A Study of Curvilinear Flight Page: 3 of 28
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.A. C .A. Technical memorandum so. 615
q (kg/S )
=rolling moment due to aileron setting,
= damping moment,
= inclination (bank),
= wind velocity,
= dynamic. pressure,
= angular speed of rotation,
= angular speed of acceleration,.
hfien an airplane describes a curve it takes a certain time
for it to turn from level to inclined position and then back to
level again. In the following, we express the motion about the
horizontal axis as "roll" or "bank" and the motion perpendicu-
lar to the vertical axis, i.e., the actual curve, as !turn."
rThe m oment of is
The moment of wetli is
Mr = cmr bP t q = I d D,
with coefficient of rolling moment cmr dependent on aileron
Therefrom follows the time' required to attain a
certain inclined position by given angular velocity* as
12 I In
-R vt dcn w dcn
2g da vk dCa
wi th k = ---
*Lachmann, "The Span as Underlying Basis in Airplane Design,"
Zeitschrift fur Flugtechnik und. Iotorluftschiffahrt, 1928, pp.
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Kruse, Helmuth. A Study of Curvilinear Flight, report, April 1931; (https://digital.library.unt.edu/ark:/67531/metadc277406/m1/3/: accessed March 20, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.