TWR and Terminal Velocity

[Northstar1989]

I do recall a number of threads suggesting to launch with a thrust to weight ratio of around 2, but I don't recall many that said it was optimal to maintain that TWR throughout the ascent.

The reason for this, I suspect, is that it's basically impossible. Using up fuel will decrease your weight, but until you stage your maximum thrust is constant, and if you run at less than maximum thrust then it means your engines are too big and their extra mass is a waste. So your actual TWR will vary throughout the ascent as fuel tanks are used up and then discarded along with their engines.

The "build for a TWR of 2" should therefore be read as "build for a TWR of roughly 2 on the launchpad". Then as people want more detail they can find the various ascent profile threads. I'll spit this out form memory so I could be slightly off, and things may have changed across a few versions, but it looks pretty much like this:

Altltude  - Target Velocity
0m        - 100m/s. Accelerate as hard as you can at launch
3000m     - 130 m/s
8000m     - 220 m/s
10,000m   - 260 m/s
16,000m   - 450m/s
20,000m+  - orbital speed, go as fast as you like.

You can throttle down to achieve a TWR of whatever you desire. Just because you have the extra engine mass doesn't mean you should use it...

As for the table, your speeds are a little slow at the start. Here's a list I copied off the Wiki a while back...

http://wiki.kerbalspaceprogram.com/wiki/Kerbin#Atmosphere

Kerbin Terminal Velocity

75 m: 100.9 m/s

1000 m: 110.5 m/s

3000 m: 134.5 m/s

5000 m: 163.7 m/s

8000 m: 219.9 m/s

10000 m: 267.7 m/s

12500 m: 342.4 m/s

15000 m: 437.8 m/s

20000 m: 716.0 m/s

32000 m: 2332 m/s

Note that taller rockets behave as if they're taking off from a higher altitude (their tops are already higher up), and launch clamps tend to produce a little spacing from the ground, so a better target at liftoff might be 102 m/s

Regards,

Northstar

Edited May 22, 2014 by Northstar1989

[Northstar1989]

I see a further problem with the deeply idealized model you have used--the efficiency of every engine in KSP increases as the atmospheric pressure decreases. This might make a "catch-up-and-cut-back" scheme advantageous; then again, you are spending more time in regions of lower efficiency if you do cut back your throttle during ascent. It's a very complicated business that, in my opinion, can't be simply boiled down to "TWR of 2.4 is best."

Trust experimental data which supports one launch profile over another.

I never said TWR 2.4 was actually best, it was just a hypothetical...

Anyways, the increasing ISP with thinning atmosphere is precisely one more factor that makes the ideal TWR greater than 2 at most times, so that you spend less altitude in the thicker atmosphere where ISP is less (as I said, it's not simply enough to catch up and then cut back to TWR = 2, as you'll end up falling behind terminal velocity as you climb with TWR = 2...)

Regards,

Northstar

[Northstar1989]

I won't contest your math, because most likely you are far better at it than I. But my experiments have shown that rockets have maximum delta-V at a much lower TWR. I've traditionally been trying to have it at 1.2, but recently I've actually discovered that the real g-force of my rockets as they leave the pad is more like 1.01.

For instance: an LV-T45 will go much, much farther with six or seven FL-T400s on it than it would with three or four.

Lower TWR gives you more Delta-V to work with in the first place because either you have more fuel or less engine mass, but you will actually spend a larger quantity of fuel with rockets with lower TWR...

As a result, for disposable rocket stages, you often want to go with more fuel and less engine (lower TWR) because that will get you further for the same rocket mass, even if you expend more fuel...

But where fuel consumption and higher TWR (attempting to keep Terminal Velocity) really start to shine is with reusable launch vehicles. OK, not really a huge deal just yet- but once they implement budgets, you'll WANT to cut down on your fuel consumption as much as possible, if the fuel costs you any kind of money, but recovering the reusable rocket gives you back the cost of all the recovered engines...

For that matter, most of this discussion about idealized ascent really only applies to the "straight up" flight profile of a (SpaceX-style) reusable launch vehicle anyways- because once you start your gravity turn, your path length through the atmosphere changes, and your ideal velocity probably isn't terminal velocity anymore... (terminal velocity being ideal was determined a long time ago by tests where the goal was to reach the highest altitude possible- which meant a straight up ascent profile, as there was no requirement that the final orbit be circular...)

Regards,

Northstar

[Northstar1989]

Certainly true, and the only consideration once you're in orbit. But at launch, things are different: Two LVT45's will be more efficient than one when the mass of the rocket passes a threshold, because the shorter duration spent fighting gravity and drag when you have twice the thrust results in less total fuel consumption than the cost incurred from the mass of the additional engine.

I think part of what he's getting at, though, is that there is a certain intermediate set of TWR values where the extra Delta-V you have to work with from having less engine mass outweighs the extra Delta-V you spend getting to orbit...

See what I had to say about reusable launch vehicles though- where fuel savings become a relatively bigger concern (especially if you operate a reusable launch vehicle off-planet, coupled with off-world fuel production, say with KSP-Interstellar or Kethane...)

Regards,

Northstar

[Northstar1989]

I didn't want to start a new thread about this question, but this seems like a good place to attach it to: Why is terminal velocity in KSP given as a fixed speed at an altitude? Terminal velocity depends on shape and other factors. Does the basic KSP aerodynamic model essentially cancel out all those other factors and you end up with a simple velocity@altitute chart?

Yeah, unfortunately that's exactly what happens in the stock aerodynamics model- drag scales directly with mass, regardless of shape; so you end up with a simple velocity @ altitude chart.

Play with FAR if you want more realistic aerodynamics- though then your ideal liftoff TWR goes even higher, as terminal velocity with a well-designed rocket starts off even higher (meaning you need more thrust to catch up...)

Regards,

Northstar

[Northstar1989]

How important is terminal velocity anyway? And, is it about equally inefficient to go either faster or slower, or will going too fast waste disproportionate amounts of fuel?

If you go too fast, the fuel-cost penalty tends to be a little less steep than if you go too slow, but the penalty to your Delta-V budget when you make stable orbit will be even greater because you had less Delta-V to work with in the first place... (lower fuel fraction, higher engine mass)

Minimizing fuel expenditures is most practical with a reusable launch vehicle (especially once budgets come out), or if you are operating on another planet with an atmosphere like Duna (keep in mind that terminal velocities will be much higher there, and you need a lot less thrust for a given TWR...) Maximizing Delta-V available after you reach orbit, on the other hand, is more practical for disposable rockets and one-off missions, and should lead to use of sub-optimal TWR from a fuel-expenditure perspective (it's better to spend more Delta-V to orbit if you have more Delta-V in the first place...)

Regards,

Northstar

[Northstar1989]

Thrust is constant (ignoring Isp altitude difference), while Weight goes down as fuel burns up, so I'm pretty sure your point is moot - TWR is never "fixed at 2".

You can fix TWR at 2 by throttling down (MechJeb has a handy readout on your TWR than you can use as a guide for when to throttle down- using the "maintain terminal velocity button won't throttle you down to 2 because you need a TWR above 2 to keep up with Terminal Velocity...)

Regards,

Northstar

[mhoram]

While building rockets optimized for payload fraction and hosting a payload fraction challenge, I came to the conclusion that it is more efficient to have more fuel and less engines (TWR starts at about 1,5 at liftoff).

If the focus is not payload fraction, other values are probably more fitting.

[Northstar1989]

There's nothing magical about a TWR of 2 that keeps you at terminal velocity (TV). The density of the atmosphere decreases exponentially with altitude, so a ship needs to accelerate faster and faster (i.e. higher and higher TWR) as it climbs if it wishes to stay at TV. It's only likely to be able to keep up with TV in the lower 25km of atmosphere. This is assuming a gravity turn ascent, jets are obviously different.

The rocket needs to accelerate faster and faster as it climbs, but it is experiencing less drag- which means the same TWR provides a greater net acceleration on the rocket...

Also, if you are performing a gravity turn as you climb, the steeper you enter into your gravity turn, the more gradual your ascent through the atmosphere- meaning less TWR is necessary to keep up with Terminal Velocity... Though, as I stated before- I'm not actually sure if ideal velocity *IS* Terminal Velocity if you are climbing at a 20-degree angle to the horizon...

That said, I find all the worry about terminal velocity a bit overblown. In my experience, an ascent below TV with TWR around 1.4 only loses a few dozen m/s of dV to aero drag while delivering a better payload fraction due to less engine mass. An ascent above TV loses more dV, but it's still not a huge amount.

A rocket with sub-optimal TWR (from a fuel-consumption standpoint) will often reach orbit with more Delta-V leftover, because it had more fuel and more Delta-V to work with in the first place. From a roleplaying perspective, low0TWR rockets also make sense, as fuel and fuel tanks are a *LOT* cheaper to purchase and maintain than rocket engines...

For a reusable launch vehicle, on the other hand, where fuel has to be replaced on every launch, but the relative cost of engines goes down (as they are re-used again and again...), it makes sense to launch with a higher TWR, closer to a fuel-optimal ascent... (you also save a tiny bit one mission control staff hours that way- as the actual ascent takes less time...)

A bit of a tangent, but one point I've always been curious about, is if in real life it actually makes more economic sense to have disposable drop-tanks on a (SpaceX-style) reusable rocket rather than making it 100% reusable...

Drop tanks (unlike engines) are going to be resilient to impacts and have a low terminal velocity (which also minimizes temperature increases from air resistance)- so I would also imagine it would be quite easy to slow them down to a safe touchdown speed to prevent damage to them (and allow re-use) with relatively small parachutes... The question is, would the extra payload capacity (and thus reduced number of required launches) on each launch be worth the extra expense of recovery and re-packing the drop tanks' parachutes, or of adding disposable drop tanks to each launch?

Regards,

Northstar

Edited May 22, 2014 by Northstar1989

[Northstar1989]

While building rockets optimized for payload fraction and hosting a payload fraction challenge, I came to the conclusion that it is more efficient to have more fuel and less engines (TWR starts at about 1,5 at liftoff).

If the focus is not payload fraction, other values are probably more fitting.

That depends a lot on the particulars of rocket design. For instance, I notices your designs used NERVA tug engines in the upper stages right from liftoff. That increases average ISP over the ascent, and reduced the redundant engine mass (utilizing upper-stage engines from liftoff is generally a very good idea), and may actually be responsible for your increased payload fraction rather than your low TWR.

It also depends on how you define your "payload"

Rockets with a TWR closer to optimal consume less fuel during their ascent, and thus will be able to carry more dry mass to orbit. While more of that weight may be tied up in upper stage engines rather than "payload", in some cases the engines from your (mostly spent) upper stage actually are part of your payload- such as when they can be detached from the upper stage and re-attached to another vessel (via docking port), essentially turning the upper stage into a giant drop-tank (no reason for the payload to pack its own engines when they can steal them from the upper stage), or when you recycle the spent upper stage with an orbital scrapping/salvaging operation...

There are also other considerations- for instance, a rocket with heavier lower-stage engines may weigh more than a rocket of approximately the same total size with lighter engines and heavier fuel tanks- and thus have a lower payload fraction even though it may actually be capable of carrying a slightly larger payload to orbit than a rocket of comparable size (not mass) with lower TWR...

And if you use Solid Rocket Boosters to bring up your TWR, forget about a direct comparison of payload fractions- SRB's are MUCH heavier than LFO fuel tanks and engines for the amount of Delta-V they provide- their chief advantage is that they pack a lot of thrust and propellant mass into a very compact profile...

Regards,

Northstar

Edited May 22, 2014 by Northstar1989

[Northstar1989]

In FAR, your terminal velocity will be high enough that you won't be able to catch up to it with any reasonable weight in engines, and high TWR makes it harder to keep the rocket stable.

So the conventional wisdom for FAR is a TWR on the pad of 1.2 or 1.3 to 1.6 or 1.7, and then full throttle unless you get structural failures.

Because your terminal velocity is usually higher in FAR, you want a TWR *MUCH* higher than 1.6 or 1.7 on the pad (if you can get it) in order to catch up to terminal velocity quickly... That won't EVER bring you up anywhere close to terminal velocity- you need a TWR of at least 2 to even maintain terminal velocity in level flight (more when ascending), FAR or not...

Even though you won't reach terminal velocity in FAR, TV is not a "magical number"- the greatest benefits actually come from the first 10 or 20 or 30% of the way to terminal velocity, with or without FAR- the fuel savings from faster ascent speed steadily drop off the closer you come to TV, until you actually reach TV, at which point you start spending more fuel as you go even faster... (this is ignoring Mach effects, of course- it can be assumed any reasonable rocket should be going quite a bit faster than the sound barrier...)

The challenge is, as stated, structural failures (I assume he means due to aerodynamic loads- the actual G's due to thrust shouldn't be any higher with FAR than firing the same rocket in a vacuum- and most rockets can withstand a TWR of at least 4 there...) and having enough surface area on the bottom of your rocket to obtain high TWR...

I imagine you could try radial thrusters to bring up your TWR, but they might wreck too much havoc on your aerodynamic profile to be worthwhile...

Regards,

Northstar

Edited May 23, 2014 by Northstar1989

[mhoram]

That depends a lot on the particulars of rocket design. For instance, I notices your designs used NERVA tug engines in the upper stages right from liftoff. That increases average ISP over the ascent, and reduced the redundant engine mass (utilizing upper-stage engines from liftoff is generally a very good idea), and may actually be responsible for your increased payload fraction rather than your low TWR.

On several occasions I had a design with a TWR near 2 during the vertical ascent and wanted to squeeze out a little bit more dV and reduce mass while still being able to reach orbit. In nearly all of these cases I reached this goal by removing engines and adding fuel.

It also depends on how you define your "payload"

I always assume that the payload does not participate in the ascent.

This means, no fuel or engines from the payload is used during the ascent.

Rockets with a TWR closer to optimal consume less fuel during their ascent, and thus will be able to carry more dry mass to orbit. While more of that weight may be tied up in upper stage engines rather than "payload", in some cases the engines from your (mostly spent) upper stage actually are part of your payload- such as when they can be detached from the upper stage and re-attached to another vessel (via docking port), essentially turning the upper stage into a giant drop-tank (no reason for the payload to pack its own engines when they can steal them from the upper stage), or when you recycle the spent upper stage with an orbital scrapping/salvaging operation...

I never counted the engines of my upper stages as part of the payload and payload fraction - the ability to use them for the payload is just a bonus of that particular design. I had a picture of this designconcept in this thread.

[Northstar1989]

Also note that reading over many of these posts will give you the impression that you want very high TWR for the upper stages of your rocket. That is simply not the case in many rocket designs. In the upper stage, you're already going like, over half of orbital velocity, and your rocket is pointed more or less parallel to the ground. The whole point of having high TWR is to waste very little fuel in counteracting gravity drag. However, there is zero gravity drag when you are pointed parallel to the ground!

It doesn't matter which direction your rocket is "pointed" (that's entirely a construct of our own analysis), or even which way a rocket is thrusting (which is what has actual physical significance), it matters which way a rocket is actually MOVING.

A rocket that is thrusting parallel to the horizon, but still has a prograde vector 20 degrees above the horizon is, first of all, losing some potential benefits from the Oberth effect (which only acts on thrust in the direction of your movement- *NOT* any component of thrust perpendicular to it).

Second, such a rocket is still experiencing loss of kinetic energy to gravity (and to drag if it has not yet exited the atmosphere). The higher your acceleration at this altitude (which should not necessarily be parallel to the horizon), the more quickly you will raise your apoapsis while thrusting in this direction. You will be able to get in more of your thrust before gravity has managed to slow your rocket down as much, allowing greater utilization of the Oberth Effect, and less energy spent raising your apoapsis at a higher altitude... (from a perspective more familiar to most players- you are closer to periapsis at 36000 meters than at 42000 meters if the final orbit you are aiming for is 100 km- as a suborbital trajectory can be modeled as a highly elliptical orbit that passes through the atmosphere and the planet itself...)

All an upper stage needs to do is raise your periapsis above ground level before you re-enter the atmosphere. Thus, upper stages often can get away with a relatively low TWR. In many cases, 0.5 is fine. I've had even less work, but there have been some rocket designs I made that needed a upper stage TWR of >1 (generally, the upper stage was a bit over-sized on these rockets). It all depends on what fraction of orbital velocity you are going when you ignite the upper stage. IN GENERAL, vacuum Isp is more important than TWR for an upper stage, but that is of course, a generalization.

Indeed, vacuum ISP is a major thing to focus on for upper stages. But you can't neglect TWR either. And, as always, it depends on the particulars- for instance the upper stage of a Space-X style reusable rocket (my new favorite launch profile) requires a MUCH higher TWR than the upper stage of a conventional rocket, as it will have almost no horizontal velocity when ignited, and won't have an apoapsis terribly high above the atmosphere in most cases...

One place where this generalization can really break down is when using asparagus staging, which I generally use for my larger rocket designs. In asparagus staging, the upper stage ends up being the central "stalk". As asparagus staging requires that all "stalks" on the rocket be firing their engines all the time, I end up making the central stalk generally similar in TWR and Isp characteristics as all the other stalks. So my upper stage ends up being a little over-powered.

There's no reason the central "stalk" needs to be the same as the outer stalks in asparagus staging. In fact, in some cases it may behoove you to use a lower-thrust, higher-ISP engine for the central stalk than for all the other engines. For that matter, the central stalk doesn't even need to be your upper stage- it's not uncommon to park an upper stage on top of an asparagus-staged lower stage. Though, generally speaking, asparagus staging of the type you are describing is never a very efficient design during an ascent in the first place- you waste a lot of fuel bringing the engines on the upper stalks up, only to throw them away a soon as the fuel tanks above them run out. Generally, it's more advisable to make use of asparagus-staged drop-tanks, and use radial boosters on the central stalk for extra thrust...

For the (successful) stock Eve lander I made, I actually used a combination of vertical staging and asparagus staging, and I DID end up using a low TWR (at least, low for Eve) upper stage (~0.8 - 1.5 or something like that).

Eve is a stinking kraken-hole, that I never intend to visit again due to the horrendous lag it puts on my computer. But if I *were* to visit it, and even try to send a Kerbal to the surface and back, I wouldn't bother with rockets- you simply expend too much fuel fighting Eve's high gravity. On Eve, it would be much better to go with a NERVA (or KSP-Interstellar Thermal Turbojet) powered spaceplane (with chemical rockets to kick it into orbit), lots of drop-tanks and really large wings, and let lift hold your vehicle up instead of thrust... (you *might* want to put the giant wings on decouplers though- so you can detach them when the atmosphere becomes too thin for them to be useful any longer- as you don't want to haul those heavy/draggy things all the way back to orbit...)

Regards,

Northstar

Edited May 23, 2014 by Northstar1989

[Northstar1989]

On several occasions I had a design with a TWR near 2 during the vertical ascent and wanted to squeeze out a little bit more dV and reduce mass while still being able to reach orbit. In nearly all of these cases I reached this goal by removing engines and adding fuel.

It depends how much fuel you added. What this did to the average ISP of your remaining engines (did you remove the least or most efficient engines? How was their TWR?) and a lot of other things... Additionally, I made no secret of the fact that you get more Delta-V with lower-TWR rockets in many cases- so you're not saying anything new. The thing is, that extra range comes at the expense of higher fuel-consumption, so if you can get the rocket to orbit with a TWR closer to ideal, you will often expend less fuel that way (which is in some ways better if you re-use just the engines, salvage them, or re-use the entire lower stages of the rocket- but inferior for a "throw-away rocket")

I always assume that the payload does not participate in the ascent.

This means, no fuel or engines from the payload is used during the ascent.

That's generally a bad assumption to make. IF your payload has engines, and you have a way to use them in your ascent and thus save engine mass on lower stages, why wouldn't you? It's almost always best to take an integrated approach to rocket design...

I never counted the engines of my upper stages as part of the payload and payload fraction - the ability to use them for the payload is just a bonus of that particular design. I had a picture of this designconcept in this thread.

It's up to you how you want to play the game. If you want to design general-purpose rockets, and try and get other players to use them (though I don't see the fun in using somebody else's rocket design- the pride of seeing something you designed soar through the sky is half the fun in KSP), then that's your perogative. Personally, I prefer to design my own specialized rocket for each mission where possible. In a worst-case scenario, I usually at least design a general frame and then make extensive modifications (a drop tank here, a lighter launch engine there due to the ability to use payload engines, etc...) based on my mission profile. As always, KSP is about learning and having fun, and open to many play styles- so do what you like, and enjoy!

Regards,

Northstar

[yaur]

The "magic" of having a TWR of 2 is not that its going to keep you at terminal velocity. I believe TV should increase exponentially while TWR is going to increase linearly for most configurations, so any configuration that can maintain TV for most of the ascent has way to much engine mass. What a TWR of 2 or less (on the pad) gets you is the ability to leave the throttle wide open for the entire ascent. If its over that you are going to need to micromanage your throttle to stay near TV.

[phoenix_ca]

You didn't fix all your typos!

I'm a sad, sad panda now.

[SkyRender]

This is the first I've ever heard of anyone referring to any TWR as a "magic number" (well, besides the obvious "greater than 1" requirement if you want to actually get off the ground). Ideally you want to hit mach 1 as fast as possible and stay there until the atmosphere is thin enough that the drag coefficient isn't eating up most of your fuel. Ie. you'll throttle down to slow your acceleration to a crawl once you get going fast enough, and gradually throttle back up as the air thins out.

[Vanamonde]

Thread moved to the gameply & how-to subforum.

[Mesons]

The whole point of having high TWR is to waste very little fuel in counteracting gravity drag.

-cringe-

Being in science makes the jargon used in our KSP community sometimes hurt a little.

[Mesons]

This is the first I've ever heard of anyone referring to any TWR as a "magic number" (well, besides the obvious "greater than 1" requirement if you want to actually get off the ground). Ideally you want to hit mach 1 as fast as possible and stay there until the atmosphere is thin enough that the drag coefficient isn't eating up most of your fuel. Ie. you'll throttle down to slow your acceleration to a crawl once you get going fast enough, and gradually throttle back up as the air thins out.

Why mach 1? That seems like a pretty "magic number" to me; as far as I know, there's no sound speed dependence in KSP so this seems like an arbitrary cutoff as well.

[Northstar1989]

Why mach 1? That seems like a pretty "magic number" to me; as far as I know, there's no sound speed dependence in KSP so this seems like an arbitrary cutoff as well.

He *might* be thinking of FAR- where you want to break the sound barrier to reduce the drag coefficient on your rocket. But with FAR, generally you don't want to stall at Mach 1, because the most difficult part is breaking the sound barrier, and after that drag increases a lot less with speed- whereas you will still see strong benefits to reduced engine burn-time if you fly faster...

Regards,

Northstar

[Northstar1989]

-cringe-

Being in science makes the jargon used in our KSP community sometimes hurt a little.

You're not the only scientist here, you know *self point*

I'm a biologist in real life...

Just learn to relax and go with the slang a little.. I'm perfectly aware of the technical "inaccuracy" of many of the terms used here too...

Regards,

Northstar

- - - Updated - - -

You didn't fix all your typos!

I'm a sad, sad panda now.

Awww, I'm sorry- what other typos do you want me to fix?

Regards,

Northstar

[phoenix_ca]

Awww, I'm sorry- what other typos do you want me to fix?

Same one I'm afraid. You have more "Ration"s in there that should to be "Ratio"s.

But with FAR, generally you don't want to stall at Mach 1, because the most difficult part is breaking the sound barrier, and after that drag increases a lot less with speed

You mean decreases, right? The drag coefficient tends to go up until Mach 1 (rising rapidly when it hits the drag divergence mach number), and then it falls pretty sharply.

Edited May 23, 2014 by phoenix_ca

[Laie]

for what it's worth:

[MarvinKitFox]

The only thing I have to say is this: It's "Trust-to-Weight Ratio". Not "Ration". We aren't handing out ready-to-eat meals here.

The only Trust-to-Weight ratio I know is my calory allowment in my diet. ;-)