Calculate the altitude after burn and then the altitude after coast of a rocket stage?

[MrHost56]

As the question states, I need to calculate the altitude a stage of my rocket will be at after it burns, and then how far it will coast.

Liftoff stage stats

Mass=15.1 t

Parts=26

Height=14.8/20m

Width=4.3/15m

Length=4.3/15m

Thrust=315

Isp=230

Burn Time=45.7s

Here's a screenshot of the rocket, showing center of thrust and center of mass for the first stage: http://steamcommunity.com/profiles/76561198130134594/screenshot/711904559423379375 (link might be buggy) As you can see, I am using the BACC solid fuel booster for the launch stage.

There is this site: http://www.rocketmime.com/rockets/rckt_eqn.html that gives me equations to work with, but I have no idea where to find wind resistance force, among many other things.

If someone could give me some equations or formulas(or whatever the term is, I swear I know how to math) along with some explanations that would be very, very appreciated.

What I have managed to calculate

Area=14.5

TWR=20.9(this was calculated with plugging in 1 for g in the Thrust-To-Weight-Ratio equation, plugging in 9.8^2 instead yields .2, if that is what I was supposed to do)

I hope I have provided enough information. Thanks in advance.

[Th3F3aR]

Basically, i'd say, forgett it. I tried it myself and you just can't get the airresistance equation get to work without a knot in your head. That's why even in real world such things are estimated and from time to time acknowledged by tests. To get it "right" you should be physicist (does one write that like that XD?) or something like that to just understand whats going on! If you still wanna give it try (although it seems totally unnessesary for KSP) check out this linky -> http://exploration.grc.nasa.gov/education/rocket/dragco.html

Nasa got all the things you need, described step by step. Maybe you get it done, i was to lazy to get all of it in my head

[LethalDose]

First, to calculate TWR, the equation is: TWR = F/gm, where F is thrust (in kN), g is 9.82 m/s² and m is vessel mass (in tons). The TWR at launch for the vessel you've provided would be 315/(9.82 * 15.1) = 2.12

For stock aero (I play with FAR), the consensus seems to be you should aim for a TWR of ~ 1.5-1.7 at liftoff, but don't take that as gospel, at least from me.

For what you're asking, Th3F3ar is correct: Getting those estimates is something of a fool's errand IMO. The end state of the flight is determined not only the starting TWR, mass, etc, but also the flight path. In general, I think stock aero takes about 4.5 km/s of dV to get into LKO with a reasonable TWR. That's a better target for vessel design than what it appears you're trying to do.

[Claw]

The type of information you are asking for is a bit difficult to calculate by hand. Really you'd need to go about it one of at least two ways:

1) Empirical Method: Build a table of information by repeatedly launching a test rocket until you can build a table based on dV at some relatively constant takeoff TWR. Like LethalDose said, 1.5-1.7 TWR at launch is about right for most stock craft.

2) Theoretical Method: Build an iterative computer program or spreadsheet that can solve all the equations for you. You might be able to build and solve a system of equations by hand, but it would get rather messy with all the calculus. But you can build an set of equations and have the computer do some iterative calculations for you. I think someone might have even done something like this and posted a few charts around here.

What's maybe more important for us to know, is why you are trying to figure out how high and how far your rocket is going to be? Rather than us trying to help you recreate a complex set of equations, there might be a simpler method to find the real information you are after.

For example, I wanted to know "how much rocket" I needed for part testing. Rather than solving a set of equations, I went through process #1 above with a few assumptions to make testing easier. Then I built a chart that shows me how much dV I need to reach a certain altitude. Now when I get those "test part X at altitude Y and speed Z," I know how much dV I need without having to over engineer everything. Some people don't find that fun and it's easier to just put the pieces together and go. So it all depends on what you want.

Cheers,

~Claw

[PlonioFludrasco]

You may get a look to the Ascent Komputron: very useful for that kind of stuff!

[MrHost56]

In response to your question on why I want to calculate it, it's because I'm playing career mode and don't want to waste money on a failed flight that could have been avoided.

Thank you for your help though.

[Pecan]

In response to your question on why I want to calculate it, it's because I'm playing career mode and don't want to waste money on a failed flight that could have been avoided.

Thank you for your help though.

Then unless you're going to orbit (~4,500m/s dV), leave altitude-dependent missions until you have wings and do them with a plane that can fly at any altitude, control its speed better and use very-efficient jet engines.

THE problem, as the others have said, is that there are so many unknown variables affecting your flight, especially those dictated by your ascent path.

If you're actually doing the 'achieve an altitude of nnnn' contracts then ... overbuild. Launch something you KNOW will go higher and watch the apoapsis marker in map view. Cut engines when it reaches your desired altitude, using tiny bursts of power to keep it there.

[Claw]

In response to your question on why I want to calculate it, it's because I'm playing career mode and don't want to waste money on a failed flight that could have been avoided.

Thank you for your help though.

Hmm... I might have been misleading with my question. I mean to say what is the end goal of calculating the numbers? Are you trying to optimize staging? Optimize payload fraction? Obtain a specific altitude/velocity for part testing? Get to orbit? That sort of thing.

Generally people who ask questions similar to yours like to avoid over engineering (I am one of those people). But there is a huge array of things to help avoid over engineering. The tool to use depends a bit on what you are trying to accomplish. Someone built charts which show the "best" engine for given a TWR and craft mass, for example. Or dV burn numbers for an optimum ascent (so you can plan stage requirements).

If you just want to figure out if your rocket will make it to orbit, then your most basic bet is to determine how much dV your rocket has (either by hand or with a plugin such as Kerbal Engineer or MechJeb). ~4,500 is required to get to orbit. When I use SRBs, I generally bump up the requirement some because they often lose more dV to drag than a dV equivalent liquid fueled engine (since you can't control the throttle mid flight). This might be where your question is coming in, as to how much dV is lost due to drag. That's a bit tough to tell in stock KSP right now because the drag model is dependent on ship mass. So real world drag equations don't strictly apply, since currently Cd of the rocket is not based on it's shape.

I think I'm starting to wander a bit, but hopefully I'm narrowing down in on what your question is primarily aimed at?

Cheers,

~Claw

[MrHost56]

It seems I have been fairly misleading as well. Specifically, yes, I want to send something into orbit, and I'm on a budget. All I need to know is how high each stage is going to go, given thrust, mass, burn time, etc. That way, if I can predict the outcome to some sort of degree, I can figure out a rocket that will work the first time around instead of wasting money on rockets that don't make it. Not so much the stages that are used to establish orbit, just the ones that get me up out of the atmosphere.

Thank you for other explanations as well.

[EtherDragon]

MrHost,

The info you are looking for can be determined from working backwards with the Delta-V provided by the other users. Estimate 4,500m/s Delta-V required to reach orbit (75km x 75km). We know from Tsiolkovsky's rocket equation that Dv = Isp*9.8*Ln(M0/M1). M0 = full mass, M1 = empty mass. For the Isp, you can estimate the average if it changes. This is true for any single stage. You can add stages together for the total mission (say you have asparagus staging, or something) by calculating this for each stage, and adding the total together:

Total Dv = Dv1 + Dv2 + ... + DvN

Then, you can then work that backwards to solve for the Full / Empty masses required for each stage. For instance, if you know that you need 4,500 Delta-V from a single-stage, and that stage needs to deliver 2,000kg into orbit:

4,500 = 350*9.8*Ln(M0/2000kg) - solve for M0:

1.312 = Ln(M0/2000kg)

I cheat and use a table I already have and find that the mass ratio is between 3.5:1 and 4:1, so I use the average of 3.75 (ln(3.74 = ~1.322)) - which means that I need 7500kg of fuel at 350 newton seconds (Isp) to get that payload into orbit in a single stage.

Or I could use the identity of e to get the actual result:

e^1.312 = M0/2000kg

3.714 = M0/2000kg

7427 = M0

Edited February 27, 2015 by EtherDragon

[MrHost56]

Thank you so much!

[GoSlash27]

Quick 'n' dirty rule of thumb for stock:

You will spend the first 1,500 m/sec in vertical boost. This phase needs 1.7:1 t/w ratio. You should burnout right around 7km altitude.

The next transstage 1,500 m/sec phase will get you to roughly 45* pitch. T/W should be 1.4:1. You should burnout around 25km altitude.

The last 1,500 m/sec is insertion. 1.2 t/w will be fine, and it can taper back to less than 1:1 as you tip prograde.

I don't necessarily use a single stage for each phase, and may occasionally have a stage bridge these phases (or even one stage do all 3).

Best,

-Slashy