GEOMETRY

PROBLEM 5.

The largest component of the prelaunch Space Shuttle configuration Is the external tank, which serves as the "gas tank" for the Orbiterčit contains the propellants used by the main engines. Approximately 8.5 minutes after launch, when most of the propellants have been used, the external tank is jettisoned. It is the only major part of the Space Shuttle that is not reused.

Fig 4.4(a) shows the launch configuration with the back view of the Orbiter, and Fig. 4.4(b) shows the side view. Fig. 4.5(a), (b), and (c) show the liquid hydrogen tank, the intertank, and the liquid oxygen tank, respectively. The intertank serves as a mechanical connector between the liquid oxygen and liquid hydrogen tanks, and contains the upper dome of the liquid hydrogen tank and the lower dome of the liquid oxygen tank.

a. Using the dimensions provided in the diagrams, estimate the volume of each of the tanks by dividing the tanks into shapes whose volumes are easy to compute.

Solution: (This is one possible solution.) The liquid hydrogen tank has the shape of a cylinder with ellipsoidal caps on each end. Since the formula for the volume of a hemisphere is better known, let us approximate the domes as hemispheres. Now the total length of the tank is given as 29.6 m, and the diameter as 8.4 m; our approximation, then, consists of two hemispheres (or a single sphere) of radius 4.2 m and a cylinder of radius 4.2 m and length 29.6 - 8.4 = 21.2 m. The resulting volume estimate is:

GEOMETRY GRAPHIC 5A.

Solution: (This is one possible solution.) The liquid hydrogen tank has the shape of a cylinder with ellipsoidal caps on each end. Since the formula for the volume of a hemisphere is better known, let us approximate the domes as hemispheres. Now the total length of the tank is given as 29.6 m, and the diameter as 8.4 m; our approximation, then, consists of two hemispheres (or a single sphere) of radius 4.2 m and a cylinder of radius 4.2 m and length 29.6 - 8.4 = 21.2 m. The resulting volume estimate is:

GEOMETRY GRAPHIC 5B.

GEOMETRY GRAPHIC 5C.

GEOMETRY GRAPHIC 5D.

GEOMETRY GRAPHIC 5E.

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