Specific impulse

Specific impulse, $I_{sp}$, is the single most quoted number in propulsion. It's a fuel-efficiency rating for rocket engines.

The definition is straightforward:

Force per weight-flow of propellant. Units come out as seconds, which is universally confusing on first contact. Here's how to read it: if your engine produces $F$ Newtons of thrust, $g_0 \cdot I_{sp}$ tells you how many seconds you could keep that thrust running if you burned propellant at a rate of 1 N of weight per second.

But the easier mental model: $I_{sp}$ is just $v_e / g_0$ in disguise. A higher $I_{sp}$ means faster exhaust, which means more push per kilogram of propellant. That's it.

A feel for the numbers

Two things to notice:

1. Chemical rockets cap out around 450 s for LH2/LOX. There's no clever chemistry left to wring more out of the energy density. Past that, you switch to electric propulsion (high $I_{sp}$, tiny thrust) or nuclear (great $I_{sp}$, regulatory nightmare).

2. Hobby motors are an order of magnitude below liquid first stages. That's why model rockets need such a high mass-fraction of propellant for even short hops — chapter 4 (the rocket equation) will make this brutally concrete.

The thrust curve

A real motor's thrust isn't constant. Black-powder motors have a sharp peak followed by a slow tail; composite motors look more rectangular. The $I_{sp}$ quoted on the label is an average; the curve is what determines your max acceleration and where the rocket leaves the launch rod.

The C6 spikes briefly above 14 N before settling into a long ~2 N tail; the H128W stays close to its 128 N average for the whole 1.65 s burn. Same $I_{sp}$ class, very different flight feel.