Relationship between payload weight to the range of a ballistic missile

Question

is it possible to talk about how much extra range a ballistic missile gets if its warhead were to shrink by say 10x?? that is without knowing other details about the missile. For example: Iran claims they have ballistic missiles that can carry a 1500kg warhead up to 2000 KMs.

if the warhead weight were to be reduced to 150kg (10x less) than how much greater range does the weapon get?? sorry I am not physicist so this might sound dumb, but I was thinking if we assume a pure ballistic trajectory (which it may not have) but if we assume that, and if total thrust from the solid rocket is constant but unknown, then maybe its possible to derive a relationship to range but I couldn't do it after a googling these equations for an hour.

Can we say the range would double to 4000 KMs if payload shrunk 10x ??

Answer 1

Yes its possible but in reality that is a difficult problem. For a ballistic missile the range depends mostly on the burnout velocity. This assumes of course that burnout occurs above the atmosphere. But the burnout velocity depends on the mass or payload among other things and on the atmospheric drag of the the missle and payload for the part of the powered flight that occurs in the atmosphere.. For short range ballistic missiles this source has some plots of mass verses range which may help you. A factor of 10 in payload is pretty large.

This study, for long range ballistic missle says that a 1,500 kg payload has a range of 7,500 km. For half that payload, the range increases to 11,000 km. This source also has data on many realistic ballistic missile systems.