When to separate SRBs? A not-so-obvious question.

[Kowgan]

I'm using Crzyrndm's mod, SRB Variable Thrust Limiter, which allows SRBs' thrust to decrease as they burn fuel, just like in real life.
The question is, what is the math used to determine the exact time when the SRB's current acceleration is the same as the vessel's acceleration, and with that, perform the separation staging?

I'm trying to achieve this effect, where at the separation moment, the SRB has just enough thrust to keep itself at the same speed as the vessel.
https://www.youtube.com/watch?v=-nwhrQXAAlM

https://youtu.be/nzN9G2LSbuM?t=40s

Thanks in advance.

Edited February 12, 2016 by Kowgan

[Snark]

I would say that it's pretty clear:  you separate the SRBs when they're completely out of fuel, because their inherent acceleration is always higher than that of the rest of the ship.  And if their inherent acceleration is not higher, it means that you're Doing It Wrong™, and the fix is to either adjust their thrust upwards, or else adjust the liquid-fueled thrust downwards, rather than to do math to figure out when to separate them.

 

Acceleration of SRB = the SRB's thrust divided by the SRB's current mass

Acceleration of the rest of the ship = the rest of the ship's thrust divided by the rest of the ship's mass

If acceleration of SRB <= acceleration of the rest of the ship, ditch it.

That answers your question... but I think your question is kind of a moot one.  That circumstance should never happen.  If that's even close to happening before the SRB runs out of fuel, then either you've got your SRB thrust limiter turned down way too low, or else you're using your liquid-fueled engines when you shouldn't be.

SRBs have much crappier Isp than liquid-fueled engines, which means that you want to burn your solid fuel before your liquid fuel.  The only time you should ever be running liquid-fuel engines at the same time as SRBs is if the SRBs are already at 100% thrust and still don't have enough power to lift your ship by themselves.

So basically, there should only be two scenarios that ever happen:

• You're over-supplied with SRB thrust.  In which case you set your SRB thrust limiters to give you the desired TWR, you take off on SRBs only, and you never activate liquid-fuel engines until the SRBs burn out.
• You're under-supplied with SRB thrust.  In which case you set your SRB thrust to 100%, and take off with all your engines (SRB + liquid fuel), using only as much liquid-fuel thrust as you have to in order to maintain the desired acceleration.

In neither of those cases do you come close to having an SRB whose inherent acceleration can't keep up with the overall vessel.

Edited February 12, 2016 by Snark

[Norcalplanner]

Or you can play RSS/RO, where the SRBs have a soft cutoff rather than a hard cutoff. Right click on the SRB and watch when the thrust level starts to fall off, then stage then.

[Geschosskopf]

17 hours ago, Kowgan said:

The question is, what is the math used to determine the exact time when the SRB's current acceleration is the same as the vessel's acceleration, and with that, perform the separation staging?

Hmm, an intriguing question.

I'm thinking that if you do figure out the formulae, they will be very dependent on a specific launch trajectory.  Therefore, if you can't fly that trajectory within very tight limits (such as by running an autopilot), any calculations  you did before launch would be invalid.  So you might just have to eyeball it, like by hitting the spacebar when the SRBs have just a tiny sliver of fuel left.

You might improve the accuracy of an eyeball method by launching the SRBs by themselves with less fuel (so they don't get too fast too soon) but the same fall-off of thrust, and see what their acceleration is when they're almost empty.  Then, during a real launch, watch the acceleration of the whole vehicle and stage when it's about the same as what you got for the SRBs.

 

[CSE]

On pure efficiency grounds, it's better to burn your lowest-I_sp fuel as quickly as possible and then drop the engines. But I sometimes reduce my SRBs' thrust and increase the burn times for easier flying:

• Because longer-burning boosters will be staged away higher in the atmosphere, which can help to give a cleaner separation with less chance of colliding with the inner stacks.
• And, if the core stage is very heavily-loaded with fuel (e.g. in 6.4x or RSS scales), then there's a less dramatic drop in TWR at staging, which makes it easier to judge the gravity turn / pitch program correctly.

[Snark]

56 minutes ago, Geschosskopf said:

I'm thinking that if you do figure out the formulae, they will be very dependent on a specific launch trajectory.

Why would it depend on the trajectory?  As long as you know the mass & thrust of the SRBs, and the mass & thrust of the rest of the ship, that's all that matters, isn't it?

(Yes, technically the altitude matters somewhat, if you have different engines with different Isp-vs-pressure curves, but in practical terms you're going to be at least a few kilometers high before staging is an issue.  Pressure drops off fast, and by that time you're mostly in vacuum anyway.)

[Gaarst]

The goal of the SRB is to carry itself and push your shuttle/rocket at the same time.

A part of the SRB's thrust will be used to push itself around and what's left will push your rocket.
If the SRB's TWR is over 1, then the SRB will push your rocket and that's fine. If the SRB's TWR is 1 then the SRB will just push itself but not your rocket. If the SRB's TWR is less than 1 then the SRB will not be able to push itself, then your rocket will start to pull the SRB.
You don't want this last thing to happen, therefore, ditch your SRB when its TWR gets under 1 (assuming decaying thrust). If it never gets under 1, then ditch it after flameout, when it will get under 1 (0 in that case).

[Ravenchant]

40 minutes ago, Gaarst said:

ditch your SRB when its TWR gets under 1 (assuming decaying thrust)

Small correction: assuming decaying thrust, ditch your SRBs when their TWR is equal to the vehicle's TWR. So the moment to ditch is when thrust(boosters) = thrust(stack)*mass(boosters)/mass(stack). Of course, that's easier said than done. The main stack's thrust should be largely constant if you have the bulk of the atmosphere below you, and I guess kOS should be able to keep track of the rest.

[Snark]

2 hours ago, Gaarst said:

The goal of the SRB is to carry itself and push your shuttle/rocket at the same time.

A part of the SRB's thrust will be used to push itself around and what's left will push your rocket.
If the SRB's TWR is over 1, then the SRB will push your rocket and that's fine. If the SRB's TWR is 1 then the SRB will just push itself but not your rocket. If the SRB's TWR is less than 1 then the SRB will not be able to push itself, then your rocket will start to pull the SRB.

The above description is mostly correct, but a slight correction:  the magic cutoff is not 1, but rather the TWR of the rest of the ship without the SRB.

That is, suppose you have a central liquid-fueled core and some radial SRBs, all firing together.  Suppose that the TWR of the central core (i.e. leaving out both the mass and the thrust of the SRBs) is 2.  In that case, the TWR of the SRBs themselves has to be at least 2, because if it's less than that, it's the rocket pulling the SRBs rather than the other way around.

Another way to picture it:  imagine that your liquid-fueled core and your SRBs were just flying along side-by-side rather than being attached to each other.  Which one would be winning the race and pulling ahead?  It had better be the SRBs, or they're not actually helping you. 

Edited February 13, 2016 by Snark

[Geschosskopf]

7 hours ago, Snark said:

Why would it depend on the trajectory?

Because the thrust of the OP's SRBs is a function of time, and if you vary the trajectory very much, you end up with rather different speeds and drags going on at different altitudes when the SRB's "timer" gets to a certain point.  And the drag is the important thing here.  If you calculate when the remaining SRB fuel will produce a harmless amount of acceleration on the separated booster once it no longer has to push the whole shuttle, that necessarily must include the braking effect of the atmosphere.  Thus separating the SRBs too high, where there's not enough drag, might result in them shooting up the sides of the main tank and hitting something important.  And OTOH, separating them too low might mean wasted thrust for the whole assembly.

I agree with your first suggestion:  hold the SRBs until they burn out.  But the OP wants to release them safely while they're still running for the style points of doing it like the real shuttle.

[Kowgan]

Now the tricky part. How to get the SRB's TWR, instead of the whole vessel's TWR? At the same time, how to get the rest of the vessel (without SRBs) TWR?

Edited February 13, 2016 by Kowgan

[Snark]

7 minutes ago, Kowgan said:

Now the tricky part. How to get the SRB's TWR, instead of the whole vessel's TWR? At the same time, how to get the rest of the vessel (without SRBs) TWR?

Well, the simple answer is to just hit F5 and then stage 'em off.  If they go shooting out way up ahead, you're too early.  F9 and repeat. 

 

[Geschosskopf]

22 minutes ago, Kowgan said:

Now the tricky part. How to get the SRB's TWR, instead of the whole vessel's TWR? At the same time, how to get the rest of the vessel (without SRBs) TWR?

I don't think you need to worry about that.  You should be able to eyeball it from just watching the acceleration.  My thinking goes like this:

1. The only reason to drop the SRBs before they burn out is if acceleration is less with them than without them.  IOW, they no longer provide enough thrust to overcome their remaining mass and the drag of having them attached.
2. The TWR and hence acceleration of the shuttle + tank (not counting SRBs whether attached or not) is increasing throughout the ascent because the main engines have been running since the get-go.
3. Meanwhile, the TWR of the SRBs is decreasing due to having been running since the get-go.
4. While the SRBs are still providing useful thrust, the acceleration of the whole vehicle should be constant or slightly increasing as the decreasing SRB thrust is countered by the decreasing mass of the whole vehicle (assuming main engine thrust is more or less constant---you haven't mentioned that part), and the decreasing drag of the thinner air is countered by the increasing drag of going faster.
5. Therefore, at the point where the SRBs have burned down to where they're doing more harm than good, you should see the acceleration of the whole vehicle start to decrease (or level off if it was slowly increasing).
6. Hopefully, by that point the SRBs are providing so little thrust that they won't go shooting up the sides when you release them, or at least you have enough Sepratrons to kick them away so they do no harm.

 

Edited February 13, 2016 by Geschosskopf

[Kowgan]

Thanks, Geschosskopf. I'll try this method.

[numerobis]

The other reason to ditch SRBs shortly before they burn out is if you can make it so when decoupling they tilt their nose away from your spacecraft. Then their remaining thrust will move them further away from the spacecraft. Of course, you could just attach a sepratron instead.

[Buster Charlie]

51 minutes ago, numerobis said:

The other reason to ditch SRBs shortly before they burn out is if you can make it so when decoupling they tilt their nose away from your spacecraft. Then their remaining thrust will move them further away from the spacecraft. Of course, you could just attach a sepratron instead.

I Kinda wish there was a stock checkbox in the VAB to auto stage when there was like 1% fuel left in the SRB so you didn't have to have the extra mass/parts count of a sepratron, I know you can kinda eyeball and do it manually, but if you're designing a unified launch system then it's good to have repeatability.

[Snark]

12 hours ago, numerobis said:

The other reason to ditch SRBs shortly before they burn out is if you can make it so when decoupling they tilt their nose away from your spacecraft. Then their remaining thrust will move them further away from the spacecraft. Of course, you could just attach a sepratron instead.

 

11 hours ago, Buster Charlie said:

I Kinda wish there was a stock checkbox in the VAB to auto stage when there was like 1% fuel left in the SRB so you didn't have to have the extra mass/parts count of a sepratron, I know you can kinda eyeball and do it manually, but if you're designing a unified launch system then it's good to have repeatability.

If you're careful about your design, you really don't need a sepratron.

I love SRBs, I use 'em all the time, practically all of my ships take off on SRBs alone.  Occasionally I lift with some LFO assistance if it's something really huge and I can't pack on enough SRBs to do the job alone.  But in any case, I use SRBs a lot, in many different configurations, and I never need to use sepratrons.

Really, all that's necessary is:

• mount the SRB as low as possible on the radial decoupler (i.e. so the decoupler is as high as possible above the SRB's CoM
• mount the decouplers as low as possible on the rocket, so that the SRBs are as far aft as possible

The high-mounted decoupler causes the SRB to nose outwards on decoupling, which causes aero forces to peel it away without any assistance at all from either thrust or sepratrons.  Mounting the SRBs down low makes it easy for your core ship to slide out from the middle without the tail ends of any SRBs tapping it on the way.

Simple, easy, works like a charm, totally repeatable, requires no fiddling with sepratrons.

[Buster Charlie]

11 hours ago, Snark said:

 

If you're careful about your design, you really don't need a sepratron.

I love SRBs, I use 'em all the time, practically all of my ships take off on SRBs alone.  Occasionally I lift with some LFO assistance if it's something really huge and I can't pack on enough SRBs to do the job alone.  But in any case, I use SRBs a lot, in many different configurations, and I never need to use sepratrons.

Really, all that's necessary is:

• mount the SRB as low as possible on the radial decoupler (i.e. so the decoupler is as high as possible above the SRB's CoM
• mount the decouplers as low as possible on the rocket, so that the SRBs are as far aft as possible

The high-mounted decoupler causes the SRB to nose outwards on decoupling, which causes aero forces to peel it away without any assistance at all from either thrust or sepratrons.  Mounting the SRBs down low makes it easy for your core ship to slide out from the middle without the tail ends of any SRBs tapping it on the way.

Simple, easy, works like a charm, totally repeatable, requires no fiddling with sepratrons.

Yeah, most of the time I do just that. But coupled with Stage Recovery I like my SRB to not crash into each other when I stage them so sometimes they need a little extra boost, or sometimes my design burns long enough it goes into the gravity turn and I have to be careful about the booster on top.

[Mahnarch]

I like separatrons because they sound like a shaken can of soda being opened.

 

Also, cuz they move stuff away, but mostly the first part.

[Kowgan]

On 13/02/2016 at 0:17 PM, Ravenchant said:

Small correction: assuming decaying thrust, ditch your SRBs when their TWR is equal to the vehicle's TWR. So the moment to ditch is when thrust(boosters) = thrust(stack)*mass(boosters)/mass(stack). Of course, that's easier said than done. The main stack's thrust should be largely constant if you have the bulk of the atmosphere below you, and I guess kOS should be able to keep track of the rest.

Could you elaborate this a bit more? Is the mass measured in tons or kgs? Do I have to countermeasure anything in the formula for having two or more boosters, or the amount of boosters doesn't matter? Thank you.

[Snark]

4 hours ago, Kowgan said:

Could you elaborate this a bit more? Is the mass measured in tons or kgs? Do I have to countermeasure anything in the formula for having two or more boosters, or the amount of boosters doesn't matter? Thank you.

The mass in that formula doesn't matter what units it is, as long as you use the same units everywhere.  However, the most common units to use in KSP is tons, since that plays nicely with thrust numbers that are usually reported in kN.  One kN pushing one ton = one m/s² acceleration.

Note that Ravenchant referred to "thrust(boosters)" meaning "the total thrust of all boosters combined", and "mass(boosters)" meaning "the totall mass of all boosters combined."

[Kowgan]

8 hours ago, Snark said:

The mass in that formula doesn't matter what units it is, as long as you use the same units everywhere.  However, the most common units to use in KSP is tons, since that plays nicely with thrust numbers that are usually reported in kN.  One kN pushing one ton = one m/s² acceleration.

Note that Ravenchant referred to "thrust(boosters)" meaning "the total thrust of all boosters combined", and "mass(boosters)" meaning "the totall mass of all boosters combined."

It doesn't quite make sense for me. Maybe I'm doing something wrong?

http://puu.sh/nn9xj/82459c60c5.png - Taken just after launch.
Thrust (boosters) = 247.2 (x2 = 494.4)
thrust(stack)*mass(boosters)/mass(stack) = 1875 * (7.5 * 2) / 73.627 = 381.99, which is smaller than Thrust(boosters).

Even though, the SRBs by themselves are clearly faster than the rest of the vessel.

---

I'm now just calculating the SRB's TWR and the main engine's TWR without the SRB's mass, and that solves the question. Now I have to figure out a way to do it automatedly.

Edited February 27, 2016 by Kowgan

[Plusck]

2 hours ago, Kowgan said:

It doesn't quite make sense for me. Maybe I'm doing something wrong?

http://puu.sh/nn9xj/82459c60c5.png - Taken just after launch.
Thrust (boosters) = 247.2 (x2 = 494.4)
thrust(stack)*mass(boosters)/mass(stack) = 1875 * (7.5 * 2) / 73.627 = 381.99, which is smaller than Thrust(boosters).

Even though, the SRBs by themselves are clearly faster than the rest of the vessel.

Precisely: The boosters' thrust (494.4) is greater than the stack's TWR multiplied by the weight or mass of the boosters (giving a total of 382), so you keep them.

Because you want TWR(boosters) to be greater than TWR(stack). The TWR is the thrust divided by weight. Weight is mass multiplied by gravity.

Thus:

thrust(boosters) / (mass(boosters) * local gravity)  > thrust(stack) / (mass(stack) * local gravity)

multiply both sides by gravity:

thrust(boosters) / mass(boosters)  > thrust(stack) / mass(stack)

multiply both sides by mass(boosters):

thrust(boosters)  > (thrust(stack) * mass(boosters) ) / mass(stack)

And the actual units don't matter since they'll cancel each other out. It was also unnecessary to include gravity to start with (i.e. to differentiate between weight and mass) since gravity cancels out too for your purposes, but I thought it best not to start saying that TWR = thrust/mass because that's wrong by definition

Edited February 27, 2016 by Plusck

[wumpus]

On 2/12/2016 at 3:59 PM, Snark said:

SRBs have much crappier Isp than liquid-fueled engines, which means that you want to burn your solid fuel before your liquid fuel.  The only time you should ever be running liquid-fuel engines at the same time as SRBs is if the SRBs are already at 100% thrust and still don't have enough power to lift your ship by themselves.

 

KSP leaves a couple of reasons for using liquid rockets and SRBs together:

1.  Stability.  My SRB-based first stages are typically controlled by a pair of AV-T1 winglets on the North and South end of the rocket (which then provide control for an E-W pitchover).  The liquid rocket typically has vectored thrust and can do the rest needed to get the rocket back on course (note: you pay not only in that extra decoupler, but also in a much worse (I assume) aerodynamic profile.  Just slap on more controlled winglets unless firing it up for the reason below as well).

2.  Re-usability.  The shuttle fired the main engines from launch presumably because it didn't make sense to provide additional thrust from the SRBs (it also let them light the engine only on the pad, but KSP doesn't care about such things).  It is much easier to bring home a first stage carried into orbit by SRBs than to recover the SRBs, so that extra thrust can be thought of as "free" (until you get bored landing them, then you need to stop fast).  Don't forget it will harm your aerodynamics.

But yes, you really have to ask yourself why you are burning fuel with an Isp of ~400 when being carried into orbit by fuel with an Isp of ~200.

[Snark]

9 hours ago, Kowgan said:

It doesn't quite make sense for me. Maybe I'm doing something wrong?

http://puu.sh/nn9xj/82459c60c5.png - Taken just after launch.
Thrust (boosters) = 247.2 (x2 = 494.4)
thrust(stack)*mass(boosters)/mass(stack) = 1875 * (7.5 * 2) / 73.627 = 381.99, which is smaller than Thrust(boosters).

Even though, the SRBs by themselves are clearly faster than the rest of the vessel.

Yes, exactly.  Since 494.4 > 381.99, it means it's not time to drop the boosters.

If it'll help, you can think of it this way:  the boosters are giving 494.4 kN of thrust, of which 381.99 kN are being "used up" in just accelerating the boosters themselves, leaving a bit over 110 kN left over to shove the rest of the vessel forward.