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