I. What is the dynamic underwater soaring project ? 

This is an attempt to use the logic of dynamic soaring in the open water. In the case of dynamic soaring, a sailing plane tries to use the wind shear that is to say the wind speed changes to gain some energy and thus to gain some altitude without motor.

Underwater, even if there isn't any current shear, we can use an unlimited energy resource in the same way; this unlimited energy resources are the water waves.

As in the dynamic soaring problematic, we will consider a sailing plane (more precisely an underwater soaring wing), that will use the different water stream direction (at different time instant) to generate thrust and thus gain speed and kinetic energy without motor. 

II. Physical consideration

For better understanding, we assume that the underwater flying wing has already gained some speed and is travelling under the waves with a speed v.

When the wing is between the bottom and the top of the wave, the wave relative to the wing is "forming" and thus the z component of the relative water stream speed will be positive, as displayed in the following image.

Inversely, when the wing is between the top and the bottom of the wave, the wave "seen by" the wing is "lowering" and thus the z component of the relative water stream speed will be negative, as displayed in the following image.

In the above images, we have also displayed the lift force caused by the waves on the wing. If the wing is correctly designed, the drag will be very small compared to the lift and thus neglectable. As seen on this images, the lift force will create on both situations a thrust that is (if the wing profile is symetric and if the drag is neglectable) always positive (relative to motion direction).

In other words if our wing is properly designed, it will fly endlessly without any need of external energy such as a motor. We can even think that if the thrust is always positive, the wing will always accelerate, gaining incredibly high speeds. Unfortunatly, in the real world the reality is different, at some high speed the drag will not be neglectable anymore and thus the thrust will become negative braking down the speed of the wing. Moreover, at low speed the wing can stall and thus the drag will also not be neglectable anymore.

But here we are, the concept seems to be interesting in large speed ranges as we will see later.

III. engineering consideration

• As we have seen, if we need a positive thrust whatever the stream incidence angle sign is, we need a symetric airfoil profile.
• We need a wing with the highest possible lift and the lowest possible drag. In fact, we need a wing profile with the highest possible lift/drag ratio.
• For simplicity and performance, we need a floating wing, in other words neither heavier or lighter than water. The wing weight W should then be around W=1000*V where V is the volume occupied by the wing.
• Some design consideration have also to be taken into account to stabilize the wing. Contact me for further informations about the wing stability.
• To minimize induced drag and maximize lift, we should consider a wing with a high aspect ratio and with an elliptic cord length distribution.
• The water stream path is not straight, thus to avoid curvature flow effect, the wing cord length should be designed as small as possible compared to the wave length, and the wing should be tailless, thus it should be an "underwater flying wing".
• Wing structure strenght should be as high as possible as the wing can encounter here very high lift forces.
• It is advised to add flaps to be able to control the wing. We can even consider jumping out of water like dolphin do.

IV Modeling and Simulation

With a matlab clone (scilab), I have modelised the thrust we can get versus the speed of the wing. If the thrust is positive, this means the wing gains speed without any use of external energy. If the thrust is null, the wing will remains at the same speed without any use of external energy. However if the thrust is negative, an external source of energy is needed (such as a motor) to maintain the speed constant.

In this modelisation, the drag has not been neglected. The lift and drag polars of a particular wing profile has been fully taken into account.

However, the water praticle circular orbit path has not been taken into account. The z speed component of the wing has not (yet) been taken into account.

Here is the result

[ The modelisation result comes very shortly, please be patient ]

As we can see, for very low speed, the thrust is negative, it is because the wing stalls so that the lift generated is too low to overcome the drag. Thus we need a motor for these speed ranges. In other words our wing will never be self startable, it will always need a motor for starting purpose.

However, when the wing gains some speed, the thrust becomes extraordinary high, thus the acceleration should become outstanding and our wing speed can become very high.

V What next ?

I have published this project on my web page to develop this project in a collaborative way. As I do not have the time, nor the materials and maybe not the skill to build a high quality underwater flying wing. I am looking for peoples that could help me to build a prototype and thus to validate this new concept.

So, If you have the skill, if you have already made some well designed model aircraft and if you are interested in this concept please fill free to contact me.  In return, I will incorporate you fully in the project and give you all the necessary plans and informations to fullfill this outstanding new concept.

If you think my english is bad (you are right) please fill free also to contact me. I will correct bad sentences right away.

If you have usefull scientific information to share please fill free again to contact me. This project is for sure perfectable.

Hope to see you soon,

Philippe Crochat