The Art of the Helicopter John Watkinson - Karatunov.net

Introduction to helicopter dynamics 63
Fig. 3.2 Profile drag must be included in the behaviour of any real airfoil. The induced drag and profile drag
add to tilt the total blade reaction backwards. Conditions at low airspeed are shown in (a). At a higher speed,
(b), the profile drag is greater, but the induced drag is less. This is only possible because it is not really a drag.
In practice the air also has viscosity that resists movement as a function of the surface
area of any body moved through it. The loss due to this effect is called profile drag. The
profile drag tilts the blade reaction further to the rear as in Figure 3.2(a). There is a
boundary layer between a moving object and the stationary air. At the leading edge, the
speed difference across the boundary layer is maximal and the drag is greatest. Further
back, the viscosity has been able to get the boundary layer moving and the drag is
reduced. Thus the drag experienced by a wing or rotor blade is a function not just of the
surface area but also of the chord. Very small objects possess disproportionately high
profile drag, which is why the wind can blow sand but not rocks. Reynolds numbers are
used to describe the relationship between dimensions and profile drag. It is important
in model testing that the airspeed used is scaled correctly. Scale speed is not used.
Instead the speed is chosen to produce the same Reynolds number in the model as in
the full-sized device and then the drag of the model will be representative.
If an airfoil is not producing lift, the induced drag will be zero and only the profile
drag will be observed. In a full-size helicopter in the hover roughly 30% of the rotor
shaft power is lost to profile drag, the rest goes in accelerating the air downwards. In
model helicopters and full-sized tail rotors profile power is proportionately greater as
the small-chord blades operate with adverse Reynolds numbers.
Figure 3.2(b) shows the production of the same lift at a higher relative velocity.
The profile drag has increased but the induced drag has reduced. This is not what
one would expect from a true source of drag. The explanation is that the airfoil is an
actuator or transducer, which accepts mechanical power as the product of the mechanical
impedance and the relative velocity in order to drive the air against aerodynamic
impedance. Accelerating air downwards constantly provides lift. The actuator reflects
the aerodynamic impedance back as mechanical impedance. The variation in angle of
attack is analogous to changing the turns ratio of a transformer or the ratio of a gearbox.
Clearly if the relative velocity goes up, to keep the power the same the impedance
must fall.
Once the concept of an airfoil as an actuator is understood, it is a small step to
appreciate that most types of actuator are reversible. Some helicopters use an electric
motor to start the engine when that motor becomes a generator. In a turbine engine, the
rotating blades in the compressor are putting energy into the air, whereas the rotating