If a supersonic nozzle is designed for less than complete expansion of the flow, some lift force can be produced without downwards deflection of the nozzle. A theoretical analysis has been made, by the method of characteristics, for a two-dimensional nozzle consisting of an upper wedge and lower parallel shroud. General trends of lift performance with the main variables have been obtained.

The success achieved in wing analysis and related problems through the introduction of triangular elements with six nodal points and a prescribed linearly varying strain or stress, naturally raised demands for a further sophistication in the idealisation process by triangularisation. In this context a practically important extension is concerned with the influence of taper in the thickness. We reproduce in what follows the theory for the special case of linear type. The paper may be considered as a generalisation of notes 2 and 3 of this series. However, the analysis is here based on the non-dimensional homogeneous triangular co-ordinates introduced in note 5, which simplify the argument considerably. A significant broadening of the applicability of the new element will be given in notes 9 and 10.

In 1954, Preston introduced a new concept of skin friction measurement in turbulent flows by using a surface pitot tube. Since then considerable controversy has risen in the use of Preston tubes for skin friction measurements. However, Head and Rechenberg investigated Preston tubes extensively and confirmed the validity of the Preston tube method. Recently Rajaratnam has given a theoretical calibration curve for the Preston tube using logarithmic velocity distribution for the boundary layer velocity profile.