Some Notes on Towing Gliders as Kites

Towing gliders is more complicated that it looks. On tow, a glider is essentially a kite and the kite equations should apply. Twelve twelfth degree partial differential equations with cross derivatives constitute the equations of motion for a glider. A kite requires 18 eighteenth degree etc. This is because the towing force affects the dynamics in complex ways. The first time I tried to solve this mathematically it took all day to invert the 18 x 18 matrix to solve the equations. Many of the terms had been guessed and I wondered how many mistakes I may have made in doing the calculations by hand, with a slide rule. I was not going to do it again. Also, the theory makes certain simplifying assumptions which I found to be unrealistic. I found that experience teaches us the main things we need to know. There are characteristic forms of kite instability that can be recognized which can guide our response. The best kite to experiment with is Bill Bigge’s Janus. (Or something similar.) This kite has slots fore and aft for fins. You can fly various combinations of fin length and plot a diagram of the forms of instability. This divides the plane into nine regions, each with a characteristic form of action. The behavior also depends on the length of the tow line and the wind speed.

The most common form of instability for towed gliders is known as yaw divergence. (It corresponds to too much tail fin / not enough forward fin. This is analogous with what glider flyers call the spiral dive, which is associated with too much tail fin / not enough dihedral.) It begins to climb, but turns off to the side. The turn accelerates. A symmetrical kite will turn either way with indifference. Asymmetry will bias the preference, but not necessarily dominate. It depends more on which way it happens to get off course at the start. This is analogous to the spiral dive of gliders, but not exactly the same, because of the effect of the string. In both cases the divergence will accelerate. In the case of the kite, pulling on the line or running faster will accelerate the acceleration. This is the natural reaction, trying to pull it into flying straight forward, but it has the opposite of the intended effect. The towed glider will spin into the ground and crash. A shorter line will make it worse, everything happens faster. In a favorable case, relaxing the line and moving in the direction the kite is moving can let it settle into a normal glide mode where normal dihedral will level the wings, then you can GENTLY ease it back into forward flight. You want to be directly upwind of the glider or it will go off in the opposite direction.

The spiral dive is caused by the fact that the kite is side slipping and the side slip pushes the fin to accelerate the yaw, increasing the divergence. At the same time, the towline force is dominating gravity, so the dihedral correction is not working to level the wings. It is working to make the belly point toward the tower. The tow force will be many times the weight of the glider and will dominate the action. You can’t pull it out of a divergence, you must relax tension and let it settle.

There are some suggestions that may help reduce this tendency. Use a longer tow line. Don’t reel it in, but run with the reel. Hold the string in your fingers to better feel and control the tow force. You need to control the speed and direction of tow. In general, reducing tail fin and adding forward fin would be recommended, but may not be appropriate for a scale glider. You can add a fin to the end of the towline, which will come off at release. You should trim CG for minimum sink and attach the tow to correspond to CG of maximum L/D. That gets you highest tow angle and longest glide. Here is a simplified discussion of trimming CG and locating the tow point.

http://www.endlesslift.com/flying-expanded-polystyrene-gliders-as-kites/

A fuller discussion may be found in Frank Zaic, 1957-58 Model Aeronautic Yearbook, page 112, “TOWLINE GLIDER STABILITY (During Tow).”

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