# How does a thickening boundary layer create form drag?

Imagine a normal wing with flow over it, and to simplify things it's at 0 AoA. Drag is being made mainly because of form drag and skin friction drag. I'm not sure on this, but I don't think there would be any induced drag here.

To add to that, drag is any force that has a component facing opposite to the direction of flight.

In this answer, it says :

It is more correctly termed "profile drag" because the growth of the boundary layer virtually modifies the profile of the airfoil seen by the airflow.

This states that there is extra drag from the air in the growing boundary layer, and it is profile drag, or form drag.

The boundary layer air isn't connected to the wing, so why would it make (form) drag? Since the force of drag is from something 'pushing' backwards on a wing or body, why would faster moving flow (flow before it reaches airfoil) encountering slower moving flow (flow inside BL) make drag?

If the whole wing was increased to the size of the boundary layer it would make sense why form drag would increase, as there is more surface for the oncoming air to push against.

However I can't seem to see why air which isn't connected to the wing would create drag in the same way.

Profile drag is the term for skin friction and form drag on a 2D body. We do not talk about profile drag on 3D bodies.

3D bodies still have skin friction and form drag.

In this picture, the thickness of the boundary layer is exaggerated.

Recall that the pressure drag around a 2D inviscid closed body will be zero. This is because everything cancels out just right.

Next, we treat the flow outside the boundary layer as inviscid. It produces a pressure distribution that pushes on the outside of the boundary layer.

Next, we assume that the pressure 'across' the boundary layer is constant (this goes with it being thin). So, we apply the pressure distribution from the inviscid flow on the outside of the boundary layer to the airfoil shape. We can integrate this pressure to get the lift.

If you really understand each of the above steps, you're ready to understand form drag. If you aren't, then re-read these steps again and think about them.

What happens to the boundary layer at the end of the airfoil?

It keeps going.

The inviscid body (around which the pressures sum to zero drag) would need to continue on the outside of the boundary layer to infinity.

But we can't deal with a pressure distribution that goes to infinity. So instead, we cut it off at the blue line I've added to this figure.

We don't apply the entire inviscid body's pressure distribution to the airfoil. We just apply the part we chopped off and kept.

Which leaves us with the problem -- we needed a full closed body's worth of pressures to cancel out and get to zero. What happens if we chop off a chunk and throw it away? I.e. we aren't dealing with a closed body?

Another way to think about it is to integrate the pressure on the outside of the boundary layer (without transferring it through to the airfoil). This integral would clearly need to extend to infinity to encompass the entire boundary layer.

Instead, when we cut it off at the blue line, and we do the integral around the BL near the airfoil -- but closed off by the blue line. What pressure do we apply along the blue line?

Since pressure is constant across the boundary layer, it will be the pressure at the outside of the boundary layer at the trailing edge.

The blue line is nearly vertical -- which means that any force we integrate across it will be in the thrust-drag direction.

Also, we know the pressure on this face (the pressure at the TE of the boundary layer). But we now see that the thicker the boundary layer, the longer the blue line. Consequently, the thickness of the boundary layer at the trailing edge is directly related to the amount of form drag.

From all this, we see that form drag is a pressure drag -- but it is a pressure drag that only exists because of viscous effects (the presence of the boundary layer).

• I tried finding out what a 2D inviscid closed body was (because I didn't really know), and after looking through google (reputable places) and Introduction to Flight, I couldn't find anything. I'm assuming that's essential to know to understand this answer? Commented Jun 6 at 1:53
• Inviscid means without viscosity which is equivalent to ignore the boundary layer. Commented Jun 6 at 2:01
• @AeroAndy Right, but I was more confused on what a 2d closed body is. It might be simpler than I'm thinking of. (An airfoil type shape) Commented Jun 6 at 2:07
• yup, don't overthink it. just a two-dimensional shape with no openings. :) Commented Jun 6 at 2:24
• Take a pencil and draw a loopy curve. If you end the curve where you started it, it is closed (say a circle). If you don't, it is open (like the letter C). Two-dimensional just means something you can draw on a sheet of paper. Commented Jun 6 at 2:45