DavidP

I have recently become interested in rocketry, and I am reading about it as I think of fun things to do. A friend and I built some very simple coke-bottle water-rockets several months ago, where we used compressed air and water to propel the rockets into the air. It was fun!

Anyways, I have been reading up on thrust on wikipedia, and I came upon the ideal rocket equation, which describes the change in velocity of a rocket given the effective exhaust velocity and the total mass of the rocket (before its fired while all the fuel is still present) and the final mass of the rocket (after all the fuel/propelant has been used up).

I don't really understand the effective exhaust velocity, however. Its equation is:

v_e = I_sp * g_0

Where g_0 is gravity (9.8 m/s^2).

I_sp is the part I don't understand. According to wikipedia, it is the specific impulse. The wikipedia article about specific impulse states that "it represents the impulse (change in momentum) per unit of propellant". Why then, is the units of specific impulse seconds?

If momentum is P = mv, then the units of momentum are kg * m/s, and thus the units for change in momentum (impulse) would be (kg * m/s) / s.

So the impulse per unit of propellant (specific impulse), would be something like ((kg*m/s)/s) / kg (assuming the amount of propellant is measured in kg). I fail to see how things cancel out to be just "seconds".

Of course, I am not the best mathematician or engineer either, so maybe you guys could shed some light on this?

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brewbuck

You can think of sp. impulse in terms of the MASS of the propellant, or in terms of the WEIGHT of the propellant. If you use mass, you get:

(kg*m/s)/(kg) = m/s

which is a unit of velocity.

If you use WEIGHT, then you get:

(kg*m/s)/(kg*m/s^2) = s

which is a unit of time.

Both are valid definitions of the specific impulse. However, the weight-based measure is what is normally used.

(This is actually explained in the second paragraph of the Wikipedia article)

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Sebastiani

Great explanation, brewbuck - very lucid and concise.

You'd make a great professor. =)

DavidP

Thanks for the clear response.

This small snippet from the wikipedia article on impulse also helped clarify things: "Impulse has the same units and dimensions as momentum"

Whereas I was dividing it by seconds an extra time.

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MK27

Hey so when I are we gonna see your pics from the "camera in a cooler" balloon?

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Bubba

No he wouldn't. He makes sense and is far too realistic and down to earth for that.
A professor's job is to take something simple and complicate it so no one understands it.
A programmer's job is to take something complex and simplify it so anyone can understand it.

I used to mess with model rockets while growing up. Went to a few gatherings filled with model rocket geeks and had a lot of fun. I wouldn't mind getting back into it or perhaps building a model rocket and/or airplane or two. Lots of fun. I never got really deep enough into it to need any equations but it sounds cool.

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Sebastiani

Hehe, well that is often true. My step-dad was actually a physics professor, and although he wasn't always entirely lucid, he definitely tried to be, and generally went to extreme lengths to explain things as well as he good in layman's terms (something a simpleton such as myself can really appreciate). Unfortunately, I was usually more interested in the qualitive (rather than the quantitive) aspect of things, and so only attained a much-less-than-expert level of understanding of the subject. Still, he did a great job of inspiring a deep passion for the field, which I will always have, I believe. Yes, good teachers are priceless, and rare.

Model rockets sound like a lot of fun, though I've never tried it, personally. I once (and quite briefly) had a remote control plane (Christmas of '81, maybe) - it was a huge wood and metal behemoth that ran on gasoline - but unfortunately, it's first flight was to be it's last. It crashed and exploded in a horrendous fireball! After that, I think I lost faith in myself as a pilot of flying machines.

Bubba

Ahh brings back memories of watching my uncle put together his model airplane. He started at around Christmas and I was able to see its progression all the way through to about July of that same year. First flight was its last as well as it nosed in hard on landing. Horrible to see all that work go up in smoke.

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abachler

Specific impulse is the change in momentum per unit of propellant. It is a measure of the overall efficiency of a rocket and rocket fuel combination. Think of it in terms of Newton seconds per gram of fuel. For a given mass of fuel, you get a specific amount of impulse, or 'push' Which can be measured as newtons of thrust over a period of time (seconds). A higher Isp means the fuel/engine combination is more efficient.

There are other considerations however. An ion engine gives a very high specific impulse, but its instantaneous thrust is so low that it cannot be used for launching payloads from the surface of the Earth.

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DavidP

Yes the definition of "change in momentum per unit of propellant" is intuitive and makes sense, I was just having trouble with the fact that it is often denoted in units of seconds, because that hardly seems intuitive, while m/s seems much more intuitive.

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abachler

its denoted in seconds because it is in seconds. Its basically the length of time a given fuel can exert a force equal to its own weight. So a heavier fuel has to have more energy in order to maintain the same Isp.

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brewbuck

The use of the word "unit" is what leaves it open to interpretation so to speak. Unit of weight is more useful in some ways because the weight of the fuel matters more than its mass at ground level.

But there are drawbacks to that, because specific impulse actually depends on your frame of reference. In a free-falling reference frame where weight is zero, the specific impulse is infinite.

As far as launching rockets, I happen to be friends with the whack-jobs who did this:

YouTube - Full Beer Keg Rocket

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Sebastiani

Awesome. Impressive rocket, too!

brewbuck

Those guys make their own propellant and motors. I think the beer keg motor was a size P. The beer that went up was supposed to be something I brewed but I didn't have it ready in time

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MK27

Wow, I am surprised you are allowed to do that without some kind of licence or something. Guarranteed Homeland Security has "these guy's" addresses and such

The cashmere/redneck beerkeg launch that youtube throws up at the end is pretty great.

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