Because of the time involved, no group was able to come to a truly definitive conclusion regarding the optimal design for the simple motor. However, as a class, most good ideas were considered and some solid conclusions were reached. Some very confusing ideas were also put forward, ideas that do not hold up very well under serious scrutiny. In this report I will summarize the work of the class and offer a few comments and questions. I will present all the ideas that I could identify, both good and bad, since they all offer opportunities to learn more about electromagnetics.
General Conclusions: The coil should have more turns, more current, less mass, smaller radius, and be in a larger field than in the original design.
Force: The force is proportional to current and magnetic field. However, increasing the number of turns will not necessarily increase the speed since the mass increases linearly with the turns. This problem can be addressed by reducing the wire size as the number of turns is increased, thus keeping the mass at least constant. Increasing the field can be accomplished by adding a magnet, by enhancing the existing field, or by putting more of the coil into a higher field region. The latter can be accomplished by making the coil smaller so more of its wires can reside within the higher field region near the center of the magnet. Making the coil too small will make poor use of available field. The best compromise is to make the coil comparable in dimensions to the magnet.
Coils and Magnets: Getting the coil closer to the magnet makes the effective field larger. Thus a square or rectangular coil should be better. Very few people found this to be the case. Rearranging the magnets also achieved mixed results, mainly because no on recognized that stacking the magnets on the battery increases the magnetic field because it lowers the overall reluctance experienced by the magnets. Some people thought that the lack of improvement they expected from relocating the magnets was because they did not use a support structure, but rather held them in place by hand. Vibration or bouncing of the coil were found to be bad, since quiet coils went faster. The best simple design was very quiet. Many people tried stacking the magnets but very few thought of shortening the paperclips to achieve the same effect. Only one person provided a really low reluctance path for the field by adding magnetic materials. In this case a C-clamp was used to hold the magnets on opposite sides of a coil. A small attempt to achieve improvement this way was made by two groups that built A-frame support structures out of forks borrowed from dining halls. The forks are too small to have the desired effect.
Batteries: Different batteries worked differently. Most had the experience of reduced performance with an old battery, but few tried more than one type of D-cell. The performance depends a lot on the internal impedance of the battery, since most found it to be the dominant term in fixing the coil current. Some people thought the coil impedance should be matched to the battery impedance, but that would maximize the losses. No one -- even the students who looked at the information on batteries in Horwitz and Hill -- thought to try a Ni-Cad battery, even though they have significantly less internal impedance. The impedance of the coil and the paper clips were not significant unless the wire size was reduced and the number of turns increased significantly.
Connections: Some people tried other materials for the battery-coil connection when they were required to use paper clips. No one tried to find paper clips made out of other materials and, I am pleased to say, no one tried to pass off a home made copper or aluminum paper clip as the genuine article. Quite a few people thought that the paper clips were aluminum -- possibly to save time in finding their conductivity -- even though every paper clip I have seen in the last two years has been plastic or was magnetic. (Testing to see whether the clip is magnetic seems kind of trivial to me.) Very few realized that thicker paper clips or doubling up the paper clips would reduce the resistance -- assuming connections are good. In the latter case, the designers re-discovered the old truism that it is not possible for a one-dimensional object like an axle touch more than two points at once. In two-dimensions this applies to chairs. On no rigid chair do all four legs solidly touch the floor. Only three-legged chairs have all legs equally loaded. Very few people tried to improve directly the connection between the coil and the paper clips.
Drag: Air drag is significant. Reducing the surface area of the coil reduces drag. Friction also plays a substantial role. A couple of people successfully applied a lubricant like WD-40. Changing the size of the axle wire also changed the loading and thus the friction. Adding a lubricant would be a good way to study losses due to friction.
Finite Frequency: Increasing the number of turns increases inductance and back emf. However, at low speeds, these effects are not big. The L/R time for typical coils is quite small when compared with the period of revolution.
Balance: Coil balance was key to good performance. When the coil would sit still and just spin, it achieved the highest speeds. Careful winding of the coil along with rigid supports helped.
Systematic Improvement: Systematic studies of motor performance with different parameters were reported by less than 1/4 of the groups. Few were able to think of a way to do this that changed only one parameter.
Motor Speeds: Motor rotation frequencies were measured, corrected for geometry. That is, the frequency measured by the multimeter was divided by 2 or 4 depending on the geometry of the coil and the position of the laser beam. The fastest with two magnets was 55 Hz, while the fastest with one magnet was 51 Hz. The slowest was 10 Hz. The mean was 21 Hz, while the median was 17 Hz.
Separating Phenomena: Few people realized that they could separate the functions of the coil and the axle. One or two realized that the benefits of fine wire could be achieved and still have a rigid axle if one used smaller gauge wire for the coil and larger gauge wire for the axle. The single wire method will make a cheaper motor, however.
Questions: There were some questions that no one addressed. I will raise them here, but not necessarily answer them.
Most people seem to have conceptualized the interaction between the magnet and the coil as between a permanent magnet and an electromagnet. In this case, the forces are due to the repulsion of like poles and the attraction of unlike poles. This caused some to consider placing a highly magnetic material inside the coil to enhance the field. Most realized that this would block the laser beam used to measure coil speed, but few recognized that the magnet material would be permanently attracted to the magnet and thus keep the coil from spinning. The second way to conceptualize the interaction is to address the force on a current-carrying wire in the field of a permanent magnet. I am sure that the two results will agree, but are there any advantages to one method over the other?
How can a lubricant help the performance of the motor when it is not a good conductor?
Few guessed at the actual distribution of energy. How do you think the energy is distributed?
Given what we have learned about the motor and the design process, what would you do next if the project continued?