Calculating dV in Complex Designs

[SR1200 THUNDER]

Calculating dV is easy enough in a single engine stage. But I am stumped when it comes to calculating it in a multi-engine stage.

dV=Ve x LN(M0/M1)

But how do I adjust that formula if I am using a Swivel engine with (2) Hammer SRB's for a small initial kick? (For the record, I am NOT building a craft with a swivel and 2 hammers, that was just a hypothetical since they use entirely different fuel sources.)

How would I go about adjusting that formula in asparagus staging? Say I am using a Swivel as the center engine, and (2) reliant engines for their additional thrust as the outside engines? All three engines are burning at the same time, but they have different exhaust velocities, and are sharing fuel loads. This is a much more common problem for me, and (at the moment) requires me to over-engineer the craft because while I know it's going somewhere, I can never be sure where that ends up being.

Edited April 3, 2018 by SR1200 THUNDER
Formula error

[bewing]

I find it faster and more fun just to cheat the ship to somewhere near the outer limits of some SOI with SetOrbit, SAS to prograde, make a note of the orbital speed, go to full throttle -- and burn every last bit of fuel, staging appropriately. Then subtract. 

 

[GoSlash27]

SR1200,
 You wouldn't alter that formula, but you're going to have to figure out the Isp of each stage and figure out how much fuel will be expended during each stage. You will then add up the DV of the individual stages.

 To figure out the Isp of dissimilar engines, you first need to figure out the mass flow rate of the engine types.

For any engine,

 R_MF= T/(g0I_sp)

where

 R_MF is propellant mass flow rate in tonnes per sec
 T is thrust in kiloNewtons
 g0 is standard gravity; 9.80665 m/sec²
 and
 I_sp is the specific impulse of the engine in question

 Note that all engines maintain their mass flow rate at a fixed throttle, regardless of changes in air density. Isp will change, but this manifests as a change in thrust rather than mass flow rate.

 Anyway... R_MF will vary linearly with throttling. R_MF is also cumulative in parallel, even with different engine types.

 
 R_MFT= R_MF1+R_MF2...+R_MFN

 Thrust is also cumulative in parallel, so you do the same thing with thrust.

 Dividing the sum of thrust by (go x the sum of mass flow rates) will yield the stage's I_sp

 

 

A lot more to follow, but it's hard to compose formulae on this forum, especially when I'm remoted into another computer.

 

Edited April 3, 2018 by GoSlash27

[Cpt Kerbalkrunch]

1 hour ago, bewing said:

I find it faster and more fun just to cheat the ship to somewhere near the outer limits of some SOI with SetOrbit, SAS to prograde, make a note of the orbital speed, go to full throttle -- and burn every last bit of fuel, staging appropriately. Then subtract. 

 

Bewing, are you a secret trial & error player? I had no idea. I hear we're in the minority around here. 

[SR1200 THUNDER]

1 hour ago, bewing said:

I find it faster and more fun just to cheat the ship to somewhere near the outer limits of some SOI with SetOrbit, SAS to prograde, make a note of the orbital speed, go to full throttle -- and burn every last bit of fuel, staging appropriately. Then subtract. 

 

I don't think I can do that on console.

I really need to join the master race.

1 hour ago, GoSlash27 said:

SR1200,
 You wouldn't alter that formula, but you're going to have to figure out the Isp of each stage and figure out how much fuel will be expended during each stage. You will then add up the DV of the individual stages.

A lot more to follow, but it's hard to compose formulae on this forum, especially when I'm remoted into another computer.

 

I apologize if I am making you do a lot of work, but thank you very much for helping me out. There is so much in this game that is either poorly explained, or not at all.

[bewing]

27 minutes ago, SR1200 THUNDER said:

I don't think I can do that on console.

Yes you can.

Do you know how to get into the debug menu?

 

Edited April 3, 2018 by bewing

[Aegolius13]

For vacuum operation, where thrust and ISP are constant, I think you could do this with calculus.   I can't put a precise formula down,  but the basic idea would be:

Acceleration=force/mass.   

Force is just the combined thrust of your engines. 

Mass can be defined as a function of time.   E.g, starting mass minus burn rate(in mass/sec)*elapsed time.   

So, the acceleration at time t can be represented by the function a(t)=thrust/(m(0)-(burn rate)*t)

Thus, to get the sum of acceleration over time (which is delta v), you can integrate that function with respect to t, from 0 to the time where your first set of rockets burn out.   Then,  repeat for the next set,  or if you only have one set of rockets left, use the rocket equation.

Note that it's going to be very complicated to get accurate delta v numbers in atmosphere,  due to the change in isp and thrust with altitude.   This is the case even with "regular" rockets that work with the rocket equation.

[FleshJeb]

1 hour ago, Cpt Kerbalkrunch said:

Bewing, are you a secret trial & error player? I had no idea. I hear we're in the minority around here. 

Even us "math" players should be looking for good ways to empirically test our results, and that's a good one. I just happen to prefer less trial, and less error. 

[Cpt Kerbalkrunch]

13 minutes ago, FleshJeb said:

Even us "math" players should be looking for good ways to empirically test our results, and that's a good one. I just happen to prefer less trial, and less error. 

It's become one of my favorite methods. Throw a ship in orbit, spin the dial to 10,000, then burn and see what I get. It works pretty well.

[GoSlash27]

Okay, so the next step is figuring out the burn time until a critical event that defines a "stage"; usually when a fuel tank that is attached to a decoupler runs out.

 For a swivel with a pair of Hammers, we assume that the Hammers will burn out first. The Hammers are not capable of drawing fuel from adjacent supplies, so the problem is greatly simplified.

 We know that the R_MF is constant and the fuel supply is fixed, so it's a simple problem to figure out the burn time.

t=M_f/R_MF

Where
t= stage burn time in seconds
M_f= Mass of fuel in the most limited tank in tonnes
and
R_MF= the cumulative mass flow rate of the engine(s) drawing from the most limited tank in tonnes per second.

For an all- lfo asparagus arrangement with various engines drawing from the outermost tanks, it's the same deal, except the cumulative R_MF of all firing engines is used, and the fuel supply is the tanks attached to whichever tanks will be dropped.

Once we have established the t for the first stage, we then figure out the fuel mass expended by the engines that are firing, but are not drawing from the most limited stage. This works in reverse from the earlier example.

M_f=t*R_MF

We then subtract that fuel mass from the subsequent stage (presumably the next most- limited tank attached to a decoupler) and proceed.

In this way, we are able to predict the burn times, TWR, and ship masses post- stage of any arbitrary combination of engines, throttle limits, fuel types, and staging arrangement. It's the same basic deal for parallel, onion, asparagus, quasi- asparagus, and drop tanks.... you just have to be certain about what defines a "stage", have to be sure that the R_MF and M_f are appropriate for the stage you're looking at, and you can't adjust the throttle during launch. This is MJ's big achille's heel; it's not always certain of what constitutes a "stage".

If you get confused, just remember this: An engine's thrust and I_sp will vary over the course of a launch, but it's R_MF will always remain constant so long as you don't move the throttle.

Best,
-Slashy

 

 

 

 

Edited April 3, 2018 by GoSlash27

[GoSlash27]

Finally, we use the same ol' rocket equation we always have.

ΔV=g0I_spln(M_w/M_d)

Which gives us the ΔV of the current stage. Rinse and repeat for subsequent stages.

HTHs,
-Slashy

 

[AeroGav]

Some people here (eg. @GoSlash27 ) have much more of a head for Maths than i have.

On another thread, there was an attempt to revive the "single tank to Tylo" challenge, this time using the mk3 liquid fuel fuselage as its basis.

Someone who is much better at actual spaceflight than myself calculated a minimum delta V of 8050 in LKO to make that work.

I managed to get a mk3 tank into LKO . with 5800dV remaining with 6 NERVs and its landing gear attached.

If you fire the separators to remove the gear and 3 of the nervs, DV immediately increases to 7800.

The design and flight profile could be optimised (I blew off the wings and nose cones while coasting to AP, should have waited till out of atmo,  one of the engines snagged on the tail fin after separation and was dragged most of the way to space) but i don't see the point in putting more effort in this if we're not even close.

It's hard to work out where I stand though when you can cast off some of your engines for the final leg of the journey.

That post includes the error strewn flight video, a link to the craft file and also a save of it in LKO after that flight, in case anyone wants to run their own calcs.

[GoSlash27]

AeroGav,

 You always have to keep in mind that mods to calculate DV can be (and regularly are) fooled, and are never accurate during atmospheric flight.

Discrepancies such as the one you describe can and will happen, especially when you stage at a point the calculator doesn't expect and can't predict.

 In this case, you didn't "gain" DV when you jettisoned your gear and half your LV-Ns. You had it all along, but MJ didn't know because it based it's calculation on the assumption that you weren't going to do that. Had you calculated it based on what you were planning, it would've been accurate.

Vacuum maneuvers are usually accurate to the predicted values so long as T/W is at least 1/2g in the local gravity well, although landings can vary widely. Atmospheric numbers, OTOH, can only ever be estimated because the Isp is constantly varying. None of the mods do a good job of predicting true launch DV in my opinion.

The mission planning cycle always works the same way. You either calculate or estimate the DV required for a phase of a mission, as well as the minimum T/W required. This is done with math and experience. You then take this mission requirement (along with the payload it will be moving) and use that to design a light and inexpensive stage that will fulfill the requirement. Thus, the mission planning moves forward in time, but the ship design works *backwards* after the mission planning is done.
 Even the rocket equation works backwards instead of forward.

When done properly, you don't find yourself in the VAB putting together assemblies and observing what DV and T/W they generate, but rather the reverse. You already know what engine and tank combo will best suit your need before you begin assembly.

Best,
-Slashy

Edited April 4, 2018 by GoSlash27

[SR1200 THUNDER]

20 hours ago, bewing said:

Yes you can.

Do you know how to get into the debug menu?

 

No. Please tell me.

[SR1200 THUNDER]

20 hours ago, Aegolius13 said:

For vacuum operation, where thrust and ISP are constant, I think you could do this with calculus.   I can't put a precise formula down,  but the basic idea would be:

Acceleration=force/mass.   

Force is just the combined thrust of your engines. 

Mass can be defined as a function of time.   E.g, starting mass minus burn rate(in mass/sec)*elapsed time.   

So, the acceleration at time t can be represented by the function a(t)=thrust/(m(0)-(burn rate)*t)

Thus, to get the sum of acceleration over time (which is delta v), you can integrate that function with respect to t, from 0 to the time where your first set of rockets burn out.   Then,  repeat for the next set,  or if you only have one set of rockets left, use the rocket equation.

Note that it's going to be very complicated to get accurate delta v numbers in atmosphere,  due to the change in isp and thrust with altitude.   This is the case even with "regular" rockets that work with the rocket equation.

Determining acceleration is a standard part of my pre-launch calculations. I have never bothered to take the extra step of figuring out how the mass changes over time during ascent. I never even really thought about it.

16 hours ago, GoSlash27 said:

Finally, we use the same ol' rocket equation we always have.

ΔV=g0I_spln(M_w/M_d)

Which gives us the ΔV of the current stage. Rinse and repeat for subsequent stages.

HTHs,
-Slashy

 

WOW!!! First of all, let me say, thank you for taking the time to explain all of that to me. I won't lie, having just read it over once, it made my head spin! lol

I am going to take some time to re-read all of that, and plug some gameplay numbers into your formulas and see if I understand everything. I might (probably) will have some follow up questions over the next couple of days.

[bewing]

1 hour ago, SR1200 THUNDER said:

No. Please tell me.

 

[SR1200 THUNDER]

1 hour ago, bewing said:

 

Thanks!