An aerodynamics question (for experts only)
 

I've tried this one before and got nowhere - maybe because it's all cr*p.

I've been looking through the books again following attendance at an instructor seminar - and am getting really confused with the "forces acting on an aircraft in flight".

Let's go for the easy option (or at least what I believe to be the easy option), let's take a light aircraft, in straight and level flight, all balanced - no acceleration, no climbing, nothing spectacular - just cruising along, drilling a hole in the sky. (first wanabee to send me £10 can log the time :D )

Trevor Thom, et al, are telling me that there are four forces acting on the aircraft - lift, weight, thrust and drag. And I've been using this since my trial lesson back in 1973.

Now, my FIC renewal has brought out the comments that we have been using the terms of the four forces for the sake of convenience but that actually there are only three forces. Weight, thrust and total reaction (TR). This TR can be broken down, by the scientists, to show a horizontal vector (not a force) which we call drag - and a vertical vector which we call lift.

I'm getting numerous arguments in favour of both camps. Anybody (who actually knows what they are talking about) care to comment? Please!

"If anyone tries to tell you something about an aeroplane which is so damn complicated that you can't understand it you can take it from me it's all balls."

- R.J. Mitchell (designer of the Supermarine Spitfire)

If you were a study of Richard Feynman et al, you would understand this concept. What it is saying is that weight and thrust are relatively constant and independant variables acting on the body.

However there is a resultant and balancing vector that is comprised of (classically) Lift and Drag.

However Drag is partially and variably dependant on Lift so it makes sense to resolve these two items as a single vector that is continuously opposing Weight and Thrust (in unaccelerated motion). Simply resolve the vector (at the instant in time that you are interested in) and you have the two (more conventional) items - Lift and Drag.

It is another way of looking at the same thing. But mathematically a single vector of these two co-dependant and variable effects is easier to manage.

Don't sweat this complex math stuff (unless you enjoy the challenge) when there is lots more to understand well before you come to this. From a human / physical perception there is no difference.

MG

Fine - tell 'em if they want to play that way that there are still four fources - weight, thrust, "total reaction" from the wing and drag from the airframe.:rolleyes:

Or tell 'em that you have resolved the forces of thrust and weight into one force, call it the "speed independant" force, and the lift and drag into another, so that there are only "two real forces" acting on the airframe... :rolleyes:

There was a discussion about this topic a while ago on the Instructors forum, but I can't find it now.

Exactly - just being clever cloggs by and bye. What are we teaching ? Maths or Flight

MG

GoneWest,

Mr Boeing states that for level unaccelerated flight, thrust and drag must be equal and opposite, and the lift and weight must be equal and opposite according to the laws of motion, you then get:

T=D
L=W

He then goes on to justify it mathematically, resulting in……

L/ ä = 1481.351 CL M2 S
D/ ä = 1481.351 CD M2 S
W/ä = 1481.351 CL M2 S
T/ ä = 1481.351 CD M2 S


Mutt.

An aerofoil presenting an angle of attack to the relative airflow will experience a single force.

That force is conveniently resolved in 2 mutually perpendicular directions; normal to the relative airflow to give lift and parallel to the relative airflow to give lift dependant drag.

Similarly, a propeller is also an aerofoil. It also experiences a force due to the angle of attack presented to the relative airflow resulting this time from both propeller rotation and forward motion of the aircraft. This force is also conveniently resolved into 2 directions, that normal to the plane of rotation gives thrust, that parallel to the plane of roatation gives 'prop drag' which is the force the engine must work against to maintain the rotational velocity.

Is there any testable difference in validity between the 3-force model and the 4-force model?

You can slice and dice forces any way you want for convenience. It's convenient to differentiate thrust from the "total reaction", but they're both contributions to the aerodynamic force on the aircraft -- so should it be a 2-force model?

Which model you pick depends on what problem you're tring to solve at the time.

If we're getting pragmatic here, why don't you concentrate on the number of forces that a P of F exam will ask about? Isn't this the final arbitrator?

Some very useful replies - (and a couple of useless, :p ), thanks guys.

MasterGreen - I like your explanation. Made it a lot clearer.

Mutt - I think it was said by many, long before Mr Boeing came along.

BEagle - you have quoted the CFS style approach to the question ......

........which really brings us to the question posed by a few of you "Does it matter?"

A different subject - but (for OZExpat, and others of the same frame of mind) one of the downsides of flight instruction is that every instructor is convinced that he/she is correct. This then brings us to the point that the definition of correct will likely be a matter of opinion - between the various instructors who state their own ideal as being the only correct one. You can read any number of threads in these forums and everybody argues that their posting is the facts of the case - and that anybody who argues is just plain wrong.

So, if that P of F exam mentioned by OzExpat, is a verbal one - administered by an examiner who may decide on the future of your position in the aviation industry - then I would think it quite important to be able to give him/her the answer that he/she wants. If it is a question of researching the individual examiners, to learn their favoured answer, then this really highlights the problem that BEagle brought up about instructor renewals being done by means of a mandatory flight and ground test with an examiner.

In which case, %MAC, MasterGreen, Checkboard, bookworm and OzExpat - it certainly does matter.

What I don't agree with is that I've spent 20 years of listening to instructors and reading Trevor Thom etc - all who tell me there are four forces and now - the people that MATTER (as far as this discussion goes) are telling me that there are only three.

Man has been flying for just short of 100 years now - surely somebody has sussed it out.

If the point that you're making is that examiners sometimes don't have a full grasp of the physics behind the questions they ask and that you sometimes have to learn an 'official' simple answer to a much more complex question, then perhaps I'd agree with you. But if that's the case here, your question is mis-titled: you mean "for examiners only", not "for experts only". :)

Most of the good examiners I've met (most of them) are not so insecure about their ability in physics as to be frightened by a little debate about a complex issue.

bookworm - agree entirely.....but what I's saying is that it's the examiners who are now suggesting that they more than fully understand the physics, and that it's their three forces is correct and that the four forces stuff that we've all grown up with is "convenient - but wrong".

The last guy I flew with was talking about this very subject and said "There is a whole generation of pilots out there that have no idea what is making the aeroplane fly"

....and, as far as the examiners are concerned, they are the ones with the full understanding and the likes of (presumably) you and I - and all the others that subscribed to the four forces theory - are in that generation......and that it is us who do not understand the physics.

Postings such as BEagles (who I greatly respect [on most topics]) confirm that there are people who agree on the three forces. I just don't understand why it is suddenly an issue - but it is fast becoming one.

An aerofoil presenting an angle of attack to the relative airflow will experience a single force.

Of course there are in fact millions of forces acting on an aircraft in flight.

What Physics does is to say can we pretend there is only one, or two or three etc and get the correct predictions (-ish) whilst making the mathematics simpler.

So the answer to your question depends on what you are trying to do. As an example if you want to explain the effects of propellor wash you are going to have to consider two lateral forces on the airframe, perhaps one at the centre of mass and one at the centre of the fin.

If you are going to the trouble to talk about resultant forces on the airplane, the answer is there are none. The sum of all forces has to be zero or the airplane wouldn't be flying straight and level at constant speed.

If all forces are in balance, the aeroplane will not accelerate. But it would continue to maintain both horizontal and vertical velocity until influenced by another force.

There is obviously only one single reaction force T to
the movement of the plane, however it is convenient
to split it into its two equivalent components Tx & Ty
which are acting at right angles to one another and
hence can be placed in opposition to the Thrust &
Weight components so as to balance in straight and
level unaccelerated flight.

To think that the three force model or four force
models are describing different things is to completely
miss the point.

-- Andrew

Sorry to be pedantic, and at risk of being flamed, but the "obviously only one single reaction force" is not, ISTM, correct. As pointed out by an earlier posting, there are really zillions of little aerodynamic forces acting all over the aeroplane - but for many purposes they can be treated mathematically as though they were a single reaction force, i.e. their "resultant", or they can resolved into two forces at rightangles, by convention called lift and drag. Neither is more right or wrong than the other, it is more a question (as yet another pointed out) of which one suits a particular purpose at the time.

Incidentally, there are also couples (twisting or turning forces) acting upon an aeroplane. Couples cannot be resolved into a single force, if I recall my maths. and engineering training correctly. For basic explanations of P of F these are usually ignored. (Any unbelievers, consider e.g. trailing edge vortices - created by apply a couple to the airflow - Newton's third law leads to the deduction that there is an equal and opposite couple experienced by the aircraft. A single prop creates another couple, in a different plane.)

When I was instructing, I had to face examiners for rating renewal and upgrades. There was always a contentious issue that happened to be that particular examiner's pet hobby horse. They would deliberately set that subject for the "long briefing".

When I hit the area of contention and addressed it in my own way, a "full and frank exchange of views" would occur. The fact is that, so long as you can explain - justify - why you've made a certain statement, you won't be failed. Well, not in my experience in Oz, anyway.

So, okay, you've been brought up to believe in four forces. Fine, so was I. I can still argue my case for that now. I can see how someone might want to believe in just three forces and that's also fine by me, so long as they can justify it. I think this is where most examiners are "coming from"... they want to know that you have an understanding of the subject and are not merely doing it parrot fashion.

I think our students have a right to expect that we can explain the particular statement or subject in any of several different ways. I'm not sure that a consideration of three forces makes it any easier for a student to understand because it's still necessary to explain how they are derived. In doing so, one has little choice other than to talk about FOUR forces.

In any event, a verbal P of F exam, which I admittedly hadn't considered in my first post, provides scope to justify your belief, whatever it happens to be.

The RAF (CFS) teaching for rotary winged aircraft uses a vector diagram for the forces acting on a rotor blade. This shows the resultant of lift and drag on a blade segment as a the "Total Reaction". This is then broken down into "Rotor thrust" acting vertically up the rotor mast and "Rotor drag" acting perpendicularly to it. Rotor thrust lifts and propels the aircraft. Rotor drag is opposed by the application of engine Torque.

Similar thing to the prop theory given by Beags. It has to be done for rotating things because the lift and drag on a rotor blade don't act coincidentally with the rotor axis. I don't think it's necessary to do it for plank wings as it over-complicates the issue.

chrisN, the situation being discussed is the analysis in two
dimensions of the forces operating on an aircraft. The
intent is to simplify as far as possible while still being
able to generate useful predictions of the actual system
behavior.

So yes, the reaction force T, is the result of the sum of
the set of reaction forces operating on each element of
the aircraft...however that is a complication that doesn't
help us understand what is happening in the system.

Its easy to make things more complicated, the trick is
simplifying while keeping the nub of the problem intact,

-- Andrew

The intent is to simplify as far as possible while still being able to generate useful predictions of the actual system behavior.

Spot on!

There are not one, two , three, four or whatever forces. There is whatever you choose to best explain what is going on.

(If anyone else doesn't understand this just try putting your hand out of each door and window in turn during the cruise. Then write back and tell us there are no forces...)

For the plane to be in S&L flight TWO things must be true...

1). The sum of all the TRANSLATIONAL (straight line) forces must be zero

AND

2). The sum of all the TORQUES/ROTATIONAL forces must be zero.

If you define LIFT(cog), THRUST(cog), WEIGHT(cog) and DRAG(cog) as the orthogonal (right angles) translational components of all the forces that act through the center of gravity then it's true that they balance to zero.

But then you have to look at the other rotational forces. If the true center of drag is a bit above the CoG then that causes a rotational pitch-up. A high thrust line creates a pitch down. The wings pitching moment causes a pitch down etc etc. All these rotational forces must also balance to zero or the plane will be rotating about it's CoG - as it flys along S&L.

Consider what happens when you put the gear down. The translational component of drag increases so you must apply more power to maintain speed. However the center of drag also moves downwards. This causes a rotational force (pitch down) which may require a trim change. The trim change adds up elevator restoring the balance between rotational forces.

The TWO types of force must balance or the plane will either accelerate in some direction or rotate.

GoneWest why don't you take thrust out of the equation and consider a glider. It has a downward force due to its Mass and Gravity.

Newtons third law of motion states that every force has an equal and opposite force known as the reaction.

So now we have a glider with weight acting vertically down and the reaction acting vertically upwards. 2 Forces.

For convenience, we resolve the reaction into 2 "man made" forces called lift and drag to explain how the glider flies.

If we add a third force Thrust, there will be an equal and opposite reaction to that force however, the two reactions do not coincide with the established definitions of Lift and Drag. If we combine our reactions into a total reaction, there are now 3 forces acting on our aeroplane, one of which can be resolved into the two forces we require for the purpose of explanation thus giving us the conventional 4 forces.

The reference to 3 forces is to make you think about the forces acting and realise that Lift and Drag are not equal and opposite reactions.

No, that's an abuse of Newton's third law. The 'equal and opposite reaction' phrasing of the law is concise, but leads to this sort of confusion. Newton's third law says that if Body A exerts a force on Body B, Body B exerts and equal and opposite force on Body A.

In the case you cite, the 'reaction' is the gravitational force that the glider applies to the earth, equal to the weight of the glider and applied vertically upward -- it has nothing whatsoever to do with the aerodynamic forces.

I think the tree-force-model has come from the aircraft and wings designing department.
Since both drag and lift are equally subject to airspeed and angle of attack for a specific wing or entire aircraft, it does make sense to calculate with one resultant vector. Otherwise, you would have to calculate lift and drag seperately and the put them together again. For all the graphs it's much easier with one resulting force.

But in the end, both models still describe the same effects, don't they? (Yes, it does fly - and yes, you need some energy to keep it doing so)

We're going round and round saying the same things - and this is from folks who understand the situation. Maybe the first real test might be to see how well a trainee grasps the concept. Perhaps its time we heard from them?

I suspect that we might be getting away from the "KIS" principle that has served us all so well, ever since the Wright Bros flew at Kittyhawk.

I have always referred to a "Total Reaction" force in a climb, for example, but this is a completely different situation to S+L flight. It's quite easy to introduce that concept at that stage because the trainee already has a grasp of the fundamentals that apply in S+L. I'm just not sure it's such a good idea to introduce the TR force in S+L, but I'm happy to accept that others can make it work without bamboozling a trainee.

Does a 3 force aircraft fly faster or slower than a 4 force aircraft???????????
Look in you student's, or examiner's face. If you see understanding - you explained it the correct way. If not - try something different.

On the subject of drag, I believe it manifests itself in three somewhat unrelated forms, one only of which is related to angle of attack/lift.

It cannot be analytically useful to consider only three forces, thrust, weight and was it TR?, but it is useful to consider thrust overcoming drag, producing speed through the air, thus acting on the airfoil and producing lift to overcome the weight, while unfortunately generating various drag forces which in turn reduce the resultant force available to produce speed through the air.

Equally unfortunatey none of these effects is linear so the equations relating to the above simplified consideration of flight are both multivariable and non linear.

I'm with bookworm on this one.

Add them, subtract them, do what ever you want. Just choose the method that explains most easily the behaviour you are trying to explain.

When teaching PofF I always used to avoid starting a discussion of the forces by looking at straight and level. Its too much of a special case. People get the wrong idea really easily about what orientation the forces are defined in, then you are really in trouble.

CPB

By definition a vector is a force with a direction (magnitude, sens and orientation).

Drag as always been a force (see defintion) in every aerodynamic books. Don't trust flight instructors but rather engineers for those issues.

cheers

Bookworm,

you say: "that's an abuse of Newton's third law"
-------------------------------------------------

NASA don't seem to be too upset by such abuse:

Quote from:
http://www.lerc.nasa.gov/WWW/K-12/airplane/newton.html

"The third law states that for every action (force) in nature there is an equal and opposite reaction. In other words, if object A exerts a force on object B, then object B also exerts an equal force on object A. Notice that the forces are exerted on different objects. The third law can be used to explain the generation of lift by a wing"

I start most of my technical groundschool by saying:..' now this is not 100% technically correct but it is the easiest way to understand..'
Usually I get the point across.
I also keep a book from the University of Delft(Holland) from the division of aeronautics as a backup for the occasional smart-ass student....'but what if..'
In that case I get the book out,show them all the formulas and tell them they are only required to know the simple version.(Right?)
One vector split in two doesn't really change the right of existence of the original one now does it?
Our whole system of mathematics is man-made and a model that exists by the grace of not been disproved....yet.
Thrust and weight can also be conbined in a single vector resulting in a single angled force.Counteracted by the lift/drag combo,back to 2 vectors.
Question: Why do we need more power in slow flight,in fact almost as much as in cruise? (Single engine GA)


Most frequent answer: high angle of attack resulting in high lift therefore higher induced drag....


How about this one: as lift works perpendicular to the wing right?
In a turn we can split the lift into a horizontal comp. and a vertical comp.
The horizontal comp. makes the airplane turn and the vert. keeps the plane in the air.
Now for the shocker....the same applies in slow flight.
The horizontal component works in the same direction as drag in the 4-forces model,therefore increasing it.Hey presto more thrust needed.
Never even thought about this till the FAA examiner for my CFI mentioned this.I will forever be grateful.......
Taught most of my students the same thing.Makes great sense after you've experienced slow flight.
Now for the big question...
Does the 1st answer disprove or overrule the 2nd one?
No ....they co-exist.
Some people tend to think their way is the only way
it's not..
I never claim I'm a 100% right,I'm just less wrong than the the people I teach and I hope the'll end up being equally right.
Not more,that's embarrassing.

To finish: Confucius say: ..many thoughts lead to a cluttered brain....

:D :D :D

Almost forgot :
The only true 4 forces acting are
lift
trust drag
faith

StrateandLevel

The quote from NASA is correct. But if you read the pages linked to from the one you cite, you'll find that at no point do they use Newton's Third Law to assert that lift, drag, or total aerodynamic force is a 'reaction' to gravity, which is what you implied.

B2N2

They don't coexist at all. The assertion that the direction of lift (or total aerodynamic force) is perpendicular to the chord line is simply wrong, and you can see that it's wrong by either:

a) inspecting any drag polar and noting that D/L is not equal to the angle of attack

b) thinking about how that rule might work when you know that changing the wing span changes the drag coefficient for th same AOA.

The problem is not that it's a little inaccurate or not 100% correct. It's not even close.

If you want to claim that your rule of thumb is a good aide-memoire for those who don't understand mechanics then fine, go ahead and teach it. But it doesn't make the physics correct, or more importantly it doesn't make the physics as correct as a proper explanation of induced drag!

> How about this one: as lift works perpendicular to the wing right?

Well err no. There is no such thing as a single lift vector..

Sum ALL the force vectors acting on the wing and you get ONE vector pointing upwards and backwards. You can split this into two orthogonal (right angles) vectors pointing in any direction you like...

But for convenience it makes sense to choose one pointing upwards at right angles to the airflow because weight normally acts downwards, also at right angles to the airflow (unless you happen to be wave or ridge soaring etc).

You could define your lift vector to act perpendicular to the wing but you don't have to.

Again, I'm with Bookworm.

It really is depressing how much people misunderstand Newton.

Even the RAF have it wrong (I used to teach air cadets, and their manual has the same mix up!).

The equal and opposite the the gravitional force of the earth on the aircraft is:

The gravitational force of the aircraft acting on the earth.

Think about the moon. Not only is it pulled towards the earth by gravity, but the Earth is pulled towards the moon.

Good thing its in Orbit really (Itchy and Scratchy).

If you jump out of an aircraft, not only do you fall towards the Earth, but the Earth falls towards you. The gravitational force is equal and opposite.

Thing is, Earth has more mass, you have relatively little. Newton also tells us F=MA, so you do most of the accelerating.

Eat lots of crewfood till you weigh the same as the Earth. Then, if you jump out, you'll meet the Earth half way.


Acheo.

Vector is an amount and a direction, not a Force and a direction.

A force is a vector, but there are many other vector quantities.

Velocity. Acceleration. Momentum.
All the rotational equivalents, to name a few.


CPB

The NASA quote......can be used to explain lift by a wing. The wing accelerates air downwards and forwards (by applying a downwards and forwards force to it), causing the wing to experience an upward (lift) and backward (lift drag) force. The more you accelerate it (by increasing the angle of attack), the greater the forces are.

What is actually going on when an aeroplane flies is enormously complicated. In order to understand it, we build simplified models. There are no 'right' or 'wrong' models; however some models explain certain aspects of flight better than others. Therefore, it is sometimes easier to think of an aeroplane as having thrust, drag, lift and weight, and sometimes it better to think of it as other forces (for example splitting the lift force into a horizontal and vertical component when the aeroplane is turning).

I think you should be comfortable with both the 3 and the 4 force model (and perhaps models with a few more forces as well to handle turning and spins and so on), but don't think that one is correct and the other is somehow wrong.

A good model should:-
Be simple as possible
Be able to explain observer results
Be able to predict future results

You're making it too complicated
 

All forces acting on a body at any instant can be resolved into a single force vector.

If the aircraft is at constant altitude then the weight and lift forces cancel out.

If the aircraft is flying 'straight and level' then the lateral forces must also cancel.

And if it is travelling at constant speed -- and thus not accelerating -- then the longitudinal forces cancel.

Therefore there is no overall force acting on the aircraft. Perfectly in line with Newton's first and second laws.

QED :D :D :D

Konkordski

Perfectly true and perfectly useless. I won't quote the usual joke.

Your statement applies equally to a stone resting on the ground.

The objective is to understand the forces acting on an airplane, taking a simplified approach at first and eventually a more refined and complex approach in order, in the case of a pilot, to understand the interreaction of the controls available to the pilot in order to equip the pilot with the ability to fly proficiently and safely.

The four force explanation of straight and level flight carries out the first steps of this path to full understanding .

A resting stone analysis fails to do this.

It seems to me we're all taking the same language. The original post was about...

><snip> actually there are only three forces. Weight, thrust and
>total reaction (TR). This TR can be broken down, by the
>scientists, to show a horizontal vector (not a force) which we
>call drag - and a vertical vector which we call lift.

Actually their are an infinite number of forces acting on a plane that sum to zero in S&L constant velocity fight - but we prefer to resolve them (break them down into) components that act in specific directions.

You could say...

The sum of all forces = 0

or

W + T + D + L = 0

or

W + T + L + TR = 0

or

W + everything else = 0

It's all means the same thing.

The important bit is that the sum = zero. If it doesn't then there
is a residual force acting on the plane that will cause it to depart
from S&L constant velocity flight.