Dynamic soaring

Dynamic soaring is a flying technique in which can attract a bird or a plane energy from a non-constant wind field ( wind shear ). Here, the bird or the pilot of the aircraft attempts to choose the flight path so that the energy gain exceeds (due to wind shear ), the loss of energy (due to the flow resistance ) in the time average.

Taking advantage of the Dynamic gliders can albatrosses few meters above the sea to cover flying very long distances. The Dynamic soaring is also practiced by glider pilots. While the albatross utilizes the energy gain for locomotion, is exploited in the dynamic soaring with gliders the energy gain to fly faster for fun on a locally approximately constant path.

• 3.1 Model Assumptions
• 3.2 Two different state changes
• 3.3 Description of the states in four places

Principle of operation

A simple model, in which the functional principle of the Dynamic gliding can be explained, consists of two layers of air with different wind speed: The aircraft is cyclically from one layer to another, and pierces repeated the interface between the layers of the atmosphere. Below this two -layer model is described in detail, in brief: When piercing and in the bends, the velocity ( airspeed ) and the speed relative to the ground change over the air ( ground speed ). In each cycle, the aircraft gains speed - that of kinetic energy. Depending on whether you look or the kinetic energy in an inertial system (such as " above ground " ) in each case with respect to the local air ( see next section), the energy increase takes place in the (upper) turn against the wind instead of ( elastic collision ) or each at the sudden increase of the relative wind in the transition to the other layer of air.

The latter approach is used in the following generalization to arbitrary maneuvers and wind fields taking into account the potential energy. Starting from the momentum equation for the plane as a mass point at which except the weight of only the air forces attack lift and drag are obtained by simple transformations a balance equation for the (specific ) energy of the aircraft. Based on this balance equation, the effect of wind shear can be seen.

Energy balance

Reference system, speeds and forces

The reference system is up to the gravitational acceleration free of slip forces. It can be a connected to the ground coordinate system ( " above ground " ) or one that is constantly moving with the mean velocity of the wind.

In such a frame of reference are the velocity vector of the aircraft and the velocity vector of the air at the place at which the aircraft is in each case just so that the airspeed is. The main effect for the time derivative of the velocity, which contains both the actual time variation of the wind field as well as the most dominant contribution of the directional derivative.

Lift and drag are used as specific sizes ( unit N / kg), so as acceleration as the acceleration of gravity, so that the mass of the airplane can shorten out.

The resistance is defined as parallel to the flow and the buoyancy perpendicular to it. The latter can be expressed by dot product as:

Momentum and energy balance

Valid according to the law of momentum

So

To gain an energy balance, the last equation is multiplied with scalar and used. It follows

Provides insertion of v = w u

If the amount of designated g and written to the parallel component of the velocity as a rate of change of height, so is thus obtained

Application of the product rule gives an assessment of the specific energy compared to air '

Also useful is the representation

Evaluation of result

The specific energy compared to air ' is the sum of, kinetic energy to air ' and potential energy. This energy is the for gliders ( or birds ) significant. An excess of, kinetic energy to air ' (too high speed to air ) can be converted into height and vice versa. For this reason, the change show variometer precisely this energy (up to a factor mg).

The time variation of the specific energy compared to air ' is influenced by the three terms on the right side: The first term is the specific power due to resistance. This term is always negative. The middle summand is the specific power of updraft or downdraft. Is upwind. That is, increase the energy of updrafts aircraft. The right-hand summand is the specific power due to the wind shear. It shows that energy gain arises from the wind shear on those portions of the trajectory where the wind component increases in the flow direction -u, ie where.

In the last equation it can be seen: When the vector of the total aerodynamic force (acceleration) in the direction of w ( of the wind speed from the average wind), it increases the energy 1/2 · V V gh. To avoid misinterpretations, should be v and w are defined as velocities relative to the mean wind speed.

For most wind fields it will not be possible to choose the flight path so that more energy is created profit - but in the ( temporal ) means you can achieve this often.

Suitable trajectories

Not every trajectory can gain energy from a wind field. But at a given wind field and aircraft to flight paths can compare to the effect how large the energy gain (per time).

If a horizontal, constant direction, but increases with altitude wind blows, as shown in the above image is suitable as a trajectory eg an inclined loop whose lowest point is the most downwind located simultaneously. The upper half circle, can ' be folded down so that an albatross or aircraft also can move transversely to the wind direction.

Even if the wind blows vertically and not constant ( such as in a field of lift ), the aircraft can gain from this shear energy: For example, if the field of lift in his heart is strong and the edge is weaker toward, it is cheaper, ' fly in in the field of lift and upwards ' down out of it to fly than vice versa.

Two -layer model

Alternatively, the energy gain of the aircraft on a two -layer model to illustrate.

Model assumptions

• Notation: v is the magnitude of the velocity vector over ground, w is the magnitude of the wind velocity vector.
• Below a separation layer rule no wind, ie w = 0 Rule above layer wind w to the right.
• The plane generating, while the separating layer is flying either above or below ( but not to ), no resistance.
• When passing the separating layer, the air forces remain independent of the separation layer thickness is limited.
• The aircraft fly through the separation layer as shown under very small angles.

Two different state changes

The aircraft experienced two different state changes:

Description of the states in four places

• Position 1: flying into the separating layer: Speed ​​vs.. Reason ( initial velocity ). Since there is no wind, the speed is prev. Air.
• Position 2: The velocity vs.. Air is increased to, speed over ground still ( plane flies to the left).
• Position 3: Here and ( plane flies to the right and has a tail wind, before it flew to left ).
• Digit 4: Well and is (regardless of the direction of flight).

This process can be repeated now. The kinetic energy of the aircraft rises to always on.