Bedford Level Experiment - Geography

[Haswellx86]

Had my Geography exam today, and this logical question has been zooming around my brain since yesterday. If you don't know, In the Bedford Level experiment, 3 poles with the same length were planted with a distance of 5km to each other in Bedford canal, England. After viewing by a Theodolite (precise telescope), the middle pole stood out longer than the rest of the two poles, stating the fact that the Earth is circular. But the way they planted the poles, shouldn't be possible (see the image attached). Because how gravity and the Earth's curvature works, the 2 poles should be planted in a slanting way when seen from the side view. Thus, all the poles should align in an equal radius and should see as having equal length. But the simplified diagram they have shown is only possible in 2 ways, if hypothetically (which is not possible because this is a real experiment), those poles were planted without being altered by the gravity and deny the declination of the terrain. The second way will be to account for the physical declination of the terrain and slant the poles themselves, so they are perfectly straight as the middle pole, which sounds a bit ridiculous.

[tikker]

On 2/16/2023 at 8:12 PM, NvidiaFirePro6900XXTX3DPRO said:

Thus, all the poles should align in an equal radius and should see as having equal length.

They are an equal height above the surface at their respective locations. Your vision doesn't curve along with Earth, so the actual heights at which you will see the poles at will be different, which the top half of the diagram illustrates. We can try a back of the envelop estimate to see what difference accounting for the change in angle would make. The Earth's circumference is ~40,000 km, spanning the 360 degrees of a circle. Over 5 km that means the angle of a pole perpendicular to the surface will have changed by 5 / 40,000 th of a degree, or 0.000125 degrees. With some triangle math we have

tan(angle) = <vertical change> / <line-of-sight distance>, 

 

or with some rearranging:

<vertical change> = <line-of-sight distance> * tan(angle)
                    = 5 km * tan(0.000125 deg)
                    = 1.1 * 10^-5 km
                    = 1.1 cm

So the change of our line of sight perpendicular to the pole we are looking through, on a perfect sphere, amounts to just over 1 centimetre change at the other pole. Meanwhile, the actual change in height due to curvature can be calculated to be 1.96 m over a 5 km distance. Based on these estimates, you can make relatively large holes to account for any errors in placement while still getting noticeable change in height.

[dalekphalm]

On 2/16/2023 at 2:12 PM, NvidiaFirePro6900XXTX3DPRO said:

Had my Geography exam today, and this logical question has been zooming around my brain since yesterday. If you don't know, In the Bedford Level experiment, 3 poles with the same length were planted with a distance of 5km to each other in Bedford canal, England. After viewing by a Theodolite (precise telescope), the middle pole stood out longer than the rest of the two poles, stating the fact that the Earth is circular. But the way they planted the poles, shouldn't be possible (see the image attached). Because how gravity and the Earth's curvature works, the 2 poles should be planted in a slanting way when seen from the side view. Thus, all the poles should align in an equal radius and should see as having equal length. But the simplified diagram they have shown is only possible in 2 ways, if hypothetically (which is not possible because this is a real experiment), those poles were planted without being altered by the gravity and deny the declination of the terrain. The second way will be to account for the physical declination of the terrain and slant the poles themselves, so they are perfectly straight as the middle pole, which sounds a bit ridiculous.

IMO the top diagram is simply ignoring the change of angle due to the placement of each pole along the curve. The curve is also likely accentuated (eg: Not to scale) in that diagram.

 

And as @tikker pointed out, the differences due to the angle due to the curve are essentially negligible over 5km. The outside poles would be slanted 1/8000th of a degree away from the center pole, on either side. I doubt you could even see 1/8000th of a degree slant with your naked eye.

[Haswellx86]

@tikkerSo basically, the poles do slant, but it is not enough to cancel out the height difference? Also, I used to think that our vision does bend if Earth's curvature, but I guess not. If not, then how don't we see the space by just looking forward? If not with naked eyes, then with a telescope? 

[dalekphalm]

Just now, NvidiaFirePro6900XXTX3DPRO said:

@tikkerSo basically, the poles do slant, but it is not enough to cancel out the height difference?

This is correct. The height difference from the curve is 178 times larger than the height difference caused by the angle.

Just now, NvidiaFirePro6900XXTX3DPRO said:

Also, I used to think that our vision does bend if Earth's curvature, but I guess not. If not, then how don't we see the space by just looking forward? If not with naked eyes, then with a telescope? 

Your eyes see straight. You can't see space by looking forward for the same reason you can't see space when looking straight up... You're looking at the atmosphere in both cases.

 

On the flip side, on a clear sky during the middle of the night (assuming no light pollution), you can see "space" by "just looking forward". Anything above the horizon is space. Now, space closer to the horizon are harder to see because you're looking through a LOT more atmosphere, which degrades and distorts the image.

 

If your sight curved with the earth, you'd be able to see around the curve, and you'd be able to see much farther than you can. You cannot do this.

[tikker]

25 minutes ago, NvidiaFirePro6900XXTX3DPRO said:

@tikkerSo basically, the poles do slant, but it is not enough to cancel out the height difference?

The height difference comes from the fact that Earth's surface curves downward away from you. The slanting of the poles affects the direction you look in, and thus by extension what you can see. For tiny holes you would have to take into account all the small variations from local terrain, slant etc. but if you make the hole big enough then, since the Earth is so big, they don't matter much over such relatively small distances.

25 minutes ago, NvidiaFirePro6900XXTX3DPRO said:

Also, I used to think that our vision does bend if Earth's curvature, but I guess not.

A textbook example of this is watching ships near the horizon. If our vision would bend with Earth's curvature you would not see ships disappear over the horizon. The fact that ships do slowly "sink" below the horizon as they travel away from you tells you that Earth's surface is curved and that our vision doesn't follow that curve. There are exceptions to this due to the atmosphere though. Atmospheric refraction allows you to see objects that are technically below the horizon.

25 minutes ago, NvidiaFirePro6900XXTX3DPRO said:

If not, then how don't we see the space by just looking forward? If not with naked eyes, then with a telescope?

You can. During the day, sunlight refracting and scattering in the atmosphere drowns out all light from space. That's why you don't see any stars during daytime. During the night, there are still other problems as you get closer to the horizon. One is that you have to watch through more of the atmosphere if you look more parallel to the ground (towards the horizon). This higher mass of air between you and space (which is aptly "air mass") will scatter or absorb more light, making it harder to see the faint stuff in space. This is also the reason why sunsets turn orange-red: the increased atmosphere light passes through causes most of the blue light to be scattered away from your eyes. The Moon has no atmosphere, which is why the "sky" on the Moon appears black.

 

Another reason is that our cities are causing a lot of light pollution. All our city lights are effectively creating the same problem that sunlight causes during the day. Man made light near the surface simply drowns out all the faint stuff from space. This even holds for looking straight up. You will see way less stars in a city with lights everywhere compared to a rural area with little to no light.

[Blue4130]

If sight curved, and eyes were powerful enough, you would be able to see yourself.

[IkeaGnome]

13 minutes ago, Blue4130 said:

If sight curved, and eyes were powerful enough, you would be able to see yourself.

This brings new meaning to the term "You better watch your a... rear"