Turn spacing for helical heating coil?
While I would be quick to jump on the &quot;just simulate it&quot; bandwagon for tasks like this, I'll take a shot

Reflections off the rods, assuming the wire of the coil radiates fairly evenly about its circumference, having a wider gap between the coils means there is a larger proportion of paths from that circumference that can either freely escape, or reflect off the rod and miss another heating coil, so the heat is spread over a wider angle on average, meaning the wire should be slightly cooler.

Resistance, The smaller the spacing, the longer the coil is in total, you cannot trip the circuit its on, so the resistance has to be high enough to not do this, equally to get the maximum wattage out of a given supply voltage you want to be as close to the ideal resistance as possible, e.g. for a 240V, 10A circuit, P = IIR, so 2400W / 10 / 10 = 24 ohms, matching the resistance of your wire to reach this resistance would be ideal

Thermal change in resistance, the larger the surface area the same heat energy is spread across, the lower the temperature on that surface, so the more turns in your coil, the lower the temperature in the wire, and the lower the temperature change from ambient, the less increase in resistance when at operating tempeature,
Based on all this, I would work to find your ideal resistance by knowing your supply voltage and current limits, find a wire thickness and number of turns that meets that at expected hot and cold temperatures, that fills as much of that surface as possible, increasing the spacing only if you need a wider angle for the heat to be spread over.