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Why solid rocket boosters or hybrid engines are favored towards larger hydrogen content, not carbon (C+LOX, C+NO2, C+N2H4O3)?

Is there any known data on Isp and issues of such combinations (both solid and hybrid with significant solid carbon content)?

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Specific impulse of an engine is directly proportional to exhaust velocity - and hydrogen, being the lightest of elements (a H2 particle being just two protons + 2 electrons), using the same amount of energy can be accelerated to much higher velocities than any other elements. A single Carbon is about six times heavier as a H2 particle - and only in compounds, like CO or CO2 it takes gaseous form (the resulting particles even heavier) - raw carbon particles are a solid (soot) that on top of having a total zero of adiabatic expansion ratio (consuming energy of combustion as heat, without producing any thrust), tends to gunk up the engine.

The development of fuels is always trying to find the middle ground between reaction as energetic as possible, and combustion products as light as possible; hydrogen reacting with many other substances can produce good energy and particles that are light - HF, HCl, H2O. Carbon can provide more energy, but with its four bounds it will necessitate much heavier exhaust compounds. While you still do gain ISp by increase of combustion reaction energy, you run into new problems: chamber pressure, chamber temperature, residue build-up, and so on. Lighter exhaust products give higher performance without these trade-offs - at cost of lower fuel energy density.

As for data, I can recommend the book Ignition! by John D. Clark. The chapter "Performance" explains the theory behind achieving as high performance as possible, and the whole book is filled with examples of more or less successful struggles to find propellants where the exhaust is as light as possible (and the even less successful ones where the exhaust products were heavier, or contained solids).

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