# Why does stall speed decrease when flaps are deployed?

I've been told that deploying the flaps on approach enables the following:

1. Potentially steeper approach
2. Slows down the plane
3. Lower stall speed

It's the last one that confuses me.

Given the equation for lift:

$L = \frac{1}{2}C_l ρ V^2 S$

with:

• $L$ - lift
• $C_l$- lift coefficient
• $\rho$ - density of the air
• $V$ - velocity
• $S$ - surface area of the wing

When we deploy the flaps, we automatically change the camber of the wing which does the following:

1. Increases the surface area of the wing
2. Increases our current angle of attack

As a result of the change in surface area of the wing, we can decrease our V in the equation and generate the same amount of lift that was needed before flaps. Does that sound correct?

For most practical purposes, your average GA pilot doesn't deal with the AOA because it can't be readily calculated so the POH typically lists the stall speed Vs. However, as I understand it, stall speed is indirectly correlated with our plane's "critical angle of attack".

What I don't quite understand is, why exactly does our stall speed decrease when we deploy the flaps?

Is it because of what I outlined earlier, that we can produce an equivalent amount of lift at a lower speed because of the change in wing surface area?

• If they didn't decrease stall speed, why bother having them? Points #1 and #2 can be achieved with flat-plate speed brakes. – Ralph J Jan 30 '18 at 0:10
• I'm not sure I take your point? I'm not debating the fact that they decrease stall speed, I'm asking how it occurs. – zoombini Jan 30 '18 at 2:09
• Do you mind marking one of the provided answers? I am curious (and I think others as well) of what have helped you -if anything did- to understand. – Stelios Adamantidis Feb 2 '18 at 13:09
• @SteliosAdamantidis To be honest, that's one of the reasons I haven't marked an answer yet - they're both extremely helpful so I'm having trouble choosing between them. After rereading them again, I went ahead and marked an answer. – zoombini Feb 4 '18 at 16:08

Your stall speed decreases because the $C_{L_{MAX}}$ of the wing increases with flaps deflected.

Deploying flaps increases wing camber and increases both $C_L$ and $C_D$ at the same AoA and airspeed. Depending on the type of flap, the critical AoA actually reduces: the airfoil with simple flaps deflected stalls at a lower AoA than without flaps.

Slats or leading edge flaps do not change the $C_L$ at the same AoA, but allow for a higher AoA and therefore higher $C_L$ before the airfoil stalls.

The flaps mostly increase the camber, which increases the Cl (albeit, with greater drag).

In quite a few cases (especially low-end GA aircraft) the flaps have little or no effect on the wing's surface area (the flaps are just a section of the trailing edge that swings downward on a hinge).

Even in those that do slide the flaps back on a track, the change in surface area is quite small compared to the change in camber (and with it, Cl).

• To be explicit (and answer the question), the increase of $C_L$ provided by flaps extension allows to produce the same lift amount with a reduced speed for the same AOA, hence just before reaching the critical AOA, the aircraft can fly level at a lower speed. – mins Jan 30 '18 at 0:41