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The Art of the Helicopter John Watkinson - Karatunov.net

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126 <strong>The</strong> <strong>Art</strong> <strong>of</strong> <strong>the</strong> <strong>Helicopter</strong><br />

Fig. 4.8 (a) <strong>The</strong> application <strong>of</strong> cyclic pitch in translational flight results in reduced induced drag on <strong>the</strong><br />

advancing blade, but increased pr<strong>of</strong>ile drag. (b) <strong>The</strong> root <strong>of</strong> <strong>the</strong> retreating blade experiences down thrust due to<br />

reverse flow.<br />

called a Coriolis force, has to be imagined to act. If <strong>the</strong> head itself is completely rigid,<br />

<strong>the</strong> in-plane blade movement due to conservation <strong>of</strong> momentum results in bending in<br />

<strong>the</strong> blade. <strong>The</strong> resultant forces are <strong>of</strong>ten called Coriolis forces. In fact <strong>the</strong> forces arise<br />

because <strong>the</strong> rigid head tends to prevent <strong>the</strong> blade conserving its momentum whereas<br />

drag hinges allow momentum to be conserved.<br />

In translational flight <strong>the</strong>re is considerable asymmetry in <strong>the</strong> conditions experienced<br />

by <strong>the</strong> advancing and retreating blades. <strong>The</strong> most obvious consequence <strong>of</strong> this asymmetry<br />

is <strong>the</strong> application <strong>of</strong> cyclic pitch in order to produce equal lift moments on each<br />

side <strong>of</strong> <strong>the</strong> rotor. This will result in <strong>the</strong> induced drag and <strong>the</strong> pr<strong>of</strong>ile drag being functions<br />

<strong>of</strong> blade phase angle and radius. Note that <strong>the</strong>se two functions are quite different.<br />

Figure 4.8 shows that <strong>the</strong> induced drag falls on <strong>the</strong> advancing blade because <strong>the</strong> angle<br />

<strong>of</strong> attack is reduced, whereas <strong>the</strong> pr<strong>of</strong>ile drag increases because <strong>the</strong> velocity <strong>of</strong> <strong>the</strong> RAF<br />

is higher. Figure 4.8 shows that, at an inboard radius, reverse flow causes <strong>the</strong> root end<br />

<strong>of</strong> <strong>the</strong> blade to develop an undesirable down force.<br />

<strong>The</strong> result <strong>of</strong> <strong>the</strong>se induced and pr<strong>of</strong>ile drag variations will be in-plane bending<br />

moments within <strong>the</strong> blade as well as overall in-plane moments at <strong>the</strong> blade root. Dragging<br />

hinges are intended to relieve in-plane root moments. However, <strong>the</strong> presence <strong>of</strong><br />

dragging hinges allows in-plane blade motion and it is important that this motion is<br />

stable. Unlike flapping, <strong>the</strong> restoring force when <strong>the</strong> blade drags away from its neutral<br />

position is quite small and so <strong>the</strong> resonant frequency is much lower than <strong>the</strong> rotational<br />

frequency. For in-plane motion, <strong>the</strong> degree <strong>of</strong> aerodynamic damping is also very small.<br />

It was seen in Chapter 1that additional damping is <strong>of</strong>ten necessary on <strong>the</strong> dragging<br />

axis to prevent ground resonance. This phenomenon will be discussed in sections 4.16<br />

and 4.17.<br />

4.7 Order <strong>of</strong> hinges<br />

<strong>The</strong> order in which <strong>the</strong> flapping, dragging and fea<strong>the</strong>ring hinges are disposed is subject<br />

to a certain amount <strong>of</strong> variation from one design authority to <strong>the</strong> next. <strong>The</strong> use <strong>of</strong><br />

coincident flapping and dragging axes is common because it allows a compact bearing

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