When 90 degrees is taken from any degree of angle other than true vertical, aka plumb, aka no slope, the 90 degree angle will not be true horizontal, aka no slope.

Therefore it will not be level when you hold a level up to it.

Now let's take a look at what one degree difference would be 69.4 miles away from true plumb aka vertical.

Yes, that's why I said you don't measure plumb based on something farther away. You measure it based on local plumb.

However, when you're building something where there's a significant enough angle between the radials at either end of what you're building, for example, with the Golden Gate Bridge, you have to account for that difference.

Q. Looking for some help figuring out how to calculate distance equivalent to degrees.

e.g.: If I have a 2 degree tolerance for perpendicularity at 20" from the joint how much is 2 degrees in inches?

how would I figure out the given tolerance in inches over a given distance.

ex: 2 degrees at 20", 4 degrees at 20 inches etc.

Thank you everyone for your help

A. By dickDate 05-08-2015 03:32

miracle point (angle-pitch) 2 degrees =.035 per inch .035x20= .7inch, 4 degrees =.07 per inch .07x20=1.4 inch

1 degree angle = .0175 pitch per inch or .210 inch per foot

No idea what you're trying to prove here, but it isn't helping your position.

Now if I build a cabinet 2 feet high by 8 feet long at true plumb and horizontal and haul it 69.4 miles away to where your house's ceilings and walls are one degree out it will be crooked.

No, it won't be, because it will be pulled level (assuming you built it correctly) by the local radial, the plumb line.

The only way it will be crooked is if you intentionally hang it crooked.

2 x .210 = 0.42 That's almost a 1/2 inch out from the corner.

8 x .210 = 1.68 That's almost 1 3/4 inches out from the ceiling.

Try getting paid after hanging a cabinet like that.

Try getting a job period when you can't understand that you don't build small things based on level measurements 70 miles away. No one will hire you because they'll think you're an idiot who doesn't know what he's talking about, because you ARE an idiot who doesn't know what he's talking about.

If you build a cabinet, and it hangs level, and you travel 70 miles away to hang it up, both you and the cabinet have moved to a different radial, and are no longer at the radial you were at when you initially built the cabinet. Both you and the cabinet have rotated the same amount as the surface of the earth, and are still vertical, because verticality is based on location, and is not the same in all locations. The only way in which it is the same is that they all point "down" to the same center of mass.

If you have a sphere of some sort at your home, say, a basket ball or soccer ball, get it out, take a pen or pencil, and hold the writing utensil so that it is upright, "vertical" on top of the ball. Now move the pen or pencil around the outside of the ball to a different location, it doesn't matter where, keeping the pen or pencil aligned to the center of the ball.

At both the starting point of the pen or pencil, and at the end point, the pencil was "vertical" relative to the ball. (NO, it was not vertical relative to YOU, OBVIOUSLY, so don't be dumb and make some idiotic comment about it not actually being vertical, because I'm trying to demonstrate something at a scale that you can understand!)

It was vertical at both locations because verticality is defined by 90 degrees from horizontal, which is the plane tangential to the surface of the ball, tangential meaning that it is the ONLY plane that intersects the sphere at one and only one point, with all other concentric points around it being equally distant from the plane. There are an infinite number of "horizontal" planes on any given sphere, just as there are an infinite number of tangents on any given circle. All of them are, by definition, perpendicular to the radial that intersects that same point that it intersects.

When you move from one point to a different point, the new radial is now the vertical one, and the first one is no longer vertical to you. I repeat, THE FIRST radial is no longer vertical

**TO YOU**. It is still absolutely (iow, "in the absolute sense") vertical in its own location, but it is not vertical relative to other radials.

This is how it works, 1m1s. If you cannot comprehend this, then I pity you.

If you REFUSE to comprehend, however, then you are a fool, and I have no pity for you.