Herr Professor Doctor Alex

[bonanova]

He's doing what? asked Jamie.

Shh.. here he comes, answered Ian. He's studying physics

on the Internet. I think we should humor him, OK?

So here's yer challenges for tonight, me boys. Alex had a

strange way of smiling when he thought he had his friends

over a barrel. He was smiling now.

[1] how can you tell a raw egg from a hard-boiled egg?

[you can't break the shell or use light, heat, sound or X-rays]

[2] compared to a still day, will a round-trip airplane ride take more,

less or equal time if there's a constant wind blowing?

[a headwind one way, a tailwind the other way]

And there's more where that came from, boys ... have fun.

[bonanova]

Why is that?

Every wind is slower than every plane? Why?

[Guest]

Say a plane is going 150mph between airports that are 150 miles apart.... without any wind the flight total will take 2 hours round trip (lets ignore added time and speed differences for takeoff/landing)

Now that same flight with a 50mph wind (head/tail depending on leg of flight) going at the same speed...

it will take 45 minutes with the tail wind and 90 minutes with a head wind.... So this flight would take 15 minutes longer total that without wind.

[bonanova]

Say a plane is going 150mph between airports that are 150 miles apart.... without any wind the flight total will take 2 hours round trip (lets ignore added time and speed differences for takeoff/landing)

Now that same flight with a 50mph wind (head/tail depending on leg of flight) going at the same speed...

it will take 45 minutes with the tail wind and 90 minutes with a head wind.... So this flight would take 15 minutes longer total that without wind.

You're giving the correct analysis.

My post asked mattkonczal13 why he says it is not possible for the air speed to equal the plane speed.

[Guest]

You're giving the correct analysis.

My post asked mattkonczal13 why he says it is not possible for the air speed to equal the plane speed.

As indicated in a prior post (I believe), a headwind equal to the plane's speed would, in fact, negate the plane to travelling at 0 mph, meaning the plane isn't flying.

[bonanova]

As indicated in a prior post (I believe), a headwind equal to the plane's speed would, in fact, negate the plane to travelling at 0 mph, meaning the plane isn't flying.

Right [groundspeed].

Wrong [isn't flying].

Flying is about interacting with a surrounding fluid in a way that permits Bernoulli's principle to overcome gravity.

Fly a kite [0 ground speed]

Watch a seagull or hang glider hover [0 ground speed]

Throw a frisbee into a really strong wind. [0 ground speed]

Fly a 100 mph airplane into a 100 mph wind [0 ground speed]

In all these cases, flying occurs when there exists a sufficient air speed to enable flight.

Even tho the ground speed may be zero.

[Guest]

or you said the tailwind aids as much as the headwind hinders,

thus the trip will take the same time.

You don't compare speeds over similar distances to get average speed.

You compare speeds over similar times to get average speed.

I believe you're mistaken.

speed = distance X time

so...

speed/distance = time

given that the headwind, or tailwind affects the air speed at the same rate: the flight times would average out to be the same as if there were no change in air speed either way.

Ex.

500 Mph. / 1000 Mi. = 0.5 Hr.

550 Mph. / 1000 Mi. = 0.55 Hr.

450 Mph. / 1000 Mi. = 0.45 Hr.

0.45 Hr. + 0.55 Hr. = 1 Hr. /2 = 0.5 Hr.

So, the average of the trip with the same wind in both ways was the same as the timing for no wind at all.

[bonanova]

I believe you're mistaken.

speed = distance X time

so...

speed/distance = time

given that the headwind, or tailwind affects the air speed at the same rate: the flight times would average out to be the same as if there were no change in air speed either way.

Ex.

500 Mph. / 1000 Mi. = 0.5 Hr.

550 Mph. / 1000 Mi. = 0.55 Hr.

450 Mph. / 1000 Mi. = 0.45 Hr.

0.45 Hr. + 0.55 Hr. = 1 Hr. /2 = 0.5 Hr.

So, the average of the trip with the same wind in both ways was the same as the timing for no wind at all.

Hi bobbyb.

Think a bit about the formulas you wrote down.

Do they make sense to you?

Do the units match?

If you double your speed do you expect the time to double?

If there were a 500mph headwind, what would happen during that leg of the flight?

Maybe you just wrote them down in a hurry.

If not, read up on the subject and then give it some more thought.

[Guest]

Spinning the egg and then stopping it would work, but here is another way I thought of:

Since the inside of a raw egg is a liquid compared to the solid part of hard-boiled egg, sending sound waves through the egge would tell the difference between liquid and solid. The faster being solid and the slower the liquid. But this would take expensive and delicate equipment and many eggs to compare making it an inconvienience.

For second:

It would take the same time since you are making a round trip the wind would slow you down on one leg and make up for it by increasing your speed on the other, assuming you are traveling at constant speed.

[Guest]

For second:

It would take the same time since you are making a round trip the wind would slow you down on one leg and make up for it by increasing your speed on the other, assuming you are traveling at constant speed.

This would be incorrect as proven by a few posts.

When a plane travels with a tail wind it isn't flying any faster, it is however traveling in a 'fluid' that is also going the same direction; so the plane is still flying at say 150 MPH but has a ground speed of 200 MPH (using a 50mph wind speed). Now on the return trip, again the air speed is the same 150 MPH but now the wind is going against the plane so it drops it down to a ground speed of 100 MPH. So it gets a 25% boost with a tail wind and a 50% drag with a head wind; that means (in my example) that the plane trip takes 25% LONGER than the same flight without any wind.

[bonanova]

This would be incorrect as proven by a few posts.

When a plane travels with a tail wind it isn't flying any faster, it is however traveling in a 'fluid' that is also going the same direction; so the plane is still flying at say 150 MPH but has a ground speed of 200 MPH (using a 50mph wind speed). Now on the return trip, again the air speed is the same 150 MPH but now the wind is going against the plane so it drops it down to a ground speed of 100 MPH. So it gets a 25% boost with a tail wind and a 50% drag with a head wind; that means (in my example) that the plane trip takes 25% LONGER than the same flight without any wind.

That's the right idea - losing speed increases your travel time more than gaining speed decreases it.

Here's a driving example:

Suppose you're traveling 60 mph on highway and hit 10 miles of 40 mph construction zone

You spend 15 minutes there instead of 10, losing 5 minutes.

Then suppose you try to get the time back by going the next 10 miles at 80 mph. Bad strategy, for two reasons.

First, that next 10 miles still takes 7.5 minutes, saving not 5 minutes as you hoped, but only 2.5 minutes.

Plus, you got a ticket.

In the plane example, it's also useful simply to calculate travel time intervals:

Suppose each leg of the trip is 600 miles, the air speed is 150 mph and the wind is 50 mph.

At 100, 150 and 200 mph ground speeds, the one-way travel times are 6, 4 and 3 hours, respectively.

Without wind, the total time is 4 + 4 = 8 hours. Avg speed = 1200/8 = 150 mph.

With wind, it's 6 + 3 = 9 hours. Avg speed = 1200/9 = 133 1/3 mph.

So the percentage change in speed or travel time is 12.5%

[Guest]

You don't have to stop the egg to tell. If it's hard-boiled and you spin it right (it's not hard) it'll stand on end like a child's top. It's actually sort of cool. I've been able to do that with every hard boiled egg I've ever come across, but have never succeeded with a raw one.

[Guest]

The answer is: any constant wind - in any direction - will increase the duration of a round trip,

provided the plane maintains a constant air speed.

This is incorrect.

Assuming the earth is round and you are flying along a straight path, a constant wind could actually decrease the duration of the trip if the wind blows hard enough. Example- I if you are going half way around the world againts the head wind and the head wind is blowing twice as fast as the plane flies, then you will reach the destination in the same amount of time as you would have if there was no wind. Unfortunately you would have been blown backwards to your destination and that is probably not very safe. Then, when you head home with the tail wind, you will fly the same distance 3 times faster. Therefore, your total time flying will be about 2/3s of the time it would have been flying with no wind at all.

I just thought I would put it out there.

The rest of what you say is correct though.

Steve

[Guest]

This is incorrect.

Assuming the earth is round and you are flying along a straight path, a constant wind could actually decrease the duration of the trip if the wind blows hard enough. Example- I if you are going half way around the world againts the head wind and the head wind is blowing twice as fast as the plane flies, then you will reach the destination in the same amount of time as you would have if there was no wind. Unfortunately you would have been blown backwards to your destination and that is probably not very safe. Then, when you head home with the tail wind, you will fly the same distance 3 times faster. Therefore, your total time flying will be about 2/3s of the time it would have been flying with no wind at all.

I just thought I would put it out there.

The rest of what you say is correct though.

Steve

Due to wing design planes speed up during a head wind and slow down during a tail wind.

It doesn't really matter though.

[Guest]

1. Spin the egg, do the stop thing, also balancing it, shining a light through it, and shaking it work too.

2. I believe it would take longer, but I'm not sure. I have a friend in aviation, so he would know better then me, but I know that wind does have very strange effects on flight in an aircraft, so I'm saying longer just to be safe

[Guest]

This is incorrect.

Assuming the earth is round and you are flying along a straight path, a constant wind could actually decrease the duration of the trip if the wind blows hard enough. Example- I if you are going half way around the world againts the head wind and the head wind is blowing twice as fast as the plane flies, then you will reach the destination in the same amount of time as you would have if there was no wind. Unfortunately you would have been blown backwards to your destination and that is probably not very safe. Then, when you head home with the tail wind, you will fly the same distance 3 times faster. Therefore, your total time flying will be about 2/3s of the time it would have been flying with no wind at all.

I just thought I would put it out there.

The rest of what you say is correct though.

Steve

LOL. That's hilarious. But it only works in situations where you fly halfway around the world. And if that were the case, you'd just fly in the direction that gives you 3x speed for both parts of the trip .

Since it hasn't been done... mathematical proof:

d: distance (one-way)

v: plane speed

x: windspeed

Time without wind:

t = 2d/v

Time with wind:

t' = d/(v+x) + d/(v-x)

= [ d(v-x) + d(v+x) ] / (v-x)(v+x)

= d (v-x + v+x) / (v-x)(v+x)

= d (2v) / (v-x)(v+x)

Compare t with t':

t / t' = 2d/v * (v-x)(v+x)/2dv

= (v-x)(v+x) / v²

= (v² - x²) / v²

For non-zero x and v, x² and v² are positive, therefore:

(v² - x²) must be less than v².

(v² - x²) / v² < 1

t / t' < 1

And assuming times are positive,

0 < t / t' < 1

t < t'

Thus, no-wind flight takes less time for all values v>0, 0<x<v, d>0.

[bonanova]

Since it hasn't been done... mathematical proof:

[proof]

Thus, no-wind flight takes less time for all values v>0, 0<x<v, d>0.

Nice job.

This holds for collinear winds [as the OP asked].

Can you generalize for cross winds [at angle x] as well?

[Guest]

LOL. That's hilarious. But it only works in situations where you fly halfway around the world. And if that were the case, you'd just fly in the direction that gives you 3x speed for both parts of the trip .

Hey, the question isn't that realistic in the first place. I just wanted to point out that it doesn't always work out to slow down the flight. There is an exception.

I would hope the people flying the plane would do the logical thing, but you have to admit that within the restraints of the equation, which are not really that realistic either, the flight time can be increased or decreased by the wind.

[bonanova]

Hey, the question isn't that realistic in the first place. I just wanted to point out that it doesn't always work out to slow down the flight. There is an exception.

I would hope the people flying the plane would do the logical thing, but you have to admit that within the restraints of the equation, which are not really that realistic either, the flight time can be increased or decreased by the wind.

Hi biosteve,

What's unrealistic? A plane flies from point A to point B and returns.

And, if the plane flies backwards instead of forwards, then it returns backwards instead of forwards.

[1] There's no wind. It takes t1 minutes.

[2] There's a wind. It takes t2 minutes.

Compare t2 to t1.

What's your answer?

[Guest]

Hi biosteve,

What's unrealistic? A plane flies from point A to point B and returns.

And, if the plane flies backwards instead of forwards, then it returns backwards instead of forwards.

[1] There's no wind. It takes t1 minutes.

[2] There's a wind. It takes t2 minutes.

Compare t2 to t1.

What's your answer?

Hi bonanova,

What is unrealistic? Well I would say a wind with a constant speed and constant direction is pretty unrealistic.

Anyways,

You may have missed something.

If you read it carefully you will see that, in my solution, the plane is not flying backwards, the wind is simply blowing it backwards. When it flies the other direction the wind pushes it forward. Also as you will see in the previous post, the proof he uses allows for my solution, meaning that there is an exception to the rule and the constant wind could potentially decrease the flight time. Making your solution incomplete.

Please edit your solution from "any constant wind - in any direction - will increase the duration of a round trip, provided the plane maintains a constant air speed." to say "Most constant winds will increase the duration of the round trip, but surprisingly there is an exception, and biosteve cleverly found it."

This edit will make your solution more complete, as well as more correct.

Just in case you don't feel like reading back through the posts here is the solution that leads to a quicker flight-

Example- if you are going half way around the world "flying east" against the head wind (imagine westerly wind) and the head wind is blowing exactly twice as fast as the plane flies, then you will reach the destination in the same amount of time as if there was no wind. Unfortunately, in this case, you would have been blown backwards to your destination and that is probably not very safe. Then, when you head home "flying west" with the tail wind (again a westerly wind) behind you, you will fly the same distance 3 times faster. Therefore, your total time flying will be 2/3s of the time it would have been flying with no wind at all.

Now... you do the math and tell me what you get for t1 and t2.

Use vectors, it will make it easier for you to understand and visualize.

[Guest]

You see, the proof he uses fails to take into account that the earth is round.

The limits at the end of proof require an x value less than v and greater than zero.

On a sphere the wind value "x" can be larger than the plane velocity "v" and still allow the plane to arrive at its destination. A more accurate proof would include all possible values for x and v while still setting their limits to >0.

[Guest]

He's doing what? asked Jamie.

Shh.. here he comes, answered Ian. He's studying physics

on the Internet. I think we should humor him, OK?

So here's yer challenges for tonight, me boys. Alex had a

strange way of smiling when he thought he had his friends

over a barrel. He was smiling now.

[1] how can you tell a raw egg from a hard-boiled egg?

[you can't break the shell or use light, heat, sound or X-rays]

[2] compared to a still day, will a round-trip airplane ride take more,

less or equal time if there's a constant wind blowing?

[a headwind one way, a tailwind the other way]

And there's more where that came from, boys ... have fun.

1) the hard-boiled egg would be hot of course as you pick it up if it just finished boiling, and warm for the raw egg..

Now, if they're both already cooled off, their weight would be different.. HB eggs are heavier.

2) equal. As long as everything remains constant.

[Guest]

I don't like the way ppl are thinking of this. I would say it would take the same time, because if a pilot is going into the wind, he could merely accelerate to compensate and reach the speed he desired. If there was a tailwind, he would deccerate to go the speed he desired. Unless of course you factor in the possibility that the headwind would be so strong he would not be able to accelerate through it, then yes, the times would be different. What you're assuming is the pilot would keep the throttle at the exact same position even though winds are varying. If you don't get what I'm saying maybe this will help, does modern day cruise control attempt to stay at the same throttle position, or does it attempt to stay at the same speed?

Edited July 17, 2008 by tekanubis

[Guest]

He's doing what? asked Jamie.

Shh.. here he comes, answered Ian. He's studying physics

on the Internet. I think we should humor him, OK?

So here's yer challenges for tonight, me boys. Alex had a

strange way of smiling when he thought he had his friends

over a barrel. He was smiling now.

[1] how can you tell a raw egg from a hard-boiled egg?

[you can't break the shell or use light, heat, sound or X-rays]

[2] compared to a still day, will a round-trip airplane ride take more,

less or equal time if there's a constant wind blowing?

[a headwind one way, a tailwind the other way]

And there's more where that came from, boys ... have fun.

Solution: Spin the egg. Stop the egg from spinning. Let go a fraction of a second later. Watch.

Explanation: If an egg is hard-boiled, the egg exists as one, nearly, solid object. Therefore, if you stop its momentum, all of it stops. However, if the egg is raw, then it is merely a solid exterior with a liquid, semi-liquid rather, center. If you stop the momentum of the solid the liquid, semi-liquid, still maintains part of its inertia, and when you let go, the inertia continues.

[Guest]

I don't like the way ppl are thinking of this. I would say it would take the same time, because if a pilot is going into the wind, he could merely accelerate to compensate and reach the speed he desired. If there was a tailwind, he would deccerate to go the speed he desired. Unless of course you factor in the possibility that the headwind would be so strong he would not be able to accelerate through it, then yes, the times would be different. What you're assuming is the pilot would keep the throttle at the exact same position even though winds are varying. If you don't get what I'm saying maybe this will help, does modern day cruise control attempt to stay at the same throttle position, or does it attempt to stay at the same speed?

Aircraft Auto Pilots, Speed Hold, aim to keep the aircraft at a constant IAS (Indicated Air Speed), since that is where all the performance specifications are calculated from ( Stalling Speed, Maximum Flap Speed, Landing Gear Speed, Maximum Speed, Manourving Speed, etc .. ).

True Air Speed = Indicated Air Speed adjusted for air pressure, tempature, huminity, alitude etc..

Ground Speed = True Air Speed + Wind Vector

Al low level flights (<10000ft) TAS and IAS are aproximatly the same. In the high level lanes, the IAS and TAS are quite different dur to the reduction in preassure.

Asuming all the constants remain the same except for the Wind Vector though, The wind will increase( or reduce) the ground speed.This can be calculated using vector Adition (or a flight computer ) to work out the direction to point the aircraft (heading) , and therefor the groundspeed in the direction ( track ).

I agree with the previously stated, that any wind will increase the time for a round trip, however in Air travel, no one is usually concerned with round trip times

[Guest]

All of you are messed up on the airplane one. Realizing of course that it is not really an airplane we are talking about here but assuming it is.

An airplane needs a HEADWIND to be able to fly. So if you had a tail wind greater than or equal to the airplane's attempted speed, it would not fly. With a tail wind the pilot might actually have to ramp up the ground speed to keep actually flying.

Of course a head wind can be strong enough to wipe out the forward groundspeed.