roll-out of only a few feet, whereas the 400 ton airliner at 150 knots needs over a mile to stop. The faster, heavier plane needs to slow down as much as it can before touchdown.

Also from the lift equation we can derive that increasing coefficient of lift, by increasing AOA, or by reconfiguring the wing, only increases lift in a linear fashion, whereas lift increases with the square of velocity.

The need for slats and flaps really depends on how slow you need to get to land safely. So does greater runway length, which allows for a slightly faster approach speed.

Further more, we find one aspect of the Fi 156 Storch rarely discussed, its 240 hp Argus AS 10 V8 and it's variable pitch prop.

This shows the designers went to great lengths to provide adequate power to keep flying in spite of the tremendous drag the slats and flaps create. It was a price to pay for increasing STOL performance, and illustrates why aircraft perform far better "cleaned up" at Vy.

Note of interest: the same engine was used with the Bf 108 "Taifun", resulting in a cruise speed 50 knots faster, landing around 45 knots. Both planes were of similar weight.

• we forgot one thing: induced drag – Abdullah May 28 at 11:39
• I’m not sure how this answers the question asked by the OP. – dalearn May 28 at 14:02
• I hope the re-write answers a bit better. – Robert DiGiovanni May 28 at 18:14