# ATPL Theory - Principles of Flight: Drag

It’s been a minute, hasn’t it! Please do accept my apologies for the hiatus in creating this next topic, much ‘life stuff’ has cropped up and eaten up my time in the last year or so.

With that said…

Welcome back to ground school once again, this time for a far deeper dive into Drag!

The Bain of every aerodynamicist’s existence, drag is inevitable when moving anything at any speed through any fluid, be that a liquid or a gas. This is true of cars, boats, trains, scooters, bikes, you name it; and especially true of Aircraft.

The biggest question on any aircraft designers mind nowadays is how can we eeek out as much performance as possible for as little fuel as possible? How can we make this airframe just that bit more efficient?
Obviously creating more efficient engine’s is a good answer. Engine technology has come a long, long way since the original can turbojets of the old days.

But there are other options too which we see and hear about all the time:

• Reduce the weight of the fuselage using new materials (Carbon Fibre springs to mind),
• Reduce the weight of the seats,
• Remove the rivets from the outer skin by using a bonded skin instead,
• Reduce the size of the tail stabilisers (Think of the MD-11)…

All good ideas and good solutions. But the above all have something in common: they all reduce drag.

How? Well, that’s what we are going to find out here. Hopefully.

Types of drag

In basic terms, drag can be broken down into two categories: Induced drag and Parasite drag. These, in turn, are broken down further but more on that in a bit.

Induced drag is effectively a by-product of the creation of lift. If lift is being created, so too is induced drag. You will often hear it referred to as Lift Induced drag for this exact reason - it is drag induced by the creation of lift.

Induced drag decreases with increasing speed proportional to 1/V^2. That is to say, induced drag decreases exponentially with an increase of speed.

Parasite drag, on the other hand, increases with increasing speed proportional to V^2. In other words, it increases exponentially with an increase in speed.

Parasite drag is then broken down further, as it is the sum of Profile drag + Interference drag.
to make it even more fun, Profile drag is the sum of Form drag + Skin Friction drag.

Keeping up? Let’s start with the easiest and work our way up from there.

Skin Friction and Form Drag

Any surface creates friction when something runs along it. That’s is a known fact. However, a fluid running along a surface creates something of a strange effect.

The fluid molecules closest to the surface of the skin of an aircraft suffer from a decrease ion speed due to skin friction. this creates a layer of air that is at a different speed to the main body of air moving around the aircraft. This layer is known as the Boundary Layer, a term you may have heard before.

The speed of the molecules against the skin its massively reduced compared to the relative airflow. the speed then increases throughout the boundary layer until the speed of the molecules is 99% of the speed of the relative airflow. The boundary layer is usually at most a few millimetres thick.

There can also be two different airflow types within the boundary layer: Laminar flow and Turbulent flow. Laminar flow is preferred as it is far, far more “slippery”, i.e. aerodynamic. This makes aerodynamicists very happy indeed. In a laminar flow, the molecules all run along in an organised, parallel way. A laminar flow layer its typically very thin.

by comparison, a turbulent flow can be anything up to a few centimetres thick. Molecules travel with little to no organisation whatsoever and carry a higher mean speed than a laminar flow. This results in turbulent flow causing higher skin friction drag than laminar flow, making aerodynamicists sad.

The point at which a laminar flow becomes turbulent is known as the transition point, and it can be causes by anything from dirt or rivets (remember the use of a carbon fibre fuselage?) to the aircraft skin being “pulled away” from the boundary layer too aggressively.

The rougher the skin, the greater the skin friction drag. With a rougher skin, the transition point also moves forward.

Another example of this would be cyclists shaving their legs for the extra marginal gains. If you’ve ever wondered why in God’s name they do that… now you know.

Form drag is a more basic principle: if something in shaped like a brick, it’s going to have less drag than something shaped like a bullet.

Easy, right? Unfortunately, this is PoF. It’s never that easy, I’m afraid.

Aircraft wings, and to an extend fuselages too, are made up of a combination of form and skin friction drag. We already know that making the surface of the wings smoother reduces skin friction drag. However, reducing the actual physical cross-sectional area (CSA) of the wing will also help reduce form drag. The shape of a wing, along with the shape of an aircraft’s nose cone, are very deliberate shapes:

The blunt leading edge creates a stagnation point, which in turn slows down the air and allows the laminar boundary layer to form. This idea will be mentioned again in a later lesson but for now, just understand that the shape above reduces drag.

Reduced form drag allows for more speed with the same thrust, thus increasing efficiency. This also decreases the noise produced - think of how loud an aircraft gets with the flaps and landing gear down. That noise its mostly due to the turbulent air flow ‘rumbling’.

Sometimes, however, we actually want to increase the form drag of an aircraft to help us slow down - maybe to avoid a violation when passing FL100 on descent (we’ve all been there!).

To do this, we essentially have to increase the size of the aircraft when looking at it head on. Devices such as flaps, spoilers, air brakes and landing gear can be used to achieve this. The opposite is true as well - streamlining its all about reducing the CSA and thus reducing form drag. A logical example would be the A380 vs the A320 family. Pictured side by side from head on, the A380 is obviously far bigger. It will therefore, by definition, have more form drag. Ii hope that makes sense.

Interference Drag

This is a weird but quick one. Simply put, when two surfaces meet at 90 degrees, or are perpendicular, interference drag between each surface’s respective laminar flow occurs, creating turbulent flow.

To fix this, filleting its used to create a curved surface joining the two perpendicular surfaces together. This can be seen on pretty much every high-efficiency aircraft flying today.

Wing filleting as seen on an old fighter plane.

Profile/Parasite Drag

So, we now have all the ingredients of the Parasite drag soup. Let’s stick it on a graph and see what happens.

Just like so.

As we heard earlier, Parasite drag increases exponentially with an increase in speed.

Remember, parasite = profile + interference.

We’ve already seen how we can influence interference drag. Let us now look at some ways to influence profile drag:

Increase Profile Drag:

• Rough surfaces
• Ice
• Wear and tear
• Damage
• Large, aggressive changes in CSA

Decrease Profile Drag:

• Smoother surfaces (remember one-piece fuselages)
• Smaller CSA
• Fairings around exposed mechanisms, such as flaps and landing gear
• Fly Slower

All fairly logical once we know what we are looking at and talking about.

Now, take a breath, grab a refreshing cup of tea and we’ll continue. This is where it starts getting fun.

[Lift] Induced Drag

Above is a Cl Alpha curve. We saw something similar in the previous lesson on lift. Don’t worry about the 16 degrees marked on the angle of attack scale, that’ll come up again in a future lesson.

I put this here because the Coefficient of Induced drag, Cd, is directly proportional to Cl^2 / Aspect ratio.

But… induced drag? What?

Well, remember how I previously said that induced drag is a result of the induction of lift? First, we need to understand that bit. Please bear with me, this is going to be awkward to explain. It’s a weird concept.

As a wing travels along, some of the relative airflow is ‘turned downwards’, known as downwash. This, in turn, actually reduces the angle of attack compared to what it “should be”, so to speak. This is known as the ‘Induced AoA’ or Induced alpha. However, due to the reduced AoA, there is now a reduction of lift. Therefore, we need to increase the AoA again to make up for the loss, probably by pitching the aircraft up. This results in an increase in drag; meet Induced drag.

In other words, the downwash reduces the effective AoA, reducing lift, to a new AoA. The difference in the two is the induced AoA.

I hope to God that makes some sense. If you’re confused, don’t be alarmed. This principle took me a good couple of weeks to fully understand when I first learned about it.

To minimise induced drag, there must be less lift at the wing tips than at the wing roots. This can be increased using wingless, sharklets, wing tip fences, split scimitars… choose your weapon.

A rectangular wing has more lift at the root than at the tips, but far greater wing tip vortices and induced drag.

Elliptical wings, on the other hand, create a constant effective AoA, which reduces induced drag.

Increasing the aspect ratio also reduces induced drag, where aspect ratio = wing span / wing chord.

Wake Turbulence

Wake turbulence is the disturbed air that forms behind an aircraft as it passes through the air. There are well documented examples of how powerful wake turbulence can be if unexpected.

Wing tip vortices are horizontal rotating spirals of air that are formed at the back of the wingtips. Interestingly, deploying flaps can actually reduce WTVs as flap tip vortices and WTVs tend to cancel each other out.

Anyway, what causes wing tip vortices? As we learned in the introduction lesson, the high pressure beneath the wing tried to spill up to the top side of the wing to find equilibrium in pressures. It does this travelling from wing root to wing tip, flowing up and over the end. This is known as span-wise flow (flowing along the wing span), and as the air curves up over the tip, the WTV is formed.

The effect can be reduced in a few ways, but the most obvious are the winglet devices mentioned earlier.

WTVs can also be reduced by:

• Flying faster (less AoA required, and therefore less induced drag),
• Having a bigger wing surface area,
• Using a tapered/elliptical wing plan form,
• Wing wash out

For those wondering - washout is where the AOA of the wing is reduced along the span, effectively creating a slightly ‘twisted’ wing.

WTVs spread out horizontally and descend behind the aircraft.

The Drag Coefficient

We’ve already seen this, but this is the formula for drag.

It’s worth noting: Cd = Cd Induced drag + Cd Profile drag

Cl can be plotted against Cd on a graph. It’s known as the Aerofoil Polar Diagram, and it looks like this:

Now, I appreciate that this monstrosity is a bit weird and difficult to read, but it’ll become a bit clearer when combined with a graph of total drag:

The point at which the two drag curves intersect is called the speed for minimum drag, or Vmd. Notice How Vmd is marked on the polar diagram too for an asymmetrical wing?

Essentially, anything that increases drag will increase the total Cd, and therefore move the curve to the right. That’s over-simplified, of course, but it will do for this purpose.

My head is hurting too. I get it. Almost there.

Induced Drag Coefficient

I’m going to throw some formulas at you now I’m afraid:

This is simply saying that Cdi = the coefficient of lift squared, divided by the wing aspect ratio. Alternatively, we could say this:

Therefore, using our knowledge of the Lift formula and knowing that, win level flight, Lift = Weight, we could say that:

We find this simply by swapping bit and pieces around in the lift formula. It becomes simple algebra by that point, once you get your head around it.

Commercial aircraft and business jets fly at high speeds. Very high speeds actually, as fast as M0.95 for some business jets. This is done because as high cruise speeds, the AoA required to maintain lift is lower, so the amount of downwash is lower and therefore so is induced drag.

due to the relatively very thin air at high altitudes, the effect of profile drag is also reduced. Remember, density of the air is included in the drag formula!!

Therefore, it is logical that commercial aircraft are most efficient when flying fast and at high altitudes. Hence why they do. Hopefully that makes sense.

Profile drag is, fairly obviously, unchanged with changes in the weight of an aircraft.

Furthermore, high lift devices such as flaps reduce the speed for minimum drag, Vmd, but as stated earlier they have a minimal effect on the amount of induced drag created.

In a banked turn, the AoA increases. This increases Cl and, therefore, induced drag. This may be one of the reasons why commercial aircraft that are not in infinite flight make such gentle, slow turns at higher altitudes.

Ground Effect

Last bit now. I promise.

Ground effect modifies the airflow around an aircraft. Hit has the effect of increasing the aspect ratio of the wings, making the wing more efficient. The effect increases progressively as the aircraft nears the ground and the height reduces, but is only really significant below the height of approximately 1/2 the wingspan.

The downwash from earlier? Remember that? Well, it returns here. due to there being a massive planet below the aircraft, that downwash has nowhere to go and, as a result, a couple of things happen. Firstly, the pressure underneath the wings is increased, producing an artificial increase in lift. Secondly, there is an artificial change in the effective angle of attack, meaning far less induced AoA is required.
This can potentially have the effect of creating a nose down pitch moment too.

Conclusion

Well, we’ve made it guys! I apologise, I appreciate this is a long, wordy lesson but they, that is the ATPLs for you. The CAA or EASA could ask you a question on just about anything I’ve mentioned in this explainer, so it’s always best to prepare for the worst.

Hopefully you’ve found this fairly interesting, feel free to leave any comments or feedback, or any questions and I will do my best to answer them.

But again, I am a pilot but II’m by no means a qualified flight instructor or theoretical knowledge instructor. These are for interest and curiosity only, though they meant help with revision.

All the best, and see you next time!

Harry

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That was an interesting read I hope you do more topics.

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Thank you very much! I certainly plan on it.

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First of all, this is fantastic! Great to see your topics again!

My first read though so far (I need to and will read it again), really interesting and some new thoughts for me to think a bit more about.

You also gave me a homework assignment: “@adit you’ll like this. I’m fully expecting a well thought out question!” (I dreamt the other night I failed an exam…one of those you know).

Ok, I’ll try one. In the section Induced Drag Coefficient you wrote: “This is done because as high cruise speeds, the AoA required to maintain lift is lower, so the amount of downwash is lower and therefore so is induced drag.”

Does not downwash for level flight (no vertical acceleration of the aircraft), have to always remain the same for a given weight? So even as IAS changes, constant downwash momentum must always be maintained so as to equal weight of the aircraft? (the total “quantity of motion,” of the downwash cannot change if weight is to be exactly offset).

But of course, the AoA needed to achieve the maintenance of this constant downwash (constant momentum of downwash) varies with forward speed.

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Anyways a really informational topic! Keep this up and everyone’s gonna be 10x smarter in no time!:)

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Good question, I love it.

I think I see what you’re saying, but no. Remember that speed is part of the lift equation, so as that increases, the Cl factor in the lift equation will naturally decrease for a constant value of lift. Therefore, induced drag, by virtue of downwash, will also decrease as the Cd decreases due to the lower Cl.

In other words, if you speed up then you will have to reduce the angle of attack to maintain constant lift, and therefore the induced drag will decrease as a result.

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So when you say “but no,” you are referring to “downwash, will also decrease?”

In other words, you are saying that downwash changes, thus disagreeing with my assertion that downwash must stay the same at all airspeeds?

Are we perhaps defining downwash differently?

What I label as the amount of downwash is the total momentum of air shifted downwards caused by the airfoil, must equal lift.

It is Newton’s 2nd Law, which expresses force as a change in momentum.

Momentum = mass x velocity.

And so: Lift = Vertical Momentum induced = mass of air moved down x velocity induced downwards.

By “induced,” I just mean the change in the momentum down (in keeping with Newton’s Law).

As Lift = Force = change in momentum = d(mv)/dt

A constant value of lift = a constant value of change in momentum.

So to maintain flight for a constant weight, momentum of downwash must be constant.

And again, the reason AoA changes is to maintain constant downwash momentum, for the purpose of maintaining constant lift.

It is true that the mass of air directed down, and the velocity trade places, but the entire momentum change “package,” the product of the mass x velocity, must stay the same.

It is certainly clear that lift production drag, or induced drag, is lower a higher speeds as the AoA declines.

But this is because in producing the constant value of downwash momentum, more mass (more air mass passing the airfoil per unit time), is available to replace velocity, in the m x v momentum product.

More air moving slower consumes less energy than less air moving faster (due to the v term being squared when it comes to measuring kinetic energy, 0.5mv^2).

This is what’s at work with the efficiency of engines with high bypass ratio.

You could say the wing is working with the high bypass ratio concept in consuming less energy at higher speeds.

It’s also what’s at work with the lethality of a firearm: Projectile and firearm both receive equal momentum, but the projectile must carry much higher kinetic energy as a result of it’s much lower mass.

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Hi!
Awesome topic sir!
I’ve even shared that with my friend who studies aerodynamics and such things for his pilot licences. He also highly recommended me to add his quote:

Drag is bad however we have to remember that turbulent flow is way more stable than laminar flow (i. e. at low speeds or when some abrupt gusts occur) and sometimes we have to sacrifice our efficiency for safety.
For example, you would install “vortex generators” near the leading edge of an aircraft wing especially in front of its control surfaces. So, even if a major part of your wing starts to stall due to low speeds while performing landing flare, you can at least level its roll and don’t get a wing tip / engine strike.

Here’s the example of 737’s vortex generators:

I find this addition really interesting since it shows us that in aviation we don’t divide everything by good and bad but sometimes we have to balance 😃

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My mental model when encountering vortex generators was that they are like little sewing machines stitching together the laminar layers of airflow, so the layers are less able to slip against each other and separate when put under stress (the vortices are the threads).

Sure the thread makes the material rougher “to the touch,” but you get the cloth held together as the overriding benefit.

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Not quite, the vortex generators create a turbulent boundary layer to increase the energy within the airflow passing over the outboard ailerons.

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I don’t see that what I said is inconsistent with maintaining energy in the airflow.

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Oh, I see tho I asked my friend again to clarify 😂 (aerodynamics is hard for people, guys)

You talk about friction increase between the layers (streamlines). Yeah, it makes the airflow more stable and the required level of air particles exchange usually meets turbulent flow criteria (although seems none of us is from Boeing’s aerodynamics branch to clarify this particular case for sure).

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I think I used the fuzzy descriptive word “slip” (like a landslip) rather than “friction,” but it goes back to what @A_Hippopotamus said about the velocity gradient (which is a source “stress” in the overall flow) as you move out from the solid surface:

About which I though you made a great point about bringing up the paradox of vortex generators to use a bit of disorder to increase the overall system order.

Kind of like back burning before the summer forest fire season, or getting a little bit sick from a vaccine to prevent a more serious disease infection.

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I’ve gotta admit, this left me hungry for more. I yielded to…chatGPT just a bit, after a lot of other searching, in trying various ways to amalgamate ideas on this. I’m just gonna list it here, without alteration, in case the rare individual finds some relevance some day (or significant rebuttal):

Why is turbulent flow more stable than laminar flow?

ChatGPT

Turbulent flow is generally more stable than laminar flow because turbulent boundary layers have greater resistance to separation and are better at maintaining attachment to the surface compared to laminar boundary layers. This increased stability in turbulent flow is attributed to several factors:

1. Energy Redistribution:
• Turbulent flow involves the random motion of fluid particles, leading to increased mixing and energy redistribution within the boundary layer. This mixing helps prevent the formation of regions with extremely low energy, reducing the likelihood of separation.
1. Reduced Sensitivity to Disturbances:
• Turbulent boundary layers are less sensitive to external disturbances compared to laminar boundary layers. Laminar flow is more susceptible to disturbances, such as surface roughness or abrupt changes in pressure, which can trigger separation and transition to turbulent flow. Turbulent boundary layers are more robust and less prone to separation in the presence of disturbances.
1. Increased Momentum Transfer:
• The random motion of turbulent eddies leads to increased momentum transfer between adjacent fluid layers. This enhanced momentum transfer helps maintain higher velocities closer to the surface, reducing the adverse pressure gradient that can cause separation in laminar flow.
1. Thicker Boundary Layer:
• Turbulent boundary layers tend to be thicker than laminar boundary layers. The increased thickness provides a buffer against adverse pressure gradients, making it more difficult for the flow to separate from the surface.
1. Shear Stress Redistribution:
• Turbulent flow redistributes shear stress more effectively within the boundary layer. This redistribution helps prevent the concentration of shear stress in localized regions, reducing the likelihood of separation.
• Turbulent flow is inherently unsteady, with the continuous formation and dissipation of eddies. This dynamic nature contributes to the stability of the flow by preventing the establishment of long, quiescent regions that can lead to separation.

It’s important to note that the stability of turbulent flow is context-dependent, and there are situations where laminar flow may be preferred, such as in certain aerodynamic designs to minimize drag. However, in many practical applications, such as aircraft wings, where resistance to separation is critical for control and performance, turbulent flow is often more desirable due to its increased stability.

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Awesome stuff, goes far deeper than my personal prior knowledge of course! Thank you very much for the contribution, as always!

Goes to show how certain aspects of different aircraft are optimised for different jobs too, something I’ve always found intriguing. The vortex generators are just one way the 737, for example, has clearly been designed with slow speed manoeuvrability in mind as a short haul, high capacity carrier!

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I was trying to understand how much the existence of the boundary layer is related to the existence and degree of viscosity (you pull a spoon from a jar of honey, and the honey against the walls hardly moves at all - that’s an extreme condition of boundary layer adhesion associated with high viscosity).

So, if I understand correctly, the boundary layer would disappear if viscosity goes to zero. And in fact a significant simplification of the Navier-Stokes equations, is assuming viscosity is zero. It massively simplifies the mathematical interrelationships for “layers” pulling on each other, but still yields useful insight into the generation of lift.

But of course, you need viscosity for specific airfoil design, because it makes a significant difference in flight performance characteristics for a real working wing.

@AlexNine99 at one point had been expressing something similar to what I was considering at one point: how to think about the void apparently left behind an airfoil in the explanation for the mechanism of lift.

This University of Michigan Professor talked about, “back circulation” being a possible solution for the void (thus invalidating that explanation)… Krzysztof Fidkowski | How Planes Fly - YouTube (17min 12sec). Sorry, this is splitting hairs, but I didn’t quite understand his reasoning until I hit upon the velocity gradient and the boundary layer (in the roll of creating flow reversal eddies), such as you explained so well in your above tutorial, and its relation to viscosity.

I think I’ll leave that point (too much micro detail).

But I mean, lift is the process of turning the air from the asymmetry of a solid creating an asymmetrical pressure drop that pulls the relative wind sideways. That gives the momentum change necessary to overcome weight. On top of that, just gotta optimize the flight parameters for performance, safety and efficiency (by not forgetting viscosity and the boundary layer when it’s design time)!

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I think it’s important to point out, this disagreement I have about the nature of downwash, goes right back to how the FAA characterizes downwash, which one supposes is a historical legacy, and really messes with the physics of the big picture of lift:
(https://www.faa.gov/sites/faa.gov/files/07_phak_ch5_0.pdf):

The very last line of that text, about the induced drag varying inversely with the square of the airspeed (which I believe you mentioned) doesn’t come out of thin air. It’s directly related to the kinetic energy content of the total downwash momentum (which is fundamental to the physical definitions of momentum vs energy). The FAA could use a sorting out of the definitions of downwash consistent with the first principles of physics.

This btw affects the nature of wake turbulence hazard.

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Very nice topic! One thing - I think this statement may be backwards…

I see on your profile you are studying for ATP, I’d be very interested in reading a post about high altitude aerodynamics (Mach tuck, coffins corner etc.)

Keep up the good work!

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