Example: Cut Volume Mars Habitat 1

Lets say you’re thinking of building a habitat on Mars. How much dirt do you need to move? Before you get bogged down in the calculus, consider the method many engineers use. The method is called Average End Area. It is especially good for irregular shapes like those found in the real world. In this example, let’s assume that the habitat is roughly spherical and the surrounding mound of dirt slopes from midway up the sphere to original ground. Start with a contour map of the site you want to build on. Then plot the contours of the inside of the sphere up to the top of the surrounding mound, then down to original ground. Now you need to determine the area inside each contour. If you’re working on graph paper, you can count squares. Make a table with the elevation and areas (square feet), average between the elevations, multiply by the difference in elevation (between contours, dFt), and add these numbers.

Make one table for dirt below original ground, and another for dirt above original ground. The dirt below is called “cut”. The dirt above is called “fill”. Some of your fill can be from the cut. See how close you can make the cut and fill to each other by adjusting the elevation of the base of the sphere.