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The Art of the Helicopter John Watkinson - Karatunov.net

The Art of the Helicopter John Watkinson - Karatunov.net

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

shaft to <strong>the</strong> boundary <strong>of</strong> <strong>the</strong> reverse flow region. Figure 3.22(d) shows <strong>the</strong> expression<br />

for d graphically and it will be seen that <strong>the</strong> reverse flow area is circular and that its<br />

diameter increases with speed. Instantaneously <strong>the</strong> rotor is turning with respect to <strong>the</strong><br />

outer edge <strong>of</strong> <strong>the</strong> reverse flow region. <strong>The</strong> ratio <strong>of</strong> forward speed to tip speed is known<br />

as <strong>the</strong> advance ratio µ which is <strong>the</strong> same as <strong>the</strong> ratio <strong>of</strong> <strong>the</strong> diameter <strong>of</strong> <strong>the</strong> reverse flow<br />

region to <strong>the</strong> blade radius.<br />

<strong>The</strong> retreating blade suffers reverse flow near <strong>the</strong> root; a small downward force may<br />

be experienced because <strong>the</strong> retreating blade effectively has a negative angle <strong>of</strong> attack<br />

due to flow reversal. Here is ano<strong>the</strong>r reason for root cut-out, to reduce <strong>the</strong> amount <strong>of</strong><br />

useless reverse-flowed blade. However, as <strong>the</strong> area is proportional to <strong>the</strong> square <strong>of</strong> <strong>the</strong><br />

diameter, <strong>the</strong> amount <strong>of</strong> disc area lost to <strong>the</strong> reverse flow region is small. For example,<br />

at µ = 0.4, <strong>the</strong> diameter <strong>of</strong> <strong>the</strong> reverse flow region is 0.2 <strong>of</strong> <strong>the</strong> rotor diameter but <strong>the</strong><br />

area lost is only 4%.<br />

Owing to <strong>the</strong> huge difference between <strong>the</strong> airspeeds, if nothing were done, <strong>the</strong> advancing<br />

blade would produce more lift and <strong>the</strong> retreating blade less. This would apply to<br />

<strong>the</strong> rotor a roll couple toward <strong>the</strong> retreating side. <strong>The</strong> gyroscopic action <strong>of</strong> <strong>the</strong> rotor<br />

would result in a response delayed by 90 ◦ <strong>of</strong> rotation corresponding to a rearward pitch<br />

effect. This rearward couple is colloquially known as ‘flapback’ and it tends to reduce<br />

<strong>the</strong> forward tilt <strong>of</strong> <strong>the</strong> machine and consequently reduces <strong>the</strong> forward component <strong>of</strong><br />

<strong>the</strong> rotor thrust, slowing <strong>the</strong> machine down.<br />

Thus sustained forward flight requires a continuous application <strong>of</strong> forward cyclic<br />

control that reduces <strong>the</strong> angle <strong>of</strong> attack <strong>of</strong> <strong>the</strong> advancing blade and increases that <strong>of</strong><br />

<strong>the</strong> retreating blade in order to balance <strong>the</strong> lift moments on <strong>the</strong> two sides <strong>of</strong> <strong>the</strong> rotor.<br />

In cruise <strong>the</strong> amount <strong>of</strong> cyclic pitch applied may be <strong>of</strong> <strong>the</strong> order <strong>of</strong> 5 ◦ . Flapback results<br />

in speed stability because it automatically opposes <strong>the</strong> cyclic control.<br />

<strong>The</strong> more forward cyclic is applied, <strong>the</strong> higher will be <strong>the</strong> forward speed. Thus in<br />

translational flight <strong>the</strong> fore-and-aft position <strong>of</strong> <strong>the</strong> cyclic stick primarily controls <strong>the</strong><br />

airspeed. If <strong>the</strong> airspeed is changed, <strong>the</strong> collective lever will need to be adjusted to<br />

maintain height because tilting <strong>the</strong> rotor thrust vector alters its vertical component.<br />

In forward flight <strong>the</strong> rotor has access to a greater mass <strong>of</strong> air. Thus <strong>the</strong> same momentum<br />

increase and <strong>the</strong> same thrust can be obtained with a smaller induced velocity and<br />

this reduces <strong>the</strong> power needed. Figure 3.23 shows that <strong>the</strong>re is a minimum induced<br />

power speed where <strong>the</strong> inflow velocity is <strong>the</strong> least.<br />

3.21 Inflow and coning roll<br />

In flight, <strong>the</strong>re is a region <strong>of</strong> low pressure above <strong>the</strong> rotor and a region <strong>of</strong> high pressure<br />

below. This pressure difference results in a tendency for air in <strong>the</strong> plane <strong>of</strong> <strong>the</strong> rotor<br />

to move upwards. Figure 3.24(a) shows that this happens for some distance from <strong>the</strong><br />

edge <strong>of</strong> <strong>the</strong> disc. Simple inertia keeps <strong>the</strong> air moving upwards so that in translational<br />

flight, <strong>the</strong> leading edge <strong>of</strong> <strong>the</strong> disc encounters upwash. <strong>The</strong> upwash ceases when <strong>the</strong><br />

downward impulse <strong>of</strong> <strong>the</strong> rotor cancels <strong>the</strong> upward momentum <strong>of</strong> <strong>the</strong> air mass.<br />

In slow forward flight, Figure 3.24(b), <strong>the</strong> low pressure above <strong>the</strong> rotor has time to<br />

bend <strong>the</strong> inflow increasingly downwards as it reaches <strong>the</strong> trailing edge <strong>of</strong> <strong>the</strong> disc. <strong>The</strong><br />

disc can be thought <strong>of</strong> as a low aspect ratio wing producing tip vortices which roll<br />

inward at <strong>the</strong> top and down through <strong>the</strong> rear <strong>of</strong> <strong>the</strong> disc. <strong>The</strong> result is a reduction <strong>of</strong><br />

<strong>the</strong> angle <strong>of</strong> attack <strong>of</strong> <strong>the</strong> blade at <strong>the</strong> rear <strong>of</strong> <strong>the</strong> disc compared to that at <strong>the</strong> front.<br />

<strong>The</strong> loss <strong>of</strong> lift at <strong>the</strong> rear <strong>of</strong> <strong>the</strong> disc is subject to <strong>the</strong> phase lag, or precession, <strong>of</strong> <strong>the</strong><br />

rotor and manifests itself as a roll to <strong>the</strong> advancing side, which is known as inflow roll.

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