Page 203 - Aerodynamics for Engineering Students

186 Aerodynamics for Engineering Students
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Fig. 4.17

The flap contributes to the lift on two accounts. Firstly, the downward deflection
of the jet efflux produces a lifting component of reaction and secondly, the jet affects
the pressure distribution on the aerofoil in a similar manner to that obtained by an
addition to the circulation round the aerofoil.
The jet is shown to be equivalent to a band of spanwise vortex filaments which for
small deflection angles T can be assumed to lie along the Ox axis (Fig. 4.17). In the
analysis, which is not proceeded with here, both components of lift are considered in
order to arrive at the expression for CL:
CL = 47rAoT + 27r( 1 f 2&)a (4.58)
where A0 and Bo are the initial coefficients in the Fourier series associated with the
deflection of the jet and the incidence of the aerofoil respectively and which can be
obtained in terms of the momentum (coefficient) of the jet.
It is interesting to notice in the experimental work on jet flaps at National Gas
Turbine Establishment, Pyestock, good agreement was obtained with the theoretical
CL even at large values of 7.

4.7 The normal force and pitching moment
derivatives due to pitching*

4.7.1 (Zq)(Mq) wing contributions
Thin-aerofoil theory can be used as a convenient basis for the estimation of these
important derivatives. Although the use of these derivatives is beyond the general
scope of this volume, no text on thin-aerofoil theory is complete without some
reference to this common use of the theory.
When an aeroplane is rotating with pitch velocity q about an axis through the
centre of gravity (CG) normal to the plane of symmetry on the chord line produced
(see Fig. 4.18), the aerofoil's effective incidence is changing with time as also, as
a consequence, are the aerodynamic forces and moments.
The rates of change of these forces and moments with respect to the pitching
velocity q are two of the aerodynamic quasi-static derivatives that are in general
commonly abbreviated to derivatives. Here the rate of change of normal force on the
aircraft, i.e. resultant force in the normal or Z direction, with respect to pitching
velocity is, in the conventional notation, i3Zjaq. This is symbolized by Z,. Similarly
the rate of change of A4 with respect to q is aA4jaq = M,.
In common with other aerodynamic forces and moments these are reduced to non-
dimensional or coefficient form by dividing through in this case by pVlt and pVl:
respectively, where It is the tail plane moment arm, to give the non-dimensional

* It is suggested that this section be omitted from general study until the reader is familiar with these
derivatives and their use.