NAVWEPS DO-ROT-80 
APPLICATION OF AERODYNAMICS 
TO SPECIFIC PROBLEMS OF FLYING 
usually means remaining over a particular 
spot on the ground, it shall be considered 
here as flight at zero airspeed. This is necessary 
because the aerodynamic characteristics of the 
rotor depend on its motion with respect to 
the air and not the ground. Hovering in a 20 
knot wind is aerodynamically equivalent to 
flying at an airspeed of 20 knots in a no-wind 
condition, and the characteristics will be 
identical in the two conditions. 
The first point to realize is that the rotor is 
subject to the same physical laws of aero- 
dynamics and motion that govern flight of 
the fixed-wing airplane. The manner in which 
the rotor is subject to these laws is much more 
complicated due to the complex flow con- 
ditions. 
Rotor lift can be explained by either of two 
methods. The first method, utilizing simple 
momentum theory based on Newton’s Laws, 
merely states that lift results from the rotor 
accelerating a mass of air downward in the 
same way that the jet engine develops thrust 
by accelerating a mass of air out the tailpipe. 
The second method of viewing rotor lift 
concerns the pressure forces acting on the 
various sections of the blade from root to tip. 
The simple momentum theory is useful in 
determining only lift characteristics while 
the “blade element” theory gives drag as 
well as lift characteristics and is useful in 
giving a picture of the forces at work on the 
rotor. In the “blade element” theory, the 
blade is divided up into “blade elements” as 
shown in figure 6.15. The forces acting on 
each blade element are analyzed. Then the 
forces on all elements are summed up to give 
the characteristics of the whole rotor. The 
relative wind acting on each segment is the 
resultant of two velocity components: (1) the 
velocity due CO the rotation of the blades 
about the hub and (2) the induced velocity, 
or downwash velocity caused by the rotor. 
the velocity due to rotation at a particular 
element is proportional to the rotor speed and 
the distance of the element from the rotor hub. 
Thus, the velocity due to rotation varies line- 
arly from zero at the hub to a maximum at 
the tip. A typical blade section with the 
forces acting on it is shown in figure 6.15. 
A summation of the forces acting perpen- 
dicular to the plane of rotation (tip path plane) 
will determine the rotor thrust (or lift) char- 
acteristics while summation of the moments 
resulting from forces acting in the plane of 
rotation will determine the rotor torque char- 
acteristics. As a result of this analysis, the 
rotor thrust (or lift) is found to be propoc- 
tional to the air density, a nondimensional 
thrust coefficient, and the square of the tip 
speed, or linear speed of the tip of the blade. 
The thrust coefficient is a function of the aver- 
age blade section lift coefficient and the rotor 
solidity, which is the proportion of blade area 
to disc area. The lift coefficient is identical to 
that used in airplane aerodynamics while the 
solidity is analagous to the aspect ratio in air- 
plane aerodynamics. The rotor torque is 
found to be proportional to a nondimensional 
torque coefficient, the air density, the disc 
area, the square of the tip speed, and the blade 
radius. The torque coefficient is dependent 
upon the average profile drag coefficient of the 
blades, the blade pitch angle, and the average 
lift coefficient of the blades. The torque can 
be thought to result from components of profile 
and induced drag forces acting on the blades, 
similar to those on an airplane. 
As in the airplane, there is one angle of 
attack or blade pitch condition that will result 
in the most efficient operation. Unfortu- 
nately, the typical helicopter rotor operates 
at a near constant RPM and thus a constant 
true airspeed and cannot operate at this most 
eficient condition over a wide range of altitude 
and gross weight as the fixed-wing airplane.