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# Could someone help with these multistage Delta-v calculations?

## Question

I have had KSP for the PS4 a total of 4 days now, and it's complexity and intricacy exceeds what I prepared for. I am happy in this, but mortified as well. I have started a science save file, and have only researched 4 additional groups including: basic rocketry, engineering 101, general rocketry, and survivability.

With the new parts acquired from researching these groups I built a simple, 3 stage ship, and have decided to try to achieve LKO. To do so efficiently, I delved into the KSP wikis and forums to find the relevant information. I understand to a certain point the rocket equation, or the "*dudes name I can't spell*'s equation".

Anyways, I found the ISP of the rockets used in each stage, and I wasn't going for complete accuracy at first, using the ATM ISP for every equation done. Then, I found the total mass of each individual stage, as well as the dry mass of the stages by themselves. In order to do so I had to take the first to stages off, and measure the total and dry masses for the last stage, then add the second stage and subtract the total mass of both stages my the total mass of the last stage to get the total mass of the second stage. Then I proceeded to do so with the first stage attached as well. I found both total and dry this way for the first and second stages.

Now that I have the ISP, M_FULL, and M_EMPTY, I figured I could calculate and add the answers together to find my overall delta-v, granted I SHOULD have more than I calculate based on the idea that my ISP for each equation will be the atmospheric ISP.

My work: (weights are rounded)

Stage 1 (final stage): pod, fuel tank, and 'reliant' thruster. -

Dv = 265 * 9.8 * In (4/3) = 747

Stage 2 (second stage): 2 fuel tanks and 'reliant' thruster. -

Dv = 265 * 9.8 * In (3.5/1.5) = 2,200

Stage 3 (first stage) 2 BACC thrusters, and 1 'hammer' thruster, with added radiator panels.

Dv = 520 * 9.8 * In (19.5/4.5) = 7,472

I am now realizing that each stage must also push the weight of the stages above them, meaning I must carry the mass of those stages into that equation, adding to the total and dry mass of the stage being figured. If this is not so and I have created a false solution, please let me know, thank you.

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Hello, and welcome to the forums!

Moving to Gameplay Questions (since Science & Spaceflight is for discussions about real-life science & spaceflight).

16 minutes ago, TrevorC42303 said:

dudes name I can't spell

Yeah, those darn Russians and their names full of consonants.  Tsiolkovsky.

16 minutes ago, TrevorC42303 said:

Anyways, I found the ISP of the rockets used in each stage, and I wasn't going for complete accuracy at first, using the ATM ISP for every equation done.

Sounds like you're off to a good start.  Just FYI:  You probably want to use atmospheric Isp for the first stage off the launch pad, but you should probably be using vacuum Isp for everything after that.  Reason:  The atmosphere falls off very quickly with altitude.  By the time you get to 10 km, you're already 90% of the way to vacuum, and engines' effective Isp will be much closer to vacuum values than ASL.  And your first stage probably takes you high enough that everything after that will mostly be in vacuum.

This doesn't matter all that much for engines like the Swivel, Reliant, etc. because their vacuum and ASL numbers aren't all that far apart.  But for engines like the Terrier or Poodle, there's a huge gap between the two (they're truly awful in atmosphere), so your numbers will be a lot more accurate if you use the vacuum Isp values for those.

16 minutes ago, TrevorC42303 said:

I found the total mass of each individual stage, as well as the dry mass of the stages by themselves.

You may be going off the rails there.  The mass of the stages doesn't matter.  What matters is the mass of the whole rocket.

For example, suppose you have a 3-stage rocket, and the total mass of the rocket sitting on the launch pad is 16 tons, and the first stage has 4 tons of fuel in it.  So, when you plug that into Tsiolkovsky's equation, the two numbers you should use to find out the dV of the first stage is the total rocket mass divided by mass of rocket minus first stage's fuel, i.e. in this case it would be 16 / 12, or 1.333333.

Then, to calculate for the 2nd stage, you'd do the same thing-- but for "total rocket mass" you'd use the total mass after ditching the first stage, and for dry mass you'd use the total-mass-after-ditching-first stage divided by the mass after burning the 2nd stage's fuel.

What you don't want to do is to use the mass of the stage itself.  It's the whole mass of the rocket at that point that matters, including the dead weight of the stages above that which you haven't activated yet.

16 minutes ago, TrevorC42303 said:

Dv = 520 * 9.8 * In (19.5/4.5) = 7,472

Aside from the fact that your math has gone off the rails because you're not using the whole rocket mass... it's also worth noting that you have a really wrong number for Isp on this one.  SRBs' Isp is nowhere near 520.  ASL Isp for a Thumper is 175, and for a Hammer is just 170.  So the value of the three of them together would be between those two numbers (closer to the former than the latter, since that's where most of the thrust is).

16 minutes ago, TrevorC42303 said:

I am now realizing that each stage must also push the weight of the stages above them, meaning I must carry the mass of those stages into that equation, adding to the total and dry mass of the stage being figured. If this is not so and I have created a false solution, please let me know, thank you.

Nope, you're exactly right in this realization, as discussed above.

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5 minutes ago, TrevorC42303 said:

it should take around 4,550 dV to reach LKO

Considerably less than that.  I haven't checked the numbers lately, but I think it's more like 3.4 km/s (the exact amount depends on various things like how streamlined your rocket is, the TWR of your various stages, your ascent profile, etc.).  It's certainly way less than 4 km/s.

5 minutes ago, TrevorC42303 said:

even with my calculations, i reach the correct height, but don't have the dV left to make the orbital burn.

What does your ascent profile look like?  What's the TWR of your rocket on the launch pad?  When you reach 45 degrees from vertical, how high are you and how fast are you going?

Ascent profile matters quite a lot, in terms of dV efficiency.  A suboptimal ascent can waste quite a lot of dV.

Could you post a picture of your rocket (say, in the VAB)?  (Screenshot it with F1, upload it to imgur.com or somewhere with a simple click-and-drag, right-click on the uploaded image and choose "copy image location", then paste the image URL here and it will automagically get converted into an embedded image.  Remember, you want the URL of the image itself, not the URL of the page where it's located.)

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You only need about 3200 for a perfectly efficient LKO ascent; I suspect you are having problems with your ascent profile? I had the same problem.

How soon are you inclining to east and at what height are you reaching 45 degrees lean?

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16 minutes ago, TrevorC42303 said:

still using ATM ISP for this, ending up with 5,685 delta-v

That number still looks way too high, to me.  Okay, so I went ahead and did some calculations of my own based on the numbers you give.

• Top stage is 4 tons, with 1 ton of fuel, is using Reliant
• Middle stage is 3.5 tons, with 2 tons of fuel, is using Reliant
• Bottom stage is 19.5 tons, with 15 tons of fuel, using SRBs

The dV of the top stage is 310 * 9.81 * ln(4/3) = 875 m/s.

For the middle stage, it's 310 * 9.81 * ln(7.5/5.5) = 943 m/s.

For the bottom stage, it's a bit complicated because you're mixing engine types.  Not just do the engines have different Isps, but also the Hammer and Thumper have different burn times and you haven't said anything about when you stage things away and whether you've set any thrust limiters or anything else.  But it probably doesn't matter all that much since it's just some SRBs we're talking about and the total dV numbers for this stage aren't likely to be super high, so for a rough estimate I'll just assume that it's a single SRB with 15 tons of fuel and an Isp of, say, 174.  So that would give a dV for the bottom stage of 1384 m/s.

Adding those together, 875 + 943 + 1384 = 3202 m/s, which is barely enough to get to orbit even if you have a perfectly optimal ascent and great streamlining.

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This has helped tremendously, I recalculated after my realization (still using ATM ISP for this, ending up with 5,685 delta-v. I figured it would most likely be a little more than that based on the idea still that I underestimated. I know that it should take around 4,550 dV to reach LKO but even with my calculations, i reach the correct height, but don't have the dV left to make the orbital burn.

11 minutes ago, Snark said:

Aside from the fact that your math has gone off the rails because you're not using the whole rocket mass... it's also worth noting that you have a really wrong number for Isp on this one.  SRBs' Isp is nowhere near 520.  ASL Isp for a Thumper is 175, and for a Hammer is just 170.  So the value of the three of them together would be between﻿﻿﻿ those two numbers (closer to the former than the latter﻿, since that's where most of the thrust is).

Didn't think to figure this, my thought process was to add all thrust in the stage to get a total thrust.

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4 minutes ago, Snark said:

What﻿ does your ascent profile look like?  What's the TWR of﻿ your rocket on the launch pad?  When you reach 45 degrees from vertical, how high are you and how fast are you going?﻿﻿

Ascent profile matters quite a lot, in ﻿terms of dV efficiency.  A suboptimal ascent can waste quite a lot of dV.﻿

My ascent profile is dreadful, it is steep, I do try and take advantage of the gravity assist in that I tilt east, but I can never quite get my ship to tilt enough for a solid profile. Also, at this point I do not have nose cones, so my 2 'thumper rockets create a heavy amount of drag, possibly the reason for the lack of control. My image is being loaded, one moment.

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Granted I am new to this, I may have used too many radiator panels, but I don't think removing them will add too much dV. I might be wrong. My image url is not cooperating.

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31 minutes ago, TrevorC42303 said:

My ascent profile is dreadful, it is steep﻿, I do try and take advantage of the gravity assist in that I tilt east, but I can never quite get my ship to tilt enough for a solid profile.

You want to tip the rocket eastwards immediately upon liftoff, and then follow all the way to orbit.  (If you're playing in sandbox, or if you're in career mode with a level-1-or-better pilot or HECS-or-better probe core, you can just set your SAS to "hold " and it'll do it for you.)  Nice thing is that when you do that, you don't have to "get" the rocket to tilt-- it'll take care of it for you and will just automatically do the right thing.  You don't have to steer at all; all you have to do is jettison stages when they burn out.

The main trick is to figure out how much to tip eastwards on liftoff.  That will be a function of your TWR and other factors, but a bit of trial and error will quickly give you a feel for it.  The key milestone on ascent is to check your situation at the point when you hit around 350-400 m/s speed.  At that point, you should be roughly 45 degrees from vertical, and your altitude should be no more than 10 km or thereabouts (possibly lower, if you've got a high-TWR rocket).  If you find that when you hit 350-400 m/s you're still a lot more vertical than 45 degrees, then you didn't tip enough on liftoff; revert to launch and try again.

31 minutes ago, TrevorC42303 said:

Also, at this point I do not have nose cones﻿, so my 2 'thumper rockets create a heavy amount of drag, possibly the reason for the lack of control.

Yeah, that's not good.  Also, I'm guessing that your TWR is probably way too high.  You mention lifting off the pad on two Thumpers and a Hammer.  That's a total of 698 kN of liftoff thrust.  I make your launchpad mass as 27 tons, so that's a TWR of 2.63, which is way too high.  Generally you don't want your launchpad TWR to be any higher than 2.0.  It causes problems (mainly, you end up going too fast while too low in the atmosphere and waste too much dV to aerodynamic drag, even if you do have nosecones).

Your upper stages have TWR that's way too high, too.  Your second stage has a Reliant (vac thrust 240 kN) pushing 7.5 tons of rocket, which is a TWR of 3.26, which is insanely high.  That would be way too high even on the launchpad-- it's especially high for an upper stage.  (In general, the higher the stage, the less TWR you need or want.)  A good TWR number for your second stage would be 1.5 at most.

Then your third stage has a Reliant pushing only 4 tons of rocket, which is a TWR of 6.11, which is just insane.  Your third stage should have a TWR of less than 1; it simply doesn't need much engine.

So, why is it bad to have a TWR that's too high?  There are two reasons:

The first reason generally applies only to the bottom stage:  if your TWR is too high, you go too fast while still down low in the thick part of the atmosphere, and waste dV on aerodynamic drag.  This applies only to bottom stage, generally, because for the second and subsequent stages, you're up where the air is thinner and you generally don't care at all about drag.

The second reason, though, applies to all stages:  Engines are dead weight.  Dead weight is bad, because it lowers your dV.  Therefore, if you have more engine than you actually need, it means you're wasting mass.  It would be better to have less engine and more fuel, because fuel adds dV whereas dead weight lowers it.  When designing stages, there are two handy rules of thumb I like to use:

• The first rule-of-thumb is about TWR.
• Launchpad TWR should be in the range 1.3 to 2.0.  (Matter of taste, it's just how one likes to design rockets.  Personally, I like 2.0, but there's nothing especially "better" about it.  But certainly you shouldn't go higher than 2.0.)
• Second stage TWR should be lower than the launchpad TWR, and in any case should never be higher than about 1.5.
• Third stage TWR should be lower than 2nd stage, and in any case should be less than 1.
• The second rule-of-thumb is about mass ratio of fuel-to-engine for a stage.
• Take the total mass of fuel in a stage, and divide by the mass of engines in the stage.  What's the ratio?
• I like to keep that number always at least 4, even for high-TWR stages.  Low-TWR stages should be more than that, like 8.

In your case, your TWR values are really big, and they're also arranged wrong (each of your successive stages has a higher TWR, when you want it to be the opposite).  Also, you've got really low mass ratios-- e.g. your top stage actually has more engine than fuel!

So what you need is more fuel and less engine.  I'd ditch the Hammer and add more fuel to your initial Reliant stage, instead-- at least double it.  Then, for your topmost stage, you want a smaller / lighter engine than a Reliant, when you can.  The Terrier is perfect for this-- try to unlock that at your earliest opportunity, it's a fantastic upper-stage engine.  Until you get to that point, though, I'd suggest swapping out the top engine for a Swivel (better vacuum Isp) and double the fuel amount there, as well.

Also, get nose cones.  They help a lot, and the "Stability" tech node is a fairly cheap one.  You'll want to grab that as soon as you can.

7 minutes ago, TrevorC42303 said:

Granted I am new to this, I may have used too many radiator panels, but I don't think removing them will add too much dV. I might be wrong.

Wait, what?  Radiator panels?!  Sorry, I see now that you mentioned those earlier, but I somehow managed to miss that.

Why do you have any radiator panels on the ship?  At all?  They do absolutely nothing to help you; you don't need them at all; and they're just wasting mass and adding a bunch of aerodynamic drag.

You're probably right that removing them won't make much of a dV difference... but they're seriously unnecessary, they literally do nothing to help you with that ship (there aren't any components on board that need radiators, like ISRU or drills), and they're using up precious part count (since I'm guessing you haven't upgraded the VAB yet and are limited to 30 parts on the rocket).  Definitely ditch them.

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8 minutes ago, Snark said:

Why do you have any ﻿﻿﻿radiator panels on the ship?  At ﻿all﻿?﻿

I laughed way too hard at this. I figured as much.

How do I calculate TWR

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This is my ship info thus far, including my recent changes.

Stage 1: a single thumper

(need more thrust) 2 fleas with the thumper?

Stage 2: a relient with 2 T200 fuel tanks, and 1 T100

Stage 3: same as stage 2 but including the pod, 1 Mk16 parachute, 2 Mk2-R radial-mount parachutes, various science gadgets, heat sheild, and decoupler.

Edited by TrevorC42303
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28 minutes ago, TrevorC42303 said:

How do I calculate TWR

• Take total thrust, in kN
• Divide by total mass, in tons
• Divide by local gravity (i.e. 9.81 m/s2, on Kerbin)

Thus, suppose you have a lone Thumper lifting a 15-ton ship off the pad.  That's 250 kN, divided by 15 tons, divided by 9.81 m/s2, gives you a TWR of 1.70, which is reasonable.

22 minutes ago, TrevorC42303 said:

Stage 1: a single thumper

Sounds good.

22 minutes ago, TrevorC42303 said:

Stage 2: a relient with 2 T200 fuel tanks, and 1 T100

That's only 2.5 tons of fuel.  I'd suggest increasing that to 4 tons at least-- say, four T200 tanks.

22 minutes ago, TrevorC42303 said:

Stage 3: same as stage 2 but including the pod, 1 Mk16 parachute, 2 Mk2-R radial-mount parachutes, various science gadgets, heat sheild, and decoupler.

Each successive stage should generally be smaller than the last one (pick a ratio you like, I usually go for about 2, i.e. each successive stage has around half the fuel mass of the preceding one).  As specified, your stage 2 and stage 3 are identical, which isn't great.  However, if you boost the fuel of stage 2 to at least 4 tons, then this one seems reasonable.  You could probably even reduce it to 2 tons (i.e. just two T200 tanks).

By the way, you don't need a heat shield yet.  If your reentry vehicle is gonna be basically just a Mk1 command pod and a few small accessories as you describe, then it turns out that it can re-enter just fine from low Kerbin orbit without a heat shield.  It'll get a bit warm, but it won't come even close to exploding.

Where you'll need a heat shield would be if you're hitting atmosphere a lot faster than LKO speeds, e.g. if you're coming back from the Mun or Minmus, because then you'll be going like 3000 m/s on reentry instead of only around 2200.  Another example of needing a heat shield would be if you have a ship that has a significantly higher ballistic coefficient, i.e. a ship that is more massive and less draggy, so it has to get a lot deeper into the atmosphere before slowing down much.  But a lone Mk1 command pod, reentering butt-end first, is very light and very draggy (i.e. it has a really really low ballistic coefficient), so it does fine (at LKO speeds) without a heat shield.

So you can leave the heat shield off for now, and save yourself nearly a third of a ton of mass.  Later on, when you go places where you do need a heat shield, it's worth noting that you almost never need a full load of ablator.  Lower that down to 10%, or (if you're paranoid) 20% at most.  Most of the mass of a heat shield is in the ablator, so you can save quite a lot of mass by reducing it.  No point in lugging all that dead weight to orbit and then coming home with 90% of your ablator still remaining.

Anyway, lifting on a single Thumper:  what's your launchpad mass?  Just eyeballing it here, let's say around 1 ton for the pod & accessories, then (assuming 2 tons fuel plus a Reliant) 3.5 tons for fuel & engine, so 3.5 tons for the top stage.  Middle stage, if it's four T200 tanks and a Reliant, would be a bit under 6 tons.  Then the Thumper itself would be 7.65 tons.  This puts your total ship mass in the ballpark of 17 tons or a bit over.  With 250 kN of launchpad thrust, that'll give you a TWR of around 1.49, which is reasonable.  In short:  if you have a ship with a mass up to 18 tons or so, it's reasonable to launch with a lone Thumper.

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3. Thumper

2. Reliant, 4 tons of fuel

1. Reliant, 2 tons of fuel

Pod

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The one thumper is enough to get me up as far as TWR goes, but it does not have the dV. My total dV for this ship is 3,704, and I would like to be around 4,500 just to be safe.

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34 minutes ago, TrevorC42303 said:

3. Thumper

2. Reliant, 4 tons of fuel

1. Reliant, 2 tons of fuel

Pod

Okay, now you're talkin'.

So, I make that 1843 m/s of dV for the top stage, 1515 m/s of dV for the middle stage, and about 730 m/s for the Thumper.  Add those together and you've got over 4000 m/s of dV now, which is enough to get to orbit with several hundred m/s of safety margin.  Your actual dV will be slightly lower because of lugging along parachute, science stuff, etc., but the point is, you're well over what you need to get to orbit now.

13 minutes ago, TrevorC42303 said:

My total dV for this ship is 3,704, and I would like to be around 4,500 just to be safe.

3700 is several hundred m/s of safety margin, and actually I think you have around 300 more than that.  (I'm guessing that you used the ASL Isp for the Reliants?  They'll be operating mostly in vacuum-- use their vacuum Isps).

4000 m/s is a big enough safety margin that you really ought to be fine.  Try flying that-- and if you still have trouble getting to orbit, the next thing we should focus on is your piloting (i.e. details of ascent profile) rather than engineering.

13 minutes ago, TrevorC42303 said:

The one thumper is enough to﻿ get me up as far as TWR goes, but it does not have the dV.

Bear in mind that the stage that lifts you off the launchpad is almost always the worst one in terms of dV (mainly because it needs a high TWR, meaning lots of engine mass).  In this case, your Thumper stage has around half the dV of the first stage above it, and that's a fairly typical ratio.  So, in this particular case, per my reasoning above, I think you do have enough dV, actually.  But if you didn't and needed more (e.g. if you were going to the Mun or something), then the way to add dV would be to add another stage, not try to boost the SRB liftoff stage's dV.

Incidentally:  Try to unlock the Terrier engine as soon as you can.  It's fantastic for upper stage engines.  If you were to take that same exact rocket but put a Terrier instead of a Reliant on the top stage, then the total dV goes up to over 5100 m/s-- a huge improvement.  So, get that when you can.

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My TWR for my first stage, if I've done my math correctly, is about .99 or 1. This doesn't seem right

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I flew a few times, and I reach 300 m/s around 50 degrees east, this seems almost perfect as this is when my solid fuel cuts and I blow my fist stage, here I realized I needed find on the second stage because my stability is off and I spin out of control. Once I did this I was able to retain a 45-50 degree ascent till my AP reached around 80km, I then cut my engine with just about a 3rd of my fuel left in the second stage. I set a maneuver nose for a prograde burn to circularize my orbit. I started the burn with my second stage and finished with about half my last stage, using the other half to create a aerobrake as it was too expensive to create an impact from the single burn, I burned till my AP reached about 40 km, then I waited to hit atmosphere, when I exited the atmosphere, I could've waited for the next aerobrake and saved all my fuel, I burned the last of my fuel, dropping my orbit into kerbin.

Thank you for your help,  I appreciate it greatly.

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Excellent, glad it all worked out!

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