Helicoptorial

AERO-DRY-NAMICS

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

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.

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

You can send your feedback and input to Chuck at chuckm@aero.com

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