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How much propellant would an ideal single stage sugar rocket with dry mass of 1 kg need to reach the altitude of 100 km in a suborbital flight when launched straight up? Let us assume the specific impulse of its motor to be 120 s.

In case more input is needed (rocket diameter etc.) please try to supply some sample numbers. Please also provide the calculation procedure.

PS. Some people are actually trying to do this - they call it Sugar Shot to Space program (SS2S) - just not with "ideal" rocket.

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  • $\begingroup$ Different but somewhat related and has some interesting answers: Why sugar is not commonly used as fuel in hybrid rocket engine? see also What properties define a good solid propellant for a hybrid engine? (e.g. why not use wood? and links therein. $\endgroup$
    – uhoh
    Commented Jun 5, 2023 at 22:26
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    $\begingroup$ As ever, there is a relevant XKCD for your challenge. $\endgroup$
    – Cadence
    Commented Jun 5, 2023 at 23:15
  • $\begingroup$ @Cadence I love it! For today's procrastination I will think about how the staging profile (that double bell shape) can be calculated - should I use Monte Carlo? A variational approach? A genetic algorithm? Brute force calculation for all possible configurations? Hmm... gonna make another cup of coffee and continue to mull it over... I wish I were a professor so I could assign it as homework just to see what happens :-) $\endgroup$
    – uhoh
    Commented Jun 10, 2023 at 0:58
  • $\begingroup$ @Cadence He's making it much more complex than it needs to be! E9-0 engines! 12% lighter and much simpler staging. I don't think it will be stable enough to reach space, though. $\endgroup$
    – Loren Pechtel
    Commented Jun 13, 2023 at 0:34

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The solution turns out to be quite simple. We can use the Tsiolkovsky rocket equation but we need to find out the delta-v needed to reach Karman line (altitude of 100 km) first. Using this answer we can realize that the delta-v needed in theory is about 1400 m/s, but for real world rocket we need to consider about 2100 m/s. The isp of 120 s gets converted to exhaust velocity of about 1200 m/s. Then we plug all this to rocket equation and solve it for m0 (initial total mass of the rocket). We can use online calculators like this or this.

The result is following:

  • ve (exhaust velocity) = 1200 m/s
  • mf (final mass) = 1 kg
  • delta-v = 2100 m/s
  • computed m0 (initial mass) = 5.75 kg
  • propellant mass = m0-mf = 4.75 kg

A single-stage rocket with dry mass of 1 kg needs 4.75 kg of "rocket candy" propellant to reach the height of 100 km.

The weights scale linearly so a 10 kg rocket will need 47.5 kg and 100 kg rocket 475 kg of propellant.

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