[Guest]

A medium-size jet has a wingspan of 120 feet. An albatross is a bird with a wingspan of about 12 feet. At what altitude would each object have to fly in order to cast shadows of equal size?

[curr3nt]

Does it matter that the albatross shadow would not be visible to the human eye?

[Guest]

Depends on the question, if only the wings are different they can both cast the same shadow by turnning and making their wing parallel to the sun-light, (as in turn 90° if it's mid-noon)

Or you could wait until night where they make no shadows...

or you can have one fly under the other so they make the same shadow...

[Guest]

I am sure we all understand what OP is trying to say. At what altitude does each have to fly in order for the wingspans (horizontal and fully extended) need to be in order for them to be equal in length when viewed on the ground.

I got they need to be 144' apart from each other.

Edited March 25, 2011 by kkehoe5

[Guest]

The Sun's rays, for all Earthly intents and purposes, are parallel.

[Guest]

We know the Moon is much larger then the tiny focused dot that appears on Earth during a Solar Eclipse.

The Sun's rays, for all Earthly intents and purposes, are parallel.

Edited March 25, 2011 by kkehoe5

[Guest]

We know the Moon is much larger then the tiny focused dot that appears on Earth during a Solar Eclipse.

Right-- however the moon is also a lot farther away than either an albatross or a plane could fly. A plane's shadow changes size very little with altitude, that is why d3k3 says the rays are parallel. They aren't exactly, but might as well be in this case because the bird would pass out and the plane would stall before either got to an altitude that would make any noticeable difference.

[Guest]

First, as d3k3 stated, on Earth sunlight is parallel, which means, that no matter the height you're flying at, you will always cast the same shadow. So you must fly way beyond the Earth's boundaries to be capable of casting a larger shadow. However, the bird should be flying higher than the jet.

The only thing left is to wait for nightfall or make the albatross fly under the jet.

[Guest]

It seems like whatever distance the albatross flies from the sun, the jet will have to be 10 times farther from the sun.

[Guest]

One will be at an altitude that is half the distance to the sun from the other.

If the sun is considered large then the formula is

(distance to sun - jet)/2 = albatross.

If the sun is considered a point, then the formula is

(distance to sun - albatross)/2 = jet.

[Guest]

Oops got my numbers wrong at the beginning. After looking at it again I have to agree that if you consider the sun to be large then the jet would have to be ten times higher than the albatross.

[Guest]

Wouldn't the time of day affect the shadow?

[Guest]

Assuming the sun is a small point (which it is not!) the albatross needs to be 90% of the distance to the sun, about 9.3 million miles above the earth. Call Icarus. Nice puzzle.

[Guest]

They don't both have to fly parallel to the sunlight. If the plane alone flew at a roll angle of 84.26 degree, while the albatross remains parallel to the ground, they could fly at the same altitude and cast the same shadow.

Depends on the question, if only the wings are different they can both cast the same shadow by turnning and making their wing parallel to the sun-light, (as in turn 90° if it's mid-noon)

Or you could wait until night where they make no shadows...

or you can have one fly under the other so they make the same shadow...

[fabpig]

So if I'm standing under the wings of a jet plane (on the ground) in the shadow, no matter how high that jet goes, I'll still be in the shadow?

[fabpig]

addenda to the above:

Imagine a jet silhouetted against the sun so that wing tip to wing tip appeared to be the same size as the diameter of the sun, at what height would the albatross have to be (relative to the jet) to give the same effect?

Edited March 26, 2011 by fabpig

[Guest]

Depends on the question, if only the wings are different they can both cast the same shadow by turnning and making their wing parallel to the sun-light, (as in turn 90° if it's mid-noon)

Or you could wait until night where they make no shadows...

or you can have one fly under the other so they make the same shadow...

no

[Guest]

They can never cast shadows of equal size

Any difference in their altitude would be negligible compared to their distance to the sun. It's those 93,000,000 miles from our planet to the sun that affect the shadows' size much more than their puny distances apart.

A medium-size jet has a wingspan of 120 feet. An albatross is a bird with a wingspan of about 12 feet. At what altitude would each object have to fly in order to cast shadows of equal size?

[Guest]

I meant 9.3 million miles from the sun, or 83.7 million miles from the earth.

[Guest]

when the albatross is flying and the jet is still, use an internal source of light (a lamp) and adjust it so that the albatross' shadow covers the jet

[plasmid]

It doesn't require a lot of experimentation in real life to realize that an object's shadow does indeed seem to become smaller as the object is raised higher from the ground, so I dismiss everyone who argues that the shadow sizes will not significantly change, because their assertion can be experimentally disproven.

I strongly suspect that the shadows become smaller at higher altitudes mostly because not all of the light that hits the ground (and therefore affects the appearance of the shadow) comes from a direct linear path from the sun. Much of it is scattered by the atmosphere (which makes the daytime sky appear blue instead of the blackness of outer space) or say a nearby tree whose leaves reflect some of the green light that hits them. This scattering will lead to an increasingly fuzzy shadow as the object is raised higher, and the amount of scattered light will be very dependent on what's in the environment, and practically impossible to calculate a priori.

So the answer to your question is: it depends to too many variables to answer as a riddle. But if you want to go conduct the experiment with pieces of paper cut to varying sizes, and then extrapolate what it would come out to with an albatross versus a jet, then go for it and let us know the answer

[Guest]

At a great height

we all know that the closer the object to the screen ,the smaller and well defined is the shadow thus the size of the umbra becomes smaller and smaller if the screen is moved farther and farther from the light source and the object the result is larger and fainter penumbra thus they both will never cast a shadow on the surface ,so 0=0 DRAW

[fabpig]

It doesn't require a lot of experimentation in real life to realize that an object's shadow does indeed seem to become smaller as the object is raised higher from the ground, so I dismiss everyone who argues that the shadow sizes will not significantly change, because their assertion can be experimentally disproven.

I strongly suspect that the shadows become smaller at higher altitudes mostly because not all of the light that hits the ground (and therefore affects the appearance of the shadow) comes from a direct linear path from the sun. Much of it is scattered by the atmosphere (which makes the daytime sky appear blue instead of the blackness of outer space) or say a nearby tree whose leaves reflect some of the green light that hits them. This scattering will lead to an increasingly fuzzy shadow as the object is raised higher, and the amount of scattered light will be very dependent on what's in the environment, and practically impossible to calculate a priori.

So the answer to your question is: it depends to too many variables to answer as a riddle. But if you want to go conduct the experiment with pieces of paper cut to varying sizes, and then extrapolate what it would come out to with an albatross versus a jet, then go for it and let us know the answer

Thanks, Plas. I was beginning to think I was in a minority of 1. I've been assuming that by "shadow", umbra is intended. Now if we substitute discs for the plane and the bird, we could put the 12ft disc on the ground and it would obviously create a 12ft shadow! Without doing any calculations, I suspect that the 120ft disc would not have to be that high (certainly not as high as being suggested) to create a 12ft shadow. In fact, 120ft is miniscule compared to the diameter of the sun and I don't think such a disc would have to be particularly high to go antumbral (ie create an annular eclipse). But I'm open to persuasion by numbers.

(I'm taking the sun to be overhead and light scattering to be nil)

[superprismatic]

Well, I tried Plasmid's experiment. I placed a white piece of cardboard in such a way that its

perpendicular pointed roughly at the sun. Then I took a foot-long stick, placed it on the cardboard

and marked the cardboard at the end of the stick. Then I moved it about 10 feet away and its

shadow still hit those marks, indicating that the shadow's length didn't change. I wasn't willing

to get up a tree or on the roof to get a larger distance. So, I think d3k3 is right, and this is

born out by my little experiment.

[plasmid]

Well, I tried Plasmid's experiment. I placed a white piece of cardboard in such a way that its

perpendicular pointed roughly at the sun. Then I took a foot-long stick, placed it on the cardboard

and marked the cardboard at the end of the stick. Then I moved it about 10 feet away and its

shadow still hit those marks, indicating that the shadow's length didn't change. I wasn't willing

to get up a tree or on the roof to get a larger distance. So, I think d3k3 is right, and this is

born out by my little experiment.

After doing some Google Image searching, I have to agree with you - there can be virtually no such scattering complicating the picture in areas where there is not always significant cloud cover. However fabpig has a good point, so I also don't agree with d3k3's call of shenanigans due to the following two facts, and I revise my own answer.

diameter of sun = 1.4 million km

distance to sun (on average) = 150 million km

Edited March 28, 2011 by plasmid

[Guest]

diameter of sun = 1.4 million km

distance to sun (on average) = 150 million km

Well, OK, if you want to be all technical, the Sun's angular size is roughly 30 arc-minutes. So, technically, if the albatross is on the ground, casting a 12 ft. shadow, the airplane will cast an umbra of the same size at roughly 11,600 ft. However, at that altitude, its penumbra will be 19 times larger, so we're talking about something that looks extremely fuzzy at best. You're definitely not going to be able to trace the edge of the umbra without some extremely sensitive equipment that probably doesn't exist. Also, we're considering the airplane to be a disk. A real airplane would cast no umbra at all at that altitude, since no part of it is more than about 30 ft. across at any point. I highly doubt any part of its penumbra would be visible to the naked eye. So... shenanigans.