Is it possible to build a jetpack using downward firing machine guns? In theory, yes, Randall Munroe (xkcd) says — although he uses an assault rifle in his example:
In the engineering world, the ratio between a craft’s thrust and the weight is called, appropriately, thrust-to-weight ratio. If it’s less than 1, the vehicle can’t lift off. The Saturn V had a takeoff thrust-to-weight ratio of about 1.5.
As it turns out, the AK-47 has a thrust-to-weight ratio of around two. This means if you stood it on end and somehow taped down the trigger (Note: Please, PLEASE do not try this at home) it would rise into the air while firing.
This isn’t true of all machine guns. The M60, for example, probably can’t produce enough recoil to lift itself off the ground.
He notes that the thrust from shooting ten eight-gram bullets per second at 715 m/s — around 13 pounds — underestimates the total thrust by ignoring the hot gasses — but he doesn’t note that some of that energy is used to cycle the action.
Read the whole thing.
I’m surprised that he didn’t label the Saturn V the Up Goer 5.
Also surprised that in this context he didn’t mention the Orion project, which is conceptually similar and actually built a working model of an explosive propelled rocket.