Loosely inspired be this thread:
Imagine you are making a really large flat area. Laser flat, not bubble level flat. At what point in size would it start to feel like a bowl, because it is separating from the ideal shape of surface of the Earth?
Or a tunnel going laser straight from A to distant B. At some length, it would feel as a downslope up to the middle (where it is closer to the center of the Earth) and the back up to the surface). At what length does this start being an issue?
If you walk 111.3 km out from the point where your flat surface is tangent to and touching the earth, gravity will tilt you 1° from perpendicular to the surface of the plane.
That’s more than enough of a slope to run an aqueduct:
Can you feel a 1 degree slope walking on it?
I’d think you could, if the distance was long enough. The tangent of one degree is 0.0175, so for every foot of distance travelled, you’d be elevated 0.21 inches. That’s a grade of 1.75%, which is just noticeable
Definitely. You could see it too. Imagine if one goal line on a 300’ football field was 3’ higher than the other.
From a quick google search it looks like 2% is a high grade for a train to climb.
Those massive climbs that you see the skinny guys on bikes suffering up are not generally much more than 5% on average. 10% or more is “beyond categories”.
ETA: Oh I mistook degrees for percent. 1.75% is even more noticeable.
If you did a straight tunnel 111.3 Km long (as per Squink’s post), how deep would it go if both ends were at the same ground level?
Radius of Earth = 6378.1 km (love how Google search gives that answer directly). Half of 111.3 is 55.65. Throw it into Pythagoras’s equation and you get a depth at the midpoint of 243m.
So we are talking a tunnel longer and deeper than any existing tunnel. So much for my idea of a tourist attraction.
Longer yes, deeper no. The Eiksund Tunnel in Norway goes 287m deep. It’s less than 8km long, though.
A straight tunnel like that can be used (at least in theory) to make a “Gravity Train” which (again, in theory) is very fuel-efficient and results in a 42-minute ride, no matter how far you go.
http://www.time.com/time/magazine/article/0,9171,842469,00.html
http://www.bbc.co.uk/dna/h2g2/A2960633
Gravity train - Wikipedia (the image here is misleading, as the idea is to go from any point to any other point, not just to the one that is directly on the opposite side of the planet)
I don’t see how this 42’ ride comes to happen. In the 111 Km example above, it looks like the acceleration would be very slow with only a 1 degree incline.
Constant acceleration is a deceptive thing. If my math is correct, with no friction a 1 degree incline will give you acceleration of 0.17m[sup]2[/sup]. After the first minute, you’ll be doing 10.2m/sec or about 36km/hr. After the first 5 minutes, 61m/sec or about 217 km/h. At the halfway point, after 21 minutes you’d be doing 214m/sec or 771km/hr.
True. Although the acceleration is not constant as the track flattens as it advances. Still, I agree that compound interest adds up quick.
Oh. Missed that, you’re right.
Another error I think is that you are misapplying Squink’s figure. It would actually be about 220km through a tunnel that lead down by 1 degree. His figure is half what it would take to go down and up.
Still, with constant albeit reducing acceleration, you can see how you get to an average high enough to get the distance in 42min.
I think the question as asked makes little sense, if any, but let me try. Since the OP mentions a flat area let us imagine we are just cutting off a cap of the earth with a plane laser and so we get a flat plane as a result. In the center of that plane the vertical will be perpendicular to it and, well, the ground will be horizontal, defining horizontal as perpendicular to vertical.
As you move towards the edge the effect will grow and will be greatest at the edge where the angle between the ground plane and vertical will be at its greatest difference from 90º. But to experience this you do not need the entire plane at all. You only need the very edge. In other words it’s just a slope. Any slope you choose.