TWR and Terminal Velocity

[Northstar1989]

I can't count how many times I've hear players say "a rocket launched with a Thrust-Weight Ratio of 2 will ascend at terminal velocity".

I've even been guilty of this erroneous statement many times myself.

However, reading up on terminal velocity on Wikipedia, I was reminded that "Scientifically, an object approaches its terminal velocity asymptotically."

http://en.wikipedia.org/wiki/Terminal_velocity

In more detail:

"This velocity is the asymptotic limiting value of the acceleration process, because the effective forces on the body balance each other more and more closely as the terminal velocity is approached. In this example, a speed of 50% of terminal velocity is reached after only about 3 seconds, while it takes 8 seconds to reach 90%, 15 seconds to reach 99% and so on."

Why does this merit a thread in the KSP Forums you might ask? Because, long ago, KSP players proved that the most efficient speed for a rocket to ascend in the KSP physics engine on a planet with an atmosphere (stock, *NOT* running FAR) is at terminal velocity.

This led many players to assume that you should launch rockets with a Thrust-Weight Ratio (TWR) of 2 on the launchpad, as that will cause the rocket to increase in speed moving upwards at exactly the same rate as if free-falling downwards, and seek to maintain that TWR = 2 at all times.

More advanced players realized that, since a rocket starts out stationary, you need to start out with a TWR greater than 2, in order to "catch up" to terminal velocity, and then drop down to a TWR of 2 in order to maintain it.

However, neither of these statements is correct.

While it is true, in an infinitely tall atmosphere, a TWR fixed at 2 would lead to a rocket attaining terminal velocity and never leaving it until it ran out of fuel; in a REAL atmosphere such as Kerbin's, atmospheric thickness falls off as you ascend, therefore causing terminal velocity to increase as the rocket ascends, and never be reached.

Therefore, as you ascend, terminal velocity is constantly increasing, and you constantly have to "catch up" to it.

A TWR = 2 rocket will NEVER keep up with the rate of increase of terminal velocity, however, even if it attains it briefly (before it drops its SRB's, for instance), as velocity will approach terminal velocity asymptotically with a rocket with TWR = 2.

What that means is, in a real atmosphere, since it takes exponentially longer for each incremental increase in velocity towards terminal velocity, a rocket's maximum velocity at TWR = 2 when thrusting straight upwards is terminal velocity, and terminal velocity is constantly increasing as the atmosphere thins, a rocket with TWR = 2 will theoretically never reach terminal velocity, so long as it is ascending straight upwards...

The obvious answer, then, is that a rocket needs a TWR that is GREATER THAN 2 in order to attain terminal velocity during the vertical portion of its climb...

Note, however, that how much greater the TWR needs to theoretically be than 2, in in order to actually attain and keep up with terminal velocity during an ascent, falls off the longer the path-length through the atmosphere- so if that TWR is 2.4 during vertical climb, for instance, it might fall to 2.3 and then 2.2 and then 2.1 as the rocket begins and then deepens into its gravity turn...

Of course, all this breaks down if you add lifting parts, or install FAR (which makes every part a lifting part, even a fuel cylinder, by adding the real-world effect of body-lift...)

The same effect persists with a scaled-up Kerbin in Real Solar System mod, but the atmosphere becomes taller and falls off more gradually, and thus the path-lengths increase: so ideal TWR during the vertical limb might be 2.04 instead of 2.4, for instance...

Regards,

Northstar

Edited May 26, 2014 by Northstar1989

[phoenix_ca]

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.

[Northstar1989]

I'd just like to clarify what I meant about lifting surfaces breaking this pattern...

If lift, rather than thrust, is being used to hold a vessel up, then the TWR necessary to maintain terminal velocity becomes 1.

Of course, if any component of thrust is used to hold a plane/rocket up (such as by angling the nose above the horizon to increase the angle of attack), then the TWR necessary to maintain terminal velocity decreases back towards 2.

A brief summary:

TWR required to maintain terminal velocity for a vessel where 100% of force used to counteract gravity is coming from lift: 1

TWR required to maintain terminal velocity for a vessel where 100% of force used to counteract gravity is coming from thrust: 2

Of course, like with a rocket, terminal velocity is approached asymptotically- meaning a plane will never actually reach terminal velocity (even in perfectly level flight, with TWR = 1, and 100% of force used to counteract gravity coming from lift) unless its TWR >1.

And, terminal velocity is *NOT* the most efficient speed for a spaceplane to ascend at anyways- as jet engines decrease in their effectiveness at higher speeds, and a spaceplane's path length through the atmosphere is VERY LONG... (terminal velocity is the ideal ascent speed during a VERTICAL ascent)

Regards,

Northstar

P.S. Wings can be built into a spaceplane at an angle, providing an Angle of Attack for the lifting surfaces even when the nose of the plane is pointed directly at the horizon. That, and angling of the engines themselves downward relative to the nose, while pointing the nose up, can allow a plane to both point 100% of its thrust at the horizon and still produce lift...

Edited May 22, 2014 by Northstar1989

[Northstar1989]

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.

Really? Focusing in on a single typo? (now fixed) You surely must have something more interesting than that to say...

Regards,

Northstar

[phoenix_ca]

Really? Focusing in on a single typo? (now fixed) You surely must have something more interesting than that to say...

Regards,

Northstar

Not really. My brain is mush right now and you pretty much covered it, I think.

[allmhuran]

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.

[Xavven]

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.

Did you mean to say thrust instead of trust?

[Mesons]

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.

[problemecium]

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.

Edited May 22, 2014 by parameciumkid

[allmhuran]

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.

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.

Edited May 22, 2014 by allmhuran

[Lukaszenko]

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?

[Guest]

Yes. KSP aerodynamics are dumb like that. If you use FAR, things get a lot more complex.

[Kasuha]

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?

In KSP, drag on a part is proportional (linearly) to the mass of the part times its drag coefficient. So yes, parts with drag coefficient 0.1 have greater terminal velocity than parts with drag coefficient 0.2. But absolute majority of KSP parts has drag coefficient 0.2 and the few different ones usually don't mean much of a change (most significant deviations are Cupola module and all SRBs). That's why it's usually safe to go with these constants-per-altitude.

In general, this thread is mostly a theoretical one. If you use MechJeb, you can instruct it to keep your ship at terminal velocity all the time and you only need to care to have TWR>=2 at liftoff - even with TWR=2 at liftoff, you'll reach terminal velocity in about 15 seconds.

And if you don't use mechjeb, there's no chance you'll keep your ship's TWR constant or proportional to the state of atmosphere and your rocket anyway. Just make sure you don't produce too much mach/reentry effects during your ascent and you're good.

I'd also say that the area of "feel free to go at any speed" starts no sooner than at 35 km.

[Temeter]

Yes. KSP aerodynamics are dumb like that. If you use FAR, things get a lot more complex.

Not sure about that. I build a purposefully unpractical rockets when testing FAR, and my terminal velocity on ground level was never lower than 600m/s. In contrary, the fast acceleration became somewhat of an issue.

[magnemoe]

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.

Yes, use trashcans or other stuff to get up to speed fast, first stage don't need to have more than perhaps TWR 1.5 after this, you however want high TWR at say 12-16 km attitude, now to make things more complex at high speed you don't need an high TWR. Aspargus staging work well using the core stage and an 0.8 TWR from 1600 m/s to orbital speed. You can even use the nuclear engines for the last part and circulating.

[Corw]

In KSP, drag on a part is proportional (linearly) to the mass of the part times its drag coefficient. So yes, parts with drag coefficient 0.1 have greater terminal velocity than parts with drag coefficient 0.2. But absolute majority of KSP parts has drag coefficient 0.2 and the few different ones usually don't mean much of a change (most significant deviations are Cupola module and all SRBs). That's why it's usually safe to go with these constants-per-altitude.

In general, this thread is mostly a theoretical one. If you use MechJeb, you can instruct it to keep your ship at terminal velocity all the time and you only need to care to have TWR>=2 at liftoff - even with TWR=2 at liftoff, you'll reach terminal velocity in about 15 seconds.

And if you don't use mechjeb, there's no chance you'll keep your ship's TWR constant or proportional to the state of atmosphere and your rocket anyway. Just make sure you don't produce too much mach/reentry effects during your ascent and you're good.

I'd also say that the area of "feel free to go at any speed" starts no sooner than at 35 km.

There are other mods that give you terminal velocity readout and you can manually adjust throttle.

[Laie]

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?

[Kasuha]

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 faster, you're losing fuel because your velocity is lost to drag.

If you go slower, you spend longer time in inefficient thrust mode (some call that "battling gravity"), using more fuel.

Of course to be most efficient it's not just about keeping at terminal velocity, you also need to follow optimal flight profile.

[Waz]

a TWR fixed at 2 would lead to a rocket attaining terminal velocity and never leaving it until it ran out of fuel; in a REAL atmosphere such as Kerbin's, atmospheric thickness falls off as you ascend, therefore causing terminal velocity to increase as the rocket ascends, and never be reached.

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".

[Red Iron Crown]

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.

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.

[Random Tank]

Does anyone know/have links of a good guide for this sort of 'best TWR' while using FAR? I'm doing the right flight profile, but I don't know whether I'm losing efficiency to over/under thrusting.

A link to a FAR plane guide would be nice too! Thanks guys!

[undercoveryankee]

Does anyone know/have links of a good guide for this sort of 'best TWR' while using FAR? I'm doing the right flight profile, but I don't know whether I'm losing efficiency to over/under thrusting.

A link to a FAR plane guide would be nice too! Thanks guys!

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.

[-Velocity-]

Yup, not only with high TWR (>2) do your engines end up weighing a lot, but I often struggle just to have enough SURFACE AREA on the rear of my rocket (especially the larger ones!) to even get to a TWR > 1.6. I frequently have to put supplementary engine nacelles. Getting in excess of a TWR of 2 on some of my larger rockets would be very difficult, and would also greatly complicate fuel flow (getting fuel to flow correctly if you're using engine nacelles and partial or full asparagus staging can be a nightmare). To be honest, it's good enough to build rockets with a TWR of like 1.7 at the beginning of each stage.

[-Velocity-]

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! 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.

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.

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).

Edited May 22, 2014 by |Velocity|

[NecroBones]

I don't consider my TWR to be overkill unless it's over 3.