ATPL Theory - Principles of Flight: Introduction to PoF

Welcome to Ground School.

This is the first post in a series I am looking to to create in order to bring real world commercial pilot theory to the Infinite Flight Community. Please feel free to leave any feedback or advice, along with any questions, below for the benefit of everyone.

Firstly, a disclaimer: although I am indeed a real world pilot, I am not a theoretical knowledge or flight instructor. This information should not be used for real world aviation per se, though no doubt it will help many other pilots out there and will definitely be applicable to Infinite Flight.

With that out the way, my name is Harry and this is an introduction to the Principles of Flight.

Forces in Flight

There are four main forces at work on aircraft, known as the ‘fundamental forces’ of flight:

  • Lift
  • Weight
  • Thrust
  • Drag

These forces act in couples, with lift counteracting weight and thrust counteracting drag.
In straight and level, unaccelerated flight, lift will be equal to weight and thrust equal to drag. The lift/weight couple would typically be far greater than the thrust/drag couple.

The Lift Formula

Now is probably the time for me to mention that these ground school lessons will be technical. They will not be simplified explainers I’m afraid, although I will do my best where I can to KISS.

Lift may appear to be some magical occurrence that ‘just happens’. Stick wings on a plane, it magically flies. Simple.
If only life were that easy.

Lift is made up of a few elements, defined in the lift equation:

Lift equation

“What are there hyroglifics?!”, I hear you ask.

Fair question, so here we go.

Cl refers to the co-efficient of lift of the wing (more on this shortly),
ρ is the density of the air around the wing,
V is the true air speed (TAS) that the wing is travelling at,
S is the surface area of the wing.

Make sense? Good, let’s get digging.

The Co-effient of lift (Cl) is based upon a number of factors. The first and most obvious of these is the shape of the wing, known as the wing planform. There are four main planforms - rectangular (like on a C172), elliptical (such as a Spitfire wing), tapered (like a P51 Mustang) and swept back (as seen one pretty much every current commercial airliner).

Aspect ratio also influences Cl. A higher aspect ratio increases Cl of the wing. Wing aspect ratio works the same way as a screen and is defined as AR = span / chord, where the span is the length of the wing and the chord is the width.

Wing camber further affects Cl. Camber is effectively the curvature of the wing, with a greater ‘curve’ increasing Cl.

Another less obvious factor is the surface finish of the wing. A smooth wing surface will allow the air to ‘stick’ to it a lot better than a rough wing surface, keeping more energy within the airflow and thus increasing the Cl.

Lastly, the angle of attack of the wing has a huge effect on the Cl. Put simply, the higher the AoA, the larger the Cl. This applies up until the stall point of the wing, known as the critical AoA, which coincides with the maximum Cl.

More on all of these another time.

Dynamic Pressure

Screenshot 2022-11-10 at 18.56.21
This is the portion of the lift equation that shows dynamic pressure. Also known as q (think of SpaceX launch streams - they refer to maximum dynamic pressure as Max q.), this is effectively the pressure that results from movement.

Have you heard of a Venturi? Or Bernoulli’s principle? Bernoulli created the equation A x V = Constant. In brief, this is the relationship between the speed of flow and cross-sectional area of a converging duct.

Assuming a constant volume flow through a converging/diverging duct, the speed of flow in the converging area will increase, and the (static) pressure will decrease. As total pressure remains the same, dynamic pressure must increase. This is the venturi effect. In a converging duct, the speed of the flow will increase and the pressure will decrease. In a diverging duct, the opposite is the case. This can be seen visually in the diagram below:

Does the shape look familiar? A wing works on this basic principle. As air is accelerated over the top of the wing, the pressure drops in that area. relatively high pressure below the wing tries to fill the vacuum, and as it does so the wing is ‘sucked’ in that direction.

Note: I say direction, as opposed to up, as this work regardless of gravity. if the aircraft is inverted, the same process happens.

Increasing the wing camber, i.e. the curvature, increases the intensity of the venturi effect, thus increasing the Cl.

Screenshot 2022-11-10 at 18.55.02

Speed is the most important part of the lift equation, due to it being squared. Whereas doubling the Cl or the surface area would result in the lift being doubled, doubling the airspeed while keeping all other factors the same would result in the lift increasing by a factor of 4 (2^2 = 4). In other words, the speed has by far the biggest effect on the lift produced.

Rho - the P - simply refers to the density of the air around the wing. The higher the density, the higher the lift. Simple when you think about it.

q is measured by the Air Speed Indicator, or ASI. The ASI shows indicated air speed, or IAS (well, sort of). In Infinite Flight, this is shown by the ticker tape on the left side of the HUD.

“Ram Air” is the total pressure. The pitot tube of an aircraft only measures total pressure. Static pressure enters the system via the static ports, positioned on the side of the aircraft.

Dynamic pressure is found by subtracting Static pressure from total pressure;

Total pressure - Static pressure = Dynamic Pressure

Speeds

Iced Tea Is A Pretty Cool Drink

One of my ground school instructors taught us this one our first day. It sounds silly, but this is a very good moniker for remembering the order and relationship between each type of speed.

As mentioned above, indicated airspeed (IAS) is what, essentially, goes into the pitot tube. However, because of its position, the reading has to be ‘corrected’ for any pressure error caused by air flow disturbance around the pitot. This is also known as Pressure Error. Correcting for this coverts Indicated Air Speed to Calibrated Airspeed.

Officially speaking, Calibrated airspeed is what the ASI shows.

Correcting Calibrated airspeed for compressibility - I’ll explain that one another time, just accept that it exists as a result of moving through air - gives us Equivalent airspeed.

Lastly, correcting Equivalent airspeed for Density altitude gives us True Airspeed.

Reading across gives ‘ICE Tea is a Pretty Cool Drink’.

EAS and TAS

EAS = TAS x the root of the relative density at that altitude.

The standard air density at sea level is 1.225 KG per cubic meter. Dividing the density at a specific altitude by this gives the relative density.

At 20,000ft, this works out at roughly 0.5.
At 40,000ft, it’s around 0.25.

Therefore, at sea level the EAS would be equal to the TAS (i.e. the TAS multiplied by the square root of 1).

Mach

Now we’re getting technical.

Mach is calculated by dividing the TAS by the local speed of sound, or LSS. This is calculated by taking the square root of the local temperature in Kelvin, then multiplying that by 38.94.

Don’t ask me why, just believe me.

Mach = TAS / LSS

As the temperature drops, and TAS in the climb remains more or less constant, the mach speed increases. This is demonstrated in the diagram below:

No matter the speed you pick relative to the others, the speeds should always appear in the same order. E-C-T-M

Think ‘Eat Chicken Tikka Masala’, as my instructors said.

So, that’s dynamic pressure and an introduction to air speeds. The last part of the lift equation, s, refers to the surface area of the wing. Logically, a bigger wing will produce more lift.

Drag

Drag opposes lift. And where there is a lift equation, there is also a drag equation.
It looks like this:

Screenshot 2022-11-12 at 13.28.58

Aside from the Cd - which, as I’m sure you can guess, stands for the Co-efficient of Drag - all other variables are the same as for the lift equation.

The Cd is made up of two separate components. Cd(Induced) and Cd(Parasite).

The Cds essentially depend on the size and shape of the wing.

Induced Drag

There are two types of drag which you probably already know of. Firstly, there’s induced drag. This can be thought of as lift-induced drag, as it forms as a direct result of producing lift with an aerofoil.

If you’ve ever heard of wake turbulence, this is what creates it. Think back to above where we discussed how a wing actually creates lift, with low pressure above the wing and high pressure below it. As the air ‘moves’ to try and fill the ‘vacuum’ above the wing, some of the movement spills over the end of the wing. This creates a rotation effect, which creates drag. Known as wing tip vortices, they are then carried away with the air flow passing the wing. They continue to expand, slowly dispersing energy, and continue to spiral for quite a while.

Screenshot 2022-11-12 at 13.59.10

Induced drag is highest at low speeds. We will go into this in more detail another time but for now, just accept that the faster you go, the less induced drag you produce.

Parasite Drag

Parasite drag is a summary of a combination of factors, but the general point is that it increases with speed. The faster you go, the more parasite drag is created. Parasite drag is influenced by skin friction, the aircraft and wing profile, and something called interference drag.

Drag Curves

The increase/decrease of the types of drag with speed can be demonstrated on a graph, as shown below.

Screenshot 2022-11-12 at 15.36.28

The point at which Parasite and Induced drag intersect is called the speed for minimum drag, or Vmd. Vmd is, technically, the most efficient speed for the wing (note, this doesn’t necessarily mean the most efficient speed to fly).

Any speed below Vmd is considered to be unstable. This is because a further decrease in speed will increase drag, which in turn will decrease speed further. In other words, the speed will exponentially decrease. There’s a saying in flying called ‘getting behind the drag curve’. It’s a potentially dangerous situation which can be difficult to get out of if heavy or at a low power setting.

Approach speeds (Vapp, Vref etc) are calculated with this in mind and allow a margin to keep the aircraft at a safe speed. It goes without saying that the drag conundrum is most dangerous on approach, when the aircraft configuration is resulting in the maximum amount of drag and is therefore most prone to loosing energy quickly.

Any speed above Vmd is considered to be stable. This is because any further increase in speed will increase drag (in this case, parasite drag) and bring the speed back to Vmd.

Again, we will go into this in further detail in the future.

Conclusion

So, that is an introduction to the Principles of Flight. I apologise for the amount of ‘more on this another time’ but I’ve tried to keep this as brief and uncomplicated as I can. There’s a lot of potential to over complicate things in aviation - PoF suffered heavily from this. This is only an introduction, after all.

I hope this has all made sense and been of use. If anyone would like me to further explain something or answer a question, please do let me know below.

If you spot any mistakes, again please point them out to me. Any feedback is absolutely appreciated.

Thank you for taking the time to read this introduction and I’ll aim to have the next one out soon.

Edit 1: changed category
Edit 2: fixed a few typos

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Wow, that is a lot of information! I will help you out here;

This should be under community tutorials I believe.

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Thank you, yeah that’s what I thought but it just says I’m unable to use the resource when I try and change it.

If someone with the power to do so could please change it, that would be fantastic.

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@moderators would be the way to go.

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If you think this is a lot, wait until I start getting in to it 😂

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Oh God, this sounds like 3 classes of physics

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EXELENT notes here, all correct to confirm your explenations

Welcome to the family, I hope you will get your licence and grow your flight hours

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Thank you very much. Waiting for my commercial licence to come in the post at the moment so hopefully not long now.

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Wait, will i need to know all this to get a commercial license?

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Love topics like this. We use to have a community member who did similar stuff like this years ago. Would be nice to see more content like this. Really quite refreshing. Excellent job!!!


Just wanted to point out that the other 4 forces of flight 😜

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This is actually awesome good job! Fun to read 😁

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In the UK / Europe, yes. This is just scratching the surface of what you will actually have to learn.

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Thank you so much, it means a lot! :)

Thank you!

Great Job! There is a lot of good information. Isn’t another name for Vmd L/D max?

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Im from Europe so 😅

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Hi again. A big contrats on your continued progress through professional training! I remember fondly our long dialogues on topics of flight. But at the same time I often burn myself out and need a re-charge.

I love that you unashamedly bring equations to the forum (it lowers my stress level to see this; and it’s stimulating). I am very happy to see moderators and staff endorsing this! You have my support!

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I’m curious about how to classify parasitic vs induced drag. I would assume things like skin friction and form resistance are parasitic(?). But vortex related drag increases with AoA so is included with Induced drag? I don’t know if my thinking makes sense, but I’m interested in the nature of required power implied by the induced drag curve.

edit: I was watching what seemed like a reliable source claim that wing tip vortices are the source of downwash. Am I imagining a contradiction?

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Induced drag is drag produced through the production of lift as air moves over the airfoil, while parasite drag is called profile drag, so any drag from the frame of the airfoil, such as rivets across the top of the wing would classify as parasitic.

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So as far as vortex formation + down wash, you would say induced drag includes both of those?

What I’m getting at: is drag due to downdraft (Newton’s 3rd law explanation of lift), not productive drag, while vortex formation drag is an unwanted byproduct of that?

In other words, vortex drag is also parasitic (you want to minimize it with winglets etc.), but because of it’s behavior with change in speed, it is lumped in with induced drag rather than parasitic?