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THE INFLUENCE OF RUNNING PROPELLERS
The forces on a single propeller are illustrated in Fig. 3.5, where ap is the angle of attack of the local flow at the propeller. It is most convenient to resolve the resultant into the two components T along the axis, and Np in the plane of the propeller. The moment associated with T has already been treated above, and does not affect Cma. That due to Np is
AC = C — — – c 5
where CN = Np/hpV2Sp and Sp is the propeller disk area. To get the total ACm for several propellers, increments such as (3.4,7) must be calculated for each and summed. Theory shows (Ribner, 1945) that for small angles CNp is proportional to ap. Hence Np contributes to both C and dCmJda. The latter is
dCmp = Sp_ dCNp dap Эс* Sc дар da
If the propeller were situated far from the flow field of the wing, then dap/da would be unity. However, for the common case of wing-mounted tractor propellers with the
propeller plane close to the wing, there is a strong upwash ep at the propeller. Thus
and
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where the constant in (3.4,9a) is the angle of attack of the propeller axis relative to the airplane zero-lift line. Finally,
Increase of Wing Lift
When a propeller is located ahead of a wing, the high-velocity slipstream causes a distortion of the lift distribution, and an increase in the total lift. This is a principal mechanism in obtaining high lift on so-called deflected slipstream STOL airplanes. For accurate results that allow for the details of wing and flap geometry powered – model testing is needed. However, for some cases there are available theoretical results (Ellis, 1971; Kuhn, 1959; Priestly, 1953) suitable for estimates. Both theory and experiment show that the lift increment tends to be linear in a for constant CT, and hence has the effect of increasing awb, the lift-curve slope for the wing-body combination. From (2.3,23) this is seen to reduce the effect of the tail on the NP location, and can result in a decrease of pitch stiffness.
Effects on the Tail
The propeller slipstream can affect the tail principally in two ways. (1) Depending on how much if any of the tail lies in it, the effective values of a, and ae will experience some increase. (2) The downwash values e0 and de/da may be appreciably altered in any case. Methods of estimating these effects are at best uncertain, and powered-model testing is needed to get results with engineering precision for most new configurations. However, some empirical methods (Smelt and Davies, 1937; Millikan, 1940; Weil and Sleeman, 1949) are available that are suitable for some cases.
