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

Revision as of 08:44, 23 April 2014

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 ${\displaystyle \Delta v}$ (variation de vitesse) est le B A Ba de la mécanique spatiale. C'est sûrement la chose la plus importante à connaître de votre fusée car c'est ce qui définit ce que votre fusée est capable de réaliser. De ce que nous allons expliquer dans ce tutoriel de base, le ${\displaystyle \Delta v}$ est probablement l'aspect le plus utile que vous aurez a appliquer dans Kerbal Space Program.

Pour calculer le ${\displaystyle \Delta v}$ de chaque étage de votre véhicule spatial, il faut commencer par additionner les masses de tous les composants de l'étage.

• Masse totale : ${\displaystyle m_{\text{total}}}$
• Masse de carburant (fuel) : ${\displaystyle m_{\text{fuel}}}$
• Masse sèche (dry) : ${\displaystyle m_{\text{dry}}=m_{\text{total}}-m_{\text{fuel}}}$

L'équation du ${\displaystyle \Delta v}$ ne nécessite que les masses totale et sèche, mais comme il est plus simple d'obtenir la masse de carburant, on calcule la masse sèche en effectuant une soustraction. Bien sûr d'autre combinaisons sont possibles.

La prochaine phase de calcul est de connaître l'impulsion spécifique (specific impulse) de votre moteur. L'impulsion spécifique caractérise "l'efficacité" d'un moteur en terme de consommation de carburant. Elle se mesure en secondes (s). Plus l'impulsion spécifique d'un moteur est grande, plus il est efficace. Par exemple, le LV-T30 a une impulsion spécifique de 370 s (dans le vide). Nous pouvons maintenant appliquer l'équation de Tsiolkovsky, une formule capitale en mécanique spatiale :

${\displaystyle \Delta v=g\cdot I_{sp}\cdot \ln \left({\frac {m_{\text{total}}}{m_{\text{dry}}}}\right)}$

Où ${\displaystyle g}$ est l'accélération de la pesanteur (${\displaystyle 9.81{\frac {m}{s^{2}}}}$ au niveau du sol), ${\displaystyle I_{sp}}$ est l'impulsion spécifique en secondes et ${\displaystyle ln}$ est le logarithme népérien.

Vous pouvez y aller : faites la somme de la masse de carburant de votre étage, puis calculez la masse totale de l'étage et soustrayez-y la masse de carburant (ce qui vous donne la masse sèche). Injectez ces valeurs dans l'équation à la place de ${\displaystyle m_{\text{total}}}$ et ${\displaystyle m_{\text{dry}}}$. Voici un petit exemple en prenant l'accélération de la pesanteur terrestre (la même que sur Kerbin), soit ${\displaystyle g=9.81{\frac {m}{s^{2}}}}$.

Exemple de fusée

3e étage (Injection trans-munaire, Mun lander, retour)
Masse totale	${\displaystyle 3.72t}$
Masse sèche	${\displaystyle 1.72t}$
Isp:	${\displaystyle 400s}$
Δv:	${\displaystyle 3027.0{\frac {m}{s}}}$
2e étage (Injection en orbite de Kerbin)
Masse totale	${\displaystyle 7.27t}$
Masse sèche	${\displaystyle 5.27t}$
Isp:	${\displaystyle 370s}$
Δv:	${\displaystyle 1167.8{\frac {m}{s}}}$
1er étage (Ascension):
Masse totale	${\displaystyle 38.52t}$
Masse sèche	${\displaystyle 14.52t}$
Isp:	${\displaystyle 350s}$ (estimée car vol atmosphérique)
Δv:	${\displaystyle 3349.9{\frac {m}{s}}}$
Total
Δv:	${\displaystyle 7544.6{\frac {m}{s}}}$

Multiple engines

To calculate the I_sp for multiple engines with different I_sp values, you need to find total thrust and mass flow:

${\displaystyle I_{sp_{avg}}={\frac {\sum \limits _{i}^{n}(thrust_{i})}{\sum \limits _{i}^{n}({\dot {m}}_{i}\cdot g_{0})}}={\frac {\sum \limits _{i}^{n}(thrust_{i})}{\sum \limits _{i}^{n}\left({\frac {thrust_{i}}{I_{sp_{i}}}}\right)}}={\frac {thrust_{1}+thrust_{2}+\dots +thrust_{n}}{thrust_{1}\div I_{sp_{1}}+thrust_{2}\div I_{sp_{2}}+\dots +thrust_{n}\div I_{sp_{n}}}}}$

This will give you the correct I_sp to use for your Δv calculation. If all engines are the same, they act as one engine in this calculation so the sums aren't needed.

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.