Problems calculating Delta-V for Multiple Engines craft

[Arch3rAc3]

Hello!

Firstly, I know questions like this one have already been made both in and out of the forums before, yet every thread I found and read do not fix my problem or give me an idea of what I'm doing wrong. Also, sorry if this ends up a bit too long and technical, I want to try and make it as clear and detailed as possible, especially when explaining the math I did, so it doesn't confuse or give the reader a headache.

 

So... I finally decided to play KSP [more] seriously, disabling "revert flight" and trying to calculate the rocket performance and everything else before launch to minimize failures. I'm playing the Enhanced Version for the Xbox, which should be pretty much a 1.2 stock for PC.

The rocket I have is comprised of two stages: the first one has 3 engines, a center Swivel one (with 2 FL-T800s on top), and two radially mounted Reliant engines in an asparagus setting (so they have one FL-T800 on top each, with both of these fuel tanks feeding into the center one directly above the Swivel - this way, once the radial tanks are expended, they will be jettisoned with the Reliant engines).

The second stage is the orbital stage, having a single LV-909 Terrier with a FL-T400 on top (will talk about it later on).

The goal of this rocket is to carry scientific equipment to a space station at a 200km circular orbit over Kerbin, where it's currently being assembled for a mission to Minmus.

The problem I initially has is that the Delta-V calculation I done for the first stage gave me a result of ~1899m/s², which theoretically should not have been enough to allow me to leave Kerbin's atmosphere (as "Delta-V out" of Kerbin is 2500m/s²). Yet, I managed to dock with the intended station with about 60% of fuel remaining in the second stage (no cheats involved, I swear).

I've done all the calculations based on what's available at wiki.kerbalspaceprogram, making use of the "Advanced Rocket Design" and "Cheat Sheet" topics. Will go over the math now:

Starting up, I calculated the average Isp of the three engines at sea Level, which was pretty much: (F1+F2+F3/(F1/Isp1)+(F2/Isp2)+(F3/Isp3) being F=Thrust at sea level. This gave me an AvgIsp of 261 (which I called Isp1). Right after, I got the total mass of the craft (M0=28556t) and the first dry mass (aka: the mass with empty radial tanks before dropping them and the Reliants; which I called M1=20556).

I also calculated the new mass right after dropping the radial tanks and with full center tanks and swivel engine (M2=16646); and dry mass for empty center tanks (M3=8646).

Based on this, I calculated 2 delta-Vs for the first stage: Delta-V1, while both the Reliants and Swivel were firing; and Delta-V2, after the Reliants were dropped and only the Swivel was firing and taking fuel from it's own tanks now.

So, Delta-V1 = Isp1(261)*g[9,81]*ln(M0/M1)[0,32] obtaining a value of ~819m/s².

Did the same for Delta-V2, calculating the Isp2 for the Swivel only part of the flight, for which I got an Isp2 of ~167.9; then Delta-V2 of 1070m/s²

I then made the sum between both Delta-Vs, obtaining that nasty odd value of ~1889m/s².

As for the second stage, it gave me a Delta-V value of 276.6m/s², adding the whole sum to 2175m/s² (which shouldn't even be enough to take me out of Kerbin's atmosphere, let alone docking. The whole flight from Launch to a circular 200km orbit should require ~4844.88m/s², more than twice what I had!

Some thought and considerations (and questions):

1. I know the Delta-V I calculated is lower than the real Delta-V, since, for all the first stage engines, I only accounted for the Sea Level Isp and ignored the Vacuum Isp - while in reality the higher I went, the more Isp I'd have, thus increasing my Delta-V - although I don't believe it would have such an impact on the Delta-V.

2. I tried being efficient during the atmospheric flight, avoiding overspeed and unnecessary drag, which caused me to lower the throttle quite a bit (especially while the 3 engines were firing) and in turn increase the engine-on time, resulting in more Isp since I was ever higher with the engines on. This goes back to point 1, since I only considered Isp for Sea Level even though half of my fight happened at high altitude / low pressure / higher Isp environments. Could this also justify the Delta-V discrepancy?

3. Is there a way I can calculate Isp at an specific altitude so I can be more accurate (instead of only taking into account the Vacuum Isp for the 2nd/orbital stage and ASL Isp for the first stage)?

4. I tried repeating the math but assuming I'd not fire the Swivel until the Reliants were dropped. In the end it gave me a noticeably higher Isp and Delta-V, although still not as high as theoretically necessary. This is kinda odd though, shouldn't firing all engines together but feeding only from the radial tanks be more effective?

 

Thanks. Would love to hear what I've been doing wrong and hope I didn't give too much headache to people trying to read this. (And yes, I'm super jealous of you PC players with all the fancy Kerbal Engineer calculating stuff!)

Cheers.

 

Edited March 8, 2019 by Arch3rAc3

[OhioBob]

First off, I usually do all the calculations using vacuum Isp.  It over estimates the delta-v a little, but you generally climb out of the thick atmosphere so quickly that you're burning at much closer to the vacuum value for most of the ascent than you are to the sea level value.  I believe that "vacuum delta-v" is what most people use when talking about delta-v to orbit.  I know that the "3400 m/s to orbit" figure that is commonly quoted is based on vacuum values.

Computing the combined Isp of 1 Swivel + 2 Reliant using the vacuum values, I get 313 s.  So computing the first stage delta-v using your mass numbers and vacuum Isp, I get the following:

Delta-V_1 = 313 * 9.81 * LN(28556 / 20556) = 1009
Delta-V_3 = 320 * 9.81 * LN(16646 / 8646) = 2056
Delta-V_total = 3065 m/s

Quote

So, Delta-V1 = Isp1(261)*g[9,81]*ln(M0/M1)[0,32] obtaining a value of ~819m/s².

Delta-v is velocity measured in m/s.  m/s² is the unit of measure for acceleration.

Quote

calculating the Isp2 for the Swivel only part of the flight, for which I got an Isp2 of ~167.9

I have no idea where you got that number.  The Swivel has sea level and vacuum Isp of 250 and 320, so it couldn't possibly be 167.9s.

Quote

As for the second stage, it gave me a Delta-V value of 276.6m/s²

276.6 m/s sounds way too low.  Are you computing that using sea level Isp?  You don't give starting and ending mass figures for the second stage, but I can make some educated guesses.  I'm estimating that your second stage should have >1300 m/s delta-v.

Quote

The whole flight from Launch to a circular 200km orbit should require ~4844.88m/s²

I don't know from where you got that number, but it sounds too high to me.  To reach a minimum orbit around Kerbin, I generally assume about 3400 m/s.  That's for a minimum orbit; getting to 200 km should add another 200 m/s.  That get's us up to about 3600 m/s.  It could be more than that if your rocket is really draggy, or if you fly it inefficiently.

If your first stage has 3065 m/s, and if you used 40% of the second stage's fuel, that's probably getting you pretty close to 3600 m/s total.
 

Edited March 8, 2019 by OhioBob

[FleshJeb]

2 hours ago, Arch3rAc3 said:

single LV-909 Terrier with a FL-T400

As Bob alluded to, the Terrier is optimized for vacuum and has a very poor sea-level ISP. (1.6.1 version is 85 ASL, 345 Vac).

I just love the rigor with which you're approaching this, and you seem like the kind of person that would appreciate it, so I'm going to nitpick your units:

2 hours ago, Arch3rAc3 said:

(M0=28556t)

That should be kg. It's working out because the units get cancelled in the dV equation, but it might come back to bite you later. It's probably best to do all your calculations in Tons (kilo-kilograms), since the engines are rated in kiloNewtons.

My handy trick for estimating TWR relies on the above--It should be extra useful for a console player.

Thrust (kN) / Mass (T) / 10 = Kerbin TWR (9.81m/s^2 ~= 10).

Or put another way, Thrust/10 is the number of tons you can lift at a TWR of 1. Very helpful for selecting engines.

For Mun, multiply by 6; For Minmus, multiply by 20.

[Zhetaan]

10 hours ago, Arch3rAc3 said:

1. I know the Delta-V I calculated is lower than the real Delta-V, since, for all the first stage engines, I only accounted for the Sea Level Isp and ignored the Vacuum Isp - while in reality the higher I went, the more Isp I'd have, thus increasing my Delta-V - although I don't believe it would have such an impact on the Delta-V.

@OhioBob is one of our resident maths wizards; there's not much for me to add here, except to say that it absolutely would have such a large impact on your delta-V.  Add to that that you get out of the thickest part of the atmosphere so quickly that even the Terrier, which has a sea-level I_sp of 85 seconds, is up to 99% of its vacuum thrust at a little over 10 km altitude, and you're underestimating your calculations severely all throughout.

10 hours ago, Arch3rAc3 said:

2. I tried being efficient during the atmospheric flight, avoiding overspeed and unnecessary drag, which caused me to lower the throttle quite a bit (especially while the 3 engines were firing) and in turn increase the engine-on time, resulting in more Isp since I was ever higher with the engines on. This goes back to point 1, since I only considered Isp for Sea Level even though half of my fight happened at high altitude / low pressure / higher Isp environments. Could this also justify the Delta-V discrepancy?

Overspeed is an issue in extremely thick atmospheres.  That applies to lower Eve, lower Jool, and pre-v1.0 Kerbin.  Post-v1.0 (and you are v1.2), the aerodynamics are somewhat better, and the gravity losses are the most important losses to attend.  That means that most likely, throttling down has cost you delta-V because you are allowing gravity (and its constant acceleration) to work on your vessel for a longer period of time.

10 hours ago, Arch3rAc3 said:

3. Is there a way I can calculate Isp at an specific altitude so I can be more accurate (instead of only taking into account the Vacuum Isp for the 2nd/orbital stage and ASL Isp for the first stage)?

It can be done, but you're likely better off estimating based on observed figures at various altitudes.

10 hours ago, Arch3rAc3 said:

4. I tried repeating the math but assuming I'd not fire the Swivel until the Reliants were dropped. In the end it gave me a noticeably higher Isp and Delta-V, although still not as high as theoretically necessary. This is kinda odd though, shouldn't firing all engines together but feeding only from the radial tanks be more effective?

Not the way you're calculating it.  The Swivel has ten seconds more vacuum I_sp than the Reliant, but its sea-level I_sp is fifteen seconds lower.  You gain a tiny amount of efficiency that way from using just the Reliants.  Also, since the Swivel is not taking fuel from the radial tanks if it isn't burning, your Reliants get more burn time at that higher efficiency.  If you're calculating with only the sea-level I_sp, then all of those little bits of savings add to quite a lot.  Of course, the Reliants alone won't muster the same thrust as the Reliants plus Swivel, so you'll spend more time in the lower atmosphere combating drag and need a longer run up to orbital speeds, which also increases gravity losses.  Take the fact that you're questioning your results in this case as evidence that you need better assumptions:  to wit, sea-level I_sp is really only valid at sea level.

I will add that there are times when choosing not to fire some engines makes sense.  For an obvious example, imagine that your rocket uses strap-on Reliant boosters to get a central Terrier-driven core to orbit.  Running the Terrier along with the Reliants at launch in an asparagus-style staging sequence is just a waste of fuel that the Reliants, despite their vacuum inefficiency, can put to better use.  On the other hand, imagine that you make orbit with a significant amount of fuel left in the boosters.  It makes sense in that case to deactivate the Reliants and use the boosters as heavier-than-normal fuel tanks because the Terrier is so much better in Vacuum than the Reliant.  Yes, the dead engines are parasitic mass, but the fuel is free:  when you decouple the empty boosters, you still have a fully-fuelled rocket.  In truth, you ought to have reduced the fuel load and added more payload, but if you're already in orbit with no reverts, you may as well use what you have.

But that's mainly a problem when you're using engines with radically different performance values in the ambient environment.  Swivels are essentially Reliants with gimbals; you should nearly always get better numbers when you use them together.

Edited March 8, 2019 by Zhetaan

[OhioBob]

11 hours ago, Arch3rAc3 said:

4. I tried repeating the math but assuming I'd not fire the Swivel until the Reliants were dropped. In the end it gave me a noticeably higher Isp and Delta-V, although still not as high as theoretically necessary. This is kinda odd though, shouldn't firing all engines together but feeding only from the radial tanks be more effective?

The Reliant and Swivel are similar engines with similar Isp, so the sequence in which you fire the engines shouldn't make much difference in the calculated delta-v.  What will change by firing only the Reliants first is the thrust-to-weight ratio.  You'll have less thrust off the launch pad, so you'll be accelerating more slowly.  This will decrease drag losses but increase gravity losses.  These effects are not seen in the delta-v calculation.  In fact, computed delta-v doesn't care at all about TWR.  The computed delta-v is just theoretical.  You can have a rocket with 3000 m/s delta-v, but if the TWR is <1, it's not going to go anywhere.  So there's more to designing a good launch vehicle than just delta-v.  What engine fire sequence works best should probably be determined by what keeps your rocket within a controllable range of TWR.

If you are firing 2 Reliant + 1 Swivel, I compute a TWR of 2.07 at launch and 3.45 at burnout.  By firing just the Reliants, I compute a TWR of 1.47 at launch and 2.38 at burnout.  Either of those will probably work, but the lower range is closer to what I typically do.  I find the higher TWR more difficult to control, so I find it harder to get the turn right.  But that's just me.  What works best for you should be determined through practice.

(EDIT)  Which method you use, low or high TWR, can also have an effect on launch cost.  But that's an entirely different conversation.  We can discuss it if you'd like, but I don't want to sidetrack the thread.
 

Edited March 8, 2019 by OhioBob

[Arch3rAc3]

Well, this is a bit embarassing, didn't notice I had made so many mistakes there (apparently this is the problem of trying to do KSP math at 00:30AM with coffee being the only thing keeping you up).

@OhioBob

10 hours ago, OhioBob said:

Delta-v is velocity measured in m/s.  m/s² is the unit of measure for acceleration.

Right, I don't know why I placed s² the first time, and just kept copying the units incorrectly.

10 hours ago, OhioBob said:

I have no idea where you got that number.  The Swivel has sea level and vacuum Isp of 250 and 320, so it couldn't possibly be 167.9s.

Correct! 167.9 was the Thrust. Apparently I calculated Delta-V1 correctly for ASL, but for Delta-V2 I used the engine's thrust instead of Isp.

10 hours ago, OhioBob said:

You don't give starting and ending mass figures for the second stage, but I can make some educated guesses.  I'm estimating that your second stage should have >1300 m/s delta-v.

Again, I done the same mistake and you are correct. I did not give you the mass for I thought there were too many numbers here already, but it's M4=5696kg and M5=3696kg. The resulting Delta-V3 was ~1463.8m/s , which does make a lot of sense now.

10 hours ago, OhioBob said:

I don't know from where you got that number, but it sounds too high to me.  To reach a minimum orbit around Kerbin, I generally assume about 3400 m/s.

This wiki page (https://wiki.kerbalspaceprogram.com/wiki/Tutorial:Advanced_Rocket_Design) at the "Delta-V map" section states that a launch to 100km Kerbin Orbit requires 4700m/s. Applying a Hohmann Transfer to increase my orbit from 100km to 200km requires 144.88m/s; summing it all up to 4844.88m/s.
It did feel a little bit too high, but I can't tell what's wrong here. Perhaps the numbers on the wiki are somewhat off

Should I do all the calculations with vacuum Isp and use this equation then:   Because I'm not sure where else I'd apply this.

 

9 hours ago, FleshJeb said:

That should be kg. It's working out because the units get cancelled in the dV equation, but it might come back to bite you later. It's probably best to do all your calculations in Tons (kilo-kilograms), since the engines are rated in kiloNewtons.

Thanks! This was a bit confusing while I was typing for here where I live we use commas as dots (decimals) and dots as commas when doing math. Therefore when I was calculating I'd write M1=12,345t for example, which would be correct here (345 would be decimals), but incorrect there. I ended up taking the comma out and didn't pay much mind to the tons there since it wouldn't make a difference right now (although it was incorrect).

2 hours ago, Zhetaan said:

the aerodynamics are somewhat better, and the gravity losses are the most important losses to attend

So I shouldn't pay much mind to the great ball of fire going towards space?

2 hours ago, Zhetaan said:

[...]I will add that there are times when choosing not to fire some engines makes sense.[...]

Hadn't thought of it like that, it made a lot of sense! Thanks!

 

Edited March 8, 2019 by Arch3rAc3

[Zhetaan]

1 hour ago, Arch3rAc3 said:

This wiki page (https://wiki.kerbalspaceprogram.com/wiki/Tutorial:Advanced_Rocket_Design) at the "Delta-V map" section states that a launch to 100km Kerbin Orbit requires 4700m/s.

That tutorial is ancient.  If you'll have a look at the picture of the example rocket, do you see that the parts look odd?  That's what KSP looked like at about version 0.15.  It's from at least version 0.15 because I can see the Runway in the background.  The delta-V map is much changed since then:  for example, there are other planets now.  Enjoy your glimpse of history, but don't rely on the numbers.  I note that the most recent edit is January 2018, but I don't know why that edit (or any other) didn't update the delta-V values.  In current KSP, you can achieve orbit typically with 3,500 m/s of delta-V, assuming decent rocket design and piloting.

1 hour ago, Arch3rAc3 said:

So I shouldn't pay much mind to the great ball of fire going towards space?

It is going towards space, isn't it?

Seriously, you're not going to hit terminal velocity unless you have insane thrusts.  If you had a heating problem causing your rocket to do its best impression of a fireball, then I would say that you have issues with the design that arbitrarily increase drag, or else you're doing something to keep your rocket in the lower atmosphere for too long.  However, you are getting to orbit with a lot of fuel to spare, and those other issues would stop you from doing that unless you had a seriously over-engineered rocket.  Fire is not, itself, a problem:  rockets are made of fire.  If you perform your post-launch pitch manoeuvre (this is what begins the gravity turn) correctly, then there is no reason not to fly at full throttle.  If you design the rocket particularly well, then you can leave your hands off the controls after the pitch and it'll fly itself to near-circular orbit with no further input from you.

Edited March 8, 2019 by Zhetaan

[Arch3rAc3]

Alright. I used to think that drag played a way bigger role, especially if I was close to burning.

As for the Delta-V, is this one accurate even for PC current version:

Spoiler

?

Thanks.
 

Edited March 8, 2019 by Arch3rAc3

[Zhetaan]

1 minute ago, Arch3rAc3 said:

As for the Delta-V, is this one accurate even for PC current version?

Yes.  It says in very greyed text in the upper left (directly under the word Kerbal) that it is accurate to KSP version 1.2.1.  However, PC has seen no changes in either gravity or aerodynamics since then; the map is still accurate for both PC and console.

[FleshJeb]

2 hours ago, Arch3rAc3 said:

Thanks! This was a bit confusing while I was typing for here where I live we use commas as dots (decimals) and dots as commas when doing math.

Ha! Yes, it gets me sometimes too, in the other direction.

This is where I go for the most up-to-date dV map (Google "ksp delta v map"):

Like @Zhetaansaid, nothing significant has changed. Nor is it likely to.

[OhioBob]

1 hour ago, Arch3rAc3 said:

Alright. I used to think that drag played a way bigger role, especially if I was close to burning.

Drag use to be a much bigger issue in early versions of the game, pre-1.0.  At that time the game used a placeholder drag model that produced insanely high amounts of drag.  That's where the 4700 m/s to orbit came from.  But with the introduction of the current aerodynamics in v1.0, things are much more lifelike now.  (The aero settings have gone through some tweaks since v1.0, but the basic model hasn't changed.)  Generally speaking, gravity losses are about ten times greater than drag losses.  Other than using common sense and making my rockets reasonably streamline, I don't even worry about drag.  It's just not that big of an issue, at least not on Kerbin.  Eve might be another story.

Quote

Well, this is a bit embarassing, didn't notice I had made so many mistakes there

Don't worry about it.  Lord knows we've all made our share of mistakes while going through the learning curve.
 

Edited March 8, 2019 by OhioBob

[Kryxal]

It's too bad there are no inline engines with about half the thrust of the Reliant ... I wonder if using Thuds instead and closing off the now-empty back node would be a good idea?  Then again, if you're managing a good gravity turn, maybe just leave well enough alone, but fuel is cheap, engines are expensive...

[Arch3rAc3]

1 hour ago, Kryxal said:

It's too bad there are no inline engines with about half the thrust of the Reliant ... I wonder if using Thuds instead and closing off the now-empty back node would be a good idea?  Then again, if you're managing a good gravity turn, maybe just leave well enough alone, but fuel is cheap, engines are expensive...

I also don't like jettisoning the engines like that. My initial idea was recovering it, so I had parachutes strapped and all, and only later noticed that the game causes objects in atmosphere to be destroyed when too far from the player.

I was thinking of having only one Reliant (as the only reason for the Swivel was the vectoring, but my ship is light and doesn't really require it), so I wouldn't have to jettison engines. But I'd have to check the TWR and if it comes too low I'd add solid boosters instead. Might do it later.

[OhioBob]

2 hours ago, Kryxal said:

It's too bad there are no inline engines with about half the thrust of the Reliant ...

That's one of the things I like about MissingHistory, it adds @Porkjet's LV-T15 engine (105 kN max thrust).

[Kryxal]

17 hours ago, Arch3rAc3 said:

I was thinking of having only one Reliant (as the only reason for the Swivel was the vectoring, but my ship is light and doesn't really require it), so I wouldn't have to jettison engines. But I'd have to check the TWR and if it comes too low I'd add solid boosters instead. Might do it later.

If you do that, it might be worth running the center engine alongside the boosters and adding extra fuel on top of the boosters.  Cross-feed on the decouplers and instant drop-tanks!