Reply by Authors to B. Etkin and G. D'Eleuterio

ONES and DeLaurier1 have undertaken a difficult task in developing methods for estimating the aerodynamic forces on aerostats and airships. We trust that their results will be of practical utility to workers in this field. However, the portion of their paper that deals with the modeling of forces in unsteady flow has errors in the theory that users should be aware of. In particular, Eq. (45) of the paper is wrong. It reads w= W+Py-Qx-Pv + Qu (1) In fact, w is defined correctly in Eq. (14) of Ref. 1, and its time rate of change w (for a quasirigid vehicle with y = x~Q) is iv= W+Py-Qx (2) This follows clearly and simply from the definitions of the quantities in Eq. (14); w is nothing other than the component, along the z-body axis, of the inertial velocity of the center of the panel (slice). The authors arrive at their incorrect equation (45) by a convoluted and erroneous argument following Eq. (40). The source of the error appears to be an invalid statement in Eq. (41). The vector r cannot be both as in Eq. (14) and in Eq. (41); according to the definition of r preceding Eq. (14), r is constant in the body-fixed frame, so that r = 0, whereas in Eq. (41) rVO. The incorrect value of w is then substituted into Eq. (38), which is the strip-theory application of an exact theoretical result. An erroneous expression for the dZ7 force component is then obtained in Eq. (46). It should read dZ7 = - 3' ( W+ Py - Qx) - k(Qu + k^Pv (3)