How do spherical SRB's compare to long skinny ones? What do their thrust curves look like?

Question

Most SRBs are long and skinny, probably because most are used low in Earth's atmosphere where aerodynamic drag is large.

But here are some very short SRBs, one seemingly spherical except for the nozzle at one end, from Spaceflight Now's NASA narrows design for rocket to launch samples off of Mars

I wonder if the preferred shape of SRB's would always be closer to spheres than to pencils if it weren't for Earth's atmosphere, or if these are short and squat of necessity due to their need to be packaged and sent to Mars first.

Considering exposed area would increase as $r^2$ for a sphere compared to $r$ for a cylinder, do they have more strongly peaked thrust curves?

This diagram illustrates one concept for a two-stage, solid-fueled Mars Ascent Vehicle. Credit: NASA/MSFC

This illustration shows a concept of how the NASA Mars Ascent Vehicle, carrying tubes containing rock and soil samples, could be launched from the surface of Mars in one step of the Mars sample return mission. Credit: NASA/JPL-Catlech

Answer 1

The STAR 37 solid rocket motor (SRM) was used as an upper stage for various vehicles. It was roughly spherical:

Its thrust-time curve looks like this

It had a 7-pointed star grain. The grain design is really what sets the thrust-time curve. Note the star grain in the upper right of the diagram here from Hill and Peterson "Mechanics and Thermodynamics of Propulsion", third printing, November 1970, page 385.

The STAR 48 SRM was used in the shuttle upper stage PAM system among many others. It's not quite spherical but has a similar curve. It also used a star grain.

Source AYAME/PAM-D APOGEE KICK MOTOR NOZZLE FAILURE ANALYSIS

Answer 2

I wonder if the preferred shape of SRB's would always be closer to spheres than to pencils if it weren't for Earth's atmosphere, or if these are short and squat of necessity due to their need to be packaged and sent to Mars first.

All other things being equal, which of course they never are, spherical casings would give the best volume to weight ratio. Spherical and stubby-cylinder casings are common in upper stage SRMs -- just as stubby and spherical liquid propellant tanks are commonly seen on upper stages. Drag-wise, the diameter of an upper stage is largely already "paid for" by the lower stage, so relatively short and squat upper stages are the rule, which has secondary engineering benefits -- less noodley, shorter duct and cable runs, possibly sharing fuselage tooling with the first stage, and so on.

For very large SRMs, I'm not sure if spherical casings would be workable in the absence of atmospheric concerns; regardless of grain-shaping, the burn rate could get awfully high.