NON-DIMENSIONAL COEFFICIENTS

Before examining how the realism of the theories introduced above might be improved, it is necessary to discuss the concept of non-dimensional coefficients. These coefficients are analogous to the lift and drag coefficients that are a common feature of aerodynam­ics. Rather than lift and drag, in the case of rotorcraft, coefficients of thrust (CT), torque (Cq) and power (CP) are used. These coefficients are defined as:

Подпись:CT =

NON-DIMENSIONAL COEFFICIENTS

CQ =

Note that power coefficient is numerically equal to torque coefficient (though, of course, they are different physically). Now converting Equation (2.7) into coefficient terms gives:

ct=2 abf u 9o+4 9i-1 *

CT = 2 as (3 90 +191 -1 *

where s is defined as the solidity of the disk that is the ratio of total blade area to disk area. Hence for a rotor with rectangular blades s = bcR I A. The relationship for thrust

CT ‘s 7 0O + л 01 T *

– 2 *

CT — 2 sa 3 0O.75 — 2 *

NON-DIMENSIONAL COEFFICIENTS
Подпись: Hence a rotor with zero twist will generate the same thrust coefficient as one with linear twist, provided the pitch setting of the untwisted blade is equal to that at the three-quarter radius on the twisted blade. Also from Equation (2.6): P — T(Vc — Vi) + 8 p bcVT RCD Thus:

Подпись:

image5

Подпись:

Подпись: — CV+i +1 sC — CT V + 8C
Подпись: — — CT VT + CT VT + 8 C This equation is frequently used in performance analysis. It shows that for a climbing rotor the power required can be sub-divided into three parts: the first term represents the useful power; the second the induced power; and the third the profile power. If the particular case of hovering flight is considered (Vc — 0) then from momentum theory the induced velocity can be related to the thrust coefficient: W —
Подпись: In addition, the power coefficient becomes:
Подпись: C — C I— +1 sC —-1- C32+1 sc '-'P _ '-'T. I 2 ^8 SCD_ T ^ 8 SCD
Подпись: Now for a given rotor with fixed solidity, provided the profile drag coefficient remains constant, then:
Подпись: CP — k—T/2 + k2
Подпись: Equation (2.8) is a very important result since it suggests that for a hovering rotor the power coefficient is directly proportional to the thrust coefficient (or aircraft weight) provided the drag coefficient remains unchanged. Likewise if the helicopter mass is

coefficient can be simplified by altering the definition of blade pitch from the blade root to a position at three-quarter radius (60.75), since:

fixed and the rotor profile drag coefficient is constant then the power required to drive the rotor will vary as )3 so that CP will remain unchanged. This simple rule forms the basis of hover performance testing and is illustrated in Fig. 2.4.

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