"One can derive the ratio of final velocity to initial velocity for a given rate of turn and a given turn L/D. It turns out that the wing loading drops out of the equations. The equation for final velocity divided by the initial velocity is:

V1/V0 = e^ (-theta/LD)

where,

V1 = final velocity

V0 = initial velocity

e = 2.7182818 (natural log #)

theta = turn angle, in radians (180 degrees = 3.14 radians)

L/D = Lift/Drag (glide ratio)

Armed with this equation, one can start to figure out the potential from dynamic soaring. Assume a delta wind velocity of 30 mph, and an L/D of 25 (good for a model sailplane). So, the airplane heading downwind has a ground speed of 60 mph (30 mph from airspeed plus the 30 mph tailwind). After crossing the shear boundary, the airspeed becomes equal to the ground speed. Therefore, the plane is flying 60 mph ground speed in the "dead air" on the backside of the hill. Now, do a 180 degree turn in the dead air. The velocity ratio, V1/V0, for a 180 degree turn is 0.8819. Therefore, the airspeed and ground speed after the turn is 52.9 mph. Now, cross the shear boundary again into the headwind, and the airspeed is now 82.9 mph. Do another 180 degree turn, and the airspeed is 73.1 mph. In a single 360 degree turn, the sailplane gained 43 mph! Eventually, if you keep doing these turns, the velocity loss from the turn will equal the velocity gain from crossing the shear boundary. But, the final velocity will be about 224 mph!



An interesting note is that the maximum potential final velocity is linearly dependent on the velocity delta across the shear boundary. So if the shear delta goes from 30 to 60 mph, the final velocity potential goes from 224 mph to 448 mph!"



In October of 1999, I watched Joe blow up two strong composite ships in one day flying in about 45-50 mph winds. He was only able to make 2 1/2 turns with each ship before the g-load in the turns caused the wings to fail. The first plane broke the solid carbon joiner that connects the wings to the fuselage. The second wing failed in the wing panel itself. It rained fiberglass confetti for at least another 45 seconds after the failure. The speed and acceleration was incredible! Since then I have managed to break 3 sailplanes in flight as a result of structural failure while dynamic soaring.

[img]http://www.liftzone.com/~ade/DS/images/whatis/julian.jpg" width="576" height="311[/img]

If we assume a wind speed of 10mph, and ignore any losses from model drag, turning etc., we can see that a model heading downwind over the top of the hill with an airspeed of 30mph and a ground-speed of 40mph (30mph airspeed plus the 10mph windspeed) crosses the shear boundary into the still air where immediately the airspeed becomes equal to the ground speed i.e. 40mph. You will notice the model wobble slightly as it accelerates.

Now if the model makes a 180 degree turn in the 'dead air' on the back of the hill and again crosses the shear boundary on its way back out towards the front of the hill, its airspeed where it crosses this boundary will immediately rise to 50mph (40mph groundspeed plus 10mph windspeed - now a head wind).
If the model now immediately turns back 180 degrees to the downwind direction where it began, its ground speed will be :

50mph airspeed + 10mph windspeed = 60mph

A gain of 20 mph in a single 360 degree turn!
Now imagine this with a wind speed of 50mph!

Obviously it is not quite so simple as there are factors which affect the net speed gain per circuit. Not least the drag of the model, the size of the circuit and the interference from the pilots thumbs.