astrophysics question!!!

[power5000]

so I got home from school and started nerding out xD so correct me if I'm wrong.

Dv=ISP*LN(total/dry)

ISP=total impulse/weight of fuel

total impulse= Thrust*time

adv srb type A

Thrust = .150T = 300lb

Time = 50 seconds

total impulse = 300*50 = 15000 lb-sec

ISP = 15000 / 3.75 = 4000

11K DV? = 4000 * LN(4/.25)

that is only for the rocket the smallest you can get it is the mass to be 5 and dry to be 1 so

6300 = 4000 * LN(5.04/1) that is a probe, rocket, and nozzle

REVISION!!!!!

Ve= effective exhaust velocity

M0= full mass

M0= dry mass

G0=9.81

F= thrust in Newtons

q=fuel rate

delta-v=ve*Ln(M0/M1)

Ve= ISP*G0

ISP=F/qG0

So our Thrust is .150kT or 1470 newtons

q= 3750/50 or 75 (kgs/s)

so our ISP = 1470/(75*9.8)=2. (seconds)

the effective velocity = 2 * 9.8= 19.6 (m/s)

the deltav=19.6*ln(4/.25)=54.3427389558997123

Edited September 5, 2013 by power5000

[K^2]

You are mixing units. That's not a good way to do things, and I'm pretty sure there is an error in your computations because of it. (But because you don't label all of your numbers, I'm not entirely sure. What's '3.75' in "ISP = 15000 / 3.75 = 4000"?)

It's possible to do all of this in imperial units, but you will pick up a factor of 32ft/s² in there due to difference between pounds of force and pounds of mass. At any rate, it is way easier to convert everything to metric.

There is also a difference of convention in I_SP. It may be defined as impulse per weight or impulse per mass. You will then get I_SP in units of seconds or m/s respectively. Your computations are set up to look as if you have specific impulse of 4,000s, which is way too much. Even NERVA only has about 800s, and to get 4,000s you need an ion drive. SRB would have something closer to 250s.

And if you define I_SP as impulse per weight, then the correct formula for delta-V is I_SP*g*ln(m1/m0). The factor of g, which is Earth's gravity by convention, ensures that your delta-V comes out in m/s. Units are important. Always check them.

Edited September 4, 2013 by K^2

[power5000]

Okay thank you very much 3.75 is in tons I'll review everything and see what i can get =)

[Michael Kim]

This is not astrophysics is it... Astronautics rather

[metaphor]

What's the question?

[power5000]

I suppose I've always been a bit confused on the difference of the two and the question is, is the math correct?

[K^2]

You got total impulse in pound-seconds and then divided it by tons? "Well, there's your problem."

If you insist doing this in imperial units, and assuming that these really are American Tons (though, metric and English ton are pretty close), then this is the correct way of walking through it.

The total impulse is, indeed, 15,000 lb-s. You can divide this by weight of fuel in pounds to get I_SP in the same convention that KSP uses. (It's also a standard one for Rocket Engineers in U.S.) So we have 15,000 lb-s / 7,500lb = 2s. This is a very low specific impulse, but that's what it works out to if this is, indeed, 300lb of thrust rocket. But lets pretend that this is correct. Specific impulse in units of seconds can be used with either units, but for sake of consistency, lets carry on with Imperial.

delta-V = 2s * 32.2ft/s² * ln(4T/0.25T) = 178.6 ft/s.

So where did these 32.2ft/s² come from? That's acceleration due to gravity on Earth and shows up because of relationship between pounds of weight and pounds of thrust. Equivalently, if you were to use this formula in metric system, you'd multiply by 9.8m/s², and in either case it has to do with your I_SP being in seconds.

Now, you seem to be using values for Advanced SRB mod. I'm not familiar with it, but I'm guessing the thrust is higher, with specific impulse closer to 200s. You should check these numbers. Thrust in KSP is usually given in kN. Also, the tons are metric tons, and each one is 1,000 kg instead of 2,000lb.

[power5000]

You got total impulse in pound-seconds and then divided it by tons? "Well, there's your problem."

If you insist doing this in imperial units, and assuming that these really are American Tons (though, metric and English ton are pretty close), then this is the correct way of walking through it.

The total impulse is, indeed, 15,000 lb-s. You can divide this by weight of fuel in pounds to get I_SP in the same convention that KSP uses. (It's also a standard one for Rocket Engineers in U.S.) So we have 15,000 lb-s / 7,500lb = 2s. This is a very low specific impulse, but that's what it works out to if this is, indeed, 300lb of thrust rocket. But lets pretend that this is correct. Specific impulse in units of seconds can be used with either units, but for sake of consistency, lets carry on with Imperial.

delta-V = 2s * 32.2ft/s² * ln(4T/0.25T) = 178.6 ft/s.

So where did these 32.2ft/s² come from? That's acceleration due to gravity on Earth and shows up because of relationship between pounds of weight and pounds of thrust. Equivalently, if you were to use this formula in metric system, you'd multiply by 9.8m/s², and in either case it has to do with your I_SP being in seconds.

Now, you seem to be using values for Advanced SRB mod. I'm not familiar with it, but I'm guessing the thrust is higher, with specific impulse closer to 200s. You should check these numbers. Thrust in KSP is usually given in kN. Also, the tons are metric tons, and each one is 1,000 kg instead of 2,000lb.

thank you that would have helped a lot but I did miss something somewhere so I went back and looks at all the things and have revised and got something a little closer to what i'd expect

REVISION!!!!!

Ve= effective exhaust velocity

M0= full mass

M0= dry mass

G0=9.81

F= thrust in Newtons

q=fuel rate

delta-v=ve*Ln(M0/M1)

Ve= ISP*G0

ISP=F/qG0

So our Thrust is .150T or 1470 newtons

q= 3750/50 or 75 (kgs/s)

so our ISP = 1470/(75*9.8)=2. (seconds)

the effective velocity = 2 * 9.8= 19.6 (m/s)

the deltav=19.6*ln(4/.25)=54.3427389558997123

Edited September 5, 2013 by power5000

[K^2]

Right. Except that 2s is extremely low for specific impulse of an SRB. I'd re-check the thrust. Also, you wrote 0.150T the first time, and 0.150kT the second. If it's kT, that's 1,000 times more thrust, giving you 1,000 times higher specific impulse. But that's too high. Could this be something like 150kN by any chance? Or .150MN? That would give you 200s specific impulse.

[power5000]

Right. Except that 2s is extremely low for specific impulse of an SRB. I'd re-check the thrust. Also, you wrote 0.150T the first time, and 0.150kT the second. If it's kT, that's 1,000 times more thrust, giving you 1,000 times higher specific impulse. But that's too high. Could this be something like 150kN by any chance? Or .150MN? That would give you 200s specific impulse.

oh no that would be my stupid mistake of trying to designate it as metric tons.

so I thought about it and may have made another mistake >.< so

F=36750

q=75

ISP=50

Ve=490

delta-v = 1358

my error was that in the adv configs it tells you how much it uses and when so it has

0 .075

50 .075

So I thought it would be .150T but it's not because it's .075T a SECOND for 50 seconds so im sorry and I'm an idiot.....

So our Thrust is .075t*50 (.075T for 50 seconds) or 36750 newtons

q= 3750/50 or 75 (kgs/s)

so our ISP = 36750/(75*9.8)=50 (seconds)

the effective velocity = 50 * 9.8= 490 (m/s)

the deltav=490*ln(4/.25)=1358.56

Edited September 5, 2013 by power5000