Avlab 1001-0139-000C Driver

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Avlab 1001-0139-000C Driver

For wake geometry computations, P is a point in the wake.

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The element of Avlab 1001-0139-000C at point P was originally shed from radial station n on the n blade, which had an azimuth angle 4 at the instant of shedding. Point Avlab 1001-0139-000C is the point at the upper larger azimuth angle end of the vortex-line segment whose contribution to the induced velocity at point P is being computed. The current age, 6. On a multi-bladed rotor the Z blade and the n blade are not always the same.

The Z Avlab 1001-0139-000C is identified by C, which is the azimuth angle by which the I blade leads the n blade. Thus, for a three- bladed rotor, ; can have three values: For example, in Fig. The Z blade is shown at three different ages: For wake geometry computations 6 is not zero at points P in the wake and Eq.

Since 6 Avlab 1001-0139-000C not needed for the age of P in airloads computations, it is normally used to replace 6. Thus the 6 used in wake geometry computations is always zero in airloads computations and the 6 used in wake geometry computations becomes 6 in airloads computations. This means that Eq.

The vectors from point P to points Pa Avlab 1001-0139-000C Pb are a and b, respectively. The nondimensional circulation of the vor- tex-line segment is ya' with positive y Avlab 1001-0139-000C going from point Pa to point Pb.

Figure 5 illustrates these definitions. The distortion vector of a point P n on the tip vorte. Avlab 1001-0139-000C that if point P is not constrained to be on the tip vortex, then D also becomes a function of the radial station n.

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Since only steady-state flight is considered here, airloads, inflow, blade motion, etc. It is, therefore, often convenient to harmonically analyze these quanti- ties. Avlab 1001-0139-000C most variables, the harmonics Avlab 1001-0139-000C written conventionally. For example, airloads: Table 1 summarizes the general rules used in normalizing variables. Exceptions to these rules will be ex- plained as they occur in the rest of the report.

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Standard heli- copter normalization is used for advance ratio y, thrust coef- ficient CT, Avlab 1001-0139-000C force coefficient CH, power Avlab 1001-0139-000C Ctorque coefficient CQ, and solidity a. As discussed previously, this model must be as simple as possible to allow efficient computation of induced velocities. The Biot-Savart relation for large distances is such that the magnitude of the induced velocity Avlab 1001-0139-000C inversely with the square of the distance between a finite element of vortex wake and the point at which the induced velocity is computed.

Therefore, when computing the Avlab 1001-0139-000C duced velocity at a point P 1the wake near point P must be treated very carefully. The wake moderately far from point P can be repre- Avlab 1001-0139-000C by relatively simple models and the wake very far from point P can be neglected.

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Avlab 1001-0139-000C The Biot-Savart relation also implies a singu- larity in induced velocity at Avlab 1001-0139-000C center of any vortex wake element having finite circulation. Since there are no infinite induced ve- Avlab 1001-0139-000C in reality, the mathematical model of the vortex wake must include physically realistic ways of avoiding these singulari- ties.

This consists of a concentrated tip vortex line, an inboard trailing vortex line or sheet, and a shed wake. The trailing wake is the wake resulting from radial variations in the bound circulation, while the shed Avlab 1001-0139-000C comes from azimuth bound circulation variations. As discussed in Subsection 1. The inboard trail- ing wake is necessary to conserve circulation. Trial runs show that airloads and wake geometry computations made both with and without it included, give substantially different results Fig.

If the trailing-wake circulation varies around the azimuth, then there must be a shed wake to conserve Avlab 1001-0139-000C. To extend th basic wake model all the way to infinity would require an infinite amount of computation, which is not prac- tical. The following approximations are, therefore, used.

For hovering cases, the basic wake model extends downward for about one rotor radius, and thereafter the tip vortex is represented by a semi-infinite vortex cylinder over which the Biot-Savart rela- tion can Avlab 1001-0139-000C integrated in closed form.