Q1: Can I increase the force of my solenoid by removing turns?
A1: Yes. This is common practice in the coin op industry. I would caution against carrying this too far, however.
Q2: Why does removing turns increase the force?
A2: It is the net result of two competing factors. Note that the strength of the magnetic field is proportional to BOTH the number of turns AND the current, BUT we generally drive coils with a constant voltage, NOT a constant current. Removing turns reduces the overall length, and resistance, of the wire, thus increasing the current, which increases the force. At the same time, removing turns decreases the magnetic flux through the center of the coil, decreasing the force.
Q3: So the factor due to increasing current is stronger than the factor due to a reduction in turns?
A3: That is correct. The equations in the paper illustrate why that is.
Q4: Can one therefore say that the increased force is due to the increased current?
A4: One could, since that factor dominates, but it is misleading because it implies that is the sole factor at play here.
Q5: If the magnetic field is proportional to both the current and number of turns, why does the current effect dominate?
A5: The resistance, and thus the current for a constant voltage, are both proportional to the length of the wire. That in turn is proportional to the average circumference of the windings, and thus proportional to the average radius. When you remove turns, however, you are removing turns from the outside of the coil, with a circumference that is larger than the average. You are thus removing more than the average resistance per turn, and this is why the increase in current dominates over reduction in turns. If you could remove turns with the average radius, the factors would be in balance and there would be no net gain in force.
Q6: So what would be a better way to describe the reason for the increase in force?
A6: Again, the most accurate way to state this is simply as the net result of the two factors. However, if you describe the resistance and current in terms of average radius, it becomes clear that the increase in current can be attributed to the removal of turns larger than the average radius. Or, you could view this as a consequence of the reduction in the average radius from removing turns. This interpretation confuses some people because it does not mention current at all. However, a reduction in the average radius does cause an increase in the current, and that increase in current does account for the increase in force. The rest of the increase in current is counterbalanced by the fact that you are decreasing N and thus decreasing the number of loops sending magnetic flux through the core. This is illustrated in the governing equations and backed up by experiment (see the paper for details).
Q7: So why shouldn't I just remove a large number of turns if I want a large increase in force?
A7: Because if you go too far the increase in current will burn out the wires in the coil. Removing turns is a convenient way to increase the force of an existing solenoid, but is probably not the most cost effective way, in terms of power, to get more force.
Q8: This is pretty complicated. Can I predict how much stronger my solenoid will be, and how much more power it will draw, when I remove turns? Or how the force of one solenoid will compare to another?
A8: All the necessary equations can be found in the following paper, or you can just use the program below