Part 1
by Chuck Meager
L = CL S V²r / 2
The subject of helicopter aerodynamics has come up in
recent conversations with readers. I don't claim to be an aeronautical engineer, so I'll try
to keep this basic enough so I can understand what I'm talking about. I will also break this
topic up into at least two parts. In Part 1, I will discuss the basics: Laws,
principles, aircraft component characteristics. In Part 2, I will discuss flight from a hover
to VNE. Please feel free write to me about your difference of opinion, if I stated
something incorrectly or if you have a different experience. One pilot wrote to me last
month and asked if I was going to discuss tandem rotors. I screamed to myself, pulled a
few hairs out, and decided that I would have to do some research.
IT'S THE LAW
Principles and laws relating to flying.
The concepts that are really important in helicopter flying are Bernoulli's principle,
Newton's three laws of motion, and gyroscopic precession or phase lag.
Bernoulli and Lift
Most aviators are familiar with Bernoulli. I sometimes refer to him as my buddy Dan.
From the principle he developed for fluid dynamics, the lift equation was born. It seems
like everyone knows the lift equation and what each of the components represent.
However for a quick refresher I attempted to clarify things below. I added an additional
box to indicate whether each element may be changed or manipulated during flight.
If you do not see a table, select our pre format version
| Element of Equation |
Description |
Adjusted by: |
| CL |
Coefficient of Lift: The design of the airfoil and the
angle of attack/incidence |
May be manipulated with collective, cyclic or
aerodynamic forces |
S |
Surface of the airfoil |
May not be adjusted (unless you hit a tree.) |
| V² |
Velocity squared - the relative speed of the rotor
blade |
Has the most dramatic effect on lift. May be adjusted
by airspeed, rpm, or aerodynamic forces. |
| r |
rho - signifies air density |
You get what you get |
The pilot has control over two parts of this equation: the CL and the velocity.
Interestingly, the design of the rotor system allows for automatic adjustments in the same
two portions of the equation. For instance, the coefficient of lift may be changed by the
pilot with the manipulation of the collective or cyclic or it may be changed by an induced
flow of air into the rotor system, which changes the resultant relative wind. Velocity may
be changed by the pilot when he/she (politically correct) changes airspeed or rotor RPM
or velocity may be changed slightly with shift in center of gravity when a blade flaps. More
on flapping later.
Newton
Newton's three laws of motion that helicopter pilots will respond to are: inertia,
acceleration, and action-reaction.
If you do not see a table, select our pre format version
| Force |
Description |
Why Do I Care? |
| Inertia |
A body at rest will remain at rest or a body in motion
will remain in motion until acted upon by an outside force. |
As the rotor turns... centrifugal force comes from
inertia... |
| Acceleration |
The force required to change a motion is proportional
to its mass and the rate of change in its velocity. |
A very important principle for helicopters. When
forces are unbalanced, motion changes. Lift, thrust, weight and drag are what we're
talking about. The greater the unbalance of forces the greater the change. Total
Aerodynamic Force is the resultant force between lift and drag. |
| Action-Reaction |
For every action there is an equal and opposite
reaction. |
Torque and anti-torque. Tail rotor for most of us,
opposite turning rotors for you tandem guys and gals. |
Gyroscopic Precession
Now that I've totally confused everyone let me add the final concept: Gyroscopic
Precession and phase lag. Rotating bodies have an interesting characteristic. Any force
applied to a rotating body takes affect 90 degrees later in the direction of rotation. (Check
it out for yourself with a spinning top.) So with a helicopter, if we want to change the lift
vector on the left side of the rotor disk, in a helicopter with the rotor turning
counterclockwise, a force is applied on the aft portion of the rotating disk. Cool huh?
COMPONENT CHARACTERISTICS
Main and Tail Rotors
Flapping
Flapping is the up and down movement of the rotor blade at the hinge or, for semi-rigid
systems, about the trunion bearing (at the mast). Flapping occurs in a blade due to
velocity. On a no-wind day flapping is equal across the disk. But add just 1 knot of
wind and you get unequal lift across the rotor disk. When wind or directional flight is
present, the rotor disk has an advancing and retreating side relative to the airflow. So the
advancing blade has greater lift than the retreating blade. This isn't necessarily a good
thing if I want to maintain straight and level flight. Remember velocity has a dramatic
affect on the lift equation. Picture the lift equation on both sides of the mast.
CL S V² r / 2 = L = r V² S CL / 2
On one side velocity has increased. On the other side velocity has decreased. This is not a
balanced equation!! This is a condition call Dissymmetry of Lift. Other
components of the equation must be adjusted to attain balance. We have already
established that neither aircraft nor the pilot can not affect "S" or "r", So the only thing
left to adjust is the CL. With the increased velocity the advancing blade will climb. As it
climbs, the angle of attack is reduced by the change in relative wind. With the blade
flapping up a new airflow is introduced to assist induced flow. This flow is a downward
flow of air which has the result of decreasing the angle of attack. Just the opposite
happens on the retreating blade so that the retreating blade has a greater angle of
attack.
Feathering
Feathering is just a term used to describe the rotation of the blade along its axis. The
rotation changes the angle of attack of the airfoil.
Hunting
Also known as Lead and Lag, it is the fore and aft movement of the blade as it rotates. As
a blade flaps up, its center of gravity shifts towards the axis of rotation. As any fan of the
French mathematician Coriolis will tell you, this causes an increase in RPM. Coriolis
called this the law of conservation of angular momentum. So the advancing blade leads
because the up flap of the blade makes it move faster; and the retreating blade lags
because the down flap of the blade shifts the cg outward slowing down the rotation. I
might add that in the semi-rigid underslung rotor, hunting is discouraged. The design of
the pivot point inhibits the shift in cg of the blade as it flaps.
Coning
The blades or rotor disk cones for two basic reasons. The blade tip is faster than the blade
root. Remembering the characteristics of our friend velocity, this causes an increased lift
at the tip of the blade. Coning is the result. In today's aircraft, engineers have taken
advantage of this knowledge to minimize coning. Using the strength and flexibility of
modern materials, they have designed blades with a twist and that have the
camber of the airfoil change along the span of the blade. But, as you add weight to the
center of rotation, the disk will also cone.
Torque
Because of Newton's third law of motion - Action-Reaction, we get an effect
called torque. Because there is a force driving the main rotor, there is an equal and
opposite reaction at the fuselage. So as the main rotor is driven in a counterclockwise
direction, the fuselage reacts in a clockwise direction. This is fun if you're on a carnival
ride but not if you are trying to fly somewhere safely. Most helicopters solve this problem
with a tail rotor. The pilot can manipulate the "lift" in the tail rotor so as to counter act
torque. Tandem helicopters solve the problem with two rotor disks which turn opposite
of each other. And now of course there's the NOTAR which uses air flow.
Next month, I hope to put this all together to describe the things that happen along the
way from point A to point B. From in-ground effect to out-of-ground effect and from
zero airspeed to retreating blade stall. Until next time - Chuck
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