Zn-S is indeed less powerful than other propellants when only the specific impulse is taken for comparison. When also the density of the propellant is taken into account the situation becomes less favorable for Zn-S. The higher the density the more propellant can be stored in a given motor or for a given dead mass. Hence the mass ratio (mass at the start divided by the end mass after burn out) will be higher. Together with the specific impulse (and the air resistance) it determines the final speed and altitude of the rocket.

Example:

Total construction mass of the rocket (including the coating of the propellant): 20 kg

Motor case volume (excluding the coating): 2500 cm³

Case 1: Zn-S with an Isp of 55s (exhaust speed of 539.5 m/s) and a density of 3.9

- propellant mass: 9750 g

- mass ratio: 1.488 (initial mass divided by the end mass)

- maximum speed (in vacuum and no gravity): vmax = 539.5 * ln (1.488) = 214.4 m/s

Case KNO3-sugar with an Isp of 135s (exhaust speed 1324.4 m/s) and a density of 1.9

- propellant mass : 4130 g (a 15% loss is assumed for the central hole – this is not necessary for Zn-S given the high burning rate).

- Mass ratio: 1.207

- maximum speed (in vacuum and no gravity): vmax = 1324.4 * ln (1.207) = 248.6 m/s

In this case the KNO3-sugar motor would be about 14 % faster. The calculated maximum altitudes under the same conditions ( Cwo = 0.4; motor diameter: 90 mm, burning time: 2s) yields:

KNO3-sugar: 2440 m

Zinc-sulfur: 1870 m