Difference between revisions of "Tutorial:Advanced Rocket Design/fr"

Revision as of 13:51, 25 March 2013

Page originale Par Vincent McConnell et Kosmo-not, traduite par Maneth. Traduction non finie.

Introduction:

Apprendre à construire une fusée basique pour un jeu de simulation spatiale comme Kerbal Space Program peut être extrêmement important pour le succès de la construction de fusées souhaitées dans le cadre d'une mission précise. Dans ce guide, nous allons couvrir des sujets tels que calculer du Delta-V de notre vaisseau, expliquer comment réussir un transfert de manoeuvre, obtenir le rapport de poussée sur poids, calculer les poussées de force gravitation (G-force) durant une séquence d'accélération particulière, ou encore calculer le Delta-V nécessaire pour un transfert Hohmann complet et beaucoup plus encore.

Delta-V

Le ${\displaystyle \Delta v}$ (changement de vitesse) est l'alpha et l'oméga de l'astronautique. C'est probablment la chose la plus importante à savoir sur votre fusée parce qu'il détermine ce que votre fusée est capable d'accomplir. Parmi les différentes choses que nous allons expliquer dans ce tutoriel basique, le ${\displaystyle \Delta v}$ est la chose la plus utile que vous appliquerez dans KSP lorsqu'il s'agira de construire une fusée. Pour trouver le ${\displaystyle \Delta v}$ de votre fusée -- chaque étape à la fois -- nous avons à additionner la masse des parts de chaque étage. Quand nous aurons additionné la masse des réservoirs d'essence (fuel tank), il devrait être plus facile de les écrire comme ceci sur votre papier :

Full Mass: x
Dry Mass: x

The reason for this is that it will be easier to calculate full mass and empty mass. So, simply sum up your entire stage mass.

The next important part of this set of calculations is to find your engine's specific impulse . Specific impulse is a measure of how fuel efficient an engine is (the greater the

Specific Impulse, the more fuel efficient it is). For example, the 

non-vectoring stock engine has a vacuum specific impulse of 370 s. So here, we must apply the [http://en.wikipedia.org/wiki/Tsiolkovsky_rocket_equation Tsiolkovsky Rocket Equation]. More informally known as "The Rocket Equation".

It

states: ${\displaystyle \Delta v=9.81{\frac {m}{s^{2}}}\cdot I_{sp}\cdot \ln \left({\frac {m_{1}}{m_{2}}}\right)}$.

${\displaystyle m_{1}}$

= total mass of the stage (including subsequent stages), 

${\displaystyle m_{2}}$ = dry mass of the stage

So

go ahead and sum up your stage's full mass with fuel. Then, go ahead 

and sum up the mass minus the fuel (this can be done by just adding up the 'dry mass' where given). Input these into the equation in the place of ${\displaystyle m_{1}}$ and ${\displaystyle m_{2}}$. So, we

will show a quick example, here:

File:Screenshot7ex.png

Stage

3 (TMI, Mun lander, Return):

Full mass:	${\displaystyle 3.72kg}$
Dry mass:	${\displaystyle 1.72kg}$
${\displaystyle I_{sp}}$:	${\displaystyle 400s}$
${\displaystyle \Delta v}$:	${\displaystyle 3027.0{\frac {m}{s}}}$

Stage

2 (Kerbin orbit insertion)

Full mass:	${\displaystyle 7.27kg}$
Dry mass:	${\displaystyle 5.27kg}$
${\displaystyle I_{sp}}$:	${\displaystyle 370s}$
${\displaystyle \Delta v}$:	${\displaystyle 1167.8{\frac {m}{s}}}$

Stage

1 (Ascent):

Full mass:	${\displaystyle 38.52kg}$
Dry mass:	${\displaystyle 14.52kg}$
${\displaystyle I_{sp}}$:	${\displaystyle 350s}$ (estimated due to atmospheric flight)
${\displaystyle \Delta v}$:	${\displaystyle 3349.9{\frac {m}{s}}}$

Total ${\displaystyle \Delta v}$: ${\displaystyle 7544.6{\frac {m}{s}}}$

Note: To calculate the ${\displaystyle I_{sp}}$ for multiple engines with different ${\displaystyle I_{sp}}$ values, you need to take the weighted average of the specific impulses relative to thrust. The equation looks like this: ${\displaystyle {\frac {I_{sp_{1}}\cdot thrust_{1}+I_{sp_{2}}\cdot thrust_{2}+\dots }{thrust_{1}+thrust_{2}+\dots }}}$

This will give you the correct ${\displaystyle I_{sp}}$ to use for your ${\displaystyle \Delta v}$ calculation.

==Calculating transfer maneuvers== The next very basic part of this tutorial is how to perform a transfer maneuver itself. This kind of action is called a Hohmann Transfer and it requires two burns at opposite points in an orbit. Adding velocity will boost our apoapsis higher. We would then simply wait until

we hit our newly established Apoapsis and then add more velocity to 

boost our Periapsis to circularize. Or, we could drop our orbit by subtracting velocity by burning retro-grade.

We can also apply some ${\displaystyle \Delta v}$ calculations to find out how much thrust we will need to perform this maneuver. We will break

this burn up into impulses. For example purposes, we will start at a 

100Km orbit and then boost into a 200Km orbit. Both circularized. The formula for the first burn is the following:

${\displaystyle \Delta v_{1}={\sqrt {\frac {\mu }{r_{1}}}}{\Bigg (}{\sqrt {\frac {2r_{2}}{r_{1}+r_{2}}}}-1{\Bigg )}}$

This

is the formula for the final burn in the transfer:

${\displaystyle \Delta v_{2}={\sqrt {\frac {\mu }{r_{2}}}}{\Bigg (}1-{\sqrt {\frac {2r_{1}}{r_{1}+r_{2}}}}{\Bigg )}}$

Where:
${\displaystyle \mu }$= Gravitational Parameter of Parent Body. (3530.461 km³/s² for Kerbin).
${\displaystyle r_{1}}$=

The Radius of our first orbit. (100 km in this case).

${\displaystyle r_{2}}$=

The Radius of our second orbit. (200 km in this case).

This

formula will give us our velocity for the burn in km/s (multiply by 

1000 to convert it into m/s). It's important to make sure that you will have the ${\displaystyle \Delta v}$ in the stage to make

this burn. Again, you can do that by using the ${\displaystyle \Delta v}$ calculations above.

Calculating fuel flow

Next, we will explain how to calculate fuel flow in mass to see how much fuel a burn uses up in a specific amount of time.

If we know the ${\displaystyle \Delta v}$ needed for the burn and the total mass

of the rocket before the burn, we can calculate how much fuel is 

required to complete the burn.

First, we calculate the mass of the rocket after the burn is complete. To do this, we use the Tsiolkovsky Rocket Equation, inputting the initial mass and ${\displaystyle \Delta v}$ of the burn. We can then solve the equation for the final mass after the burn. The difference between these

two masses will be used to determine the length of time that is needed 

to complete the burn.

The equation for mass flow rate of fuel, given ${\displaystyle I_{sp}}$ and thrust, is:
${\displaystyle {\dot {m}}={\frac {\frac {thrust}{9.81{\frac {m}{s^{2}}}}}{I_{sp}}}}$
where ${\displaystyle {\dot {m}}}$ is the mass flow rate of fuel consumed (in seconds)

Dividing the difference between initial mass and final mass for the burn by the mass flow rate of fuel, we arrive at how many seconds are required.

Note: The

mass flow rate of fuel can be converted into the consumption rate of 

the fuel units used in KSP (Liters, I presume). The conversion ratio is 1

mass unit per 200l of fuel.

Orbital velocity

Rather easy is the formula to calculate the orbital velocity of an orbit. This assumes circular orbit or the velocity of a specific point in an orbit. For this, we simply do this calculation:

${\displaystyle {\sqrt {\frac {\mu }{r}}}}$

Where:
${\displaystyle \mu }$

= Gravitational Parameter of parent body. (km³/s²)

${\displaystyle r}$

= radius of orbit. (km)

If we input the radius of the orbit in Kilometers, our orbital velocity will come out in Kilometers per second. In a 100km orbit, our radius will be 700km. Meaning our velocity will be ~2.2458 kilometers per second (km/s), or 2245.8 m/s.

Delta-v map

A ${\displaystyle \Delta v}$ map consists of approximate amounts of ${\displaystyle \Delta v}$ needed to get from one place (whether it is on the ground or in space) to another. The ${\displaystyle \Delta v}$ values we have for our ${\displaystyle \Delta v}$ map are approximate and include a fudge factor (in case we slip up on our piloting). Our map is as follows:

from Mun and return to Kerbin: || 1000 m/s

If

we design our rockets to have 7600 total ${\displaystyle \Delta v}$, 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 ${\displaystyle \Delta v}$ can accomplish this goal, but it is less forgiving of less efficient piloting.

==Thrust to Weight Ratio== Calculating Thrust to Weight Ratio is only three very simple steps.

It is important to know the thrust to weight ratio of your rocket to ensure your rocket will actually liftoff.

If your TWR is less than 1, you can bet that you won t make an inch in 

altitude when starting from the launch pad. The minimum optimal TWR to have for your rocket at launch is 2.2.

The formula for this is simply the thrust of all of your current stage engines divided by the weight (mass * 9.81 m/s²) of your ship, fully fueled. At the same

time, this will give you the minimum G-force you can expect on the 

current stage. Your peak G-force will occur instantly before fuel depletion. The way to calculate this is to simply divide thrust by the dry mass of your stage+the fully fueled stages above it.

In

conclusion: This guide will hopefully have helped with designing your 

rockets to allow you to get the job done -- whatever it may be -- with no test flights first. We hope this guide has been helpful to new and continuing KSP pilots alike.