Pencil, paper and calculator Heiwa. Thats the only way to do it so you can then go back over it and verify you didnt make any errors.
No wonder you come up with such wildly inaccurate numbers.
Paper and pen? Calculator?? Inaccurate numbers??? What's wrong with a fresh brain and using it for simple calculations?
You claim to work in a responsible engineering position and ask this? Wow!
You are just jealous I assume.
You assume wrong.
Question is how to brake a 1000 kg spacecraft incl. 500 kg fuel. The initial speed of the spacecraft is 7000 m/s. However, the velocity of the fuel exhaust is not 4500 m/s, but a more realistic 2800 m/s. So what is the speed of the 500 kg spacecraft, when all 500 kg fuel has been burnt and ejected as exhaust?
Although this isn't my area of expertise, this sure seems like a routine application of the
Tsiolkovsky rocket equation[nb]It's been ages since I've done this stuff. I admit I had to look it up again to be sure of the details.[/nb]
Delta-
v is your change in velocity,
ve is your exhaust velocity,
m0 and
m1 are the starting and ending masses, respectively (
m0 -
m1 is the mass of the spent fuel), and ln is the natural logarithm function (use the
ln, and not
log, function on your scientific calculator or Excel).
Since we're calculating change in velocity, and
ve is relative to the rocket, the starting velocity is irrelevant. Using a typical 4500 m/sec for
ve as originally specified by Heiwa the change in velocity is:
D
v = 4500 m/s * ln(1000 kg / 500 kg)
= 4500 m/s * ln(2)
= 4500 m/s * (0.6931)
= 3119 m/s.
If it's a braking maneuver, then the final velocity
v1 is the initial velocity
v0 minus the change in velocity D
v.
v1 =
v0 - D
v = 7000 m/s - 3119 m/s
= 3881 m/s
I'm not sure how the 2500 or 2800 m/s he mentions apply. It seems like Heiwa's subtracting
ve 4500 m/s from
v0 7000 m/s to get 2500 m/s, for some reason. If he wanted the velocity of the exhaust relative to the frame of reference
v0 is measured against, for whatever reason, and since it's a braking maneuver, he should
add those quantities and get
7000 m/s + 4500 m/s = 9500 m/s 11,500 m/s, shouldn't he?
Also, using the kinetic energy of the exhaust seems like it's unnecessarily complicated (if it is workable at all - I'm not sure it is). Using
momentum might be easier, but even then... Compounding this by "doing it all in his head" so his different result can't be examined does not lend much confidence in his work.
[Edit] Crap! This is what happens if I try to do math in my head without writing it down.
Removed added. Also, fixed typo.