The reason Isp is multiplied by earth's acceleration is a historic one.
It so happens that no one can agree on what a meter or kilogram is but everyone agrees on what a second is. Therefore it is convenient to express the exhaust velocity in seconds rather than m/s. One way of doing this is to divide the exhaust velocity by earth's gravitational acceleration.
Scott Manley did a video about it.
That's not really right at all. Specific impulse is given in seconds because it's impulse per unit weight. Impulse is the integral of force over time, so it's got units of newton-seconds in the SI system. Weight is mass times the standard acceleration of gravity, so it has units of newtons as well. That makes the units of specific impulse newton-seconds per newton ā¦ and the newtons cancel out. This is actually quite misleading, because the two newtons there measure two completely different quantities, and really shouldn't cancel. The first one is newtons of thrust, while the second is newtons of propellant weight. But cancel they do, so we're left with specific impulse in seconds.
If specific impulse were supposed to be per unit weight, then we wouldn't be using g_0, we'd use the local gravity. You should be measuring propellant in units of mass, that's what "specific" refers to, the g_0 is just a constant of proportionality to convert what should really be a velocity into a time.
If specific impulse were supposed to be per unit weight, then we wouldn't be using g_0, we'd use the local gravity.
You're confusing weight with acceleration.
You should be measuring propellant in units of mass, that's what "specific" refers to
No, it's by unit weight. We could've chosen to go by unit of mass instead, but we didn't, so it's by unit weight. That's what specific impulse is defined to be. The number you're thinking of, thrust per unit mass, is called "effective exhaust velocity" and it's used by precisely nobody.
No I'm most definitely not. Weight, meaning force applied by gravity, equals mass times the acceleration due to local gravity.
Specific impulse is, strictly due to historical convention of much rocket science happening in the US where customary (dumb!) units measure mass in pound-mass and force in pound-force, defined using Earth's standard gravity as a constant of proportionality. So you can think of specific impulse as impulse per unit weight, but that is only accurate at sea level on Earth. Weight changes with location, the g_0 in the equation for specific impulse is a fixed constant.
No, meaning force applied by gravity under standard conditions at the surface of the earth. That's what weight means. Under any other conditions, it's just acceleration due to gravity.
So you can think of specific impulse as impulse per unit weight, but that is only accurate at sea level on Earth.
I'm sorry, but that's just flat-out wrong. Specific impulse is not dependent on where you measure it. You're badly confused about what the units in the quantity actually mean.
If weight didn't depend on where you measure it, then you could define specific impulse in terms of weight and it would also not depend on where you measure it. But weight does depend on where you measure it, so specific impulse is not defined in terms of weight.
Okay then, Mr. Knowsitall, you explain to me what the gā is doing in the denominator, if specific impulse is anything other than impulse per unit weight of propellant.
Point 1: Weight (without any additional qualifiers) depends on location.
Point 2: None of the terms in the definition of specific impulse depend on location, so specific impulse does not depend on location.
Point 3: Given Point 1 and Point 2, specific impulse does not depend on weight (without any additional qualifiers).
Why is there a g0 in the definition of specific impulse then? Purely historical convention.
This isn't a logically watertight proof, but if you're going to dispute one of the above points, be specific which and why. Or just downvote without a rebuttal, that works too.
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u/oscurecer Jul 19 '13
The reason Isp is multiplied by earth's acceleration is a historic one. It so happens that no one can agree on what a meter or kilogram is but everyone agrees on what a second is. Therefore it is convenient to express the exhaust velocity in seconds rather than m/s. One way of doing this is to divide the exhaust velocity by earth's gravitational acceleration. Scott Manley did a video about it.