Mass Delta-V

[The Thyroid Man]

For a while now I've been trying to get to the harder places in the Kerbol system, like Tylo, or Moho, or Eeloo, but it has always eluded me. I can't seem to get my Landers' or transfer ships' Delta-V up as High as I need. It seems if I add more fuel tanks at a certain point, my Delta-V goes down, not up. (Yes, I have kerbal engineer, so I would know this) Can anyone help me with my ship design?

[Streetwind]

On 5/24/2016 at 1:28 AM, The Thyroid Man said:

For a while now I've been trying to get to the harder places in the Kerbol system, like Tylo, or Moho, or Eeloo, but it has always eluded me. I can't seem to get my Landers' or transfer ships' Delta-V up as High as I need. It seems if I add more fuel tanks at a certain point, my Delta-V goes down, not up. (Yes, I have kerbal engineer, so I would know this) Can anyone help me with my ship design?

The rocket equation may look confusing at first glance, due to the logarithm term, but conceptually, it's actually very simple. It's just a multiplication of three numbers, a * b * c. That's all.

One of those numbers is a constant, which you can ignore up until you actually want to do the math. The next one is your engine's specific impulse (Isp). The remaining number is (the logarithm of) your rocket stage's mass fraction. The mass fraction, in turn, is the result of a simple division: mass of the stage full of fuel ("wet mass") divided by the mass of the stage when it's empty ("dry mass").

Why am I telling you this? Because this is perhaps the single most important insight when it comes to building rocket stages. If you build a rocket stage, usually you already know what engine you want... especially in a vacuum. It's either going to be a ~350s Isp LFO engine, an 800s Isp NTR, or a 4200s Isp ion drive. Since you know Isp ahead of time, it is (mathematically speaking) a constant. As a result, you can simplify things, and just ignore Isp altogether while you build your rocket stage. And by defining as constant two of three numbers that define your dV, you end up in a situation where only a single variable truly controls your final dV. And that is the mass fraction. It is the single most important number of every single rocket stage you ever built, and will ever build.

That is the dirty little secret of rocketry. Which normally isn't dirty at all, but Bob spilled the mystery goo earlier...

 

You can get a nice visualization of this by simply solving a few of those logarithms for certain mass fractions.

Example 1: Let's say your rocket stage contains 50% fuel by mass. This means: the mass of the engines plus the mass of the empty tanks plus the mass of structural elements and other assorted greebling plus everything sitting on top of this stage, fuel and all, is ultimately equal to the mass of fuel contained in this stage alone. In this case, your wet mass is exactly twice your dry mass. And it doesn't matter how heavy your rocket is exactly - a division where the numerator is twice as big as the denominator always gives the result of 2. Thus your mass fraction is 2.

Taking the natural logarithm of 2, for which you use a calculator because nobody in their right mind memorizes this stuff nowadays, gives you roughly 0.693. Then you multiply in that one constant we ignored up until now, which is standard gravity at 9.80665. The result of this is about 6.8. Now all you need to finish the rocket equation is to multiply this number with your engine's Isp.

Or, in other words: a rocket stage - any rocket stage, in fact - with a mass fraction of 2 (where 50% of the total mass is fuel) will have roughly 6.8 times Isp worth of dV. Always. Guaranteed. If you use a Poodle, it's 6.8 times 350. If you use a LV-N, it's 6.8 times 800. If you use a Dawn, it's 6.8 times 4200. The first time I truly understood this, I had a small "holy crap" moment.
 

Example 2: You do the same math for a rocket stage in which 20% of the total mass is fuel. Independent of your rocket's actual mass, the mass fraction is always going to end up as 100 / 80 = 1.25. One logarithm and one gravity constant later, you arrive at 2.188. That means, again, that any rocket stage with a mass fraction of 1.25 will have roughly 2.188 times Isp worth of dV. If you add a Poodle, it's 2.188 times 350. If you add a LV-N, it's  2.188 times 800. If you add a Dawn, it's  2.188 times 4200.
 

Example 3: A fun result of this relationship is that every rocket stage has a theoretical maximum amount of dV which it cannot exceed, no matter how much fuel you add. That maximum is defined by the mass fraction of the fuel tanks themselves. In KSP, even if all parts except fuel tanks were completely massless, every tank** would still add 1 ton of dry mass for every 8 tons of fuel it carries. The mass fraction of a fuel tank is 9 / 1 = 9. One logarithm and one gravity constant later, you arrive at 21.548.

This means nothing other than: even if you add fuel tanks equal to the mass of the entire observable universe, your rocket stage will not exceed roughly 21.55 times Isp worth of dV. In fact, since engines and structural elements and payload actually have mass, and you don't have the mass of the entire observable universe at your fingertips, you're not going to get anywhere near 21.5. You're not even going to get anywhere near 20, either. Even getting to 15 is probably going to involve significant effort - a mass fraction of greater than 4.6, which means that you need 3.6 times as much fuel by mass in one single stage as the entire rest of the stage (including stuff on top) weighs. By that time, you're going to get significant diminishing returns from adding more fuel already.

 

You can derive a nice rule of the thumb from this: each rocket stage should probably have an amount of dV that's a sensible, healthy multiplier of engine Isp. If you look at your rocket and discover that all of your stages have roughly five times engine Isp worth of dV, you will instantly know that you've been building inefficiently. You could easily add more fuel without suffering much in the way of diminishing returns. On the other hand, if you discover a stage that has as much as 15 times Isp worth of dV, you should probably split that into two stages (unless you have a good reason why a single stage must carry that much, such as total recoverability). But if your stages are all somewhere between 7 times and 11 times - roughly mass fractions between 2 and 3 - that looks pretty healthy. You're getting your money's worth out of your engines and structural investments without running into serious diminishing returns with your fuel load. Of course, this is disclaimed a bit by TWR. KSP's engines don't have very much of that, and you may find that a launch stage without room for more engines may not be able to load that much fuel and still get off the ground. But once you are in space, TWR becomes much less of an issue.

Another lesson you can derive from this - and which actually is automatically implemented if you follow the above rule of the thumb - is that all of your rocket stages should probably have similar mass fractions. It makes sense, if you think about it: the dry mass for any given stage includes everything that is sitting on top of that stage, including upper stages and all of their fuel. This means that if you overload an upper stage, giving it much more fuel than the average for your rocket's stages, this adds additional dry mass to the stage below it, reducing its mass fraction and therefore its dV - and since that stage is now heavier, that adds additional dry mass to the stage below that, too... and so on and so forth. It's a chain reaction of reduced mass fractions for every stage below. If there are enough stages below, and you overload an upper stage deep into diminishing returns, you could potentially run into a case where adding fuel reduces the rocket's total dV, just because you choke the lower stages that much! The only way to combat this is adding more fuel to each of the lower stages in turn... and suddenly you are back in a situation where every stage has roughly the same mass fraction. It's a natural equilibrium. Ultimately it makes economic and practical sense for upper stages to be a little heavier loaded than lower ones (remember TWR?), but you should not stray too far.

The one stage you're allowed to overload freely (funds cost nonwithstanding) is the launch stage, because that one has no stages below it that could be choked. All you have to keep in mind with this one is that your atmospheric (!) TWR mustn't fall below roughly 1.2. At that point, your rocket would become so slow in lumbering off the pad that gravity losses would eat more dV than you get from adding more fuel. I personally like to go no lower than 1.35, even. And because of the already mentioned low TWR of KSP's engines, this may mean that an overloaded launch stage is a fairly rare thing to encounter.

 

** All tanks? No, not all tanks. That rule currently only holds true for LFO tanks. LF and Monoprop tanks are fairly similar, but not exactly the same; and xenon tanks are much, much worse. The mass fraction of those is less than 2.3 (EDIT: this number has changed over the years) as opposed to 9. So even though the Dawn has a huge Isp, it is much harder to get a good mass fraction due to the poor tanks, so the Isp doesn't give you as good results as you might think it should.

Edited February 27 by Streetwind

[Empiro]

Adding fuel should never decrease your Delta-V unless the fuel isn't being used. Check to see if you need fuel lines connected up.

Other than that, try using LV-N engines with the tanks that only contain liquid fuel. That should give you loads of delta-V, and are perfect for transfer stages.

[Superfluous J]

What @Empiro said, with the addition of "If I could see a picture of your ship I may be able to tell you exactly what's wrong."

[Venusgate]

Consider making your payload relatively small at first, too. It's going to be hard to get 12k dV with a 20 ton payload

 

[wumpus]

The only possible ways I can think of to add fuel and lose delta-v (in vacuum and not in a gravity field, so the way KE and the rocket equation calculates it) is to either use the wrong fuel or not connect the fuel lines.

I originally thought that adding "fuel" to a LV-N (nuclear) rocket would eventually decrease delta-v (you want "plane fuel" without oxidizer), but a quick test proved false.  Best guess is that something is blocked by a decoupler and possibly blocked by something that didn't block things in 1.0.5 (Squad seemed to block some sneaky tricks such as turning off batteries).  Note that if you have oxidizer, expect KE to "use it up" the moment your chemical engines are staged, although this should always *add* to your delta-v (unless you really expected to use the fuel in the nukes and carry around the oxidizer as an unused reserve).

As far as I know, all the KSP fuel tanks are fairly close in efficiency.  To lose delta-v you would need to add amazingly inefficient fuel tanks to a rocket that was mostly wildly efficient fuel tanks (this might be possible with adding tiny fuel tanks with big decouplers.  Of course in that case the delta-v would go down with the decoupler and up once the fuel tank (and fuel lines) were added.  But maybe not back to where you started).

[The Thyroid Man]

Turns out my problem was that I didn't remove the oxidizer! Thanks, @wumpus and @Streetwind!

Edited June 20, 2016 by The Thyroid Man
I hate autocorrect!

[Snark]

40 minutes ago, The Thyroid Man said:

Turns out my problem was that I didn't remove the oxidizer! Thanks, @wumpus and @Streetwind!

Also... if you're using LV-N's, don't just take a regular LFO tank and remove the oxidizer.  If you do that, you're using a tank that's twice as big as it needs to be (you're toting around a lot of empty space where the oxidizer used to be), and therefore wasting a lot of mass on unnecessary dead weight.

Instead, use fuel tanks that are LF-only from the get-go.  Either use one of the stock ones already in-game, or use a mod to give you additional options (since the current selection of LF-only tanks are quite skewed towards spaceplanes, and aren't super friendly for rocket designs).

Another thing to bear in mind, when you're going to places like Tylo or Eeloo or Moho:  Are you trying to send a ship that goes there, lands, takes off, and comes home?  Depending on circumstances (ship design, mission parameters) that can be very inefficient.  Getting from low orbit around a body down to the surface and back is a big chunk of dV right there.  The ideal design for a surface-capable ship is different from an orbit-only ship.  Landers need good TWR.  Orbital transfer vehicles need high Isp, and minimum dead weight (i.e. engines), so tend to have very low TWR.  Trying to build one ship that's good at both things often leads to lugging around a lot of dead weight that you don't need to.

A design that works really well is to have an optimally-designed transfer vehicle that gets to low orbit around the target body, and then parks there while you undock a small lander that goes down to the surface.  That way, you're not lugging the massive transfer vehicle down to the surface and back.  The lander can have a low-Isp, high-TWR engine that's good for planetary landings.  When the lander's finished on the surface, it goes back up to orbit and docks with the transfer vehicle for the trip home (ideally, leaving behind any landing-specific hardware that's not needed for the return journey).

[ForScience6686]

A method I use for high dv is to drag your fuel tanks behind the ship and release tanks as they become empty (not sure of the actual name, I've heard centipede staging before).  This helps shed weight as fuel is exhausted resulting in less mass to carry the remainder of the journey.  It becomes tedious as I calculate by hand, and each tank requires another calculation since mass is lost.  I haven't tested fully if it is much more efficient as this requires many decouplers which add weight.

 

Beyond that, it is critical to keep the payload as light as possible to do the job and no more.  My early days consisted of building in lots of redundancy, however that killed me efficiency wise and would take twice as much to do the same job.  

[Snark]

8 minutes ago, ForScience6686 said:

A method I use for high dv is to drag your fuel tanks behind the ship and release tanks as they become empty (not sure of the actual name, I've heard centipede staging before)

I've heard the name "bamboo staging" for this.

But there's nothing special around the "drag behind"-- it can work just as well for tanks that are attached radially, or in front, or wherever is convenient for your ship design.  The main idea is, use "drop tanks"-- i.e. engineless fuel tanks that you drop when empty.

[Wcmille]

4 hours ago, Snark said:

I've heard the name "bamboo staging" for this.

But there's nothing special around the "drag behind"-- it can work just as well for tanks that are attached radially, or in front, or wherever is convenient for your ship design.  The main idea is, use "drop tanks"-- i.e. engineless fuel tanks that you drop when empty.

I think the chief reason to drag behind is stability. Thrust applied to a long tank attached in front, which has wobbled off-center (say from turning), creates a destabilizing torque force that will make that tank more off-centered. A tank attached at rear, which has wobbled off-center, has a stabilizing torque force.

[Snark]

1 hour ago, Wcmille said:

I think the chief reason to drag behind is stability. Thrust applied to a long tank attached in front, which has wobbled off-center (say from turning), creates a destabilizing torque force that will make that tank more off-centered. A tank attached at rear, which has wobbled off-center, has a stabilizing torque force.

Yes, but in my experience, ships that use droptanks are very low TWR (if they cared about TWR, they'd have engines on the tanks they're dropping), so it tends not to be an issue.

[Vaporized Steel]

The trick is to use seperatable vessels with docking ports, launched as one single rocket.. Don't stare blind at your total delta v from the launch pad. Just get enough delta v on your nuclear stage once in LKO to reach the main soi of your destination and spare fuel to.get back. (lets say its jool) and have a detachable lander thats alot lighter to land on the moons. It can then use up all its fuel to land and back to orbit and dock and even refuel at the tug for a landing at a secondary joolian moon. Doing it on all 5 moons is the jool 5 challenge and thats a whole ordeal to accomplish. Make use of Oberth transfers and gravity assists from and to jool and changing your pe/ap around Jool.

Same works for eelo and moho. Youtube for mission videos for both destinations and youll find out its not just the rocket design and total delta v and amount of fuel but the piloting with the.methods i.e I just described.

Edited June 21, 2016 by Vaporized Steel

[wumpus]

12 hours ago, Wcmille said:

I think the chief reason to drag behind is stability. Thrust applied to a long tank attached in front, which has wobbled off-center (say from turning), creates a destabilizing torque force that will make that tank more off-centered. A tank attached at rear, which has wobbled off-center, has a stabilizing torque force.

IMPORTANT NOTE TO NEW PLAYERS: this only works between planets (when your biggest instability issue is docking port wobble).  Building a "Goddard-style" rocket with the rockets at the top is called the "pendulum fallacy" and is always less stable than putting the engine at the bottom (at least for rockets capable of achieving LKO, in space things are a bit different).

Sticking a tank or two on top (and then refueling manually and jettisoning the top fuel tank) works well for early missions exploring local moons.  It also saves a bit of cost for for the extra decoupler and fuel lines, which is more significant for those early flights.