Re: How does a spirit (carpenter's) level work?

Hi! I'm sorry this has taken so long to get answered, but your question has been sent to several of our scientists and nobody seems to be able to completely understand the question well enough to answer it!! But I am going to take a stab at answering.

I think I understand the question: A line level (or carpenter's level) uses a line to mark level. But we live on a sphere (the earth), so how can a level line give a true level?

Actually, the answer to the question is that the line indicates a tangent to the earth! That is, if the line is truly a straight line then the ends of the line farthest from the level (which is usually at the center of the line) are not at the same distance from the center of the earth as the level is. But for the kinds of things that a line level is used for the error is ridiculously small, so we can ignore the departures.

Let's run some numbers to see how big (or small!!) the "error" is. Assume the radius of the earth is 4000 miles (roughly!), and that the line to which the line level is attached is 200 feet long. Assume also that the level is in the middle of the line. We assume the line is tight enough to not sag. So the level is 4000 * 5280 feet = 21,120,000 feet from the center of the earth, and each end of the line is 100 feet from the level. Since the angle between the line and the radius of the earth is a right angle all we have to do is calculate the hypotenuse, which comes out, on my calculator, to 21,120,000.00023674 feet, which is only 0.00023674 feet longer than the radius of the earth. So the ends of the line are only about 0.0028 inches higher (with respect to the center of the earth) than the level, and this error is insignificant compared to the types of things we use line levels to measure!

I do hope this helps!

John Link
MadSci Scientist