I need a science whiz for some calculations.

[philipma1957]

okay I have a noontime sun  it shines downward at a 90 degree angle say at 12 noon

I have four drones holding a 10 by 10 tarp.

on the ground that tarp would have a 10 by 10 foot area of shade

so if the four drones lift the tarp 10 feet in the air the shadow will be larger than 10 by 10

how large.


and if the drones go to 20 foot high

how large is shadow.

I read a lot about shadow length calculations

cant find info on shadow expansion.

obviously for a really perfect example 12 noon on the equator.

but not necessary to be perfect.

just assume sun is at high noon shining downward on the tarp.

I used drones and 10 by 10 tarp

but it could be poles and a ten by ten tarp

or blimps and a 200 by 200 tarp if blimps the tarp could let a lot of air pass through it as long as it blocks sun.





actually a 2000 foot high set of blimps holding a 200 by 200 foot tarp makes a shadow of what size on the earth below?

 would be my question

it would be larger than 200 by 200  but how much larger?

[decodx]

The size of the shadow cast by an object is the same size as the object regardless of how high it is above the ground. That's because the sun is very far from the earth, so the sun's rays are effectively parallel when they reach the surface of Earth. The only difference you will notice is that the edges of the shadow are less sharp the further away the object is from the surface.

[philipma1957]

The size of the shadow cast by an object is the same size as the object regardless of how high it is above the ground. That's because the sun is very far from the earth, so the sun's rays are effectively parallel when they reach the surface of Earth. The only difference you will notice is that the edges of the shadow are less sharp the further away the object is from the surface.

well interesting idea,

 but why do I cast a long shadow in the morning and a short shadow in the afternoon and a long shadow in the evening.

if the sunlight was parallel the shadow would not wax and wane.



according to your idea the shadows  are exactly the size of the cloud casting them correct?





I have a reason for bringing this up. The Arctic ,Greenland and Antarctica  all have long summer days. So how hard is it to cast long shadows to cooling the melting ice. I am near latitude 45 n and for 1 hour in the morning and 1 hour in the evening I cast very long shadows.

Why can't we shade the ice during the long days of summer the sun is low and would cast very long shadows from 9pm to 3am. just saying why not.

[decodx]

The size of the shadow cast by an object is the same size as the object regardless of how high it is above the ground. That's because the sun is very far from the earth, so the sun's rays are effectively parallel when they reach the surface of Earth. The only difference you will notice is that the edges of the shadow are less sharp the further away the object is from the surface.

well interesting idea,

 but why do I cast a long shadow in the morning and a short shadow in the afternoon and a long shadow in the evening.

if the sunlight was parallel the shadow would not wax and wane.

During morning and evening, the Sun is at a low angle in the sky. This produces long shadows on horizontal surfaces. As such, shadows cast during these times are longer than those cast when its high noon. It's so obvious that I'm not sure what to explain about this. In your initial question you said "a 90 degree angle say at 12 noon".

according to your idea the shadows  are exactly the size of the cloud casting them correct?

Yes, when the Sun is directly above at 90 degrees, the shadows cast by clouds will be approximately equal in size to their own dimensions. (Only possible around the equator at midday.)

[NotFuzzyWarm]

During morning and evening, the Sun is at a low angle in the sky. This produces long shadows on horizontal surfaces. As such, shadows cast during these times are longer than those cast when its high noon. It's so obvious that I'm not sure what to explain about this. In your initial question you said "a 90 degree angle say at 12 noon".

Exactly. Your shadow is long because your head is no longer pointed at the sun so your body is not in line with the light rays. Lean over (or use a stick unless you can be propped up) so you are again pointed at the sun and the shadow shrinks again.

Now as to why the edges of a shadow get fuzzier the further away from the edge you get, that is caused by diffraction. To explain *that*, https://en.wikipedia.org/wiki/Diffraction In simplest and broadest terms it's kinda like the turbulence produced when air mores around things.

[philipma1957]

So the original thought I had was knocked out by your  response that does make sense . I knew the long shadow part would work.

which then made me switch to second part of idea. midnight sun casts very long shadows for 90 days from 9pm to 3am.

Sun is close to horizon for 6 hours of the 24 hour daylight.

So shading Greenland cap, arctic and antarctic for six hours out of 24 hours for 90 days seems cheap and easy.

Shading equator is a no go due to 90 degree angle casting small shadow.


Next part of question becomes. If sun is 10 degrees about horizon and I have a 50 by 50 foot curtain

How big is the shadow? Far larger than 50 by 50 for sure.

Finally part of question is the sun at what angle during those 6 hours of the midnight sun time.

Seems to me not that hard to shade the fuck out of those ice sheets if we want to for 90 days a year during the summer in these cases.

Am I wrong that

https://www.amazon.com/Be-Cool-Solutions-Outdoor-Canopy/dp/B079KJHZZZ/ref=sr_1_1_sspa?

setting rows of these up could shade huge sections of ice during the summer months?

So this is a cheap fix can shade huge sections of ice for what  millions of dollars? say a billion dollars and you shade 10 percent of greenland's ice cap.

[NotFuzzyWarm]

Length of the shadow is simple trig. Use http://www.carbidedepot.com/formulas-trigright.asp
You are looking for length of leg 'b'
'a' is height of shade above the ground
'A' is the angle of sun above the horizon

now 'b' is the length from away from the edge furthest away from the sun. The same effect will happen to the leading edge so with a horizontal shade, the 2 cancel out and the shadow is same size as the shade. Same size, just displaced from under it. Only if 'a' is a vertical wall do you get a long shadow.

[odolvlobo]

Now as to why the edges of a shadow get fuzzier the further away from the edge you get, that is caused by diffraction.

Sorry, the fuzziness of a shadow is not caused by diffraction. The edges are fuzzy because the sun is not a point. A solar eclipse, which is the shadow of the moon on the earth, demonstrates the effect well. In the fuzzy part of the moon's shadow, you see see a partial eclipse.

This is the appropriate wikipedia article: Umbra, penumbra and antumbra

[PowerGlove]

okay I have a noontime sun  it shines downward at a 90 degree angle say at 12 noon

I have four drones holding a 10 by 10 tarp.

on the ground that tarp would have a 10 by 10 foot area of shade

so if the four drones lift the tarp 10 feet in the air the shadow will be larger than 10 by 10

how large.

[...]

My trigonometry is pretty rusty, but here is how I would think about the problem (ignoring the curvature of the earth and soft shadow effects):

             /|\
            / | \
           /  |  \
          /   |   \
         /    |    \
        /     |     \
       /      |      \
      /       |       \
     /        |        \
    /         |         \
   /---------------------\
  /           |      |    \
 /            |      |     \
/---------------------------\

If D is the distance to the sun (about 491 billion feet) and T is the width/length of your tarp (10 feet), then at an elevation E, the angle A at the top of the above triangle [1] is: 2*atan((T/2)/(D-E))

[1] Just think in terms of inverse functions (i.e. asin/acos/atan vs. sin/cos/tan) and the SOH-CAH-TOA mnemonic (sine = opposite / hypotenuse, cosine = adjacent / hypotenuse, tangent = opposite / adjacent).

Then, to calculate how large the shadow would be, you can use: 2*tan(A/2)*D

-------------------------------------------------
| Elevation  | Angle (radians)  | Shadow length |
------------------------------------------------
| 10 feet    | 2.0366598778e-11 | 10.0000000002 |
| 100 feet   | 2.0366598782e-11 | 10.0000000020 |
| 1000 feet  | 2.0366598819e-11 | 10.0000000204 |
| 10000 feet | 2.0366599193e-11 | 10.0000002037 |
-------------------------------------------------

As you can see, the size of the shadow isn't meaningfully affected by the elevation of the tarp because of how small the angle is (due to the distance between us and the sun). Even if you placed the tarp as far away as the moon (about 1.3 billion feet) the shadow would still be ~10.027 feet (i.e. the shadow would only be bigger by about 1/3 of an inch).

Here's some rough python code for the table above, in case you'd like to experiment:

Code:

import math

def noonShadow(elevation, tarpLength=10):

    distanceToSun = 491 * 1000 * 1000 * 1000

    angle = 2 * math.atan((tarpLength / 2) / (distanceToSun - elevation))

    shadowLength = 2 * math.tan(angle / 2) * distanceToSun

    return (elevation, angle, shadowLength)

print(noonShadow(10))

print(noonShadow(100))

print(noonShadow(1000))

print(noonShadow(10000))

[NotFuzzyWarm]

Now as to why the edges of a shadow get fuzzier the further away from the edge you get, that is caused by diffraction.

Sorry, the fuzziness of a shadow is not caused by diffraction. The edges are fuzzy because the sun is not a point. A solar eclipse, which is the shadow of the moon on the earth, demonstrates the effect well. In the fuzzy part of the moon's shadow, you see see a partial eclipse.

This is the appropriate wikipedia article: Umbra, penumbra and antumbra

Umbra etc are the names of the regions of shadow but I stand by the effect itself being caused by diffraction. Specifically what is caused by a knife-edge - in this case the edge of the tarp - as light is partly occluded as it passes by the edge. https://en.wikipedia.org/wiki/Diffraction#%22Knife_edge%22.

For all intents & purposes of the OP the light coming from the Sun is reasonably collimated due to the distance from us. Yes it is a disk but a point source has nothing to do with it. Back in 1975 while in the Air Force I did several installations of C3 relay sites that used diffraction 'scatter' from beaming microwaves over mountain ridges to link with sites that were on the other side in the shadow of the ridges/mountains. A microwave dish is hardly a point source emitter but *is* highly directional. As long as about 1/3 of the microwave beam actually hit the ridge line the scatter had enough strength to be easily received as close as 1mile from the ridge and up to about 20miles away from it.

[odolvlobo]

Now as to why the edges of a shadow get fuzzier the further away from the edge you get, that is caused by diffraction.

Sorry, the fuzziness of a shadow is not caused by diffraction. The edges are fuzzy because the sun is not a point. A solar eclipse, which is the shadow of the moon on the earth, demonstrates the effect well. In the fuzzy part of the moon's shadow, you see see a partial eclipse.

This is the appropriate wikipedia article: Umbra, penumbra and antumbra

Umbra etc are the names of the regions of shadow but I stand by the effect itself being caused by diffraction. Specifically what is caused by a knife-edge - in this case the edge of the tarp - as light is partly occluded as it passes by the edge. https://en.wikipedia.org/wiki/Diffraction#%22Knife_edge%22.

For all intents & purposes of the OP the light coming from the Sun is reasonably collimated due to the distance from us. Yes it is a disk but a point source has nothing to do with it. Back in 1975 while in the Air Force I did several installations of C3 relay sites that used diffraction 'scatter' from beaming microwaves over mountain ridges to link with sites that were on the other side in the shadow of the ridges/mountains. A microwave dish is hardly a point source emitter but *is* highly directional. As long as about 1/3 of the microwave beam actually hit the ridge line the scatter had enough strength to be easily received as close as 1mile from the ridge and up to about 20miles away from it.

Of course there is some diffraction, but it is negligible in this case. The fuzziness of the shadows that we see are caused by the apparent size of the sun. I don't doubt your microwave diffraction experience, but the the wavelength of visible light is 400 - 700 nm and the wavelength of microwaves is 150000000 - 300000000 nm. That difference in wavelengths has a huge effect on diffraction.

Try this: view a shadow of yourself on a wall when lit with a larger source like a lightbulb and when lit by a smaller source like a phone's flash, both at the same distance. You will see a difference due to the change in the the size of the light.

Ask any photographer and they will tell you that the size of the light determines the softness of the shadows.

[PowerGlove]

Now as to why the edges of a shadow get fuzzier the further away from the edge you get, that is caused by diffraction. [...]

Sorry, the fuzziness of a shadow is not caused by diffraction. The edges are fuzzy because the sun is not a point. [...]

Umbra etc are the names of the regions of shadow but I stand by the effect itself being caused by diffraction. [...]

In image synthesis (ray tracing), soft shadows show up as soon as you start sampling the light sources in more than one position (i.e. not treating them as points). Unless I'm missing something obvious (wouldn't be the first time) I agree with @odolvlobo that diffraction isn't the right physical mechanism to be thinking about at these wavelengths. If you wanted to synthesize pedantically realistic images, then you'd have to account for diffraction, but as an explanation for why shadows don't have hard edges, I don't think it's the right one.

[decodx]

I also agree with @odolvlobo on this. The fuzziness of the shadow edges in daylight is caused mainly because the light source is not a point, but also because there is an effect called Rayleigh scattering. In short, due to the scattering of the sun's rays in our atmosphere, the whole atmosphere acts as a secondary light source.

[odolvlobo]

I would also like to point out that although it is commonly said that the rays from the sun are parallel, the ray are actually approximately parallel. If the rays were perfectly parallel, then shadows would be sharp (except for the small amount of fuzziness caused by diffraction).

I also agree with @odolvlobo on this. The fuzziness of the shadow edges in daylight is caused mainly because the light source is not a point, but also because there is an effect called Rayleigh scattering. In short, due to the scattering of the sun's rays in our atmosphere, the whole atmosphere acts as a secondary light source.

The light from the sky doesn't contribute to the fuzziness of shadows, but it does explain why shadows are not completely dark. Since the light in a shadow cannot come from the sun, it must come from elsewhere, such as the sky and reflection off of surrounding surfaces. The light from the sky is what makes things in shadow look a little blue.

[philipma1957]

So the original thought I had was knocked out by your  response that does make sense . I knew the long shadow part would work.

which then made me switch to second part of idea. midnight sun casts very long shadows for 90 days from 9pm to 3am.

Sun is close to horizon for 6 hours of the 24 hour daylight.

So shading Greenland cap, arctic and antarctic for six hours out of 24 hours for 90 days seems cheap and easy.

Shading equator is a no go due to 90 degree angle casting small shadow.


Next part of question becomes. If sun is 10 degrees about horizon and I have a 50 by 50 foot curtain

How big is the shadow? Far larger than 50 by 50 for sure.

Finally part of question is the sun at what angle during those 6 hours of the midnight sun time.

Seems to me not that hard to shade the fuck out of those ice sheets if we want to for 90 days a year during the summer in these cases.

Am I wrong that

https://www.amazon.com/Be-Cool-Solutions-Outdoor-Canopy/dp/B079KJHZZZ/ref=sr_1_1_sspa?

setting rows of these up could shade huge sections of ice during the summer months?

So this is a cheap fix can shade huge sections of ice for what  millions of dollars? say a billion dollars and you shade 10 percent of greenland's ice cap.

Lots of nice info on why shading the pacific at the equator will not work.


But the second part of shading the icecaps and Greenland, for 6 of 24 hours during the summers seems more possible.

We have all seen the long shadows in the morning and the evening correct?

and the angle would be much different.

So I need to find angle of the sun during midnight suntime?

To see if it magnifies the shadows cast by the white shade cloth I linked here.

https://www.amazon.com/Be-Cool-Solutions-Outdoor-Canopy/dp/B079KJHZZZ/ref=sr_1_1_sspa?

if a 20 foot high cloth wall casts a 200 foot shadow and costs 10000 usd to make a mile long

26 of those walls make 1 square mile $250,000

104 make 4 square miles about 1 million bucks

4000 square miles about 1 billion bucks

400000 square miles about 100 billion bucks and ½ the size of Greenland gets 6 or more hours of shade during the midnight sun.