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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?

illustration of one concept for a two-stage, solid-fueled Mars Ascent Vehicle, NASA/MSFC

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

illustration of concept of how NASA Mars Ascent Vehicle carrying tubes containing rock and soil samples could be launched from the surface of Mars, NASA/JPL-Catlech

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

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    $\begingroup$ The thrust versus time curve of a spherical SRM is still controllable via shaping the interior grain; if you start by boring a narrow cylindrical hole vertically, the length of the burning area decreases over time while the diameter increases. $\endgroup$ – Russell Borogove Apr 23 '20 at 13:47
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The STAR 37 solid rocket motor (SRM) was used as an upper stage for various vehicles. It was roughly spherical:

enter image description here

Its thrust-time curve looks like this

enter image description here

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.

enter image description here

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.

enter image description here enter image description here

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

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    $\begingroup$ I get quite a "kick" out of these motor designs! $\endgroup$ – uhoh Apr 23 '20 at 14:31
  • $\begingroup$ @uhoh there is another motor described in the same paper, SVM-2, which has a more bell-curve shaped thrust v. time curve, but I could not find any description of its grain shape, so I omitted it. The quality of the document scan gets pretty poor in that part so I might have missed it. $\endgroup$ – Organic Marble Apr 23 '20 at 14:39
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    $\begingroup$ The fluting visible in the elevation cross section of the Star-48 is interesting; there's also similar fluting in the drawing of the Iranian SRM shown here. $\endgroup$ – Russell Borogove Apr 23 '20 at 14:54
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    $\begingroup$ @RussellBorogove the Thiokol data sheets in the document linked call the STAR 37 just "star" but the STAR 48 "radial-slotted star". Maybe the fluting is what is referred to by the term "radial-slotted". $\endgroup$ – Organic Marble Apr 23 '20 at 15:02
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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.

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