3 ms·

The equation is about mass, not velocity. The mass a rocket can lift into space is inversely proportional to the mass of the propellant. To increase the payloa

• ben_w 3y ago
  Δv = I_sp * g_0 * ln(m_0/m_f) Or are you talking about a completely different equation? This one, which is the only one I know of to get this moniker, is about mass fraction, not absolute mass. You can perfectly compensate for making m_f bigger by making m_0 bigger by exactly the same ratio, hence for fixed Δv, m_0 increases linearly with m_f. Two rockets joined horizontally has twice the mass of one rocket alone, and accelerates twice as much payload to the same relative velocity as a single rocket. Two rockets joined end-to-end, with the second rocket being the payload for the first, makes the ultimate payload of the second stage go faster than if it had only been propelled by the second stage with no boost from the first, but significantly less than twice as much faster. You can also see this example by asking the inverse: if it was exponential with regards to absolute payload rather than the payload as a mass fraction, that would mean that dividing any given payload into two or more parts, launching them separately to the same ultimate velocity, and having them join together in space, would save fuel — it doesn't, QED. (There are other reasons to build in space, like "our rockets aren't big enough and nobody wants us to build bigger ones", but that's a political equation, not rocket science).