I’ve never actually understood his water level experiment and how it 100% proves the earth is not a globe
I feel a bit thick to be fair like
In some ways the theory is sound, but scale and accuracy screw it up.
A spirit level on water that is perfectly level will essentially sit on the tangent to the curve of the earth. Imagine sticking a 50cm spirit level on a football and balancing it. That is what you get only the earth is much bigger than a football. So if the football curves away then logically the earth will too. Being on water doesn't actually matter at this stage, but it stops the terrain of the earth being a problem.
So how much will the earth curve away by? Lets scale it up and go with a 2 meter long spirit level to ease calculation, that is 0.002km long, but if the middle of it is the point sitting on the earth then you are looking at a drop over half the length so we want to know what the drop is over 0.001km.
The formula for calculating the height of the drop from level is
h = r - r * cos (d / r)
h is the height of the drop, our magic number to observe
r is the radius of the planet (or ball), in this case 6,371km
d is the distance along the ground.
If you try this on a smaller scale with a football it works, but also works on the scale of a planet. That is the beauty of maths, we are just talking about a straight line on a sphere or because the line is a 2d object, we can slice the sphere and go with a circle.
Sticking these figures into the formula gives us a drop in height due to the curve of the earth of
= 6371 - 6371 * cos (0.001 / 6371)
= 0.00000 km
Well clearly that is not right, so lets multiply by 1000 to give the answer in meters. After all, we measured our spirit level in meters so lets see if that gives us a better figure.
= 0.0000000782165 meters
Oh, erm what does that mean? Lets multiply by 1000 again to give millimetres.
= 0.00007821654 mm
A human hair is about 0.06. So here we are trying to fit a 2m builders spirit level (accuracy of about 0.5 degrees) in a bath, trying to measure the curve of the earth and we are looking to see if we can see a drop 1000 times narrower than a human hair. Still not working is it? Lets disregard the surface tension and slight attractive force seen in water, like when you hold your finger just above the surface of the water it will curve up and seem to cling around your finger end. That just makes trying to see anything impossible.
So rather than laugh, lets think again. What is a reasonable distance to be able to detect with the naked eye, assuming we have our spirit level absolutely perfectly level and it is 100% accurate? 4mm should be easy enough to see. That allows us to rephrase the question as:
If we place the centre a spirit level perfectly level on the surface of an absolutely still body of water, then how long would it need to be before we can detect a drop of 4mm?
If we rearrange our equation then we get:
d (distance on ground) = r * acos ( (r-h) / r)
But we need to remember to work in the same units, in this case back to km. Only a nutter would put mm in one part of an equation and km in another. It would be like having miles and inches in the same equation - just plain wrong. So a drop in height of 4mm is 0.004m and 0.000004 km. Sticking these in an equation it gives us a result of 0.22576 km. That looks like a reasonable number, or multiply by 1000 to give us a result in meters, and we get 225.76 meters.
That is a length we can work with. But remember it was the middle of the spirit level that was on the water, so we need to double that figure.
Our experiment means that to calculate a drop of 4mm, enough to be detected by the naked eye, we would need a really accurate spirit level of 451.52 meters long. Rather ironically trying to put that distance into a scale we can visualise, then it is almost exact to the meter the walking distance between the Cooper Rose Wetherspoons at the top of Holmside and the William Jameson Wetherspoons at the bottom.
My local screwfix is sold out of such an instrument.
So before you laugh too much at his experiment, remember that the logic is sound, you just need the scale and accuracy to match something that is measurable and now we know a reasonable length spirit level to start with. Who is up for giving it a go?
