## Key Relationship Between Volume and Wetted Area

Figure 3.9. Controlling drag, that is skin friction resulting from wetted area, is the key to higher lift-to-drag ratios.

40,000 60.000

Propellant Volume (ft3)

Figure 3.9. Controlling drag, that is skin friction resulting from wetted area, is the key to higher lift-to-drag ratios.

with different missions and propellants. Figure 3.9 shows the approach. Normally, to increase its volume a vehicle is made larger, as in photographic scaling. That is, all dimensions are multiplied by a constant factor. This means that the configuration characteristics remain unchanged except that the vehicle is larger. The wetted area is increased by the square of the multiplier, and the volume is increased by the cube of the multiplier. This can have a very deleterious impact on the size and weight of the design when a solution is converged. The McDonnell approach (and as probably practiced by Lockheed and Convair in the 1960's) used the cross-section geometry of highly swept bodies to increase the propellant volume without a significant increase in wetted area. As shown in Figure 3.9 the propellant volume is plotted for a number of geometrically related hypersonic shapes as a function of their wetted area. The correlating parameter is "wetted area'' divided by the "total volume'' raised to the 2/3 power and it is the reciprocal of the AFFDL parameter in Figure 3.8. The corresponding range of this parameter is 10.5 ± 2.0. As this parameter reduces in value, the wetted area for a given volume reduces. The most slender configuration is characteristic of an aircraft like Concorde. If a 78-degree sweep slender wing-cylinder configuration (S = 26.77) were expanded to stout blended body (S = 9.36) the propellant volume could be increased by a factor of 5 without an increase in wetted area. If the original configuration were grown in size to the same propellant volume, the wetted area would be three times greater. So the friction drag of the S = 9.36 configuration is approximately the same, while the friction drag of the photographically enlarged vehicle is at least three times greater. Moving to a cone, the propellant volume is 6.8 times greater for the same wetted area. That is why the McDonnell Douglas Astronautics Corporation, Huntington Beach, Delta Clipper Experimental vehicle was a cone. It could accommodate the hydrogen-oxygen propellants within a wetted area characteristic of a kerosene supersonic aircraft

The correlating parameters with the area in the numerator and a volume raised to the 2/3 power in the denominator are characteristically used in the United States. The European correlating parameters associated with Dietrich Kiichemann have volume in the numerator and area raised to the 1.5 power in the denominator [Kiichemann, 1960]. The two approaches can be related as in the following equation set.

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