How to use Tsiolkovsky's rocket equation to find out my total delta-v

[team.leit]

If i have the initial total mass of my rocket, the finial total mass of my rocket, and the Isp of the engine, how do i use the Tsiolkovsky rocket equation to find out my delta-v, i guess what i mean is, how do i plug them through the equation to see if it matches a known delta-v? I am trying to do this for school, but i need help figuring out how to work the equation

Thanks

~Boomer

Edit: Thanks everybody for taking the time to answer this thread and my questions

Edited September 12, 2013 by team.leit

[blizzy78]

http://en.wikipedia.org/wiki/Tsiolkovsky_rocket_equation - it's the first equation at the top. Also note the Isp subformula right below that.

[Johnno]

What part of using the equation are you having difficulty with?

"Plugging" in numbers into an equation is just that, you put in all the numbers and then solve the equation. You only have one unknown which in your case would be the delta-v, so it should be really straightforward.

Equation explanation is here. Everything you need is linked from that page, natural logarithms (which I suspect you'll just be pressing on your calculator) and standard gravity.

You'll have to try and explain further exactly what you don't understand.

[mellojoe]

Delta V = ISP x ln(TOTAL MASS / DRY MASS) x Gravity

Delta V = Thrust Effeciency of your engines TIMES the natural log of the ratio of total mass divided by the dry mass, where dry mass is the total mass minus the mass of just the fuel. If your ISP is in seconds (which it is in KSP) then you need to multiply by the Gravitational constant, 9.80665.

[capi3101]

If you've got the figures, you just plug them into the equation.

Okay, practical example time. My Fireball 7 rocket on the pad has an Isp of 225 (RT-10s only in that stage to keep things simple; there are seven of them but of course it's the same engine all around so 225 is what you use). The rocket weighs 104.1725 tonnes before the stage is lit at 81.44 when it's dry.

So plug it in: delta-V = ln(104.1725/81.44) * 9.81 * 225 = 543.3844 m/s. Thus my launch stage has 543.4 m/s of delta-V.

Next stage: after sloughing off the SRBs, the rocket's next stage is 77.47 m/s full and 29.47 dry. She's using LV-30s/45s at that point, which have an Isp of 320 (bit higher than that but I use the low end for planning purposes).

Plug it in: delta-V = ln(77.47/29.47) * 9.81 * 320 = 3,034.093 m/s.

Add that to the previous stage and so far the Fireball's got 3577.478 m/s.

Just keep doing that for all the stages of your rocket. Easy peasy.

That natural logarithm (ln) might be tricky...you'll need a scientific calculator to figure it up unless you happen to know how to calculate it (which I don't know if anybody does in this day and age). MS Excel also has the command =LN() which will do the same thing.

[team.leit]

cut.. delta-V = ln(104.1725/81.44) * 9.81 * 225 = 543.3844 m/s cut..

cut.. That natural logarithm (ln) might be tricky...you'll need a scientific calculator to figure it up unless you happen to know how to calculate it (which I don't know if anybody does in this day and age). MS Excel also has the command =LN() which will do the same thing.

it was the natural logarithm that was getting me, thanks for the practical example it most certainly helped, to everybody else thanks for your help, what i am trying to do is write it all out on a sheet of paper to show it to my dad as proof of work. So if i did my math right a rocket with a filled weight of 10.61 ton and a dry weight of 2.16 ton using a lv-909 engine should get me a net total of 8,141.4 m/s of delta-v right?

~Boomer

Edit: never mind it gets me a vacuum delta-v of 6,089.6 m/s, but still thanks for the help though

Edited August 28, 2013 by team.leit

[capi3101]

6,089 is right in vacuum, yes. And at launch, you'd have 4,684 m/s (because the 909's Isp is different in atmo).

Edited August 29, 2013 by capi3101

[iStickyDuck]

If trying to figure it ll out is a bit confusing then try using the Kerbal Engineer Redux plugin which displays Delta-V and other things about your ship

http://forum.kerbalspaceprogram.com/showthread.php/18230-0-21-1-Kerbal-Engineer-Redux-v0-6-1-0

[Space_Pirate_R]

Delta V = ISP x ln(TOTAL MASS / DRY MASS) x Gravity

...then you need to multiply by the Gravitational constant, 9.80665.

Can somebody please explain further.

Given that 9.80665 is the local (acceleration due to) gravity for Kerbin, shouldn't delta-V change when you move into a different sphere of influence? Or is it implicit that delta-V is measured with respect to the gravity of our home planet? If that is the case, wouldn't inhabitants of other celestial bodies calculate different delta-V values for the same ship (even though using the same units of meters per second?)

[team.leit]

What I am trying to do is write it out on a piece of paper to show my dad as proof that i did my school work

[capi3101]

@Space_Pirate_R: the 9.81 m/s figure is used as a conversion constant for specific impulse into effective exhaust velocity. You can read up on it at Wikipedia. In how it's used, it is measured in respect to the effect of surface gravity of Earth on objects in vacuum (a concept known as standard gravity).

Beings on other planets would probably use their own standard gravity values - whatever floats their boat, right? Of course, it'd make no sense for them to use meters and seconds; they'd have their own designations. But they would still have their own units of measure for distance and time, and that's really what matters. There'd be conversion factors - just like there are on earth between metric and Imperial units, for example.

Kerbals use metric. That's kinda suspiciously convenient, like they're actually under the control of a game company based in, say, Mexico or something...

[blizzy78]

Given that 9.80665 is the local (acceleration due to) gravity for Kerbin, shouldn't delta-V change when you move into a different sphere of influence?

No, because delta-v is calculated using exhaust velocity:

Now while exhaust velocity is calculated using Isp:

this does not matter for delta-v calculation, because the exhaust velocity stays constant regardless of gravity.

The only thing that actually changes would be Isp:

So aliens on lighter planets would get higher Isp values, but that does not affect delta-v calculations. You can set any value for g0, which will modify your Isp value, but putting it all together the two g0's will cancel each other out, with the effect of leaving exhaust velocity a constant mathematically.

[mellojoe]

^^ This.

ISP is calculated as a ratio using the gravitational constant. If you change gravity, you change the ISP. Your delta-v would remain the same.

[Space_Pirate_R]

... putting it all together the two g0's will cancel each other out...

That's what I was missing. Thanks.

[blizzy78]

You're welcome. I wasn't sure my wording was good enough to get the point across.

[team.leit]

Again thanks for the help everybody, but could a mod or someone else that is able do it, move this thread to the science labs please?

[tavert]

^^ This.

ISP is calculated as a ratio using the gravitational constant. If you change gravity, you change the ISP. Your delta-v would remain the same.

No, Isp does not depend on local gravity. It depends on g0, or standard gravity, which is a constant that never changes. It's an artifact of imperial units being careless about the distinction between weight and mass. If some other culture developed elsewhere and used a similar concept of specific impulse as a time instead of effective exhaust velocity, then they would be using a different value of g0, but considering we're talking about unit systems that actually exist on earth, this is not the case. Specific impulse changes with ambient atmospheric pressure, but not local gravity.

[RadHazard]

It's also worth mentioning that in the KSP universe, the Isp given for all the engines is calculated with g0 = 9.82m/s^2. I'm not sure why, but that's the constant used in the code. As previously mentioned, this is just a conversion factor, independent of the actual gravity of your SoI.