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[Tutorial] A Guide to Basic Kerbal Rocket Design Through Rocket Science.


VincentMcConnell
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A Guide to Basic Kerbal Rocket Design:

By Vincent McConnell and Kosmo-not.

Introduction:

Getting to learn basic rocket science for a space game like Kerbal Space program can be very important to the success of building rockets that can perform a desired job. In this guide, we will be covering things like calculating the full Delta-V of your ship, explaining how to perform transfer maneuvers, getting Thrust to Weight Ratio, calculating the Peak G-force experienced during a particular burn, also calculating Delta-V needed for a full-Hohmann transfer and much more.

Delta-V (change in velocity) is the bread and butter of rocket science. It is probably the most important thing to know about your rocket because it determines what your rocket is capable of achieving. Among the several things we will explain in this basic tutorial, Delta-V is most likely the most useful thing you will apply to Kerbal Space Program while building a rocket.

To find the Delta-V of your rocket -- each stage at a time -- we have to sum up the part masses of every single part of the stage. When summing up fuel tank masses, it may be easier to write them like this on your paper:

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). In the case of the non-vectoring stock engine has an vacuum specific impulse of 370. So here, we must apply the Tsiolkovsky Rocket Equation. More informally known as �The Rocket Equation�.

It states: Delta-V = Isp*9.81*ln(m1/m2).

m1 = total mass of the stage

m2 = 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 mass. Input these into the equation in the place of m1 & m2. So, we will show a quick example, here:

screenshot7ex.png

Stage 3 (TMI, Mun lander, Return):

Full mass: 3.72

Dry mass: 1.72

Isp: 400 s

Delta-V: 3027.0 m/s

Stage 2 (Kerbin orbit insertion)

Full mass: 7.27

Dry mass: 5.27

Isp: 370 s

Delta-V: 1167.8 m/s

Stage 1 (Ascent):

Full mass: 38.52

Dry mass: 14.52

Isp: 350 s (estimated due to atmospheric flight)

Delta-V: 3349.9 m/s

Total Delta-V: 7544.6 m/s

Note:

To calculate the Isp for multiple engines with different Isp values, you need to take the weighted average of the specific impulses relative to thrust. The equation looks like this:

(Isp_1*thrust_1 + Isp_2*thrust_2 ...)/(thrust_1 + thrust_2 ...)

This will give you the correct Isp to use for your delta-V calculation.

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 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:

e92122ee1e648aa7cfc689d7d1f65844.png

This is the formula for the final burn in the transfer:

54622804d7426a2bed1a1f425de5bb04.png

Where:

u= Gravitational Parameter of Parent Body. (3530.461 km^3/s^2 for Kerbin).

r_1= The Radius of our first orbit. (100 km in this case).

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 Delta-V in the stage to make this burn. Again, you can do that by using the Delta-V calculations on pages 1 & 2.

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 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 (russian guy) equation, inputting the initial mass and 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 Isp and thrust, is:

m_dot = thrust/Isp

where m_dot 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.

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:

sqrt(u/r).

Where:

u = Gravitational Parameter of parent body. (km^3/s^2)

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 ~2.24578 kilometers per second (km/s), or 2245.8 m/s.

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

Launch to 100km Kerbin orbit: 4700 m/s

Trans-Munar Injection: 900 m/s

Landing on the Mun: 1000 m/s

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

Total delta-v: 7600 m/s

If we design our rockets to have 7600 total 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 delta-v can accomplish this goal, but it is less forgiving of less efficient piloting.

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 engines divided by the weight (mass * 9.81 m/s^2) of your stage, 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.

Edited by sal_vager
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Thanks for your efforts. However, i\'m having an issue with the formula...

Lets look at an example from one of my rockets. 3rd and 4th (final) stage has

144000kg Full

72000kg Dry

So 144000 / 72000 = 2

Nice round halving of mass.

Then the natural log...

ln(2) = 0.693

Impulse is one of those big new engines at 330s

So...

Delta-V = 330 * 0.693

which is 228.69 m/s

Now I know that is wrong... but I don\'t know why.

EDIT:

This http://www.strout.net/info/science/delta-v/

Gives me a delta-v of 2243.16 m/s

So this i think is from: Delta-V = specific impulse * 9.80665 * ln(full mass / dry mass)

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Thanks for your efforts. However, i\'m having an issue with the formula...

Lets look at an example from one of my rockets. 3rd and 4th (final) stage has

144000kg Full

72000kg Dry

So 144000 / 72000 = 2

Nice round halving of mass.

Then the natural log...

ln(2) = 0.693

Impulse is one of those big new engines at 330s

So...

Delta-V = 330 * 0.693

which is 228.69 m/s

Now I know that is wrong... but I don\'t know why.

EDIT:

This http://www.strout.net/info/science/delta-v/

Gives me a delta-v of 2243.16 m/s

So this i think is from: Delta-V = specific impulse * 9.80665 * ln(full mass / dry mass)

Forgot to add standard gravity to the equation.

dV = Isp*9.81*ln(m1/m2)

It will be fixed later today.

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with no test flights first.
Nothing replaces the value of test flights, though. Skipping those is a good way to get 500m over the surface of Mun before realizing that you didn\'t put a decoupler between your descent stage and lander. :D
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Skipping those is a good way to get 500m over the surface of Mun before realizing that you didn\'t put a decoupler between your descent stage and lander.

Build checklist. =P Write up a list of all the important parts on your command stage and when you build a vehicle, check them off one by one. That will take practically no work compared to all the other stuff you\'ll be writing down while you build. Because of the things in this guide, I have only four rockets built in my stock KSP folder at the moment. But all of them work and they worked on the first try.

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The engineer plugin did that, and it helped me design my rockets much faster. It no longer works in 0.16, meaning I had to go back to the pencil-and-paper way. Hopefully the guy who made the engineer plugin will update it for 0.16. I did ask about it on the thread a few days ago.

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Why would you need to do that?

The alternative to a spreadsheet is pad, pen, and calculator. With a spreadsheet I should simply be able to plugin the parts for each stage, and get all the delta-Vs. The spreadsheet has all the formulas and details of the parts (full and dry mass and impulse). I created one today, but I still need to add in all the numbers for the parts.

However, working on it has raised another question. How do you deal with SRBs that separate from a liquid fuel stack? I would think the SRBs would be considered a stage, but the 'empty' mass would depend on how much liquid fuel is left. Is there any way to work this out?

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However, working on it has raised another question. How do you deal with SRBs that separate from a liquid fuel stack? I would think the SRBs would be considered a stage, but the 'empty' mass would depend on how much liquid fuel is left. Is there any way to work this out?

What you have to do in this case is calculate the fuel consumption rate of the engines to get how much mass the liquid engines have used while the SRBs were running (25 seconds for small, 30 seconds for large). You find the weighted average of the Isp\'s related to thrust like in the tutorial and proceed from there.

For small SRB: Isp=442s

For large SRB: Isp=204s

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I have another question. Let's say if I want a stage to land on the mun but not be able to take off. I want it to be able to slow me down to 0m/s in speed, will I only need half of the amount of force required to lift off of the mun? Meaning that I only need 1000/2 = 500m/s in Delta-V to land (if I do it well)?

EDIT: Also if I have three landing engines on my mun landing stage. (Landing engines, 400 impulse each in vacuum). Will my calculation be this:

(400*4) * 9.81 * ln(m1/m2)

When I did that I got 9715 of Delta-V which is absurd, so I did something wrong.

Edited by Olsson
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I have another question. Let's say if I want a stage to land on the mun but not be able to take off. I want it to be able to slow me down to 0m/s in speed, will I only need half of the amount of force required to lift off of the mun? Meaning that I only need 1000/2 = 500m/s in Delta-V to land (if I do it well)?
That should be approximately correct, if the landing and ascent stages do the same thing. If the landing stage just has to get down from a low munar orbit, but the ascent stage has to get back to Kerbin, it may need a higher ΔV.
EDIT: Also if I have three landing engines on my mun landing stage. (Landing engines, 400 impulse each in vacuum). Will my calculation be this: (400*4) * 9.81 * ln(m1/m2)

When I did that I got 9715 of Delta-V which is absurd, so I did something wrong.

Isp is not thrust, but can be thought of as thrust per unit of propellant burned. Multiple engines with the same Isp will act like a single larger engine with that exact Isp. Multiple engines with different Isps will give the rocket a net Isp in between the various values.

Short version: you want ΔV = 400*9.81*ln(m1/m2) ~=2429 m/s

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I have another question. Let's say if I want a stage to land on the mun but not be able to take off. I want it to be able to slow me down to 0m/s in speed, will I only need half of the amount of force required to lift off of the mun? Meaning that I only need 1000/2 = 500m/s in Delta-V to land (if I do it well)?

Use up all your fuel on landing, then it won't be able to lift off. I don't understand what you are asking past the first sentence.

EDIT: Also if I have three landing engines on my mun landing stage. (Landing engines, 400 impulse each in vacuum). Will my calculation be this:

(400*4) * 9.81 * ln(m1/m2)

When I did that I got 9715 of Delta-V which is absurd, so I did something wrong.

Specific impulse is a measure of the efficiency of the engine. Adding more of the same engines will still give you the same efficiency.

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Use up all your fuel on landing, then it won't be able to lift off. I don't understand what you are asking past the first sentence.

Specific impulse is a measure of the efficiency of the engine. Adding more of the same engines will still give you the same efficiency.

Alright, thanks for responding :) What I ment is that in the OP it says that you need 1000m/s of Delta-V to land on the mun and 1000m/s of Delta-V to take-off from the mun. This means that it takes the same amount of Delta-V to land and to take off from the mun. What I ment is that what if my Delta-V is instead 500m/s, this will mean that I can't take off from the mun but what I'm asking is it if is enough to land on the mun. If it is enough to slow me down to 0m/s but not to lift me off the mun.

Shit I realize how stupid this sound. TL;DR: If I use half of the Delta-V required to take-off from the mun will it be enough for me to get my velocity to 0m/s to JUST land on the mun with the stage?

EDIT:

That should be approximately correct, if the landing and ascent stages do the same thing. If the landing stage just has to get down from a low munar orbit, but the ascent stage has to get back to Kerbin, it may need a higher ÃŽâ€V.

Isp is not thrust, but can be thought of as thrust per unit of propellant burned. Multiple engines with the same Isp will act like a single larger engine with that exact Isp. Multiple engines with different Isps will give the rocket a net Isp in between the various values.

Short version: you want ÃŽâ€V = 400*9.81*ln(m1/m2) ~=2429 m/s

Thanks for responding and thanks for teaching me! :) Let's say that I would want to do a re-entry on Kerbin or a landing on mars. But this time I'm not using engines but I'm using parachutes to slow me down. How does this change the calculation and what else do I need to know? Is it another calculation? You don't have to respond to this I'm just curious since landing on Murs in the next patch is going to be a pain :D

Edited by Olsson
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Well you'd need to know the drag of the chute. Calculating descent rates with a parachute for ÃŽâ€V is going to be quite a bit harder.

Alright. Unless it is another calculation where you take the gravity, atmosphere, drag and weight into effect?

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It's my understanding that with the Hohman Transfer, unless you're actually changing your orbit (say to get into a geostationary one) you don't actually want to do the second burn. You want the first burn to put you on a path that intersects your destination body's SOI then you want your second burn to be one that puts you in orbit... or not, depending on the mission.

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MilkTheFrog, what you describe is known as a direct ascent, when the Mun (or Minmus) is in the correct position it is possible to make a single continuous burn to intercept the other body, then do a second burn after you have changed Sphere of Influence, this was the method that was going to be employed by the Soviet N1 rocket btw.

The more common method is to attain a parking orbit and then wait for the opportune time to begin a transfer burn.

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Alright, thanks for responding :) What I ment is that in the OP it says that you need 1000m/s of Delta-V to land on the mun and 1000m/s of Delta-V to take-off from the mun. This means that it takes the same amount of Delta-V to land and to take off from the mun. What I ment is that what if my Delta-V is instead 500m/s, this will mean that I can't take off from the mun but what I'm asking is it if is enough to land on the mun. If it is enough to slow me down to 0m/s but not to lift me off the mun.

**** I realize how stupid this sound. TL;DR: If I use half of the Delta-V required to take-off from the mun will it be enough for me to get my velocity to 0m/s to JUST land on the mun with the stage?

No. The delta-v is for each stage. According to the OP it takes 1000m/s of delta-v to land on the Mun. It takes the same amount of delta-v to take off from the Mun. (I am going by the OP, so no idea if that is accurate.) Which means if you want to land AND take off again, you need to have at least 2000m/s of delta-v total once you are on your landing sequence.

You seem to be asking how much delta-v does it take to just land on the Mun, in which case, it is just 1000m/s of delta-v. If you halve that to 500m/s of delta-v you will probably end up making a new crater on the Mun.

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