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Engines and fuel management are very expensive to develop, and for smaller launch providers and space agencies this could prevent them from entering the market. My question is, would the cost savings made on solid propellant, presumably at least, in both R+D and actual production outweigh the ISP cost? Is there a point where it becomes more cost-effective to switch to a more expensive but more efficient fuel as the required delta-v increases, and is this point greater or less than that required to reach orbit?

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There have been a few purely solid-fuel orbital rockets over the years. The first was the Scout from 1961; the only ones in current use are the Long March 11 and the Minotaur/Minotaur-C family. There are more "nearly-pure" solid-fuel rockets such as the Shavit-2. These use three or more solid-fuel stages to get into an orbit, and then a liquid-fuel top stage to reach exactly the desired orbit.

The above hints at why these rockets aren't more common: they've got a number of drawbacks.

  • Large numbers of stages. Solid-fuel rockets have at least three stages; five stages is not unknown. Compare to liquid-fuel rockets, where 2 or 2.5 stages is the norm.
  • Low payload fraction. The Minotaur-C has a payload fraction of 1.9%, while the Scout had only 0.7%. Compare to the Falcon 9, which has a payload fraction of 3%, or the Delta IV, with 4.5%.
  • Lack of precision. Once you ignite a solid-fuel stage, you've got to let it burn to fuel exhaustion, which means you'll almost always overshoot your intended orbit.
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    $\begingroup$ There have been solid fuel stages that could be stoped by blowing a hole into the hull. $\endgroup$
    – Uwe
    Apr 30, 2021 at 10:38
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    $\begingroup$ @Uwe, the ones I've seen do that by blowing the front off, so that thrust out the back is balanced by thrust out the front. Kind of a problem when you've got a payload in front. Unzipping the sides of the rocket body could also work, but now your payload is orbiting in a cloud of fresh space debris. $\endgroup$
    – Mark
    Apr 30, 2021 at 20:22
  • $\begingroup$ One could possibly disconnect the payload as the solid rocket booster travels through the intended orbit.. have the payload mounted on the side, for instance $\endgroup$
    – Innovine
    May 1, 2021 at 14:53
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The SS-520 is a solid fuel rocket and is described in detail in my answer to Do launchers using only solid propellant exist? SS-520-5 has put the Tricom cubesat into orbit, therefore it also qualifies as a "completely solid fuelled orbital rocket".

The second attempt at becoming the smallest orbital launching rocket was made on 3 February 2018. Liftoff from Uchinoura Space Center occurred at the opening of a ten-minute window at 14:03 local time (05:03 UTC), successfully deploying the TRICOM-1R CubeSat.

SS-520-4 rocket. From http://spaceflight101.com/ss-520-4-rocket-launches-on-experimental-mission/

above: SS-520-4 rocket. From Spaceflight 101, Image: JAXA

Related:

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I can't say how all-solid launchers compare cost-wise with liquid or mixed launchers, but they're viable.

The Minotaur I and Minotaur IV rockets are all-solid, four-stage orbital launchers.

The R&D and production costs for the Minotaurs were offset to some degree by the use of converted ICBMs.

The Vega rocket is a 4-stage orbital launcher with solid rocket motors on the first three stages. The upper stage is liquid-fueled, but that's mainly to allow precise control of the final orbit and provide roll control during ascent.

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ISAS, now a part of JAXA, has a long history of using solid fuel to launch scientific satellites. Eight different vehicles, not including the SS-520.

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The ISRO had two fully solid fuelled launch systems called the Satellite Launch Vehicle ( SLV ) and Augmented Satellite Launch Vehicle ( ASLV ). SLV was a four stage launch vehicle with a payload capacity of 40kg to LEO and ASLV was 5 stage with 150kg to LEO.

Both launch vehicles were considered as experimental and never intended to have a long service life. Both the vehicles had 4 launches each. They were the first launch systems to be developed by India. It was easier for ISRO to experiment with solid launch systems as it had no experience and less funding.

After these two rockets ISRO switched to liquid fuel for increased efficiency. The curently operational PSLV ( Successor to ASLV ) has 2 solid and 2 liquid stages to increase performance and provide precise orbital insertions.

Satellite Launch Vehicle :

Satellite Launch Vehicle

Augmented Satellite Launch Vehicle :

Augmented Satellite Launch Vehicle

Sources : Wikipedia, isro.gov.in/launchers

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