Conservation of linear momentum

[cristina]

The height that a model rocket launched from Earth can reach can be estimated by assuming that the burn time is short compared to the total flight time, so for most of the flight the rocket is in free-fall. (This estimate neglects the burn time in calculations of both time and displacement). For a model rocket with specific impulse Isp=100s, mass ration m0/mf = 1.2, and initial thrust-to-weight ratio r0=5. Estimate a) the height the rocket can reach and b) the total flight time. c) Justify the assumption used in the estimates by comparing the flight time from part (b) to the time it takes for the fuel to be spent.

I never heard of impulse Isp, I know it is measured in seconds so it has to do with time. Initial thrust-to-weight ratio?? This is really torturing; I had to go to chapters we didn’t cover where they discuss r0= Fth/(m0g), and Isp = Fth(Rg). I can't get the height from The rocket equation (vertical componets). For b) The only equation that has time t in it is the (velocity of the rocket, vertical component),but again there is no Isp nor r0 in it. I am completely lost!

 

[jdavel]

cristina posted: "I never heard of impulse Isp, I know it is measured in seconds so it has to do with time. Initial thrust-to-weight ratio??"

Not quite.

Impulse is the momentum change that the rocket engine gives to the rocket in some specified amount of time. For a constant thrust, it's just F*t, where F is thrust and t is the time. the SI units are kg*m/s.

Total impulse is the momentum change the engine gives to the rocket over the engine's total burn, in other words when t in the above equation is the time for all the fuel to burn. Again the units are kg*m/s.

Specific impulse is a little more subtle. It's the thrust in Newtons (or pounds) divided by the rate that burned fuel is coming out in kg*g/s (or lbs/sec). That's where the overall unit of seconds comes from (lbs/(lbs/sec)).

For a given rocket engine, the specific impulse is a measure of how efficient the burning fuel is at producing thrust. That's because it tells you how much thrust you'll be getting when burned fuel is shooting out the back at some flow rate (lbs/sec). The more thrust you get for a given flow rate, the faster you're going to be going when you run out of fuel. To say it the other way around, if it takes a really big flow rate of burned fuel coming out of the rocket engine for just a little bit of thrust, then your fuel will all be gone before you get going very fast.

Hope that will at least get you started. And don't be "tortured"; this stuff is fun!

 

[cristina]

Do you know how to get the total flight time and the height rocket can reach?