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?