Here’s the technical information. It uses a piston engine to spin two smallish propellers. At first look it seems inefficient: the propellers are so small (diameter 1.7 ft so radius is 0.26 m) so the air mass flow is low and hence the velocity of the jet must be high, meaning high power needs for the thrust. (Mind you, it’s efficient compared to a peroxide rocket or a low bypass turbofan engine that have been used for jetpacks in the past.)
But let’s look closer. Engine specs. It’s a two stroke 2.0 liter V4 that produces about 150 HP at 6000 RPM and it weighs 60 kg. The quite high RPM means it produces quite high power.
If the engine spun at a lower speed, you could use bigger props, but the engine would produce less power.
If it spun at a higher speed, you could have higher power for little mass growth in the engine and then use a gearbox to still use the same size or even bigger props (if you geared it down further). But gearboxes are heavy, expensive and often unreliable.
6000 rpm is 100 Hz (rpm is a totally weird unit for spin rate anyway, why is it always used?). Speed of sound is 320 m/s. Hence at 100 Hz the supersonic radius would be 0.5 meters (100 1/s * 2 * 3.14 * 0.5 m = 307 m/s). At the Martin Jetpack’s 0.25 m blade radius it’s about half the speed of sound. At the 7058 max RPM it’s 180 m/s or about 60% of Mach 1 – the transonic region should be easily avoided. Maybe they could be even slightly bigger.
It’s a compromise design. With the small props you can use relatively high engine speeds so your engine stays light – and you avoid a complex expensive failure-prone gearbox. The machine also stays safe as there is no free flailing propeller. With a larger propeller (or two) you would have to give up the shroud(s) since their weight would be prohibitive. On the other hand, fuel consumption would go down and hence the range could increase. It’s a fascinating design space.