In PHAK, I saw that There is two types of downwash
in phak 5-7 It said 'This induced downwash has nothing in common with the downwash that is necessary to produce lift'
My question is Does first type of downwash (necessary to produce lift) also produce induced drag? I keep searching about this and they always say about wingtip vortices induce downwash not that 'necessary to produce lift' downwash.
I really don't know why they waste time and effort in the "PHAK" writing and teaching this stuff.
Fundamental in aviation is that the moving aircraft interacts with the air, producing drag. Heavier than air craft must make lift to counter-act gravitional force.
This is done by increasing angle of attack from a zero lift state, AKA D0. Any drag associated with lift production is Dinduced, or Di.
Drag = D0 + Di
Downwash and tip vorticies are the result of lift production. To say they are unrelated is nonsense.
Downwash is flow from the trailing edge. In the simplest explanation, the mass of air pushed down = the weight of air craft pushed up.
Tip vortexes form because increasing angle of attack (creating lift) causes a pressure differential between upper and lower wing.
The lift equation is:
Lift = Area × Density × Lift coefficient (including AoA) × Velocity$^2$
When velocity is high and AoA is lower, these tip vorticies can spill harmlessly away from the wing tip and not affect lift or drag. When the plane slows down and AoA increases, the vortex may start to impinge on the upper wingtip surface$^1$.
So, the answer is that neither downwash or tip vorticies produce drag. They are the result of the velocity and angle of attack one flys their aircraft at.
The most important concept to grasp is that the best combination of Velocity and Angle of Attack is at Vbg. That's where one wants to be if the engine fails and a safe landing area is available to glide to.
$^1$ this has a secondary effect. The aircraft must increase AoA or speed to maintain lift, resulting in more drag, directly translating into more fuel consumption.
There is a very common form of incorrect reasoning on display here. In a steady flow we observe two apparently distinct phenomena A and B. We then ask which is cause and which effect. This is almost always wrong, because usually both A and B are effects of causes that operated before the flow became steady. @Robert DiGiovanni is correct to consider how the flow evolves starting with zero lift. To say that "these tip vortices can spill harmlessly away from the wing tip and not affect lift or drag" is however seriously misleading.
A and B here are what are often called the bound vorticity and the free vorticity. Vorticity is a vector whose direction is the local spin axis of the fluid, and whose magnitude is the spin intensity. Mathematically, the vorticity can be deuced from the velocity, and usually the velocity can also be deduced from the vorticity. They are alternative descriptions of the flow. Therefore we can pretend that either of them is the cause and the other the effect. This will not be a problem as long as we only consider steady flows.
So we can imagine that the trailing vortices, rather than "spilling harmlessly away", "reach back" to affect the velocity on the wing. This is "induced incidence" and is the "cause" of "induced drag". This mechanism is reduced for high aspect-ratio wings and is absent for two-dimensional wings.
The statement in PHAK that "A has nothing in common with B" is completely ridiculous scientifically. Its only possible purpose is to prevent pilots from worrying about things they have no reason to worry about. In fact classical wing theory is a well-established university-level subject that is found hard by many students because it gets quite mathematical, but leads to many fascinating conclusions. For those who are merely curious, a description that I am assuming to be true of @aviii there should still be satisfying explanations. Let me try.
The purpose of a wing is to produce downwash, and the simplest explanation is indeed that "the mass of air pushed down = the weight of air craft pushed up". A fuller analysis of the vertical momentum also includes the pressure, which changes with velocity according to Bernouilli's Law. Just behind the wing, there is "lifting downwash" produced by the pressure difference needed to achieve lift, and also "induced downwash" produced by (or at least associated with) the trailing vortices. In sum, these must combine to conform with the geometry of the wing, so the presence of induced downwash reduces the lifting downwash and therefore reduces the lift. It also results in drag.
I hope this helps but there are better explanations available. I could recommend one if I knew more about your level of interest.
