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There are some unsourced refutations of the value for the Isp of gunpowder in the table shown below can be found under What kind of engine does this Isp = 1600 refer to? Is it cubesat-friendly?

Alas the links to the source of the table no longer work. While the values for Kerolox, LH2+LOX, H2+nuclear and H + electrical arc all seem plausible, an Isp of 350 seconds for "gunpowder" does make one scratch one's head.

update: per comments there's an archived version of the page here: https://web.archive.org/web/20170112071028/http://web.csulb.edu/colleges/coe/ae/engr370i/ch05/ch4.html

Question: What is the Isp of gunpowder likely to be? Could this table be right? Can it even be determined?

        Fuel          Isp(seconds)
gun powder               350 
kerosene + LOX**         360
LH2 + LOX**              462
H2 + Nuclear             800 
H + electrical arc      1600 
 
  *Measured on the surface of the Earth
  **LOX: Liquid Oxygen

table of some unusual Isp values from California State University Long Beach's course ENGR 370I, Astronautics and Space

above: Table from this page from California State University Long Beach's course ENGR 370I, Astronautics and Space.

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    $\begingroup$ I was busy doing work, so I missed the opportunity to provide an answer. The two answers that have already been provided are in agreement, and are in agreement with my thoughts. That value of 350 seconds is extremely dubious. More likely, that value is beyond dubious and is flat-out wrong. $\endgroup$
    – David Hammen
    Aug 6, 2021 at 10:25
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    $\begingroup$ A capture of the page can be found on archive.org. It's...rather badly dated, claiming that most solid rockets use double-base nitroglycerin/nitrocellulose propellant and suggesting composite propellants use potassium perchlorate and asphalt. web.archive.org/web/20170112071028/http://web.csulb.edu/… $\endgroup$
    – Christopher James Huff
    Aug 6, 2021 at 12:18
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    $\begingroup$ As for the meaning of "gunpowder", for rockets it almost certainly refers to black powder, which can be rammed into a solid mass. Rockets used in fireworks are almost exclusively of this sort. Other types of rockets have used similar materials to those used in smokeless powder, but cast into a solid propellant grain. The same source specifically refers to these as "double base" solid propellants. $\endgroup$
    – Christopher James Huff
    Aug 6, 2021 at 18:00
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    $\begingroup$ Early rockets (before the 20th century) used the same kind of gunpowder that everyone else did. And the early rocket engineers, like Goddard and the gentlemen of the Verein für Raumschiffahrt, knew very well that gunpowder didn't have enough energy to get a rocket into space, so they struggled from the beginning with liquid fuels. That makes me think the listed Isp for gunpowder is too close to that of liquid oxygen and kerosene to be correct. $\endgroup$
    – Greg
    Aug 7, 2021 at 21:14

2 Answers 2

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For the interpretation of "Gun Powder" as "Black Powder", which is the normal usage thereof.

In a normal well-build but conventional black powder rocket, operating at about 100PSI, at sealevel pressure, the ISP peaks at about 90s, with most pyrotechnic or amateur-safe rockets achieving 68s-93s

Some references:
https://www.rocketryforum.com/threads/mass-ratio-of-black-powder-motors.142715/
What's the Isp of a model rocket "D-size" engine, compared to the Isp of engines that do reach space?
Which includes this table for commercial ESTES rockets.

Specific impulses for several commercially available Estes rocket motors

Engine Total impulse (Ns) Fuel weight (N) Specific impulse (s)
Estes A10-3T 2.5 0.0370 67.49
Estes A8-3 2.5 0.0306 81.76
Estes B4-2 5.0 0.0816 61.25
Estes B6-4 5.0 0.0612 81.76
Estes C6-3 10 0.1223 81.76
Estes C11-5 10 0.1078 92.76
Estes D12-3 20 0.2443 81.86
Estes E9-6 30 0.3508 85.51

With a perfect combustion chamber and infinite nozzle operating in vacuum, one can achieve 158s.
This is the theoretical maximum, according to the rocket motor combustion product program PROPEP.

p.s. Just to show how far out that first figure of 350s is: The Space Shuttle's solid boosters, operating with a much fancier fuel than mere gunpowder, only managed a sealevel ISP of 242s (268s in vacuum, but they did not reach vacuum)

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  • $\begingroup$ The normal spelling is "gunpowder" all-one-word which makes me wonder if this actually refers to something like gun-cotton $\endgroup$
    – MikeB
    Aug 6, 2021 at 13:58
  • $\begingroup$ These days, gunpowder refers to modern smokeless powders. (At least among those who use it in guns.) If you mean the older black powder (still used in antiques & reproductions), you specify that. I don't know what the ISP of modern gunpowder would be, but it's certainly quite a bit higher than that of black powder. $\endgroup$
    – jamesqf
    Aug 6, 2021 at 17:13
  • $\begingroup$ The gunpowder used in rockets is black powder, modern fireworks and small amateur rockets continue to use compositions based on black powder. $\endgroup$
    – Christopher James Huff
    Sep 18, 2021 at 13:45
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"Gunpowder" is ambiguous, as it is a mixture of several components, usually optimised for other uses than rocket propulsion.

Nevertheless, I remember reading a rather nice analysis called "Model Rocket Engines Theory and Designs", and after some digging I was able to find it online.
For black powder specifically, they show a specific impulse in the range of 70-80s, way lower than the suspicious value in your table.

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