how do airplanes fly?

Great Debates
21

Ugh, this is going to take some effort to clear up.

First let me say this. In my 4 years of courses getting my BS in Aeronautical Engineering I have never seen any contradiction or debate as to “How planes fly”! Those links given are flat out ridiculous. They simply tell a different half story that basic science books do with the Bernoulli Principle.

First lets explain away that how “I’ve been mislead by my Physics Book” claim is bunk. The book isn’t trying to explain how a aircraft flies! It is trying to explain the Bernoulli Principle. As such it is correct in using a airfoil as a example. Was anyone tested on Aerondynamics or Compressible flow in Grade or High School? I doubt it. I’m sure not a single book claims that the Bernoulli Principle is the only effect acting on a planes flight surfaces, it simply uses it as a common real-world example of a complicated principle at work (a rarity in most physics).

Second, the explaination that most people have given is correct, and every engineer is fully aware of the fact. This isn’t a “duality of light” type debate amongst intellectuals.

Some points to correct. bantmof said:

This is 100% false, most aircraft do not, but it most certainly is possible, if not practical in general use. Many planes do infact use this during take off to initiate the needed angle of attack for climb.

One arguement one may make (while a moot point in reality) in saying “Lift is created by the Bernoulli Principle”, is by claiming the definition of Lift is just that. Force created by pressure differential. As such one would classify the Newtonian effects as a different force entirely. Not that it actually changes the reality of the effects, it all depends on what scale you examine the force diagram.

One misconception that is being propogated is that:

This is false. As long as laminar flow is maintained the air DOES rejoin with itself at the training edge. The “magical” reason you refer to is this. What would replace the air if it didn’t? If the air above the wing doesn’t accelerate to meet with the air passing below the airfoil, what is going to fill its place? A vacuum? That’d make life REALLY easy for engineers. Or is matter created? Maybe dark matter? Of course if the wing is in stall or creaing turbulent flow then the wing ceases to create lift and the air is not rejoining.

Now one factor that is being overlooked. Much of the Newtonian effect is already included in the Bernoulli effect. The leading edge of the airfoil is not a fixed point. It depends on the AOA and as the AOA increases the airflow is slpit at a different point. The “Newtonian” effects are measured as pressure change. So even though “air is forced downward” is is measured as a lifting force in context of the Bernoulli Principle. As the AOA increases the top camber gets larger, ergo the pressure ratio gets haigher and lift values reflect that effect. Bernoulli and Newton are not contradictions, they are different ways of measuring teh same effect. Newtonian physics are generally extremely difficult to quantify when dealing with a compressible fluid. The force lost in compression is very complicated to measure. Bernoulli uses his relationships to side step that complication. It doesn’t contradict anything Newton claimed.

I’m probably losing my train of thought, so I’ll step back and see if I need to clarify later.

22

Woah, easy there pardner :). Unfortunately I won’t be able to check this thread very often since the new board software doesn’t work very well with my primary computer.

: First lets explain away that how “I’ve been mislead by
: my Physics Book” claim is bunk.

I don’t think it is. There is a LOT of misunderstanding (even on your part; see below, and surely on mine too) about on this subject. Like I mentioned, there are many texts that try to explain flight solely by invoking Bernoulli, which completely ignores Newton’s law (and the fact that you can derive Bernoulli from Newton), and downwards acceleration of the air, so you have high school graduates who are completely unaware of it.

I’m not claiming people with PhDs are misunderstanding it - just the average gradeschool student is not being well served by the way it is being explained. This leaves the general public with some incorrect impressions.

: This is false. As long as laminar flow is maintained
: the air DOES rejoin with itself at the training edge.

I’m talking about real airplanes here, in the real world, involving both laminar and turbulent flow. In nearly any real life flight situation, the air does NOT rejoin with itself at the trailing edge. This is a well understood topic with a huge amount of research that has gone into it, from wind tunnel testing to CFD simulations. You can’t claim it’s all bunk just like that :-).

You can see the result of a pulsed smoke wind tunnel visualiation in this graphic, or any of several zillion similar ones in print:

The details change, but basically for unstalled airfoils producing lift, the air does not rejoin in the manner you think it does. I’ve seen many, many such flow visualizations (mostly 3D ones, but the principle is the same) and I can’t recall seeing one (outside of trivial non-lift producing cases) where things behave as you’re claiming. If you have one (a photo, not somebody’s diagram of how they think it works), I’ll eat some crow. :-). I think the best you can do is to find a case where the effect is so small it isn’t immediately apparent - but it will still be there if you measure carefully.

BTW, this is just a simple 2D example, but the CFD models show the same basic thing.

: What would replace the air if it didn’t?

More air, of course; it doesn’t leave a vacuum :). Among other things, air flows around the end of the wing, since the local region beneath the wing has a pressure greater than the free stream pressure, and region above, less. This results in a span-wise flow along the top and bottom wing surfaces, as well as wingtip vorticies near the ends of the wing. There is also a downward local flow of air from above the wing. There are a lot of things going on which aren’t immediately apparent by inspecting the simple 2D diagrams; it becomes more clear when you look at the 3D vector field.

Surely you aren’t suggesting that air cannot be displaced by the passage of the wing? If so, then you need think about it some more :). If that was true, lift would not be produced. In reality there is some local flow pattern induced by the passage of the wing, which will subside afterwords, but leave the air perturbed from its original location, and one effect of this perturbation is the sort of lateral displacement shown in the gif above.

: Now one factor that is being overlooked. Much of the
: Newtonian effect is already included in the Bernoulli
: effect.

I agree; they are just different aspects of the total system. My only point is just that many people don’t even know that Newton is involved, and is in a large way the foundation for quite a bit of fluid flow analysis, such as Euler or Navier-Stokes. I’m not arguing that Bernoulli isn’t in the picture; clearly he is.

: Newtonian physics are generally extremely difficult
: to quantify when dealing with a compressible fluid.

True, but for the purposes of teaching gradeschool students, compressibility can be entirely ignored; it isn’t hugely significant at low airspeeds anyway, so you can get a good understanding of how a wing works without knowing anything about it.

: It doesn’t contradict anything Newton claimed.

Agreed again. I’m not saying it does.

And, FWIW, you’re right about the 0deg AOA case; there is a positive lift coefficient. My mistake! I was trying to say that aircraft don’t fly like that; they fly at positive angles of attack throughout the entire flight envelope. (I’ll leave open that there might be some types of a/c that fly at 0deg AOA, which I’m not familiar with).

23

Forget about gradeschool students - I used to teach ground school to pilots, and every single text I could find was wrong when it came to describing how lift is created. So you’ve got an awful lot of pilots flying around who don’t really understand why their airplane is still in the air.

24

The following comes from the US Army (FM-102 Fundamentals of Flight. Sorry, I can’t post the diagrams.

[quote]
As the relative wind strikes the leading edge of the airfoil, its velocity is reduced to zerop. This point of impact is called the stagnation point. The pressure at this point on the airfoil is equal to total pressure (dynamic pressure plus static pressure). This area of high pressure creates pressure waves which are propagated ahead of the airfoil at the speed of sound. These pressure waves cause the wind moving toward the airfoil to deflect over and under the airfoil beginning some distance ahead of it. This air flows smoothly around the airfoil following its shape and deflects at a slight downward angle off the trailing edge of the airfoil. The air following the shape of the airfoil has a greater distance to travel than if it had not changed direction; therefore, the air must speed up or a partial vacuum would be created after the airfoil passes. Nature does not allow the existence of a vaccum in the earth’s atmosphere. To prevent this vacuum from forming, the airflow over and under the airfoil increases in velocity. As the velocity of the airflow increases, the dynamic pressure above and below the airfoil also increases.

According to the law of conservation of energy, an increase in one component of energy must be accompanied by a corresponding decrease in another component of energy. Total energy (total pressure) cannot change. To accommodate the increase in dynamic pressure around the airfoil, static pressure decreases above and below the airfoil. The air has a greater distance to travel over the upper surface of the airfoil than over the bottom surface. This causes a greater velocity (dynamic pressure) increase and static pressure decrease over the top surface than over the bottom surface of the airfoil. This static pressure differential across the airfoil produces the total aerodynamic force created by the airfoil. The pressure differential between the upper and lower surfaces of the airfoil is about 1 percent. Even a small pressure differential produces substantial force when applied to a large area.

Because of the viscosity of the air, some of it sticks to the surface of the airfoil. This thin layer of air near the airfoil surface is called the boundary layer. Because of the stickiness, the layer of air molecules against the skin of the airfoil has no movement with respect to the airfoil. Each succeeding layer of air molecules increases in velocity as the distance away from the airfoil increases. The boundary layer is considered to end where the velocity of the air molecules reaches 99 percent of the velocity of the airflow around the airfiol. This distance is about the thickness of a playing card. This boundary layer forms the transition between the air and the airfoil. Without it, the airfoil would produce very little lift.

Bernoulli’s principle states that as velocity increases, dynamic pressure also increases; this causes static pressure to decrease. [a figure, 2-8 in the book] shows how this principle works as flow is constricted in a stream tube. Thus static pressure on the upper surface of an airfoil decreases when velocity increases. The static pressure on the upper surface is less than the static pressure on the lower surface. Even if the static pressure on both surfaces is less than the atmospheric pressure, the airfoil will still produce lift. The important point here is the pressure differential that develops across the airfoil*
Here’s Bernoulli’s equation:

H = p + 1/2rhoV**2; or H = p + q

where H = total pressure, p = static pressure, rho = air density, V = velocity, and q = dynamic pressure.

25

For the sake of clarity, the block-quote was supposed to end with “The important point here is the pressure differential that develops across the airfoil.”

was not part of the text I quoted, but appears in the “appendix” of FM-203.

Another correction: The manual is FM-203, not FM-102. My left hand shifted over a space when I was typing. Sorry about that. FM=203.

26

Hey, bantmof and Omniscient, I think there might be a little miscommunication between the two of you. bantmof isn’t denying that air starts touching air again at the wing’s trailing edge. He’s just saying that the molecules which run into each other aren’t necessarily the same as the ones it was next to before the leading edge split them apart.

Here’s my analogy. You’ve got a whole bunch of American married to foreigners, coming back through customs. Foreigners take longer to go through U.S. customs than U.S. citizens do. In order for each foreigner to be rejoined with the appropriate American spouse, the foreigners would have to run to catch up. This is the magical force that bantmof is debunking - the molecules that get separated by the leading edge are not married; they don’t particularly care to rejoin the same air they were with.

Omniscient, if you are arguing that the air molecules rejoin their appropriate spouses, then maybe there is no miscommunication, and you two are actually on opposite sides of this issue. Which leaves me slackjawed in the middle.

My summary of this deal, which I encourage you to correct if I’ve got it wrong, is that the whole lift thang is caused by less air pressure on the top surface than on the bottom surface. The Bernoulli emphasizers talk more about top air pressure being lower than normal; those partial to Newton talk more about bottom air pressure being higher than normal (the compression/displacement caused by angle-of-attack). Is that right?
And can we measure air pressures and compare them both to normal air pressure to see which effect is greater?

27

There’s an equation in my last post. :slight_smile:

28

No, the Newtonian guys are saying that the airmass behind the aircraft has a net downwards vector such that the total change in kinetic energy of the air mass after the aircraft’s passage exactly equals the force required to provide the lift for the aircraft, minus whatever heating effects might be involved.

Think of a wing as a reaction engine, just like a rocket. A rocket gets thrust by using chemical explosions to hurtle mass in the opposite direction of motion. A wing uses the Bernoulli effect and flat plate effect to hurtle a mass of air in the opposite direction, providing lift.

Anyway, that’s how I’ve always thought of it. The Bernoulli effect causes lift in exactly the same way that igniting LOX provides thrust - they are both mechanisms for achieving the goal of applying a Newtonian force.

One comment about laminar flow: One reason you might be disagreeing about whether the air particles truly meet again is that one of you is considering a real wing, and the other is considering an idealized wing. A typical laminar-flow wing maintains laminar flow to only about 50% of the chord, whereas a non-laminar wing usually only maintains laminar flow to about 25-35% of the chord.

Also, I’d think that the air would not meet up at the trailing edge because of friction from the boundary layer, which is an energy sink on the airstream.

29

First, bantmof, your link was a white page…no help.

Boris, I think we’re both fairly clear, and I am indeed saying that the theoretical foreigners meet up with the American spouses. A better anaolgy would be that the interior rows of people in both lines get stuck and spin in circles (boundry layer flow) and the boundary layer abates a huge amount of friction. The remaining exterior rows of foreigners do speed up to catch up with their spouses, the success rate of rejoining gradually decreasing as you move rows further away from the boundary.

Sam I have no idea how your analogy of a chemical reaction compares to a physical reaction of lift. If it works for you, cool, but it lost me.

Sam is indeed onto something.

This is the assertion, and here lies my problem. I don’t disagree that part of the lift (flat plate effect) is caused my a reaction of kinetic energy in the downward vector. The proportion that the “Newtonian” camp is claiming I feel is way off base. The true ratio is determined by the flight profile of the airfoil in consideration. In MOST common flight cases the Newtonian effect is very small. The exception being near stall speed flight, and climb. Newtonian flight is very inefficient and engineers go to great lengths to avoid it.

A good analogy is with a ship sailing through water. Understand air is a viscous fluid. As such it has bouyant qualities. These qualities are related to the Bernoulli effect. The example. As a ship sails, the water beneath it supports it, comparing it to the arguement at hand the Newtonian camp would argue that the boat forces a equal weight of water down. It most certainly doesn’t, the water presses in all directions against itself resisting the displacesment by the ship. A wing works similarly, and Bernoulli quantifies this resistance to the displacement of the air.

A quick Aerospace cliche. “If you have enough thrust you can make a toaster (or bus, or Pinto depending on who says it) fly”. This is a joke the highlights the Newtonian effect. If you can muster the energy you can cause the least aerodynamic shape to fly. It would fly by driving a flat edge at a high enough speed to deflect enough air beneath it to equal its weight. This is the Newtonian effect is essence. The fact is that virtually all aircraft would burn too much fuel to rely heavily on the Newtonian effect.

dhanson…tell me about it, I took flight school after my senior year. I was consistently correcting my instructor and ground school teacher, and putting things in context. Luckily, a pilot has no more need to understand the intricacies of aerodynamic principles, than does a driver need to understand the force diagram and friction coefficient of his wheels.

bantmof, I am not convinced there are any grade school texts that have “flight” chapters, and intend to teach how planes work. I stand by my assertion that they feel the need to explain the principles of the Bernoulli Principle, merely using flight as an example, and make no efforts to wholly explain the specifics of flight. If you can show me a text that offers a Bernoulli based equation that expresses the force created by his effect and equates it to the weight of the aircraft, I’ll recant. Since every text I saw in college ALWAYS considered both effects I doubt anything in HS was different. I don’t think a HS kid is going to react as well being shown a Laminar Tube experiment when being taught about Bernoulli, as he would seeing a airfoil in work (even a incomplete description). The fact is, these texts don’t claim it to be a complete explanation.

30

No, the Newtonian guys are saying that the airmass behind the aircraft has a net downwards vector such that the total change in kinetic energy of the air mass after the aircraft’s passage exactly equals the force required to provide the lift for the aircraft, minus whatever heating effects might be involved.

Think of a wing as a reaction engine, just like a rocket. A rocket gets thrust by using chemical explosions to hurtle mass in the opposite direction of motion. A wing uses the Bernoulli effect and flat plate effect to hurtle a mass of air in the opposite direction, providing lift.

Anyway, that’s how I’ve always thought of it. The Bernoulli effect causes lift in exactly the same way that igniting LOX provides thrust - they are both mechanisms for achieving the goal of applying a Newtonian force.

One comment about laminar flow: One reason you might be disagreeing about whether the air particles truly meet again is that one of you is considering a real wing, and the other is considering an idealized wing. A typical laminar-flow wing maintains laminar flow to only about 50% of the chord, whereas a non-laminar wing usually only maintains laminar flow to about 25-35% of the chord.

Also, I’d think that the air would not meet up at the trailing edge because of friction from the boundary layer, which is an energy sink on the airstream.

31

Thats some serious lag in the multipost…

32

Omniscient: Would you agree that for an airplane to fly the wing has to do work? If so, what is it working on, and what is the net result of that work?

The ‘classic’ diagram showing a wing carving a nice clean laminar path through the air, leaving it the same behind as in front, depicts a situation in which no work is being done.

I don’t like the boat analogy, simply because the force IS applied uniformly to the submerged surfaces. A better example would be a hydrofoil. Could you explain how a hydrofoil works, using nothing but Bernoulli’s principle?

33

And I thought this thread was not going to live for more than 2 or 3 posts!

: First, bantmof, your link was a white page…no help.

Yeah? Bummer. See if this works any better: GIF Collection, Airfoil Misconception

: Boris, I think we’re both fairly clear, and I am indeed
: saying that the theoretical foreigners meet up with the
: American spouses.

Sorry, they don’t, at least not in real flight. (I’m speaking of the real world here, not some simplified textbook example). This is well understood both theoretically and emperically. See the above link for one photo that clearly shows this. I will provide another in a bit, and I can also point you to a little gadget NASA put together that will show you the same thing. There are many examples in print as well. If you want to argue that the air meets up again, you’ll be in the position of contradicting a huge mountain of scientific evidence, from agencies as esteemed as NASA, so you’ll need a pretty convincing argument if you want to falsify everybody who’s looked into it for the past 75 years or so :).

: In MOST common flight cases the Newtonian effect

Actually, in slow speed flight (i.e, your 172 tooling along at 90 knots, as opposed to your F15 at M1.2), Newtonian effects are most of the deal. If you don’t understand this, then you don’t understand flight on even a very basic level. Euler and Navier Stokes fluid flow equations are derived from just the sort of Newtonian effect you claim isn’t significant. I will provide web based references for this assertion in a bit; I can also provide printed ones if given some more time. For slow speed, flight, the mass times the acceleration of the displaced air is (to a 1st order approximation) equal to the lift. Even NASA maintains this is so.

: A good analogy is with a ship sailing through water.

No, that’s a terrible analogy. That would be more apropos to dirigables and other lighter than air craft.

: Newtonian camp would argue that the boat forces a
: equal weight of water down.

We would argue nothing of the sort. The ship weighs less than the water it displaces, so it floats. Airplanes do not weigh less than the air they displace. Trivial proof: a ship does not have to move to float. An airplane cannot fly without significant forward velocity.

: A wing works similarly

Not really. There is fluid involved in both cases, and you can use N-S to analyze water flow around a hull (and drag from that water), but that’s about where the similiarity ends.

: bantmof, I am not convinced there are any grade school
: texts that have “flight” chapters, and intend to teach
: how planes work.

I’ll provide one web based reference, and I can (if you give me a while) provide the names of books that show incorrect diagrams with bad explanations.

Actually, I think I’m going to put the references in the next post to keep these suckers down to a managable size. See my next post for references supporting what I’m saying above. They will be from universities and NASA and so on, not cheeseball web wackos. I can provide university-level textbook references too, but those will take me longer to dig up.

Anyway, isn’t this more fun than yet another “Does God Exist?” thread? :slight_smile:

  • b
34

Ok, as promised, a bunch of references.

A good one to start with is this page from the University of Frankfurt:

http://www.rz.uni-frankfurt.de/~weltner/Flight/PHYSIC4.htm

Allow me to quote from its abstract briefly (emphasis mine):

“But a higher streaming velocity is the effect of a lower pressure and never its cause. The cause of the aerodynamic lifting force is the downward acceleration of air by the airfoil - which depends on the angle of attack and its velocity.”

The whole page goes into a moderate amount more detail. Another quote from this page which corroborates what I’ve said in my post above:

“Adjacent air before the separation indeed does not meet behind airfoil. Figure 2 shows experimental evidence of air streaming along an airfoil… This disapproves the arguments based on differences in path length.”

Second reference, an article by a fellow from the University of Washington, and another from the National Accelerator Laboratory (titled, appropriately enough, “Why airplanes fly: according to Newton”).

http://64.45.7.163/theory/lift.htm

It discusses the common misconceptions arising from a purely Bernoulli-based analysis. A quote from this paper that corroborates what I’m saying about the air not rejoining:

“One can see that the air that goes over the top of the wing gets to the trailing edge considerably before the air that goes under the wing… So much for the principle of equal transit times.”

Third reference: this is a NASA web site for school children, so it is somewhat simplified, but absolutely correct as a 1st order approximation:

http://www.lerc.nasa.gov/WWW/K-12/airplane/shed.html
and
http://www.lerc.nasa.gov/WWW/K-12/airplane/bernnew.html

Frmo this web page:

“Lift is the force which holds an aircraft in the air. From a Newtonian perspective, lift is generated by turning a flow of air. The flow turning creates a downwash from the wing which can be observed in flight.”

“One important aspect of airplane lift that is included in the Newton theory and does not appear in the Bernoulli theory is downwash. To generate lift, the flow must be turned in a direction opposite to the lift, which is downwash.”

This page has a nice photo at the top showing this as an airplane flys over a cloud bank. Another page which is mostly unrelated to this debate, but does show a wind tunnel flow visualization of air across a delta wing is here: http://www.eng.qmw.ac.uk/aerodyn.html . The picture is near the bottom - you can clearly see the air shoved rather drastically downwards by the wing.

Fourth reference: NASA has built a simple airfoil simulator you can run in a javascript equipped browser:

http://www.lerc.nasa.gov/WWW/K-12/airplane/foil2.html

It’s only a simple 2D simulation, but by playing around with it you can clearly see (1) in lift producing situations, air split on the trailing edge does not rejoin off the leading edge, and (2) there is a downward velocity component to the air after the airfoil passes through.

Finally several points to ponder: a helicopter rotor is basically a rotating wing. It’s slightly different in that the airspeed is different across the rotor span, but as a zeroith order approximation, it’s just a wing moving through the air. Do you deny that there is enough air shoved downwards to support the weight of the vehicle? If not, then how does moving the wing though the air linearly instead of via rotation change the basic concept that enough reaction mass must be moved to generate the required level of lift?

Finally (really finally this time :), if the above references don’t convince you, I can supply a whole barrage of others. This is really not something about which has been in debate for almost a century. I claim that you yourself harbor the very misconceptions you claim don’t exist. (You’re not alone, FWIW - I used to think exactly the same things - i.e, that air rejoins, that there wasn’t a significant downward acceleration of air, etc). Other people in this thread have also admitted to thinking the same things. So: if so many intelligent people all have the same misconceptions, where are they coming from?

35

Sam Stone says:

: Think of a wing as a reaction engine,

Yep - that’s a good way to think about it, IMHO. The wing is basically just an air pump. The power required for it to do it’s job is supplied by the a/c’s engine (or gravity, in the case of a glider), which is dragging the entire assembly through the air. The result is largely mechanical displacement of air. At low airspeeds such as you find in general aviation aircraft, heating isn’t a big factor, and after the plane passes through, the air is all at the ambient pressure again. So what happened to it? Work was done on it, which moved it around a bit.

Oh! Here’s another thing I just though of. Consider our humble little 172 again. What’s moving it though the air? The prop up front. What’s the prop doing? It’s shoving air (a reaction mass) backwards, to provide forward thrust, again as described by F=MA. What’s the prop? It’s just a wing! Yes, there is a low pressure region on one side and high pressure on the other, as with any other wing, but do you (genetic you, not Sam :slight_smile: ) tend to think of the prop as creating a pressure difference, or as accelerating enough air backwards to provide the desired level of thrust?

36

In the thread that spawned this discussion the analogy was made that attempting to argue with the well-known principles of flight and asserting instead that planes were held up in the air by the “happy thoughts” of the passengers was patently ridiculous.

The “happy thoughts” theory is looking better to me all the time.

37

Why do you have to have such in depth links for me to read, damn it.

This isn’t going to happen now, but I’ll try and respond to all the points in kind. A few bites to start with:

I fully agree, and when I made the exception for “in near stall speed flight” I probably should have expanded it to read “slow” flight which is identical to what you’ve said. This relatively slow flight envelope is however not the most common or practical situation.

OK, the boat is water was a shity analogy, I take it back.

After I get some sleep maybe I’ll think clear enough to return some of the information.

38

I have been reading http://www.monmouth.com/~jsd/fly/how/htm/airfoils.html plus the other 20 chapters of that work and it is extremely interesting!!

I am still struggling with the mechanics of landing in a strong crosswind but on the topic of this thread I have absolutely no doubt the force that keeps an airplane aloft comes from accelerating air downwards. Anything else would violate the conservation of momentum. It would also allow helicopters to hover and fly without pushing air down as the blades of their rotors are rotating wings. If anyone can show me a helicopter that does not push air downwards I will change my mind.

39

I am not omniscient, but…

For an airplane in level flight, it is not working against gravity, so I guess it is working against air friction. Is that what you were looking for?

40

The previous post was in response to Sam Stone.

But…the wind doesn’t follow the inside of the sail. Even more importantly, the wind drives the sailboat fastest when the boat is moving at right angles to the wind. How do you explain that by deflection?