The Flight of Insects. Conchospirals
- Author:
- Irina Boyadzhiev
- Topic:
- Parametric Curves
How do insects orientate themselves when they fly in the night? They try to keep a constant angle, say between the direction of the flight and the direction to some light source. They also keep a constant angle with the direction “down-up”.
When the light source is very far away (like the moon), the light rays are practically parallel and the flight is on a straight line. When the light source is a light bulb, the rays are radial and the flight is on a conchospiral (see reference).
Assuming the light source is at the origin of the coordinate -system, and above the insect when it starts flying, we can describe the initial position of the insect by the vertical distance to the source and angle .
The trajectory is a conchospiral winding on a cone with a vertex at the light source and opening of . The trajectory cuts the light rays on the surface of the cone at a constant angle .