Calling all mathmaticians

[S13driftAZ]

If you hold a glass of water under a tap water faucet/soda fountain/what have you, and you motion the cup up and down, closer and farther from where you are getting the liquid from, will it fill your cup faster than if you just hold it still?

[Gooberman]

It depends how close you are to c.

[snoopy]

I'm an engineer, so I'll tackle it from my perspective:

The amount of liquid coming out of the tap is constant, no matter what you do with the cup.

So, the only way it'd make a difference is if it had an effect on the amount that splashed out.

Other than that, the higher the cup, the earlier the last bit of water will be in it.

[Spidey]

Lol, if you hold a glass of water under a tap, it won’t matter what you do with the glass, because it’s already a “glass of water”…

[Drakona]

If, and only if, when you finish moving the cup, it is closer to the faucet than when you started.

Do you stay drier if you run through the rain?

[ccb056]

I'm an engineer, so I'll tackle it from my perspective:

The amount of liquid coming out of the tap is constant, no matter what you do with the cup.

So, the only way it'd make a difference is if it had an effect on the amount that splashed out.

Other than that, the higher the cup, the earlier the last bit of water will be in it.

Snoopy, not entirely true.

While the mass flow rate out of the tap is constant, the flow into the cup does not have to be. The mass flow into the cup is dependent on the relative velocity of the cup with the fluid velocity out of the fountain. If the distance between the fountain and ground were infinite, and the fountain was off, and you dropped the cup, then turned on the faucet, the mass flow into the cup would be zero. Likewise, if you move the cup up while filling, the flowrate into the cup would be greater than if it were stationary.

[Duper]

Lol, if you hold a glass of water under a tap, it won’t matter what you do with the glass, because it’s already a “glass of water”…

lol

there is only so much water that is coming out of the tap. This is simple enough to try at home. give yourself a couple of controls and do a set. I think you'll find that up and down won't make any difference. if it does, the amount of time will in 100th's of seconds. more likely you would see it in moving a cup into a flowing steam that is falling a distance, say oh. 2 meters. move the cup rapidly UP the stream. THEN you will see a difference. But just your avarage at home "up and down" probably won't be significant. This echos in extreme what Drak said. ... now that i've read it.

Oh Drak, running IF it's a straight down pour. Or rather falling straight down.

[Pandora]

If, and only if, when you finish moving the cup, it is closer to the faucet than when you started.

Of course! I would have missed that.

[Foil]

If, and only if, when you finish moving the cup, it is closer to the faucet than when you started.

Exactly.

[snoopy]

If, and only if, when you finish moving the cup, it is closer to the faucet than when you started.

Do you stay drier if you run through the rain?

I agree.

In practical terms, you'll never know the difference in a real-life sink.

do you stay drier if you run through the rain? -> My guess is that you'd end up approximately equally wet, in different spots.

Here's a more complete answer:

Think about the extremes, and what the result would be.

If you move infinitely slowly, you will get an infinite amount of rain on the top of your head.

If you move infinitely quickly, you will run into all of the rain that's in your path (a significant amount of rain), on your front, with nothing landing on your head.

More speed = more frontal area = more wetness/second.

Less speed = more time in the rain = a longer time for the wetness/second to accumulate.

So, we know that moving infinitely slowly isn't the answer. What I don't know is if the total wetness keeps going down with increase in velocity, or if there's an optimal speed that yields the least wetness.

[Krom]

Mythbusters did the whole running vs walking in the rain thing and determined that you get more wet running (although the difference was small).

[Floyd]

Mythbusters did the whole running vs walking in the rain thing and determined that you get more wet running (although the difference was small).

did they only test vertical rain or also inclined rain?

[AlphaDoG]

If I remember correctly they tested both.

[Drakona]

Yeah, I remember that mythbusters. I remember being enlightened and irritated that it disagreed with my math.

Being a mathematician, I had, of course, assumed a spherical pedestrian.

[snoopy]

Yeah, I remember that mythbusters. I remember being enlightened and irritated that it disagreed with my math.

Being a mathematician, I had, of course, assumed a spherical pedestrian.

Did you re-calculate, based on a rectangular person?

If so, did you find an optimal speed?

[ccb056]

Draw a control volume.
Draw the fluid velocity.
Do a mass balance.

If the rain is comming straight down and you run you get less rain on you.

If the rain is comming from behind and you run you get less rain on you.

If the rain is comming from ahead, I would have to run the calculations, but intuition says there is a peak run speed and angle.

[Duper]

Being a mathematician, I had, of course, assumed a spherical pedestrian.

why is that??

[Drakona]

Being a mathematician, I had, of course, assumed a spherical pedestrian.

why is that??

'cuz it's what we do.

No, I didn't redo the work with a rectangular pedestrian. I mean, I solved the spherical version of the problem, and Mythbusters solved the practical version. Might be interesting to abstract, but I had other spherical cows to think about. . .

[Duper]

...oh...


o_0


but ... my amp goes to 11.....








(i get it and it does make sense... a bit of a bad practice, like playing a piano and not keeping your wrists up.) lol, it's just that I've always thought of people as rectangle ... but that's me thinking like an artist. Thanks for the answer, that was simpler than i had expected.

[Tunnelcat]

LOL, this whole argument reminds me the Mythbusters segment that tested whether an aircraft could take off when it was sitting on a conveyor belt that was moving backwards.

http://txfx.net/2005/12/08/airplane-on-a-conveyor-belt/

http://mythbustersresults.com/episode97

[ccb056]

LOL, this whole argument reminds me the Mythbusters segment that tested whether an aircraft could take off when it was sitting on a conveyor belt that was moving backwards.

http://txfx.net/2005/12/08/airplane-on-a-conveyor-belt/

http://mythbustersresults.com/episode97

It will. Aircraft dont need wheels to take off...

[Dedman]

Being a mathematician, I had, of course, assumed a spherical pedestrian.

Ah yes, you assumed a Southern pedestrian.

[Lothar]

LOL, this whole argument reminds me the Mythbusters segment that tested whether an aircraft could take off when it was sitting on a conveyor belt that was moving backwards.

http://txfx.net/2005/12/08/airplane-on-a-conveyor-belt/

http://mythbustersresults.com/episode97

It will. Aircraft dont need wheels to take off...

Yep.

A lot of people mistakenly think of an airplane as a car that drives really fast and then, when its wheels have pushed it up to speed, it takes off.

Airplane wheels serve two functions: they let it move when the engines push it along the ground, and they provide it with a small amount of braking. That's it. There are no motors attached to the wheels; they don't drive it at all. The airplane gets its speed from propellers or jets, and as long as those can push enough air to get the airframe up to takeoff speed, it doesn't matter whether you're on a runway, a big patch of ice, or a giant conveyor belt, the airplane will take off.

[Sniper]

The thing that I don't understand about how planes on a treadmill works is this...

What makes a plane take off?
Is it the simple fact that the wheels are moving? No.
Is it the simple fact that the engines/propellers are running. No.

What makes a plane take off is the amount of air running over the wings, creating that pressure differential. Lift.

If a plane is on a treadmill, and the engines are running, and the plane is not moving - are we all saying that it will take off because the engines/propellers are creating enough lift alone? What if it was a rear engine/propeller plane?

That's what I don't understand. I don't understand how a stationary plane can take off from a treadmill. I would think there would need to be airflow over the wings??

[Lothar]

What makes a plane take off is the amount of air running over the wings, creating that pressure differential.

If a plane is on a treadmill, and the engines are running, and the plane is not moving

If the plane is NOT MOVING, then the plane won't lift off the ground (unless it's got vectored thrust and a thrust-to-weight ratio of greater than one, like a Harrier, or the outside wind speed is greater than the aircraft's stall speed.)

The treadmill doesn't have anything to do with it. The treadmill won't hold the plane stationary, and if you have a way to hold the plane stationary, you don't need a treadmill. The treadmill may as well be replaced with normal ground in this problem; the speed of the airplane's wheels has NOTHING to do with whether or not it will take off.

If you rephrase the question as "if you tie a rope to a plane so that the plane doesn't move, and run the engines up to full speed, will it lift off?" then the answer is usually no (except in the cases I mentioned above.)

[Spidey]

The question was stated “on a conveyor going backwards” I doubt a plane could take off if the conveyor could prevent the plane from reaching “air speed”.

Now if it was just a free spinning conveyor…it would have no effect.

Note: air speed is in quotes here because it is meant to be the minimum speed at which the craft can remain airborn. (not true airspeed)

[ccb056]

The treadmill essentially changes the no slip assumption at the wheel and the ground to a slip assumption.

http://en.wikipedia.org/wiki/Slip_(vehicle_dynamics)

It other words, a plane taking off a treadmill is no different than a plane taking off from a sheet of ice.

[Lothar]

... if the conveyor could prevent the plane from reaching “air speed”

A conveyor won't do that.

If you want to say "the airplane doesn't reach its airspeed" then you have to have it held into place. A conveyor won't hold it in place, it'll just make the tires spin extra fast.

EDIT: Spidey, the term for the minimum speed at which an airplane can stay aloft is "stall speed".

[Spidey]

Yes, but tc phrased as “on a conveyor going backwards” .

[Spidey]

I get it…DOH

[ccb056]

You're missing the point.

Planes work using thrust, not driving wheels.

[Spidey]

See last post…

The “trick” part of the question was working on me…

Then I got it…

[snoopy]

... if the conveyor could prevent the plane from reaching “air speed”

A conveyor won't do that.

If you want to say "the airplane doesn't reach its airspeed" then you have to have it held into place. A conveyor won't hold it in place, it'll just make the tires spin extra fast.

EDIT: Spidey, the term for the minimum speed at which an airplane can stay aloft is "stall speed".

Now, I think you're wrong.

My conveyor goes a billion miles an hour, and it over-heats and seizes the bearings in about 1 second, thus introducing grip on the tires, and throwing the airplane backwards into the wall that I've set up behind the plane.

Maybe it's just my conveyor, though.

In seriousness, there are two factors involved:

1. The plane cares about airspeed, not ground speed. Within normal bounds, ground speed is completely irrelevant to the lift generated by the wings. The bearings on the wheels act to make the ground create very little friction to slow the plane down- like you're roller skates.
2. The engine/prop (or turbine) work to generate thrust against the air (thus directly generating airspeed), instead of against the ground like our cars do.

But then, I'm pretty much preaching to the choir, since you all seem to be totally on top of this one.

[Tunnelcat]

It's funny you guys got sucked into this one! There were tons of posts on the AVSIM forum on this very topic, so much arguing going on back and forth that the moderators threatened to shut the nonsense down it was generating so much topic discussion. I'd post the link, the discussions were a riot, but they were hacked not too long after that and all the older topics vanished.

Most of you got the logic correct. An airplane gets it's thrust from either the propeller or turbine/jet engine acting acting against the atmosphere and that is INDEPENDENT or DISSCONNECTED of any motion on the ground. Unless the wheels and bearings have too much friction for the thrust to overcome, moving backwards on a conveyor belt will not stop a plane from taking off. That same friction, say it even had locked up wheel bearings, would also impede a stationary plane. However, if the plane has enough thrust, it will just drag the stuck wheels across the runway anyway. Thrust will overcome the backwards motion of a conveyor belt very quickly.

[woodchip]

With a infinitely long conveyor belt propelling the plane rearward and at a speed that increases as it detects any forward motion of the plane, the plane will not generate enough lifting force to ever get off the ground. Correct?

[Krom]

Incorrect. The plane would eventually lift off because it doesn't push against the conveyor belt, it pushes off the air around it to move forward. A conveyor belt would never be able to stop a plane from accelerating and lifting off the ground.

Think of it another way, a conveyor belt trying to push a plane forward would also have no impact in the amount of time required for the plane to take off.

[Floyd]

i can't believe this topic spawns such a huge discussion. how would a conveyor belt affect the relative speed between the plane and the air?

relative speeds of the ground vs. the plane or the air have nothing to do with lift (be it this unnecessary experiment or a kite in strong wind). the wheels of a plane have nothing to do with its speed instead of creating drag, they are just there to reduce friction to the ground, to steer it, and to not have it fall on the ground. this is how an airplane works:

[Tunnelcat]

That's what was funny about the AVSIM forum discussion. These are mostly people that either fly airplanes for real or at least use a flight simulation program, so you'd think they would now how an airplane flies. The discussion generated over 10 pages of arguments on just this ONE topic, LOL! The moderators couldn't wait until that particular Mythbusters segment finally aired to shut people up. Even then, it STILL continued on for a little while.

I see woodchip is still a little unclear on the concept. Like Krom said, the airplane pushes against the AIR, not the ground, so even if the plane was going backwards at high speed, it would still be able to use the thrust against the air to eventually start moving forward.

Now, you can fly an airplane backwards. I used to know a friend who owned a Piper Cub. The plane had a very low takeoff speed. If the wind was blowing hard and constant enough, he could actually take off and fly backwards if he throttled back a little. He used to do this all the time to entertain people whenever we had fast, constant winds down the runway. If it blew hard enough, he could've easily taken off with very little forward motion. But being a pilot who wasn't totally crazy, he never attempted that in those conditions. He also wouldn't have been able to generate enough thrust to overcome the wind speed and be able to move forward to a point he could make a safe landing on that same runway anymore. The hazards of a really light aircraft.

[Drakona]

No, Woodchip is right, as snoopy hinted. A sufficiently fast conveyor belt will prevent the airplane from taking off. The wheels might be low friction, but they aren't zero. You just have to spin them fast enough. I mean, really fast enough.

It's all in the posing of the problem.

If you say \"the conveyor belt goes backwards as fast as the airplane goes forwards\", then it takes off no problem.

If you say, \"the conveyor belt goes backwards fast enough that the airplane holds still,\" then it doesn't take off. It's also an insanely fast conveyor belt.

Funny, every time I hear this problem posed, I'm always tempted to bring up the supersonic conveyor belt. I usually restrain myself, though, because it sows so much confusion, and apparently the mere distinction between ground speed and air speed sows enough confusion . . .

[Duper]

the whole question is poorly and even incorrectly phrased.

You would have mechanical failure of the wheels before the plane stopped. And in that case, \"no friction\" can't be called and thus the system breaks down. ..I think the phase is \"insanely fast...\"