Calculating Available Dv

[Usonian]

I normally rely on BurnTime MFD to tell me how much Dv a spacecraft can deliver, but I am currently stacking up some Velcro stages and BT MFD shows Dv for each individual vessel, without adding the mass of the stages attached above. (Clever Velcro does include the mass of attached vessels, so the attachments do effect performance.)

I suppose I could briefly reconfigure each stage, adding the mass of upper stages and payloads, and then use BT MFD to get a true reading of Dv. Then again, it might be time to learn something new.

I found the Tsiolkovsky rocket equation at http://en.wikipedia.org/wiki/Rocket_equation which seems simple enough:

Dv = Ve In m0/m1

Ve is the exhaust velocity Isp * g (which is simply the Isp figure used in Orbiter)
m0 is the mass of the vehicle including fuel
m1 is the empty mass of the vehicle

But the wiki article does not define In. Perhaps it is some common function known to all math wizards and needing no further explanation --like the "equal" sign and "division" slash -- except for dolts like me.

Anyone willing to tutor a math moron?

 

[synonys]

lol, ln is the natural logarithm. Also it L - N in lowercase.

http://en.wikipedia.org/wiki/Natural_log

 

[Urwumpe]

Exactly. In many math programs and on PC hardware, log is often defined to be ln (instead of the correct base 10 logarithm), in case you have not found it yet.

 

[Zatnikitelman]

It's the inverse operation so to speak of Euler's number to a power approximately 2.72, symbolized as e. So if you ever want to solve for a different variable in Tsiolkovsky's equation, it will be e^(rest of equation).

 

[martins]

It is actually quite simple to derive the rocket equation yourself from Newton's second law

F(t) = m(t) a(t)

and the definition of the fuel-specific impulse

F(t) = Isp dm/dt

which gives you the differential equation

Isp dm/dt = m(t) a(t)

Just integrate, and you're there (and if you remember that \int 1/m dm = ln m, then you also know where the logarithm is coming from).

 

[Usonian]

lol, ln is the natural logarithm. Also it L - N in lowercase.

Up until 48 hours ago I would have been inclined to say something self-deprecating about my being a "mathlete" medalist in Special Olympics... but I guess Obama beat me to that self-inflicted wound.

Ever since high school I have devoted my life to avoiding any career or activity that would involve logarithms -- didn't understand them then, and I still don't. However, I do have a calculator with a LOG button. I find that if I divide masses, then mash the LOG button, then multiplying by Isp I come out with a figure that agrees with BurnTime MFD (for a stand-alone vessel).

So now I can confidently add up attached masses and develop a correct Dv budget -- and I can do it all without any real depth of understanding! Ain't science somthin'?

Thanks for the replies (and mild put-downs)!

 

[Urwumpe]

Ever since high school I have devoted my life to avoiding any career or activity that would involve logarithms -- didn't understand them then, and I still don't.

Actually, you lost the ability to work with logarithms in elementary school. It was found out by psychologists, that humans have a natural aptitude for logarithms, which gets destroyed by the traditional schooling with emphasis on linear relations.

 

[EtherDragon]

Actually, you lost the ability to work with logarithms in elementary school. It was found out by psychologists, that humans have a natural aptitude for logarithms, which gets destroyed by the traditional schooling with emphasis on linear relations.

Which is precicely why I got an "A" in 6th grade math for writing an essay about the "Inconcistencies of Teaching Linear Mathematics in a Non-Linear Universe"

The essay was way over my teachers head, and earned an "A."

 

[Usonian]

Time to feast on a little crow...

Now that I (nominally) know what I am doing with the calculations, it turns out that BurnTime MFD is showing the accurate figures for Dv, correctly reflecting the added mass of Velcro-attached stages and payloads. My orginal problems amount to pilot error -- both Velcro and BurnTime are smarter than me! Still, I learned something from the exercise, and now have a use for that funny LN button on my calculator.

As for observations on the shortfalls of early education, I concur. In my schooling, it seems that math was presented as a method for rendering a complicated, multidimensional world into "comprehensible" linear form. Well, my elementary school taught me to read, write and cipher to the rule of 12. I am grateful for that. But having given me those tools, it would have been nice if they had stepped aside and let me pursue my own interest from that point forward.