Did
you know that a high performance sailplane can stay up on a day with no lift,
but only pockets of strong sink? Most
sailplane pilots regard sinking air as an enemy and of no value, but there is
just as much energy in downward moving air as in upward moving air it’s just
more difficult to utilize. A companion
paper called** Calculations on Soaring Sink** goes into the details of getting
energy from down gusts. Here we’ll look at the basic energy picture.

There
is a lot of energy in large-scale air turbulence and often we can extract this
energy with a sailplane. A sailplane
can get energy from the moving air.
Using up and down gusts in opposition to each other is particularly
effective. On days when the air is
smooth and calm, ** then** there is no way to stay up without a motor.

How
are we going to stay up on “sink” anyway?
Perhaps a parallel to basketball players will prove illuminating. The players want to get the ball up and
through the hoop. There are two ways to
do this; they can throw (lift) the ball up into the air so that it goes up and
through the hoop. Or (if they are
tricky) they can push the ball ** down** so that it bounces off the
floor then goes up and through the hoop.
In the second case there is no “lift” involved, rather a

How
can we do this in a sailplane? Assuming
we are flying fairly fast in an approximately wings level attitude and hit an
area of strong sink, we can push the stick forward and go into negative gee so
that the ** downward **moving air pushes us

Let’s
take a general look at sailplane energetics.
An understanding of vectors and vector math can be very helpful when
working in this area, but we’ll try to keep things from getting too “hairy”.

First
of all, how does a glider get energy from the air? A glider (or any other object) gets energy by being pushed ** in
the same direction that it is moving**. The opposite is also true; an
object loses energy by being pushed (or pulled) in a direction opposite to its
direction of motion. As examples: a
glider loses energy via drag which pulls it backwards (opposite to its motion);
a glider in a thermal gets energy from the upward lift force on the wing as it
climbs (both the force and the motion are upward).

The
rate that energy is gained or lost can be called power; it can be positive or
negative. When the glider is getting
more energy let’s call that positive power and when its loosing energy let’s
call it negative power or loss.

To
calculate power we multiply the force in the direction of motion by the speed. The units can be a bit messy here, but if we
take the speed in MPH, multiply by the force in Pounds and divide by 377 we get
Horsepower. As examples: an 800 lb.
glider with a 40:1 L/D has 20 lbs. of drag, if we multiply by 60 MPH and divide by 377
we find that it is loosing energy at a rate of about 3.2 HP. The same glider being pushed upwards in a
thermal at a vertical speed of 1000 feet/minute (about 11 MPH) is getting
energy at a rate of (800 x 11) / 377, or about 24 HP.

In
vector math terms the power going into the glider is the “dot” product of the
velocity vector and the force vector. A
dot product is a measure of how much two vectors point in the same direction,
if they point in opposite directions the dot product is negative. If the vectors are perpendicular the dot
product is zero.

Now
back to soaring. To get the most power
from the atmosphere we want the air to push our glider in the same direction
that the glider is moving as much as possible.
The way that we normally do this is by spending as much time as we can
in upward moving air, where the air is pushing the wing upward and the glider
is moving upward. The faster we are
moving upward the greater the power of energy transfer. The upward force of the air on the wing
averages out to be the weight of the glider.

We can also look at the challenge of getting energy in another way. The conservation of energy law tells us that instead of concentrating on how much energy the glider is getting; we can look at how much energy the atmosphere is loosing. The two are equal (when we consider the glider’s drag losses) and the second way of looking at the situation can be easier when understanding dynamic soaring.

How do we make the atmosphere lose energy? By pushing on the air in a direction opposite to its motion. But first let’s clarify our terminology, the energy we are talking about is large-scale kinetic energy due to air motion, which is the kind of energy a sailplane can use. Heat energy and micro-turbulence are of little use (that’s where the sailplane loses energy via drag).

Once again, to make the
atmosphere lose energy we push on the air** opposite to its direction of motion**. As the atmosphere loses energy the sailplane
gains it. In what direction can a
sailplane push on air? Well-- in any
direction. The wing of a sailplane is
designed to push on air in a direction perpendicular to the wing surface and
towards the landing gear. The wing can
also push in the “negative gee” direction (away from the landing gear), but the
airfoil is less efficient when used that way. By banking and maneuvering the
glider we can orient the wing to push air in any direction: up, down or
sideways.

What
about gravity? Oh Yeah! The wing has another job besides extracting
energy from the atmosphere and that’s holding the glider up, opposing the force
of gravity. This limits our energy
manipulations somewhat, but we can work around it. In fact it is the dual job of the wing that makes upward moving
air such a good source of energy. To
hold the glider up the wing needs to push air down. Upward moving air loses its
energy when pushed down. This is very
convenient; the glider can gain the energy lost by the upward moving air and
hold itself up at the same time.

So
getting energy from upward moving air is relatively easy for a glider, it just
needs to stay in the “lift”. What about
getting energy from sideways and downward moving air; what are the
opportunities and what are the limits?
Because of the above mentioned dual duty of the wing (holding the glider
up as well as extracting energy from the air) it is more difficult to get
energy from sideways moving air and especially from downward moving air, yet it
is still possible. And in some
circumstances it may prove very useful.

To make use of the energy in upward moving air we can use the downward force of gravity to help us push on the air. To push on air that is moving in other directions we can make use of the glider’s inertia. Inertia is the property of mass that causes a body at rest to remain at rest and a body in motion to remain in motion. When a massive body’s motion (velocity) changes a push (force, impulse) is exchanged between the body and its surroundings. When a body’s inertia carries an impulse over a distance it is in the form of momentum.

In the case of a glider there are three kinds
of forces in action: gravitational forces, which act between the glider and the
Earth; aerodynamic forces, which act between the glider and the surrounding
air; and inertial forces, which appear when the glider changes speed or
direction. The gravity force is
constant and acts to pull the glider downward with a force equal to the
glider’s weight. The aerodynamic force
is more complex and depends on air speed, angle of attack, and air
density. Inertial forces can be
measured by “gee meters” (accelerometers) and vary with the glider’s
motion.

The
aerodynamic and inertial forces are the ones we play around with when dynamic
soaring. By pulling pack on the stick
we can increase the aerodynamic force; by pushing the stick forward we can
reduce or reverse the force. By banking
the glider we can tilt the aerodynamic force sideways. As we maneuver, the inertial forces vary in
magnitude and direction so as to remain opposite to the glider’s
acceleration. Centrifugal force is a
good example of an inertial force (which, by the way, the hard core physicists
call a “pseudo-force”). The total
(vector) sum of the three types of forces is always equal to zero. That is to say that; the three types of
forces continually cancel each other out.

More
about inertia … by using the glider’s
inertia we can push on air in any direction at least for a short length of
time. When we use glider inertia as a
basis for pushing air the glider accelerates in a direction opposite to the
push. This is in accordance with
Newton’s famous law F = m a (Force equals mass times acceleration). Acceleration is a change in velocity. An acceleration of one gee corresponds to a
change in velocity of 32 feet per second each second (or a change of 22 MPH per
second). So if we want to limit our
velocity change to 88 MPH we could use our inertia as a basis for pushing at
one gee for 4 seconds in a particular sideways direction. If we wanted to use our inertia to push
upward on downward moving air we would be limited to two seconds because then
both the aerodynamic force on the wing ** and** gravity would be accelerating
the glider downward.

Note
that a velocity change of 88 MPH does not mean a speed change of 88 MPH. When we make a 180 degree turn at a constant
speed of 50 MPH we experience a velocity change of 100 MPH, (50 MPH to 50 MPH in the opposite
direction). When we talk about velocity
the ** direction**
of motion is important.

How much energy (or power) is available from moving air and how efficiently can a wing extract the power? To answer this question we first must clarify what we mean by “moving”. Motion is relative; and in order to get energy we must be able to access both parts that are moving relative to each other. For example, we could be inside a closed window train speeding along at 100 MPH and yet not be able to get any energy from the enclosed air, unless we could somehow connect a force to the outside stationary world. This is similar to drifting along in a glider on a stable windy day; there is lots of energy in the sideways motion of the air, but we can’t make use of it. A kite, on the other hand, can do fine, because the string provides a force connection between the ground and the air, which are in relative motion.

Gravity
provides a sort of downward pulling string that enables us to get energy from
upward moving air. Inertia and momentum
can provide a sort of temporary dynamic string that allows us to get energy
from the relative motion of air masses in any direction, so long as the
distances involved are not too great.
How do we figure what distances will work and what is too far? That depends on how “clean” our sailplane
is. A high performance ship can use its
inertia to carry momentum over longer distances (for the same energy loss)
compared to a draggy ship. Lift to drag
ratio and the relation of stored kinetic energy to the energy dissipation rate
are both measures of momentum carrying ability. Faster ships are relatively less effected by the constant 32
ft/sec^{2 } acceleration of
gravity and can carry momentum more effectively over vertical distances.

The
distance that a particular sailplane (at a particular speed) can effectively
carry momentum before the drag losses eat up any potential dynamic soaring
gains defines an area of operation, which can be specified in terms of distance
or in terms of a time interval. If one
is circling, distance may prove most significant; when flying in a more or less
straight line, time may prove to be a better parameter. The (possibly weighted)
average motion of the air inside the dynamic soaring operations area defines a ** local
inertial reference frame**.

Let’s
consider dynamic soaring with horizontal wind shear and see how it is
done. When we do this we are using our
sailplane as a sort of dynamic windmill.
A windmill is fixed to the ground on a tower and uses the Earth as a
basis for pushing against the moving air.
A dynamic soaring glider transfers push (force, impulse, momentum)
between fast moving air and air that is at rest, or air that is moving more
slowly, or (best of all) air moving in the opposite direction.

The
Albatross is famous for soaring the wind gradient over the open ocean in this
way. How can we do it in a glider? First we connect with the fast moving air
and push on it opposite to its motion.
We do this by banking the glider belly into the wind and pulling back on
the stick; this extracts energy from the moving air and gives the glider extra
momentum in the direction of the wind.
We then maneuver into the air that is not moving (often at a different
altitude) and we bank to push on this air in a direction opposite to the
initial push. This transfers the
glider’s extra momentum into the still air.
Some energy may be lost in this second push (if the air is not at rest),
but overall we can gain energy in the cycle.
We then maneuver back to the fast moving air and repeat the process.

The
energy gained is equal to three factors multiplied together: the force of the
initial push opposite to the air movement, (times) the duration of the push,
(times) the difference in velocity between the two blocks (or layers) of
air. For example, say we bank the
glider and can get a sideways push of 800 lbs. for 3 seconds and the velocity
difference between the two air masses is 20 mph. (800 x 20 x 3) / 377
equals

127 HP-seconds, which
is the energy extracted (we need that 377 constant factor for these Pound and
HP units). If one whole cycle takes 15
seconds we have an average power of about 8.5 HP, which could be a reasonable
amount of power to sustain a maneuvering sailplane. This example is presented for illustration purposes only. Messing around with radical maneuvers near
the ground or ocean (especially in high winds) is very hazardous and is-- how
you say? “For the birds.” There are
many instances of wind shear at altitude however, and these may prove to be a
terrific source of energy for the sailplane pilots of the future.

Let’s
look for a moment at the sailplane’s energy losses; for the energy we can
extract from the air by dynamic soaring is of no benefit unless it is greater
than the additional losses (negative power) caused by the extra maneuvering
required. Sailplane energy losses can
be divided into three categories: basic friction drag (also called parasite drag),
basic induced drag (drag due to lift), and control drag (a combination of extra
friction and induced drag due to control surface deflection etc.). Drag times true airspeed equals power loss.

The
negative power (or loss) due to friction is equal to a constant times the
glider’s airspeed cubed. The negative
power due to induced drag equals a constant times the lift force on the wing
squared divided by the glider’s speed.
Control drag losses can be measured experimentally by wiggling the stick
and observing the increase in sink rate (we don’t have a simple formula for
that one).

We’ve seen how the dynamic power extracted from the atmosphere is equal to the velocity of the air (in a local inertial reference frame) multiplied by how hard we can push against it with the wing. Or similarly, how the power of energy flow that the glider gets from the air is equal to how hard the air is pushing on the glider in its direction of motion times the glider’s speed in the local inertial frame.

In the future there will be instruments designed specifically for dynamic soaring, but here, let’s look at some dynamic soaring techniques that we can use with standard instrumentation. Standard instrumentation in this case consists of: a total energy vario, an airspeed indicator, a yaw string, and a sensitive (gee force sensing) “seat of the pants”.

First
let’s look at vertical gust soaring.
Thermals are often bumpy; how do we make the bumps work for us? As explained above, the general rule in
dynamic soaring is to push on the air opposite to its motion. The faster the air is moving the harder we
should push. This leads us to the first principle of dynamic soaring-- Increase
the gee force in lift, decrease or reverse it in sink. When we feel a bump of extra powerful “lift”
we should pull back on the stick and increase the gee force. Vice versa when the “lift” suddenly poops
out we should reduce the aerodynamic force on the wing by pushing forward on
the stick. One of the difficult aspects of this technique is figuring out what
part of the gee force is from the air’s motion and what part is due to our
control stick movements; experience helps a lot with this!

Working the bumps in this way can increase
the power extracted from the air and thus increase our rate of climb or running
speed. The technique produces a sort of
roller coaster ride and probably will not be popular with passengers. Also extra care is needed if there is other
traffic. How vigorously do we work the
bumps in this way? We can “over do it”
and waste more energy than the extra we’re getting if we are not careful; this
is because the average induced drag increases when the lift force on the wing
is not constant. So some
experimentation is necessary to see what works under various conditions. All
things considered it is best to err on the gentle side.

As we fly faster induced drag is a smaller
percentage of the total drag; this is one reason to fly faster in bumpy
lift. If we are running a cloud street
and flying fast we can work the bumps more vigorously without so much concern
about increasing induced drag.

A
situation where dynamic technique can be particularly effective is when we fall
out of the side of a thermal. In this
case we are suddenly in sink and know pretty much where the lift is (behind us). We want to get back into the lift quickly
and lose a minimum of energy to the sinking air. We could lose a lot of energy in a hurry by pushing downward on
downward moving air. So the first thing
to do after entering the sink is to reduce the aerodynamic force on the wing by
pushing forward on the stick, in an extreme situation perhaps even to somewhat
negative gee.

Next
we can bank up to 90 degrees or so and perform a maneuver similar to the second
half of a wing over (the low gee state can enhance roll rate). Once banked up we can increase the gee force
since we don’t lose any extra energy by pushing ** sideways** on

Now
let’s look at dynamic soaring with side gusts.
This may or may not prove practical, but if we find ourselves in a
situation where the yaw string keeps blowing off to one side or the other (and
it’s not due to uncoordinated flying) we may be able to work the side
gusts. If the string blows to the left,
that indicates a gust from the right and that we should bank left to extract
the energy. One way to do this is to
use the stick alone (no rudder) to initiate the bank, because that will also
straighten out the string and restore the (low drag) nose into relative wind
attitude.

This
is the second principle of dynamic soaring-- Bank away from side gusts. As in the vertical gust case there is an
energy cost to maneuvering, so the amount of bank must be tailored to the
strength of the gust.

In
an ideal case the gusts will oscillate side to side and we can make a series
of “S” turns and get energy. In another case there may be a wind shear
with altitude where we can create our own side gusts by diving and zooming in
conjunction with “S” turns or a racetrack oval course. Here is a link to a diagram showing Side Gust Soaring.

Another
very interesting form of dynamic soaring is flying in a thermal vortex
ring. A vortex ring is like a smoke
ring, only without the smoke, and in the case of a thermal it is moving
upward. This is an unusually smooth
form of dynamic soaring and we may not even know that we’re doing it.

On
the bottom side of a thermal vortex ring there is an inward flow of air; on the
top side the flow is outward from the core.
If we are spiraling on the lower side our bank angle will cause us to be
pushing ** outward** on

Here's a link to a diagram showing Smooth Dynamic Soaring.

In summary, there are many situations where dynamic soaring technique can provide an extra source of energy for the glider pilot. The general rule for getting energy from the atmosphere is-This completes our discussion of dynamic soaring, hopefully the ideas presented here will advance the state of soaring art, producing longer, faster, and funner flights. Techniques for getting energy from the velocity fluctuations in the atmosphere may open a whole new era in motorless flight.

Taras K Ó 2001 tarask@icarusengineering.com