# 36 Some Aerodynamics (RC flying)

The aircraft can rotate around three axes: the fore-and-aft axis (or the
_roll_ axis); the spanwise (nose-up/nose-down) axis or the _pitch_ axis;
and the nose-left/nose-right, or _yaw_ axis.

Speed:

The cross-section of the wing has a shape called an _airfoil_. It has the
property that when it meets the air (usually at some small angle, called
the _angle_of_attack) it generates an upward force (lift) for a small
backward force (drag). The amount of lift (and drag) depends on the
airspeed and a value called the _lift_coefficient_ (and a few other
things like surface area and density of the air). If the plane is in
unaccelerated flight, the upward force (approximately equal to the lift)
is equal in magnitude to the weight of the plane, which is a constant. It
thus follows that the total lift generated by the wing is always constant
(at least in unaccelerated flight). [One example of accelerated flight is
turning---see below]

The above mentioned _coefficient_of_lift_ (abbreviated Cl) depends on the
angle of attack. Usually, as the A-of-A is increased, Cl increases; to
keep the lift force constant, speed can decrease. So to fly fast, we
decrease Cl (and A-of-A); to slow down, increase Cl (and A-of-A). Since
the wings are fixed, we alter the A-of-A by pitching the entire plane up
or down. This is done with the elevator. The elevator is thus the speed
control.

Turning:

To turn a body moving in a straight line, a sideways force must be
applied to it. For a plane, the best method for generating a force is to
use the wings. To get them to act sideways, we roll the plane: now part
of the lift is acting sideways and voila! a turn. To roll the plane, we
use the ailerons (the movable surfaces at the wingtips). Also, notice
that now since part of the lift is acting sideways, the lift force in the
upward direction is reduced; but the upward component of the lift needs
to be equal to the weight of the plane i.e. we need a little more lift
from the wings, which we can do by increasing Cl---i.e. by pulling a bit
of up-elevator. That's why to turn in a plane you push the stick sideways
in the direction of the turn and then pull back a bit to keep the nose
level.

What happens if you try to turn with the rudder alone? The application of
the rudder will cause the aircraft to yaw, and it will continue to travel
in the same straight line (more or less), skidding. (Think of a car on a
perfectly slippery road---if you try to turn just by turning the wheel,
you'll skid but won't turn). So we need a roll to turn.

But most of the trainers we see don't have any ailerons! How do they
turn? They use a configuration of the wings called _dihedral_ (or, for most
gliders, _polyhedral_).

```     Flat                  Dihedral                     Polyhedral
~-_                     _-~
-------O--------     ~~~----___O___----~~~        ~~~~~~~----O---~~~~~~

^                       ^                 ^           ^         ^
0 angle between       small angle between        small angle between 2 wing
2 wing panels         2 wing panels              panels and also small angle
OR
0 angle between 2 wing panels
and small angle within each
panel (Olympic 650)
```

When we apply rudder (say left rudder) to a plane with dihedral, what
happens? The plane yaws; the right half of the wing then sees a greater
angle of attack than than the left half:

```		      / / / / / / <--- airflow direction
._______________________.
|___________|___________|
left wing    right wing
```

(You can try this out if you don't believe it: take a piece of paper and
fold it slightly, like dihedral; then look at it end on, but slightly
off-center, i.e. from the point of view of the approaching airflow. You
will see that you can see more of the underside of one half than you can
of the other.) And what does an increased angle of attack do? It
increases the Cl and the lift generated by that half! So we now have the
right wing generating more lift and the left less; the result is a roll
to the left. With polyhedral we get the same effect, only to a larger
extent.

The Stall:

If you try to fly slower and slower by pulling back on the stick (i.e.
applying up-elevator) you will reach a point where the plane "falls out
of the sky" or the stall. What happens is that an airfoil will only
"work" up to a certain angle of attack. When that angle is exceeded, the
airflow above the airfoil breaks up and the result is an increase in drag
and a drastic decrease in lift, so that the wings can no longer support
the plane. The only remedy is to reduce the A-of-A i.e. to push the nose
down. This may be a little difficult to do when you see your plane
falling---the natural tendency is to pull back on the stick, to "hold the
plane up."

A development of the stall is the spin. Volumes can be written about it,
and have been; go to the library and check any book on introductory
aerodynamics.

If you want to know more about Aerodynamics as it applies to Model
Aircraft (the small Reynolds' number regime, as it is sometimes called)
check "Model Aircraft Aerodynamics" by Martin Simons [Argus Books,
ISBN 0 85242 915 0].

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