Nice pic.Except the Katyusha is a tactical battlefield weapon with a degree of flexibility. The V-1 is a strategic weapon that can only hit a target that's in the direction of its launch ramp and is big enough to be hit by the not very accurate rocket. It's a bad strategic weapon and it would be an even worse tactical one, and I am saying that as the person who drew this:
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I drew this up several years ago, it's a Karl Gerät self propelled 60 cm. siege mortar and ammo carrier converted into a V-1 launcher, like your pic the V-1 here has RATO rockets attached to assist in launching.
Seven Gerät motars were built IOTL the first one entering service in 1941. If the Heer (army) instead of the Luftwaffe had shown an interest in the weapon as a form of long range artillery, I could see something like this being produced in mid to late 1940 but I can't guess what the number of these weapons would be but I'm sure it would be more than seven and a lot cheaper and less time consuming than the Karl Gerät.
Still, not a game changer or a war winner but an interesting alternate weapon system.