Calculate (and plan) a flight - How much fuel do you need, what weight ist okay...

[Akeno]

Hey,

since I play this game, I'm very interested in this whole physics stuff. After few hours in the game, I found out, what NASA is doing and especially how they do do things. Before, I had no clue^^.

I know that the game simplifies everything so everyone can play it without being a physicist or so. Anyway, the game is still more realistic than other games. And it's a great fun to play Kerbal Space program .

And as I like numbers and formulae, I would like to learn how to calculate things in Kerbal Space Program.

Currently, I randomly connect parts to my spaceship without looking for their values and information. I take some parts and test them. Mostly, it goes terribly wrong and I have to adjust the parts or exchange them many times, before the launch works. That's because I don't really know what information are given when I mouseover a part. The only thing I know is the mass or the elctrical charge.

I would like to change this. I want to calculate how much fuel I need to get into orbit/to another planet according to the mass of my spacecraft. Or how much delta-V my ship has (although I still don't understand why a ship can have delta-v. I thought delta-v is the additional velocity that is needed to change orbit or something).

I know, it might be difficult, but I'm keen to try learning this. Of course not in the way NASA is doing this^^, but the more "simple" ways.

Unfortunately, I couldn't find any tutorials on how to do this. I just found this in the wiki:

http://wiki.kerbalspaceprogram.com/wiki/Tutorial:Advanced_Rocket_Design

On this page is explained how to calculate delta-v. I understand that except for this:

This ln*(m1/m2). How do I calculate this? According to wikipedia(http://en.wikipedia.org/wiki/Natural_logarithm) it's a natural logarithm. But I don't get it:confused:

And then: What can I do with this delta-v? Okay, I know what my rocket can achieve but how do I know if my ship can even launch?

I have much more questions but I think I should understand the basic things first.

I hope the text is not too confusing . It's just hard to explain.

Thank you for reading this post and sorry if it's the wrong forum. I didn't know where this topic fits.

Greetings,

Dennis

[Godot]

dV is the most important value for most of your game it says how much your current rocket can change its speed with the fuel and engines available at this stage.

As everything in space can be expressed as chang in orbits (and other things, like drag play only a marginbal role in vacuum) you just need to work with the speed change that is needed to get your orbit to the desired orbit to get a good approximation of the fuel needed (as a fraction of your total rocket weight) (which is given by 1-m1/m2).

For example ... to get from a 100km orbit around Kerbin to the Mun you just have to increse your speed so much that the apoapsis reaches to the 11.000 km orbit around mun for which you need a dV of ~800 (that is, you have to get 850 m/s faster than you are now)

(of course this number is just an ideal ... and doesn´t tell you where you have to start the burn to get the orbit in a way that you really hit mun at the time your rocket is at its apoapsis and there may be other circumstances that increase the real dV you need (and it also doesn´t tell you anything about the ~300 m/s dV you need to slow your rocket down afterwards to get into a circular orbit around mun, instead of using mun as the center for a gravitaional slingshot out of Kerbins SoI ) )

Calculating the logarithm naturalis is easy ... usually all scientific calculators (including the one you have in the utilities for windows) have a button for this ...

so you just have to divide the mass of your rocket after the fuel of this stage is expended by the total mass of the rocket before the stage is fired

(with other words, you calculate the logarithm more or less on basis of the fration that the "dead" mass of your rocket stage (i.e. the mass that is not fuel) takes)

(and with still other words ... the whole term represents how your rocket gets lighter with the use of fuel ... from 1 (full weight of the rocket with fuel) to 0.something (frational weight of the rocket after fuel of the stagehas been expended)

I can btw. definitely recommend the Kerbal Engineer Redux - Mod.

It calculates dV, ISP, TWR and many more values on base of your current rocket (and includes an inflight item that you can use to monitor many important values during flight) ... for my spaceflight an absolute must

Edited June 2, 2013 by Godot

[Specialist290]

As for the specifics of the rocket equation itself, Atomic Rockets can break it down better than I ever could.

To answer a few of the other concerns that might make things a bit easier to understand:

1. Ships "having" delta-v: You're correct; "delta-v" is basically short for "change in velocity." Rockets work by accelerating a volume of propellant out an opening at one end; because of Newton's Third Law of Motion, this exerts an equivalent force on the rocket in the opposite direction. The more efficient your engine is, the faster it can get the propellant moving, and thus the more your rocket will accelerate for every bit of fuel it uses.

Imagine for a moment a rocket standing still in a featureless volume of space with no other forces acting upon it. Let's say that, for instance, this particular rocket has a delta-v rating of 1000 m/s. What that means is, if we burn all of it's fuel in one continuous burn, by the end of that burn the rocket will be moving in a straight line at a velocity of 1000 m/s. If we only burn half of that fuel, it'll be moving at 500 m/s; if we then turn it around and burn the other half of that fuel against our direction of travel, the rocket will come to a standstill again. In short, a rocket's "delta-v" represents how much you can change that rocket's velocity with a given fuel load.

2. "How do I know if my ship will even launch?": That's actually governed by another number entirely, known as your "thrust-to-weight ratio."

Every rocket engine has a certain maximum thrust rating (though I think the game calls it "Power" in the VAB parts listings, which isn't an entirely accurate term). Again, a rocket engine exerts this thrust as a force pushing the rocket upward. At the same time, gravity exerts a force trying to pull your rocket downward ("weight"). The way to find your rocket's weight on the launchpad is to take its mass, then multiply by 9.8 m/s^2 (the value for surface gravity on Kerbin, identical to that for Earth) to find the total force exerted by gravity, then divide that into the total force exerted by your active engine's thrust. If that number is less than 1, then you are not going into space today.

3. Natural logarithms: If you take a number and raise it to a power with an exponent, you get a second number. Relative to that second number, the exponent is the logarithm, and the first number is the base. For example, the logarithm of 1000 using 10 as the base is 3, since 10^3 = 1000.

Now, the natural logarithm of a given number uses a very special number called e (or Euler's number) as its base. Better minds than mine can tell you exactly how e is derived, but suffice it to say that it's a Very Important Number for a lot of different calculations, to the point that any good scientific calculator should already have a handy "LN" button you can press to get the natural logarithm of any number.

[Uberick]

Seeing as how this question has already been answered, I'm gonna toss in my 2c seeing as how it can't hurt.

First of all, that Atomic Rockets link is BRILLIANT,thanks Specialist.

Also worth reading(if you like calculations), is http://forum.kerbalspaceprogram.com/showthread.php/16511-Tutorial-Interplanetary-How-To-Guide

As a side note, you can find the gravity values for all the planets and moons on the KSP wiki. Substitute those into the equation in place of 9.81 to see if your ship will take off of THAT planet. As an example, Duna's value is 2.94, vs Kerbin's 9.81. As such, you need about a third of the thrust to lift a rocket on Duna. You can use that to pack the minimum amount of engines required, so you don't have any dead weight.

[Akeno]

Wow! You're awesome Thank you very much! That helped me a lot.

I think now I mostly understand delta-v. But I have still some questions about it:

1. When you want to go to a 100km Kerbin orbit you need about 4700 m/s (according to the wiki). In the example, Stage one 3350 m/s and Stage 2 1168 m/s. Together, they almost achieve 4700 m/s. But only by using two stages. Is this profitable? If yes, what is a good altitude to start the next stage? I guess, it should be the edge of the atmosphere? Or would it be okay to reach orbit with one stage (that has a delta-v of about 4700 m/s) as well?

2. But how does this number (4700 m/s) come about? Does this have sth. to do with the orbital velocity?

3. What is the context of the Thrust-Weight-Ratio and delta-v? I might have a clue. I read this in the wiki:

If we design our rockets to have 7600 total , and the acceleration of the launch stages are adequate, we can have confidence that our rocket is able to land on the Mun and return to Kerbin. A rocket with a little less can accomplish this goal, but it is less forgiving of less efficient piloting.

So I think, we need both values to be high enough. If the ship has a delta-v of e.g. 7600 m/s but just a TWR of 0.5 it won't start. The explanation might be that you need a big acceleration to escape Kerbin. If you have small engines, they would reach 7600 m/s. But just very slowly and if there is gravity they can't even reach it.

Is that right?

4. What's when the value of TWR is extremly high, e.g. 5 or something. Does it mean, the ship accelerates faster than with a value of 1? I know, that's not really important, it's just for understanding what that means .

5. @Godot: The mod is great^^. But one question: It shows me two values of delta-v (e.g. 2700 / 8500 m/s). What does that mean? What value is the "right" one?

And also with mass. First, I thought it would be "dry mass / full mass". But the difference is sometimes to small (e.g. 42 000 kg / 46 000 kg). I don't get it. Sometimes I get with these values the right delta-v(which is written in the table) when I calculate it manually and sometimes not. That's confusing

@Uberick: Thanks for the link. I definitely try this out but later on^^. It sounds a bit complicated

And again, thank you for helping me

[Godot]

1. Well, all in all it doesn´t matter too much how many stages you need (although using multiple stages could be a little bit more efficient if you set it up right) ... what matters is that the dV (if calculated right) is >= the dV needed ... what matters more with regards to the dV needed to get into Kerbins 100km Orbit is, how you perform your gravity turns ... peforming the right turns at the right altitudes can indeed make a difference between needing 4500 dV to get to the 100k orbit, or needing 5000+ (something that btw. is dependant on the individual rocket ... many people have taken up the standard practice of taken gravity turns at 10, 20 and 30km)

2. You already cited the formula with which dV is calculated. All in all you can sum it up with ... the more efficient your engine is (expressed by Isp) and the more percent of your rocket is taken up by fuel (or more correctly, by fuel that can be used by the current stage to produce propulsion (in contrast to fuel that only gets used in latter stages ... this counts as payload for this stage) the higher your dV. One might

3. It determines how much much more than its own weight the engine can lift (or, if calculated for a rocket/stage ... how much more than the rocket weight the engines of this stage can lift) ... so, if you have a TWR of 1.0, your rocket engines might (if your rocket currently is in air and facing upwards) just be able to keep your rocket at the same height, but not be able to ligft it up ... if it is below 1, then it might even just be able to slow the fall of the rocket, if your rocket currently is floating in the air and facing upwards. Therefore you should always try to have a TWR > 1.0 for your ascent stages (at least those stages that are active below ~60km ... in later stages you try to propel your rocket sideways -> TWR doesn´t play too much of a role in those stages ... for the interplanetary stages the role of TWR becomes rather insignificant (at least if you don´t mind the time needed to have your engines active to reach a certain speed)

4. Yep, the higher the TWR, the faster your Propulsion ... for your ascent a TWR of 2.2 is more than sufficient as it allows you to reach terminal velocity (which you shouldn´t exceed if you want to have an efficient ascent ... if you exceed terminal velocity you lose more energy due to atmospheric drag, than you lose due to gravity)

5. The first one is the dV of the stage you are looking at, the second number is the sum of all preceding stages ... lets say you are looking at Stage 11 (which becomes active after stages 13 and 12) and it says 1100/4300 then 1100 is the dV of stage 11 and 4300 the sum of stages 11+12+13.

As for the mass ... mass of this stage vs. total mass of the rocket

Edited June 3, 2013 by Godot

[Akeno]

Thank you

But I still don't get why it's 4700 m/s. I know, it's the delta-v you need to go into Kerbin's orbit. But this number doesn't depend on your engines, or? I mean, it doesn't matter what rocket you are flying with, you still need 4700 m/s delta-v to reach orbit. Or am I wrong?

[Specialist290]

Regarding point 3 in particular, it's best to keep in mind that the one factor that delta-v and TWR have in common is mass.

Because of Newton's second law of motion (F = ma), we know that a rocket's rate of acceleration is proportional to both the thrust of its engines and the total mass of the rocket. If we reduce the overall mass while keeping the same engines, our rocket will accelerate faster because it's pushing a smaller mass with the same amount of force.

Likewise, the delta-v potential of a rocket is proportional to the propellant fraction and the efficiency of the engines used. If we reduce the size of the payload while keeping the same engines and propellant load, we increase the delta-v, because a smaller overall mass means our rocket has less momentum to overcome in order to reach a given velocity.

In light of both of those facts, we can come to the conclusion that ultimately, the best rocket for a given mission is the lightest rocket that can accomplish that mission.

In fact, it might help to think of the delta-v equation in terms of mass management. A rocket needs propellant in order to move its payload, but until that propellant is burned, it's just "dead weight" that needs to be carried along, and thus you need more propellant to boost both the payload and the propellant you already have... and those costs add up quickly. This is why SSTO craft capable of carrying any signficant payload are so difficult to build, and why staging is so popular for many launches -- dropping unneeded mass at strategic points allows you to change how the equation is calculated in midflight.

EDIT: Yes, the delta-v requirement for reaching a stable orbit around Kerbin is the same, assuming an ideal flight path. If you have a rocket that's capable of lifting you off Kerbin's surface and getting up to that delta-v target, it'll get you there regardless of how big the rocket itself is or how many engines it has.

Think of it in the same way you think of money. Let's say you want to buy a train ticket that costs $100. It doesn't matter if you pay with a single $100 bill, 5 $20 bills, 10 $10 bills, or 10,000 pennies although I really wouldn't recommend actually trying that last one in real life... As long as you can afford to pay the fare, you can get on the ride. If you're even a penny short, though, then you're out of luck, Chuck.*

* Disclaimer: This applies equally to all individuals, regardless of whether or not your name is actually Chuck.

Edited June 3, 2013 by Specialist290

[Akeno]

Okay, but to say it with your example: I understand that you can buy the ticket with either one $100 bill or 10 10$ bills. But what I don't understand is, why does the ticket costs $100? Why not $1000 or $50?

So why is the delta-v 4700 m/s and not 6000 m/s or 500 m/s?

You can't calculate it with the formula I posted above, because you need the mass and the Isp. But 4700 m/s is a general value. So how do you get this number?

Sorry for annoying you, I just want to understand it

[Specialist290]

That's perfectly alright If you're honestly trying to learn, there's no such thing as a stupid question.

Again, I find that Atomic Rockets explains things much better than I can, but to summarize as best as I can:

Every planet has a minimum cost based on that planet's size and mass. On top of that, as you're lifting off, you're fighting against both gravitational drag (i.e. drag exerted as a force on your rocket as it tries to pull you back down) and atmospheric drag (drag exerted by the atmosphere pressing against your rocket and trying to slow it down as it tries to fly upwards). (Since Atomic Rockets doesn't provide any information on atmospheric drag, you'll probably have to use the data from the KSP wiki page here to figure that out.)

I'm going to admit that I'm still wrapping my head around the atmospheric math myself, so if you want more details on that, you might want to wait for someone more knowledgeable to chip in. (Maybe alterbaron is still around; that sort of question would be right up his alley...)

[triffid_hunter]

Okay, but to say it with your example: I understand that you can buy the ticket with either one $100 bill or 10 10$ bills. But what I don't understand is, why does the ticket costs $100? Why not $1000 or $50?

So why is the delta-v 4700 m/s and not 6000 m/s or 500 m/s?

You can't calculate it with the formula I posted above, because you need the mass and the Isp. But 4700 m/s is a general value. So how do you get this number?

you start off at some altitude, with some horizontal velocity from the planet's rate of spin.

When you are in orbit, you have a higher altitude and a higher velocity (unless the planet is spinning more than fast enough to tear itself apart). You need a particular velocity at any given orbital altitude which reduces as you get further from the planet. If you don't have enough horizontal velocity, you will fall back into the atmosphere and burn up.

On kerbin, you start off with a horizontal velocity of something like 220m/s at an altitude of about 50-60m above sea level. The atmosphere ends at 70km and you need about 2300m/s velocity at that altitude to remain in orbit.

So a kerbin launch requires you to gain 2100m/s in horizontal velocity and lift your launch mass by at least 70km vertically. I usually go for at least 90km so I don't risk grazing the atmosphere during rendezvous maneuvers, and prefer 125km since I can warp faster there.

It takes energy to push mass up a gravity well. it also takes energy to impart higher velocity to that mass when remaining at the same 'height' in the gravity well.

That accounts for most of the dV required to get off the planet (I guess at least 3400m/s). The rest is consumed by atmospheric drag- it takes energy to push all that air out of the way on the way up!

fwiw I'm finding that it's possible to achieve orbit with as little as 4400 m/s dV these days, have a play with my Fuel Tanker no MechJeb.craft and see how you go. It also demonstrates asparagus staging which gives a _huge_ boost to dV by dropping empty fuel tanks and superfluous engines as early as possible.

ps: note that the dV figure has already taken the mass of your craft into account, and balanced it vs the thrust of your engines and their fuel efficiency. That's why the required dV is approximately the same for both very large and very small craft!

[architeuthis]

Okay, but to say it with your example: I understand that you can buy the ticket with either one $100 bill or 10 10$ bills. But what I don't understand is, why does the ticket costs $100? Why not $1000 or $50?

So why is the delta-v 4700 m/s and not 6000 m/s or 500 m/s?

You can't calculate it with the formula I posted above, because you need the mass and the Isp. But 4700 m/s is a general value. So how do you get this number?

Sorry for annoying you, I just want to understand it

Hi Akeno,

Great questions:) Imagine you are on ice skates standing stationary on a nearly frictionless frozen lake. In one hand you are holding one end of a spring which is attached to an old piling jutting out of the ice. Consider it a fixed point. If you are at rest and the spring is totally unstretched then there is no energy present in this system. Now say you start skating. Since you are still holding the spring you are rotating about the post (the spring doesn't tangle up, its on free rotating bearing or something...its not a perfect analogy). As you skate faster and faster what do you expect to happen? Your radius of rotation will increase won't it? In this case energy is present in the system, in the form of the kinetic energy of you the iceskater, and of the potential energy of the spring. Again not a perfect analogy, gravity isn't quite like a spring, gravitational force decreases with distance, whereas spring force increases with distance. But, it turns out that since energy is conserved (assuming no friction:)) the energy of the total system remains constant and we get an equation called the vis-viva equation we we take the sum of the kinetic energy and the gravitational potential energy to get the total energy of the system (if you multiply all of the terms of each side of the vis-viva equation by m for mass, after a little bit of algebra it becomes the conservation of energy equation). If you happen to know what the radius of your orbit is and the gravitational parameter mu for the plant you are orbiting, you can use the vis-viva equation to calculate your orbital velocity. If you recalculate with a different r, and compare the different values of v you have your delta-v... mind you this is your total delta-v, not the delta-v required for say a Hohmann transfer orbit. Does any of that make sense?

Edited June 4, 2013 by architeuthis

[Akeno]

Thanks for the replies

I read through the Atmic Rockets page and your answers. Some things are now a bit clearer.

__________________________________________________

Okay, so when I want to go to orbit I have to consider 3 things

• The horizontal speed that I need
  
• The vertikal speed which includes gravitational and atmospheric drag
  

And the sum of theese amount to the total delta-v I need to go into orbit.

Is that right so far?

How do I calculate the horizontal speed? According to Atomic Rockets it's this equation:

-> dVo = sqrt[ (G * Pm) / Pr ]

My question about that is: on the Atomic Rockets page they write, this is the delta-v which is need to achieve orbital velocity. But what orbit do they mean? 70km? 100km? Or is this changeable by changing the radius of the planet? (i.g. 700 000m for a 100km orbit?)

And the gravitational Speed:

-> Apg = A / g

-> dVd = delta-escape / Apg

A = spacecraft's acceleration (m/s^2). How do I calculate this? I think in the game is only the thrust, not the acceleration. Or did I overlook something?

g = acceleration due to gravity on planet's surface.

According to the Atomic Rockets page, you can't simply calculate the atmospheric drag. Is that important?

___________________________________________________

As for the vis-viva equation:

what is a in this equation? I read through the article on wikipedia, but it seems to be very complicated.

___________________________________________________

Now a more general question: On the Atomic Rocket page, they often write about gravity or acceleration. But as unit they use m/s instead of m/s^2. Is that right or is it a typo?

___________________________________________________

Okay, now I think I should get practise with the basic stuff, such as delta-v calculation, TWR and building a good and light rocket.

If I have a question, I will post it here .

Thank you in advance

Akeno

[Specialist290]

Thanks for the replies

No problem!

I'll preface this by stating once again that there are others who probably understand the math much better than I do, at least when it gets beyond the more basic ideas.

Okay, so when I want to go to orbit I have to consider 3 things

• The horizontal speed that I need
  
• The vertikal speed which includes gravitational and atmospheric drag
  

And the sum of theese amount to the total delta-v I need to go into orbit.

Is that right so far?

Sounds about right.

How do I calculate the horizontal speed? According to Atomic Rockets it's this equation:

-> dVo = sqrt[ (G * Pm) / Pr ]

My question about that is: on the Atomic Rockets page they write, this is the delta-v which is need to achieve orbital velocity. But what orbit do they mean? 70km? 100km? Or is this changeable by changing the radius of the planet? (i.g. 700 000m for a 100km orbit?)

If my understanding of this particular equation is correct, it's the minimum horizontal velocity you'd need to achieve at the altitude index level (aka "sea level") in order to maintain a stable orbit around the planet just above the surface, assuming a perfectly smooth spherical surface, no atmosphere to provide drag, and instantaneous horizontal acceleration. In practice, of course, you really can't rely on any of those to be true.

And the gravitational Speed:

-> Apg = A / g

-> dVd = delta-escape / Apg

A = spacecraft's acceleration (m/s^2). How do I calculate this? I think in the game is only the thrust, not the acceleration. Or did I overlook something?

You're forgetting one of the two basic equations I mentioned earlier: Force = mass * acceleration (F = ma). Solved for acceleration, a = F/m. It's the same procedure you use to calculate TWR, only you're measuring the ship's raw acceleration without taking the extra step of dividing acceleration due to gravity into it.

g = acceleration due to gravity on planet's surface.

(Something to watch out for: A stage's final maximum acceleration is going to be higher than it's initial maximum acceleration, because you're burning fuel throughout the process, which is reducing its mass at a constant rate (assuming you don't touch the throttle during the burn). The actual average acceleration for the whole burn is probably going to be the mean between the initial and final maximum values for that one stage -- and calculating each stage individually by hand is a long, arduous, repetitive, and potentially maddening affair, the sort of tedium that people who really want to work it out tend to create spreadsheets for so that they can just plug in the values that they want. Plugging in a flat value of 20 m/s^2 -- a little over 2g -- can give you a very rough idea of what the ideal ascent delta-v should look like, though.)

According to the Atomic Rockets page, you can't simply calculate the atmospheric drag. Is that important?

Here on Earth, that's because the atmosphere is not a universally uniform blanket of pressure. On Kerbin it is, meaning that you could in theory calculate the total acceleration due to drag over the course of your burn time to get a reasonable approximation. I'm still wrapping my head around how exactly would be the best way to do this myself...

As for the vis-viva equation:

what is a in this equation? I read through the article on wikipedia, but it seems to be very complicated.

The value a is for an orbit's semi-major axis, which is one of the parameters that defines the shape and position of an orbit relative to its central body. In game terms, you find the sum of your orbit's apoapsis and periapsis and the planet or moon's diameter, then split that total in half.

Most of the orbits you're really going to worry about are going to be ellipses, with the body in question at one focus. The other two types are parabolas and hyperbolas, which can get... interesting and confusing compared to ellipses. I don't know how much geometry you've studied before picking up this game, but I'd recommend this page if you need either a crash course or a refresher. Specifically, the semi-major axis is exactly half the length of the orbit's major axis.

Now a more general question: On the Atomic Rocket page, they often write about gravity or acceleration. But as unit they use m/s instead of m/s^2. Is that right or is it a typo?

Yes, if it's written like that, it's most definitely a typo... unless you're seeing it as m/s², which is correct; the caret ("^") is just a way to represent that the following number is an exponent when typing in a format that doesn't support superscripts.

Hope this all helps!

Edited June 5, 2013 by Specialist290