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While going through Sutton's propulsion elements text, I came across an example where he compares the values of impulse-to-weight ratio to that of specific impulse and deems it a "fair design".

The value of the impulse/weight ratio was 187s and the specific impulse was 240s.

I'm having trouble wrapping my head around how comparing the two value lets you determine this.

The specific impulse of a propulsion system measures how much impulse you get per unit mass of propellant consumed.

The impulse/weight ratio (actually impulse/mass, and sometimes called system specific impulse) measures how much impulse you get per total mass of a launcher or stage.

A theoretical "perfect" rocket, with zero mass for structure, engine, tankage, avionics, and so on, would have the same impulse/weight ratio as the propulsion system specific impulse, but this is obviously impossible; the non-propellant components have mass. So the specific impulse is an unreachable upper limit to the impulse/weight ratio. If you have very little dry mass in your design -- very thin tanks, minimal structural weight, engine whittled by elves from an Unobtainium billet, etc., then the impulse/weight ratio is closer to the specific impulse.

The example design reaches 78% of the limiting specific impulse.

Delta IV Heavy has a system specific impulse of about 352 seconds; some rough calculations tell me its propellant-mass-specific impulse averages around 389 seconds, so it gets to about 90% of the limit.

Falcon 9 FT system specific impulse is about 259 seconds and its propellant-mass-specific impulse averages around 307, so it's about 84%.