Any which way the wind blows (physics brainteaser)

Fine. Now two more questions:

1. If the pilot cannot see out of the cockpit, what is the bare minimum of instruments necessary in order to be able to control the aircraft?

If control is the only requirement (rather than say navigation), an artificial horizon will suffice. This allows the pilot to know whether wings are level or not level and by how much.


2. If the pilot has no instruments at all, what is the bare minimum of visual clues necessary in order to be able to control the aircraft?

A good pilot could keep an airplane under control with just a view of the sun, or a single cloud (if not in said cloud).

JB
 
A good pilot could keep an airplane under control with just a view of the sun, or a single cloud (if not in said cloud).


I assume the pilot also sees the horizon. In this case he can easily control the plane without seeing the sun or any clouds. Of course he may end up flying in a giant circle.
 
And once again, there's nothing in the problem stating that you can't use "clues outside the cockpit" to fly the plane.

And that access isn't denied in the original problem nor in any following post.
I'll quote your original message again for reference:
"Can a pilot of an uninstrumented and unpowered soaring aircraft make any useful determination regarding which direction the wind is blowing at flight level *without* using clues seen outside the cockpit?"

Why not set it up like this?
You are the pilot and in control of a soaring aircraft. You can see the horizon and the sun, but no features on the land or in the air around you. You have no instruments on board. As a pilot, what, if anything, could you do and/or observe to determine the direction of the wind at flight level?

I found your version poorly worded, especially in a forum where relativity is discussed pretty much daily. It sounded like a relativity problem in the sense you could be asking, "the wind is moving at some velocity relative to the earth. Can you without reference to the earth determine what direction it's going?"

I know that's not what you meant, but it's not a silly interpretation. I, for one, imagined myself sitting inside a cockpit wondering about what scientific experiments I could perform. I figured I could steer the thing, but what would be the point if I couldn't look outside the cockpit and had no instruments?

Also, a reasonable person could argue that your setup is faulty. You tell us that clues outside the cockpit are needed to fly an aircraft. You say you need to fly the aircraft a certain way to solve the problem. Therefore, you need clues outside the aircraft to solve the problem.

That's just how I see it.
 
This fails for all sorts of reasons and I'll pick only one for now:

The spot you marked will only remain under that plumb bob as long as the pitch angle (think nose to tail) remains the same. Once the aircraft leaves the ground, changes in pitch from speed and lift changes will alter the planes orientation relative to vertical ... meaning that the bob can hang in many different spots, even in still air.

An example of this would be: if I'm flying in a straight line in perfectly still air @ 60knots and I mark the plumb bob spot and then I speed up to 70knots, the bob will now hang *forward* of it's previously marked location. This happens simply because to speed up I had to reduce the angle of attack of the wing and I did that by lowering the nose. This alters the aircraft orientation relative to vertical and is reflected in the new bob position.

The position you marked on the ground will reflect all sorts of things unrelated to it's positions in flight including something as simple as how much air is in the aircraft's tire(s).

JB
How about a plumb bob and a bubble level?
 
How about a plumb bob and a bubble level?

That seems sort of redundant. I don't see what you get from one that you don't get from the other. I don't think either one will tell you which way the wind is blowing either. You could fly loops or barrel rolls all day long with both the plumb bob and the level showing dead-level.
 
That's just how I see it.

You notice that pilots, and particularly soaring pilots understood it and solved it rather quickly? You notice it's the non-pilots in particular who are struggling with it? That's why the "pilot" introduction was given.

It's difficult for non-pilots, and even non-soaring pilots to understand a scenario where you can use visual clues to fly the plane, but those same visual clues are useless to determine wind direction. It's even harder for them to imagine begin able to collect information regarding wind direction from clues coming only from the 'seat of the pants' and one's internal clock -- but it can be done and is done.

Yes, it looks like it could be a relativity problem. Brainteasers often look like things they are not.

That's just how I see it.

JB
 
How about a plumb bob and a bubble level?

Looking forward to hearing about how you're gonna use that plumb bob and level to determine wind direction, but for the moment I'm going out on a limb and saying it won't work.

I'll keep an open mind though.

JB
 
If it's a really long bob you could lower it to the ground and measure the angle using the level.
 
That seems sort of redundant. I don't see what you get from one that you don't get from the other. I don't think either one will tell you which way the wind is blowing either.
I don't know anything about flying, so I was really only responding to ThinAir's response to Tumbleweed's first idea.

I'm not sure how Tumbleweed was answering the question with a plumb bob, but since the problem with it was that the plane isn't known to be level, I was thinking you could use a bubble level to help. I guess it's more than just that--imagine a bubble level built into a rectangular frame that holds a planar surface (like a card) parallel to it. Then a plumb bob hanging from the level with "down" being toward the card.

Then you could do whatever Tumbleweed was suggesting. Hold the level so that the bubble tells you it's level and mark the position of the plumb bob on the card.

I assume it's using the plumb bob to tell you the direction of acceleration and using that to figure out the wind direction. But again, I don't know anything about that stuff.

You could fly loops or barrel rolls all day long with both the plumb bob and the level showing dead-level.
Really?
 
You notice that pilots, and particularly soaring pilots understood it and solved it rather quickly? You notice it's the non-pilots in particular who are struggling with it? That's why the "pilot" introduction was given.

Yeh, you "may" need "some" information is a great instruction. Nobody has ever written a brainteaser using the word "may" to throw people off the scent, have they?

Then again, if people with specific knowledge solve it rather quickly, it's not really much of a brainteaser anyway, now is it?

I noticed more people confused by the question itself than contributing to the solution. Even one pilot who solved it said, "When reading your puzzle description I think perhaps a few of us (but definitely me!) assumed more than you meant by the statement about not being able to use things outside for clues."

So, you can take the constructive criticism and present it in a way that involves people who don't fly and who have never heard of the technique before. That would make it a good brainteaser. Or you can continue to be all defensive about it and present it to fellow pilots who will answer it rather quickly.
 
Yeh, you "may" need "some" information is a great instruction. Nobody has ever written a brainteaser using the word "may" to throw people off the scent, have they?

Then again, if people with specific knowledge solve it rather quickly, it's not really much of a brainteaser anyway, now is it?

I noticed more people confused by the question itself than contributing to the solution. Even one pilot who solved it said, "When reading your puzzle description I think perhaps a few of us (but definitely me!) assumed more than you meant by the statement about not being able to use things outside for clues."

So, you can take the constructive criticism and present it in a way that involves people who don't fly and who have never heard of the technique before. That would make it a good brainteaser. Or you can continue to be all defensive about it and present it to fellow pilots who will answer it rather quickly.

No need to get all in a wad just because you couldn't solve it.

JB
 
...since the problem with it was that the plane isn't known to be level, I was thinking you could use a bubble level to help....

It's a good thought, but there's actually a brainteaser within the brainteaser. Plumb bobs and levels don't really tell you what's level or vertical. They tell you what direction you're accelerating in. If you happen to be stationary in an inertial frame (i.e. not accelerating) that ends up being vertical and level. But think about hanging your plumb bob from your rear-view mirror. Take a left turn and watch what it does. The bubble level will do the same thing.
 
If control is the only requirement (rather than say navigation), an artificial horizon will suffice. This allows the pilot to know whether wings are level or not level and by how much.

A good pilot could keep an airplane under control with just a view of the sun, or a single cloud (if not in said cloud).

Thanks. Another question:

When an aircraft gains altitude by soaring around a thermal, it's making use of the difference in speed between the air in the thermal and the surrounding air. Say the vertical speed of the air in the thermal is V relative to the surrounding air, is the rate of gain in altitude of the aircraft:

- less than V?
- equal to V?
- greater than V?
or can it be any of the above, depending on the technique used?
 
Thanks. Another question:

When an aircraft gains altitude by soaring around a thermal, it's making use of the difference in speed between the air in the thermal and the surrounding air. Say the vertical speed of the air in the thermal is V relative to the surrounding air, is the rate of gain in altitude of the aircraft:

- less than V?
- equal to V?
- greater than V?
or can it be any of the above, depending on the technique used?

When we thermal we take advantage of the vertical speed of the air in the thermal to gain altitude. Thermals pretty nearly always have a rotational speed also, but we only use that in a second order manner. By circling opposite the rotation of the thermal, you can circle closer to the core of the thermal without going around the thermal as rapidly. This permits you to be closer to the core with lower bank angle (and thus more useful lift).

The rate of altitude gain is simply the vertical speed of the air in the portion you're "coring" minus the sink rate for your given flight condition (speed and bank angle). Faster flying speed and greater bank angle increase your sink rate.

In typical thermal flying we don't really take advantage of the difference in wind speed in and out of the thermal. We just take advantage of the absolute vertical wind speed in the thermal. There are techniques (e.g. dynamic soaring) in which you can take advantage of the relative velocity of air masses. Birds and R/C models definitely use this technique. I don't think full-scale soaring craft have done this though.

In traditional thermal flying we just think of the thermal as an elevator. We get in it and ride it up.
 
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When we thermal we take advantage of the vertical speed of the air in the thermal to gain altitude. Thermals pretty nearly always have a rotational speed also, but we only use that in a second order manner. By circling opposite the rotation of the thermal, you can circle closer to the core of the thermal without going around the thermal as rapidly. This permits you to be closer to the core with lower bank angle (and thus more useful lift).

The rate of altitude gain is simply the vertical speed of the air in the portion you're "coring" minus the sink rate for your given flight condition (speed and bank angle). Faster flying speed and greater bank angle increase your sink rate.

In typical thermal flying we don't really take advantage of the difference in wind speed in and out of the thermal. We just take advantage of the absolute vertical wind speed in the thermal. There are techniques (e.g. dynamic soaring) in which you can take advantage of the relative velocity of air masses. Birds and R/C models definitely use this technique. I don't think full-scale soaring craft have done this though.

In traditional thermal flying we just think of the thermal as an elevator. We get in it and ride it up.

Thanks for the explanation. Now I understand the difference between normal thermal soaring and dynamic soaring. These were the sort of questions I should have asked before trying to solve the problem :)

Since the aircraft is moving upwards slower than the thermal, here's something interesting that struck me: although the spiral that the aircraft makes relative to the ground carries it in the direction of the wind, the fact that the aircraft is moving upwards slower than the air of the thermal means that its mean speed in the direction of the wind is slower than that of the wind. This means that the spiral the aircraft makes relative to the air is angled the other way.
 
Since the aircraft is moving upwards slower than the thermal, here's something interesting that struck me: although the spiral that the aircraft makes relative to the ground carries it in the direction of the wind, the fact that the aircraft is moving upwards slower than the air of the thermal means that its mean speed in the direction of the wind is slower than that of the wind. This means that the spiral the aircraft makes relative to the air is angled the other way.

Edit: I've just saw that I misinterpreted what you said Michael. At first I thought you were wrong, but now I realise that you are talking about an aircraft climbing in a thermal (and staying in it) and also that you're talking above its path relative to the air. So, what follows below is not really relevant. Probably best that you ignore it completely, but I'll leave it here in case it might help someone else.

If the motion of the air through which we're flying is uniform, then we can fly in "perfect circles" relative to the air (if we also ignore the up/down dimension). I.e. Viewed from above, we are flying around and around in a circle - and this is basically the closest we can get to maintaining a fixed horizontal position in the airmass and also be "stable". Of course, diving straight down (relative to the air's horizontal movement) towards the ground also works, but only for a short time before you encounter a problem!

In a glider, we must always be descending relative to the surrounding air if we're also maintaining a constant airspeed. But if that air is rising (relative to the ground) faster than the aircraft is sinking through it, then the aircraft still gains height. For our purposes here, the vertical movement doesn't change what is happening when you restrict your view to what is happening in the horizontal plane.

So the solution to this brainteaser is relying on the fact that we can essentially always maintain a fixed position relative the air in the horizontal sense (by circling) while at the same time the position (relative to the ground) of the region where a particular thermal exists is fixed. This means a circling aircraft is (on average) drifting sideways compared to the location of the thermal. To correct for this and maintain his position in the thermal, the pilot always has to spend more time flying into the wind than in the other direction and this gives away the direction of the wind. The amount of compensation decreases if the aircraft is climbing inside the thermal and increases if it is descending (and also staying in the thermal) but the effect will always exist unless the aircraft could climb at the same rate as the air rose in the thermal.
 
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Thanks for your explanations, Clive, they have been very helpful. Let me ask you this. Suppose I'm motorcycle going down a straight highway. When I encounter a crosswind of sufficient strength I noticeably have to compensate for it. If I didn't, I would drift off the highway.

Okay. Now suppose your soaring aircraft is going straight relative the highway just like me. You're not in any thermal at this point, so I guess it's just a steady glide down. Suddenly you enter a thermal where for meteorological reasons unknown to me the same crosswind I encountered on the motorcycle is also pushing the thermal into a leaning tower.

When your aircraft enters the thermal, what happens? Do you shift "off" the highway like my motorcycle would if I did nothing to compensate?
 
Thanks for your explanations, Clive, they have been very helpful. Let me ask you this. Suppose I'm motorcycle going down a straight highway. When I encounter a crosswind of sufficient strength I noticeably have to compensate for it. If I didn't, I would drift off the highway.

Okay. Now suppose your soaring aircraft is going straight relative the highway just like me. You're not in any thermal at this point, so I guess it's just a steady glide down. Suddenly you enter a thermal where for meteorological reasons unknown to me the same crosswind I encountered on the motorcycle is also pushing the thermal into a leaning tower.

When your aircraft enters the thermal, what happens? Do you shift "off" the highway like my motorcycle would if I did nothing to compensate?
Thanks for the vote of confidence UncaYimmy! However, don't rely too much on what I say without confirmation from other sources. I've not been a practising pilot for decades, and in any case have very little actual gliding/soaring experience.

I'm also not 100% sure I understand your question properly but I'll take a stab at it anyway. It actually seems to relate to something I've been trying to get my head around also with respect to this particular puzzle and that concerns how a horizontal wind and a vertically moving thermal might "mix". The answer to your question may partly depend on how realistically we want to treat our thermals!

In the real world (and without any significant wind), a thermal is generated by an area on the ground that heats the air immediately above it. That becomes less dense than the air above it as a result, causing it to rise. But something also has to replace it as it rises, and mostly (I would think) this is air flowing in "sideways" from the surrounding areas. Possibly though some air from above is also sinking down through the rising warmer air simultaneously (maybe more so at the start of the process). Anyway, the "replacement air" also gets heated, starts to rise, and our thermal grows taller and taller. It won't go up forever though. The air warmed at ground level gets cooled and mixed with other air as it rises. Eventually it'll end up being close enough to the same temperature as the other ("non-thermal") air at that same altitude and so the thermal won't go any higher. In fact you end up with a giant circulation pattern, with (as was mentioned earlier by others) the strongest part of the thermal being a relatively small region of quite fast rising air, and a larger surrounding area of slowly sinking air. There's also going to be some turbulence created around the sides of the thermal as air masses with different velocities move past each other.

Now lets add some wind to this, and we'll assume it's also a simplified situation like the puzzle set-up - in the same direction and speed at all altitudes. Imagine a hot air balloon in a wind. It basically gets carried along (sideways) with the wind at the same speed as the wind even though it could be rising at the same time. The air in our thermal isn't physically enclosed like the warm air in a balloon, but in my guess is that it will often tend to act in a similar way. Still, the whole column of rising air can't be sitting there blocking the wind like some kind of solid barrier. I think JB used an analogy earlier of a stream of bubbles rising from a source at the bottom of a flowing stream. I imagine the actual main body of a thermal is going to be a bit like that also if you looked at it closely. Bubbles of warmer air rising (and also moving sideways) each much like a rising hot air balloon, but there will also some "cold air" blowing through (and maybe down and around also) as the surrounding wind meets the thermal at that height and the two streams interact. I really don't know exactly what's happening down at the finest levels - this description is really just me having an educated guess - but hopefully it's close enough to suggest the situation around and inside a real thermal on a windy day is likely to be quite complicated.

Having said all that, whether you are considering a parcel of cooler air that was blown into the region "occupied" by the thermal as part of "the wind", or whether you're looking at a smaller bubble of warm air rising (but also moving sideways "with the wind") you're always basically considering air that is still moving sideways at windspeed. (Mostly!)

Ignoring the real world turbulence and other complications of that kind, in the puzzle we can probably get away with the simplified picture that all the air (in the thermal or outside) is moving horizontally at the same speed and direction as the wind even though the "bubbles" of warmer air that give our thermal it's nature are also rising upwards at the same time.

In that context, if you are gliding (and presumably also descending) in a straight line in an area of "sink" (outside a thermal) and then run into a thermal, you should not expect to be moved sideways like your motorbike rider. All the air (in our simplified world) is moving sideways at the same speed. However, once in the thermal we will now also be in the region where the average vertical speed of the air is "upwards" so as we cross the boundary we should expect to feel a "push upwards" (acceleration) a bit like we've just stepped from a level floor onto an upwards moving escalator. And once we're in the region of air that we've been calling the thermal, we're actually experiencing some kind of quite complex mixture of air moving in different directions. On average though, it is "rising" and that's probably all that counts for aircraft of the sizes we are talking about.

One last warning, as already noted these are really only my own thoughts about roughly what might happen as steady sideways wind mixes with a thermal and I haven't really researched this at all. Therefore, treat what I say with caution! :)
 
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Again, Clive, thanks. I have full faith that others will chime in with corrections if needed. And for the record, I'm not trying to "set up" so I can prove the so-called brainteaser incorrect. I'm just asking some questions because I find it interesting and because I had some wacky ideas as I was falling asleep last night. Fortunately, I feel no shame in asking questions about things that might seem silly to those know a field well.

The wacky idea I had involved entering the thermal and rotating the wings to be perpendicular to the ground. That would create a profile to "catch" the most wind if you had a thermal moving east to west and you entered it from the north or south. Of course, if have the wings parallel did the same thing, then the point idea had no legs.
 

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