ATPL Theory - Principles of Flight: Lift

Welcome back to ground school and our first proper lesson on the principles of flight.

In this lesson we will be taking a closer look at Lift. What is lift, what is the lift formula and how can it be affected. Then we’ll look at some Cl-alpha graphs. Please do refer back to my Introduction to Principles of Flight post for further information. There I explained the basic idea of how lift is created.

I should warn you now that we will start getting technical now. So you might want to grab a cup of tea/coffee first.

Lift

As the thing that makes our aircraft fly, we have all heard of lift. There should not be a pilot on this planet who doesn’t know, at least in a general sense, what lift is.

But for those of you virtual pilots who don’t yet have a clue… lift is a force. This means it’s measured in newtons. Again, I explained how lift is created in my previous post linked above. But to briefly go over it again:

If is created by having a low pressure area above the wing and a relatively high pressure area below the wing. As the higher pressure air tried to move into the area of low pressure, the wing ‘gets in the way’ and is moved in that direction.

I hope that makes sense.

What I didn’t mention before is that lift always acts perpendicular to the relative air flow around a wing. It’s created when a mass of air is accelerated - i.e. has its direction changed.

Influencing Lift

Increasing the angle of attack (AoA) increases lift. For a cambered wing, this also moves the centre of pressure forward. Think about it - when you’re flying along in Infinite Flight, what happens when you pull up? You go up, right?

This happens because by increasing the angle of attack, you increase the co-efficient of lift (Cl).

Cl is a part of the lift formula, and by far the most technical one at that. All the others are easy by comparison:

More speed increases lift, fairly obviously.
A bigger wing will produce more lift.
Denser air will, indeed, produce more lift.

But the co-efficient of lift… What on earth is that?

Cl is essentially a summary of a number of factors. As can be seen below, it is part of the lift equation. Cl is calculated through experimentation by the manufacturer.

Notice how I said AoA influences lift? But there is no AoA in the lift equation? That’s because it is one of the factors that effects Cl.
Increasing AoA increases lift. For a cambered aerofoil, it also moves the centre of pressure forward.

Time to talk about centre of pressure.

Centre of Pressure

As you already know by now, wings work on pressure. Pressure movements, pressure changes.

For a cambered aerofoil, most of the pressure decrease occurs over the front half of the wing - the most curved part of top surface would be another way of thinking about it. This is shown by the light blue areas in the diagrams below. As the angle of attack increases, the pressure in the light blue area decreases. Therefore, the ‘average’ point of the pressure across the top surface shuffles forward - also known as the centre of pressure.

When talking about centre of gravity, we assume this is the point upon which gravity acts on the object, right? Like the ‘average’ point of all the mass of the object.

Assume the same with lift on a wing. Then call it the centre of pressure.

Below are some diagrams. As you can see, the higher the angle of attach, the more the pressure changes and, therefore, the greater the lift created.

What they also show is how this pressure creeps forward, thus moving the centre of pressure forward.

Cambered vs Symmetrical

This effect is only true for a cambered aerofoil. For a symmetrical aerofoil, the centre of pressure remains the same regardless of AoA.

A symmetrical aerofoil is an aerofoil inn which the chord and camber are alined. In other words, where there is no curve to the wing.

Another notable difference between symmetrical and cambered aerofoils is what happens when you have zero angle of attack.

For a cambered aerofoil, lift is produced at 0 AoA. A cambered aerofoil stops producing lift at around -4 degrees AoA. This is demonstrated on the graph below, known as a Cl-alpha graph because it shows Cl vs Alpha (AoA):

You can clearly see the curve intersect the ‘Lift’ axis above the origin. This shows that at 0 AoA, there is lift. Now take a look at the same graph below, only this time for a symmetrical wing:

This time the curve slices straight through the origin. 0 AoA = no lift. Furthermore, the centre of pressure does not move with a change in AoA.

Changing camber

As we said earlier, camber has an effect on the co-efficient of lift of a wing. Therefore, it stands to reason that with an increase in camber (for a given AoA) will come an increase in lift.

The opposite is also true. Keeping AoA constant, a decrease in camber will reduce lift.

This can be seen on the graph below:

What is also shown is that by increasing camber, the maximum Cl also increases, and is achieved at a lower AoA.

Therefore, the wing will achieve greater lift and achieve it at a lower AoA. However, Cl Max is also the point at which the wing stalls. The coinciding AoA is know as the critical AoA.

This is a highly useful property of wings. We’ll talk about it more in the future but for now, a hint: Flaps take advantage of this exact principle.

Effects of Aspect Ratio

One of the other factors of Cl is aspect ratio.

The shape of the curves actually follow the same patterns when talking about changing aspect ratio for symmetrical and cambered wings.

I’ll insert them below and you can have a look for yourselves. But what you’re looking for is a change in the slope of the curve with a change in AR:

First is the graph for symmetrical wings. We can see that the amount of lift each AR produces is the same at 0 AoA. From there, wings with a higher aspect ratio increase Cl quicker for a given change in AoA than the equivalent low AR wing.

Effects of Wing Sweep

The last segment of lesson on lift is the effects of wing sweep. Straight wings, like those seen on most light aircraft such as the C172, PA28, PA44 etc, along with the A-10.

Wing sweep has the effect of lowering the maximum Cl while increasing the maximum AoA. The Cl-alpha curve of a swept wing is far shallower than for a straight wing. This partially explains why commercial aircraft pitch so high on climb out despite climbing at a fairly normal rate.

See below the graph for different wing sweeps:

Screenshot 2022-11-16 at 18.36.19
(Please forgive my handwriting! I scribbled this down during a lecture)

So, that is a lesson on lift and the Cl-Alpha graph. As always, please feel free to leave questions and comments below and I’ll answer them as best as I can.

Please be forgiving - I’m a pilot, not an aerodynamicist!!

See you next time, probably for drag.

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You’re insane dude! Keep it up!

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Thank you very much! I’ll do my best 😂

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I really appreciate this collection of info which is not so easy to come by in such an informative format. In particular, the graphs are great - symmetrical vs cambered (and degree of camber) vs AoA. What you put together is really well thought out.

Just playing devil’s advocate for a moment:

That was certainly obvious to me in the beginning, but the more I thought about it, the less sure I was. In the L equation the rho v squared over two term certainly tells you this. It’s basically the kinetic energy density of the relative wind (TAS). More TAS is more air kinetic energy (of relative wind) available for lift. But why doesn’t “borrowing” that kinetic energy from the relative wind not increase drag so much that it pushes D too close to L in the L/D ratio(?) It’s just an interesting question, I might call “the magic of flight” question.

Centre of pressure is not something I’ve thought much about. From reading a post graduate aeronautical engineering discussion on this, it seems it is well predictable, but not completely explainable. I don’t know if this is the universal academic view or not. It’s certainly not clear to me right off how this works.

edit: another thing I’ve found quite interesting. Bernoulli vs Venturi vs Newton’s 3rd law. I find the fact that debate arises to be fascinating. We know how to engineer efficient reliable aircraft. So what is the nature of the debate? What “force” makes the debate exist at all?

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I always love your questions adit. You never fail to make me think!

Firstly, thank you for the kind words. I appreciate that what I’m doing with these is totally different to what is normal for this forum so it’s nice to hear people still enjoying them!

As for your question…

I should probably have clarified this, but that statement in your quote is assuming all other factors within the lift equation remain constant.

I’m not entirely sure on the exact kinetic mechanics of how lift works - that’s far, far above my level of education unfortunately. It is indeed an interesting question though, thank you!

All I would say is that the generation of lift is so efficient and advanced nowadays that the drag created is absolutely minimal during the cruise. Not to mention that lift and drag are not a couple - thrust is the couple to drag, and we fly around at pretty much full power all the time.

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what is this, haha great work

this can be a good introduction to aircrafts physics

I believe the whole issue of efficiency that makes “the magic” of forward flight possible (high L/D ratio), is the same cause of increased efficiency in turbine engines when you increase the bypass ratio. For a constant level of thrust (or lift in the case of downwash), moving a large mass of air slowly consumes less energy than moving a smaller mass of air very fast.

They’re both related to the difference between momentum = mv
versus kinetic energy = (1/2) mv^2

The change in momentum of air gives you the force.
But the ingredients with which you bake the change in momentum derived force makes all the difference.

Increasing bypass ratio, as with increasing speed of a wing moving forward, gives you more mass to bake into the momentum at the expense of speed of that mass. And the effect is seen as reduced energy consumption because kinetic energy goes up with the square of speed.

So increase mass at the expense of speed in a change in momentum derived force, and you effectively have energy gearing.

I think that’s right anyway(?).

edit: so you have the kinetic energy of the aircraft ke = (1/2)mv^2
As the kinetic energy of the aircraft goes up, the ke required for the downwash lift keeps decreasing because more downwash speed is being replaced with more mass of air.

So that presumably is why the induced drag curve falls as it does with increasing speed, and therefore thrust is more optimal at the bottom of the total drag curve. You have that energy gearing effect that takes less and less out of the aircraft’s kinetic energy.

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Wow, fascinating! Thank you so much for that, that makes a lot of sense!

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You’re welcome. But I still wish for a more intuitive way to explain that energy momentum relationship, rather than just pointing to the formulas. I’m having trouble thinking of an everyday experience way to relate it. I like to be able to explain it to myself in the simplest terms. Momentum is “the quantity of motion” and kinetic energy is “capacity to do work”, is still a step too far removed from where I’d like to be.

Kind of like the way you phrased:

It makes immediate sense.

The question of why induced drag decreases with airspeed always confused me, as speed increases lift and lift creates induced drag. But my most recent flight instructor finally explained it in a way that made sense.

Wingtip vortices are a big part of induced drag, and they are the most dangerous when an airplane is heavy, clean, and slow. Slow being the key word in this, as it means the aircraft has a higher angle of attack than in normal cruise. A higher AoA means there’s a greater difference in pressure between the top and bottom of the wing. This means, as AoA increases, so does wingtip vortices and vice versa.

The faster you go, the lower angle of attack you need to maintain the same amount of lift. Thus, as speed goes up, AoA and wingtip vortices decrease - meaning induced drag also decreases.

Awesome thread!

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edit: Thinking about it some, from the best I can tell, I disagree.

Higher AoA as you slow is to keep the pressure difference steady to keep lift constant. So yes, on its own increasing AoA increases the pressure difference. But your speed has been decreasing to exactly counter the pressure increase offered by higher AoA (assuming you maintain constant lift). You completely trade one for the other. So the pressure difference remains the same.

So this cannot explain stronger vortices at lower speed.

I believe wingtip vortices are the more minor part of induced drag. The major part of induced drag is likely downwash that directly results in lift generation. I say likely a minor part because vortices drag acts as a “parasitic” fractional loss of the energy that goes into that downwash. That is it’s “skimmed off the top” of the core process of lift generation.

So pure downwash is what you want, but vortices come with that due to the inevitable geometry of the wings having to end at the tips, causing a leakage loss of the main use of energy. The leakage takes the form of non-directional turbulence (rotational - it sucks up energy without adding to directional lift momentum).

So again, I believe wingtip vortices are not the key cause of the shape of the induced drag curve.

The main physical reason for drag falling with AoA, is the same process as why bypass turbines are more efficient - the displaced mass of air causing the force (Thrust in the case of the engine; Lift for the wing), is more energy efficient when more mass is added moving at a slower speed.

With the wing, you don’t have to curve the air as much (lower AoA), because you are relieved of less vertical movement of downwash, in a very non-linear way: faster mass flow of air saves you energy.

End of Edit

I need to think for a while about what you said about wingtip vortices proportion of induced drag at low speed.

I’ve also read the pressure differential is higher at higher AoA. But I don’t understand that right off because it seems like the total pressure differential should always be the same for unaccelerated flight: is there not one single, total pressure differential at a given weight(?). And that’s why you increase AoA, so that you maintain the same pressure differential as speed decreases(?) Good comment!

The classic every day experience:

Stick your hand out the car window and point it into wind. Then change its angle relative to the wind and see what happens

Nailed it. This is indeed why, so thank you for this comment. I’ll try and explain it as best as I can in the drag lesson.

As a side note, discussions like these are what I was hoping for on these posts!

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I meant about how to relate that mass carries less energy content than speed, in providing a given force from a change in momentum. Which is really the essence of the efficiency of flight. I can’t think of a good relatable example, other than flight itself, which is the thing trying to be explained.

Edit: I kind of came up with one - The fact that handheld firearms are possible.

A single explosive force propels the projectile at far faster speed than the weapon recoil due to the difference in mass. Both weapon and projectile are given exactly the same momentum. But the weapon body assumes far less energy than the projectile because of the weapon’s much higher mass.

So high bypass ratio is like the firearm body. More mass at slower speed for the same change in momentum (thrust), lowers energy consumed for that amount of thrust.

Helicopter with small engine but large blade to move larger mass of air more slowly.

Fixed wing, fly faster to move a larger mass of air down per unit time. Again, change in amount of air momentum down stays the same (lift), but induced drag declines because less energy is consumed with the larger mass moved down. So less thrust is required (and or descent rate).

Edit: So after thinking about it, I disagree. (see comments in my reply above)

End of Edit
AoA lift causes more drag than camber lift?

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Heya, I’ve finally uploaded a new lesson, on drag! I go into detail about why this is the case in there - hopefully it’ll be approved promptly for you to have a read of :)

@adit you’ll like this. I’m fully expecting a well thought out question!

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