Help with calculating delta v and twr

[GoSlash27]

A spreadsheet, Slashy? I thought you were a pencil and sliderule sort of person.

Kidding aside, I have to agree that the dV calculating mods don't answer all the interesting questions. They answer one question really well, "What is the delta V of this design?", and that is enough for many players (and often enough for me, tbh). But if you want to answer questions like "How much fuel and engine mass do I need to give this design x delta V and y TWR?" or "How much payload can this tug push to body x?", then they become a bit tedious to use and a spreadsheet or calculating by hand becomes better.

RIC,

Oh, that's just to do one-off design problems that I'm not liable to encounter again. For anything I do regularly, I set up a spreadsheet. Laziness is the mother of invention and I'm *very* lazy!

It's enough for me to know that I could work it out on paper again if I ever needed to.

Although... Everything that I do with a spreadsheet was first worked out on paper. I'm not sharp enough to figure out the math on the fly, so I kinda have to. And plus algebra...

Best,

-Slashy

Edited June 27, 2015 by GoSlash27

[Starhawk]

I have to plug Meithan's Engine Charts here. A great tool that does exactly what is being discussed. Given a delta-v range, TWR, atmospheric stats, and number of engines desired, plots a graph showing which engine is superior at a range of given values. Also displays the 'next best' solution at the same time.

It's only updated to 1.0.2 at the moment, so I guess that's the case for having a spreadsheet.

Happy landings!

[GoSlash27]

I have to plug Meithan's Engine Charts here. A great tool that does exactly what is being discussed. Given a delta-v range, TWR, atmospheric stats, and number of engines desired, plots a graph showing which engine is superior at a range of given values. Also displays the 'next best' solution at the same time.

It's only updated to 1.0.2 at the moment, so I guess that's the case for having a spreadsheet.

Happy landings!

Thanks for plugging that! I'm surprised it wasn't mentioned already.

I'm a big fan of Meithan's work in this area. I just sent him the corrections this morning for the LF&O engines, so hopefully it won't take long to update.

His approach is excellent for identifying broad trends, while the spreadsheet excels at designing for a specific requirement. They fulfill slightly different roles, so I don't really argue for the use of one over another.

I find that Meithan's charts are best for mission planning, a spreadsheet is best for vehicle design, and KER is best for live on-the-fly info.

Best,

-Slashy

[Starhawk]

I find that Meithan's charts are best for mission planning, a spreadsheet is best for vehicle design, and KER is best for live on-the-fly info.

That's interesting. I'm still somewhat too far to the trial-and-error side of things, but I'm becoming more methodical. I have to laugh a bit when I imagine how many hundreds of times easier my Eve Rocks mission would have been with a spreadsheet like yours.

I homed in on a very efficient design eventually, but it took a lot of tries! KER was definitely invaluable, though. I couldn't have done it without that. (Not least because I didn't even know the rocket equation at that point.)

Happy landings!

[Chaos_Klaus]

Yeah, the math definitely isn't for everyone.

It's really not math ... it's just typing things into a calculator ... math is deriving these formulas.

People are afraid of symbols like "ln". How can you be afraid of a button on your calculator?!?

[Falkenherz]

I am at war with math, I do not understand the language the formula´s are written in, too detailed and thus too complex.

Something I understand:

- TWR is a comparision of the ship total weight and the engine trust divided by 10. An equilibrum is an TWR of 1, which makes your ship hover in a given planet´s gravity.

- To lift off Kerbin ground, you need at least > 1 TWR, while floating in space in theory anything above 0 TWR pushes you ahead, but in practice you get only a good acceleration within reasonable time if you are around 0.5 TWR.

Something I just remotely understand:

- deltaV tells me how far a rocket can accelerate away, measured against a given planet´s gravity pull.

- deltaV gets higher the more fuel the craft has, but lower the more mass it has; there is a sweet spot where adding more fuel won´t increase deltaV anymore.

- The trust-to-weight ratio and something called "specific impulse of the engine" mess this figure up, too; higher specific impulse allows for farther flight, but if TWR is too low, a high specific impulse won´t help because gravity pull (and the rocket´s own inertia?) is stronger than what the impulse can overcome.

For me it is weird that we cannot describe things properly in normal language and need math for the ultimate precision. Maybe we should learn how to communicate only in math!

Edited June 29, 2015 by Falkenherz

[Red Iron Crown]

I am at war with math, I do not understand the language the formula´s are written in, too detailed and thus too complex.

Something I understand:

- TWR is a comparision of the ship total weight and the engine trust divided by 10. An equilibrum is an TWR of 1, which makes your ship hover in a given planet´s gravity.

- To lift off Kerbin ground, you need at least > 1 TWR, while floating in space in theory anything above 0 TWR pushes you ahead, but in practice you get only a good acceleration within reasonable time if you are around 0.5 TWR.

TWR changes with the reference body, and is calculated as thrust divided by ship weight, or on Kerbin thrust divided by (ship mass * 9.81). A TWR >1 is required to lift off, though 1.3 or more is generally considered more desirable.

Something I just remotely understand:

- deltaV tells me how far a rocket can accelerate away, measured against a given planet´s gravity pull.

- deltaV gets higher the more fuel the craft has, but lower the more mass it has; there is a sweet spot where adding more fuel won´t increase deltaV anymore.

Delta-V doesn't care about gravity, it's an expression of how much a vessel can change its velocity. It is a good indicator of which destinations a vessel can reach.

More fuel is always more delta-V, though it is diminishing returns and there are theoretical limits for how much a single stage can have.

- The trust-to-weight ratio and something called "specific impulse of the engine" mess this figure up, too; higher specific impulse allows for farther flight, but if TWR is too low, a high specific impulse won´t help because gravity pull (and the rocket´s own inertia?) is stronger than what the impulse can overcome.

Specific impulse has no effect on TWR. Though it happens that the higher specific impulse engines also have lower TWRs.

[Falkenherz]

...

Delta-V doesn't care about gravity, it's an expression of how much a vessel can change its velocity. It is a good indicator of which destinations a vessel can reach.

More fuel is always more delta-V, though it is diminishing returns and there are theoretical limits for how much a single stage can have.

...

See, this is something I do not understand. When I stack fuel tanks on an engine, there clearly are diminuishing returns on the deltaV, up to the point where you don´t get much increase any more. Why is this then?

[Red Iron Crown]

See, this is something I do not understand. When I stack fuel tanks on an engine, there clearly are diminuishing returns on the deltaV, up to the point where you don´t get much increase any more. Why is this then?

It's asymptotic. It gets ever closer to the theoretical maximum for a single stage, a maximum determined by the engine specific impulse and the ratio of wet mass to dry mass of the best tanks. So adding more fuel always adds more delta-V, but the amount gained gets smaller and smaller.

[Falkenherz]

Is there a way to eyeball the theoretical or a practical maximum figure for deltaV? Like, for TWR its mass times ten equals trust means equilibrum. I can still grasp this, but I fail to estimate something "asymptotic".

[*Aqua*]

Just in case you missed it:

Scott Manley posted a video 2 weeks ago in which he shows the delta V and TWR calculations.

[Red Iron Crown]

Is there a way to eyeball the theoretical or a practical maximum figure for deltaV? Like, for TWR its mass times ten equals trust means equilibrum. I can still grasp this, but I fail to estimate something "asymptotic".

The best mass ratios for tanks is the same for all engines except for ions and SRBs in KSP, so it's not too hard to estimate for them. The theoretical limit for these is Isp*21.6. Practically speaking, getting about half the theoretical limit is about as far as is practical for a single stage with any sort of payload, getting two thirds of the limit requires an awful lot of fuel.

[GoSlash27]

Is there a way to eyeball the theoretical or a practical maximum figure for deltaV? Like, for TWR its mass times ten equals trust means equilibrum. I can still grasp this, but I fail to estimate something "asymptotic".

Falkenherz,

The theoretical maximum DV for LF&O rockets is limited by the mass efficiency of the tanks. For an infinitely large tank, the rocket will weigh 9 times more when full. The DV would therefore be Isp*9.81*ln(9), or roughly 21.6*Isp. Rounding it off to make it easy, about 20 times the engine's Isp. *edit* Ninja'd!

As a practical matter, this isn't a useful way to design a stage since you need to keep acceleration above a minimum and you must move payload. Instead of asking "how much more DV can I get", you need to be asking "what do I need to do to get the DV and acceleration I need for the payload".

You define the requirement by DV, payload mass, and minimum acceleration, then design the stage to match it. I have linked to the procedure upstream, but here's the quick version.

Start with your selected engine. How much mass can one of these push at my required acceleration? thrust/10 for 1G, or thrust/5 for .5G.

Now how much of your mass needs to be fuel to meet the DV budget? [e^(DV/9.81Isp)-1]*mass

And how much needs to be tanks to hold the fuel? fuel mass/8

So now you have a single engine rocket that can move a payload the needed DV and acceleration. How much payload can it move?

total mass-engine mass-fuel mass-tank mass.

Now it's just a matter of scaling it to work for your payload. If your payload is 10 times what a single engine rocket can lift, then you'd scale the entire rocket up 10 times.

Best,

-Slashy

Edited June 30, 2015 by GoSlash27

[Chaos_Klaus]

Other people already stated the theoretical limit of delta v per stage to be about 21.6*Isp. However that assumes that the payload and engine mass is infinitely small compared to the rest of the rocket. That means, this figure is what you get if you put an infinite amount of fuel on your rocket! That is obviously impractical

In practice, you never even want to go beyond 10*Isp, because that is where more fuel starts to give you less and less delta v already. Use this as a rule of thumb. Sometimes it is practical to stage earlier.

There is two reasons why you get less delta v for each added tank:

1.) As the others stated your wetmass/drymass-ratio can never be better than that of a single fuel tank. In KSP this ratio is 9/1 for most fuel tanks.

2.) In the rocket equation this ratio is wrapped inside the ln-function (the natural logarithm). That too has the effect that you get less and less delta v.

The beauty of the delta v concept is that it is completely independent of actual thrust! It is also indpendent of the parent body's gravity. Gravity and aerodynamic drag might nullify some delta v that you spend, but your craft has the same initial delta v budget regardless.

Specific Impulse (Isp) is simply how much delta v your rocket can gain using a certain amount of fuel. Double the Isp, you get double the delta v.

However, sometimes high Isp engines have other problems. They often have low thrust (which disqualifies them for launches on high gravity bodies), bad atmospheric performance and the LV-N in particular is quite heavy. The weight of the engine will add to your dry mass and can decrease your delta v.

Edit:

I do not understand the language the formula´s are written in, too detailed and thus too complex.

I think you do what I've seen a lot of people do. You see a formula and immediately assume that you can not understand it. I mean ... you can propably add, substract, multiply and devide numbers, right? You also heard that a function is some thing where you put in a number and it spitts out another. Things in brackets are to be done first. And there you have it: You can solve the rocket equation! :]

ÃŽâ€v = Isp * 9.81 * ln ( m0 / m1 )

There is really nothing to it. Devide m0 by m1. Take the natural logarithm of that number (use your standard calculator). Multiply by 9.81. Multiply by the Isp of your engine. Done.

Don't be scared. It's not hard. You just don't know where to begin and what to look for. But I bet you are assuming it is really hard, while it is actually not.

Edited June 30, 2015 by Chaos_Klaus

[Falkenherz]

Very helpful, thanks!

Goslash, I read your post in the other thread but as I said, I am a bit math illiterate: "e^(DV/9.81Isp)-1*mass" just kills my brain. What is "e"? Eyeballing this expotential function is hardly possible, but sure, those are very helpful steps indeed for preparing a spreadsheet! Is the engine mass part of the "defined payload"?

Would it thus be a rough eyeballing to say: Isp times 10 is the practical max deltaV; deduct increasing chunks from this total value per ton of "payload" (includes engine mass and dry tank mass). For eyeballing the "increasing chunks", I am still missing a handle.

[Red Iron Crown]

e is the base of the natural logarithm, about 2.71828.

ln(x) and e^x are reversals of each other.

[Chaos_Klaus]

10*Isp is a practical delta v value per stage. You can get more in one stage, but it would be more reasonable to just add another stage.

Delta V is largely dependent on the ratio between drymass (payload+engines+fuel+empty tanks) and wet mass (payload+engines+fuel+full tanks). Together with the natural logarithm there is no way to eyball this in an easy way.

Most of us use a mod like Kerbal Engineer Redux that does these calculations on the fly. This way we don't need to torture our calculators all the time.

For design, I go like this: I build the payload I need to move, then add some fuel and an engine. Looking at the delta v readout of KER I then decide if I want to put more ore less fuel in that stage. I'm not at all accurate about this. If a stage has 11*Isp or 9*Isp, I really don't care. Often I go with far less than that if I don't need the delta v, or want a small lander, ect. If a stage will be used for launch or landing, I look at the TWR (possibly the atmospheric values) and go for an initial TWR of 2.

Edited June 30, 2015 by Chaos_Klaus

[Falkenherz]

Thanks! Very helpful!

[GoSlash27]

Very helpful, thanks!

Goslash, I read your post in the other thread but as I said, I am a bit math illiterate: "e^(DV/9.81Isp)-1*mass" just kills my brain. What is "e"?

Ninja'd by RIC

Eyeballing this expotential function is hardly possible, but sure, those are very helpful steps indeed for preparing a spreadsheet!

That would definitely be the easy way to go, and yeah... computing the DV of a stage isn't something that can be eyeballed. Unfortunately, you've got to do some math.

Is the engine mass part of the "defined payload"?

No, it's part of the stage. Payload mass+fuel mass+tank mass+engine mass is your total stage mass.

Would it thus be a rough eyeballing to say: Isp times 10 is the practical max deltaV; deduct increasing chunks from this total value per ton of "payload" (includes engine mass and dry tank mass). For eyeballing the "increasing chunks", I am still missing a handle.

It really wouldn't work that way. For a rocket to generate a DV and minimum thrust/ weight, the payload can only be a fixed percentage of the stage. Exactly what percentage depends on the engine you're using and it varies a lot with engine specs and the amount of DV you build into it. It has to be computed.

You can use KER and mix/ match parts in the VAB and eventually hit on something that'll work, but you never know for sure if you've found the best (lightest and/ or cheapest) solution. Finding the best solution requires doing the math.

Luckily, you only have to do it once if you set up a spreadsheet.

Best,

-Slashy

[Falkenherz]

Heh, your last point got me, thanks. I hate never knowing if I found the most efficient setup!!!!

I used to play EVE Online and had quite my share of spreadsheets. In fact, I learned a great deal about spreadsheet´ing while playing that game... ah, happy times...

[GoSlash27]

Heh, your last point got me, thanks. I hate never knowing if I found the most efficient setup!!!!

I used to play EVE Online and had quite my share of spreadsheets. In fact, I learned a great deal about spreadsheet´ing while playing that game... ah, happy times...

Falkenherz, there's an error in the process I outlined upstream. I'll correct it when I get home. I'll also walk you through a simple example to show you how it works.

Best,

-Slashy

[Falkenherz]

Hm, I just get error messages trying to reproduce your euler-formula in google spreadsheet. How about a link to a demonstrative google spreadsheet?

Here is my first small rough incompetent try; I opened the sheet for read+write.

Edited July 1, 2015 by Falkenherz

[Chaos_Klaus]

You need to use the brackets appropriately.

rearranging the Rocket Equation:

DV = Isp * 9,81 * ln (m0/m1)

to solve for the mass ratio m0/m1 goes like this:

DV / (Isp * 9,81) = ln (m0/m1) _______ // devided the whole equation by Isp * 9.81 so that it cancels out on the right side and appears on the left

EXP( DV / (Isp * 9.81) ) = m0/m1 ______ // here I did the dance with "ln ()" beeing the inverse function of "EXP()"

=EXP(DV/(Isp*9.81)) ________________ //this the spreadsheet friendly version without spaces.

Now that you know the ratio between m0 and m1, you can calculate how much fuel you need to bring in relation to your dry mass (payload+engine+empty tanks).

Edited July 1, 2015 by Chaos_Klaus

[GoSlash27]

Falkenherz,

Apologies, my internet was out last night and I wasn't able to post. my example.

I'll post it here in sections and update as I go. It'll be a wall of text, but hopefully helpful.

So for my example, I'm building an early career manned rocket to collect science in orbit. It needs to stay within the 18 tonne limit since none of the facilities are upgraded.

I decide to go with a 2 stage design, upper using an LV-909 and lower using the LV-T30.

The payload including the decoupler is 1.7 tonnes, so we start there.

Upper stage mission requirement: 1.7 tonnes payload, 1,800 m/sec DV, and minimum acceleration of 1G. Engine specs LV-909: Thrust= 60KN Mass= .5 t, Isp= 345 sec

Process overview:

1)Design a single engine example

1a) Determine maximum stage mass for defined minimum acceleration

1b) Determine fuel percentage for defined Isp

1c) Determine payload mass of single engine example

2) Determine number of engines needed

3) Determine fuel & tankage mass

4) Set throttle limiter

1a) Based on our engine's thrust and acceleration, determine the maximum mass of a single engine stage.

T/(9.81*Glim)

60/(9.81*1)= 6.12 tonnes

1b) Determine the fuel percentage of our single engine example (this is the part I had screwed up)

Our wet/ dry ratio (Rwd) is defined by our Isp and DV requirement.

e^(DV/9.81Isp). 2.718^(1800/(9.81x345))= 1.702

This is the ratio of our mass when fueled to our mass when empty, but we need to know what percentage of our fueled mass is fuel, so it works like this:

(Rwd-1)/Rwd

(1.702-1)/1.702= .423. 42.3% of our mass is fuel.

1c) Determine payload mass of single engine example

Since our tanks weigh 1/8 of our fuel, our tanks are .423/8 of the total mass; .0529

fuel percentage* total mass = fuel mass and tank percentage* total mass = tank mass.

.423*6.12t=2.59t fuel mass

.0529*6.12t=0.32t tank mass

and of course

engine mass is .5t and total mass is 6.12t.

therefore...

total-engine-fuel-tank=payload

6.12-.5-2.59-.32= 2.71t

Our single engine example could handle up to 2.71 tonnes and still meet the need.

2) Determine number of engines needed

Since our payload is less than what a single engine can do, we're simply going to use 1 engine.

In the event it's not enough, we have to scale the design up.

(Our payload/ max payload) rounded up to the nearest whole number of engines is how many we need.

N= roundup(Mp/Mp1),0

3) Determine final fuel & tankage mass

The mass of tankage will be (Rwd-1)(Mp+NMe)/(9-Rwd) where

Rwd is the wet/dry ratio (step 1b)

Mp is our payload mass

N is the number of engines

and

Me is the mass of a single engine.

For our upper stage, it would be (1.702-1)(1.7+(1*.5))/(9-1.702) =.212t

and since our fuel is 8x heavier than our tanks, Mf= 8*.212=1.69t

So there's our design: 1.7t payload, a single LV-909, 1.69t of fuel, and .212t of tankage. It weighs 4.11t total.

last step for this stage

4) Set throttle limiter

total mass/(N*max mass)= throttle

4.11/(1*6.12)= .67, or 67%.

Edited July 1, 2015 by GoSlash27

[Falkenherz]

Thanks for your help and, no harm done; I will be away now on holdiday for about a week, anyways.