The V2 rocket was the first to cross the Karman line. To pass it you need at least 1.4 km\s. How much delta V did the V2 rocket have?
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asked Jul 28, 2022 at 18:56
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$\begingroup$ Delta V depends on payload. How much payload do you think of? $\endgroup$– UweJul 28, 2022 at 21:10
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$\begingroup$ You won't reach the Karman line with 1.4 km/s of velocity. You can't ignore air resistance when throwing objects at supersonic speeds. $\endgroup$– notovnyJul 29, 2022 at 12:44
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1 Answer
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I am finding significantly different specifications for the V2 from different sources (Astronautix, Wikipedia) -- probably because they weren't all built the same -- but assuming a gross liftoff mass of 12805 kg, mass at burnout of 4008 kg, and sea-level specific impulse of 203 seconds, the Tsiolkovsky rocket equation
$$\Delta v = v_\text{e} \ln \frac{m_0}{m_f} = I_\text{sp} g_0 \ln \frac{m_0}{m_f}$$
tells us that the delta-V would be around 2300 m/s. The specific impulse would increase with altitude to a maximum of 239 seconds in vacuum, so the delivered delta-V might be closer to 2500 m/s.
answered Jul 29, 2022 at 3:39