Eve terminal velocity charts

[rogerawong]

The Kerbin wiki has a terminal velocity chart that gives you a rough yet practical and useful sense of the relationship between air resistance and altitude. 

So I went looking for the terminal velocity chart for Eve, but didn't find it in the wiki, despite many old articles referencing it. Old articles got me thinking "I bet it existed at one time". And so it did. About 9-10 years ago, the Eve wiki page had a terminal velocity chart. And then someone unceremoniously and without explanation, deleted it.

The following table gives terminal velocities at different Eve altitudes. These are also the velocities at which a ship should travel for a fuel-optimal ascent from Eve, given the game's model of atmospheric drag.[3]

Altitude (m)	Velocity (m/s)
0	58.4
1000	62.5
5000	82.0
10000	115
15000	162
20000	228
30000	450
40000	888
50000	1 760
60000	3 470

Maybe the drag model changed, maybe something else happened 10 years ago. Who knows.  

So, what would the equivalent of this be in modern times?  I'd like to add this back to the wiki. I found it useful for Kerbin. It would likely be helpful for Eve.

[king of nowhere]

a terminal velocity chart doesn't make any sense.

terminal velocity is not a function of the atmosphere. it is, first and foremost, a function of the object moving through it. its drag coefficient, its mass, its aerodinamic characteristics. even for a generally rocket-shaped object, the square-cube law makes a lot of difference.

what is actually used to calculate such a graph? what is taken as a reference? how can it be extrapolated to different ships? besides, if you need to know the terminal velocity of your speed, you can easily see it from the aerodinamic window, when drag equals weight.

all in all, i fail to see how such a graph would be useful

[Spricigo]

18 hours ago, king of nowhere said:

terminal velocity is not a function of the atmosphere. it is, first and foremost, a function of the object moving through it

well..it's actually a function of both.

 V_t=√(2mg/dAC_d)m n

g and d  depends on the atmosphere* while m, A and C_d depends on the craft.

Which indeed means that such chart wouldn't make sense if only the atmosphere is referenced. There is a table that give the terminal velocity for a imaginary body in diferent elestial bodies there https://wiki.kerbalspaceprogram.com/wiki/Atmosphere 

18 hours ago, king of nowhere said:

how can it be extrapolated to different ships

Using the formula above, I suppose. I guess an spreadsheet would help. Seems a bit impractical for me.

On 1/31/2024 at 11:26 PM, rogerawong said:

The Kerbin wiki has a terminal velocity chart

mm,mmno, there is no chart like that. Look for yourself. https://wiki.kerbalspaceprogram.com/wiki/Kerbin 

The chart there with density and pressure for altitude may be used to construct the chart you talking about but as pointed above you also need the values for the craft.

 

On 1/31/2024 at 11:26 PM, rogerawong said:

About 9-10 years ago

At the time KSP was at beta and had a very different and unrealistic drag model.  Anything from that time regarding drag have no use for today KSP.

 

 

 

*technically g depends on the celestial body and height. However so is d    ...technically

[Zhetaan]

On 1/31/2024 at 9:26 PM, rogerawong said:

The Kerbin wiki has a terminal velocity chart that gives you a rough yet practical and useful sense of the relationship between air resistance and altitude. 

Rough is correct, for reasons mentioned above.  Terminal velocity is dependent not only on the characteristics of the atmosphere, but on the characteristics of the craft, and can change dramatically over the course of the flight (as a case-in-point, this is how parachutes work, though I admit that I do not know whether this is how their simulation works in the game).

On 1/31/2024 at 9:26 PM, rogerawong said:

So I went looking for the terminal velocity chart for Eve, but didn't find it in the wiki, despite many old articles referencing it. Old articles got me thinking "I bet it existed at one time". And so it did. About 9-10 years ago, the Eve wiki page had a terminal velocity chart. And then someone unceremoniously and without explanation, deleted it.

I can give you an explanation.  That chart was an attempt to provide information that would be useful to players who had to work with few mods, few stock indicators, and a weird atmospheric model.  None of those things is still true.  It comes from this challenge:

If you're not familiar with the Goddard problem, the short version is that it is an efficiency problem.  The slightly longer version is that it is the question of how best to control a rocket to get the most altitude out of its propellant while taking into account the drag and atmospheric characteristics.  It's of practical use because more efficient control means getting more out of a given load of propellant, but because of the reasons mentioned above, it's very specific to a particular rocket in a particular atmosphere.  It's also only useful for a particular trajectory:  straight up.  Reaching maximum altitude is rather useless when the goal is to achieve orbit:  the principles are different and the optimum solutions have almost nothing to do with one another.

That being said, KSP is great for simulating these kinds of problems because it offers true reproducibility.  It's also terrible for getting practical results from simulating these kinds of problems because it's not simulating other real concerns such as unavoidable variations in manufacturing the rocket, changing atmospheric conditions, or a fully-accurate aerodynamic model, among other things.

However, at the time that it was made, that chart did provide some useful information.  I'll provide details in the spoiler, mainly because it discusses completely outdated game mechanics and I don't want to create confusion.

Spoiler

At the time, KSP calculated drag with a modified version of the drag equation:

F_d = 1/2 * C_d * m * ρ * v²

Where:

F_d = drag force
C_d = drag coefficient (though described in-game as a parameter maximum_drag, which may have mattered)
m = object mass
ρ = atmospheric density
v = velocity

For illustration, the real version is this:

F_d = 1/2 * C_d * A * ρ * v²

Where A is the cross-sectional area of the object facing towards the direction of travel.  The other parameters are the same.

I really don't have time to describe in detail how wacky the KSP version was, but for example, it meant that a part with twice the weight experienced twice the drag if all else was equal, and if you're not familiar with aerodynamics at all, then please understand that there is no reason why this should be true.  This led to interesting behaviours such as full propellant tanks falling at the same rate as empty ones when in an atmosphere, because terminal velocity is simply that velocity where weight equals drag.  If both depend on mass, then the mass cancels out and the terminal velocity becomes a function of only the local gravity and atmospheric density.  Because area was not part of the calculation, it also meant that rocket profile meant nothing:  there are old pictures of pan-shaped rockets flying just as well as needle-shaped ones.

There were other wacky things in the simulation, too, such as the fact that engines operating in an atmosphere would consume more propellant rather than lose thrust, and the less said about the semisolid slurry that passed for an atmosphere, the better.

Anyway, the important part is that this silly mass term made a number of calculations absurdly simplistic.  The optimum ascent profile in terms of drag is one where the drag force equals the force of gravity (mathematical proof here, but the general idea is that for the least amount of propellant expended to gain altitude, you want your engines to fight drag and gravity equally, and the velocity where that happens is equal to the terminal velocity--but in the opposite direction, of course), but when drag is calculated from the mass and ignores cross-sectional area, the masses cancel out and it all simplifies to TWR = 2 in all cases.

In such a circumstance, a terminal velocity table makes sense, especially when you're using a navball that doesn't show TWR, and velocity is the only useful indicator that you have.  Remember, this is when people were playing KSP with spreadsheets, not Kerbal Engineer.  The table isn't really meant to convey terminal velocities as the useful part, but rather to convey those velocities (and altitudes) that indicate a TWR of 2.  If you follow the table and hit those velocities at those altitudes, then you are staying close to the magic TWR = 2 and thus have an efficient ascent.

Now, drag accounts for cross-sectional area, at least somewhat, and doesn't include mass.  There are still problems with the aerodynamic model, but it is worlds better than it used to be.

However, the table is still no good.  Terminal velocity gives an efficient ascent profile for going straight up.  Once you deviate to the horizontal, it's no longer the optimal solution, but you must deviate to the horizontal to achieve orbit efficiently--as I mentioned above, the Goddard problem and orbit are two different things.  Terminal velocity also no longer correlates directly to thrust, because the area of the rocket matters now.  So do the drag coefficients of the front-facing parts:  once upon a time, people didn't use nosecones because the extra mass made the rocket less efficient both in delta-V and drag.  Now, nosecones are almost required for atmospheric flight, albeit there are exceptions.

The point is that because the drag model takes into account specific properties of the individual rocket, the terminal velocity changes with the rocket and cannot be generalised very easily.  There are some general rules that can apply (similar problems in getting to orbit from Eve breed similar solutions), but there are also new mechanics that override those rules.  For example, it is often necessary to limit thrust and speed on Eve because overheating is a problem on ascent (it's a problem for descent, too, which is why you'll see powered Eve landers), and if the overheat speed is lower than terminal speed, then you're not going to reach terminal speed.  It doesn't matter that it's efficient if it's not available to you.

That being said, I think that this is actually a very interesting piece of KSP history, because this is from 2012 and people were still trying to figure out the mechanics of the game (and for a lot of them, spaceflight in general).  Have a look at these cutting-edge graphics:

Note the lack of lights, gear, and abort action groups.  Also note that SAS was in the staging and had a finite capacity.  Note the lack of info panels and KSPedia.

Suffice it to say that there once was a time when people got to orbit by launching straight up and out of the atmosphere, then turning over and burning horizontally to make orbit ... hopefully before falling back into the atmosphere.

At the time of this challenge, the atmospheric model was something like ten times more dense than what it ought to have been.  Eventually, people settled on a hybrid approach to ascend in something (very) roughly approximating a gravity turn.  What you see here is some of the experimentation that the players performed on their own to try to figure out those optimal ascent and control profiles.

The terminal velocity table came from that.  It worked at the time, so it made it into the wiki.  After version 1.0 and the new model, someone noticed that a table of terminal velocities and altitudes no longer made sense for general use.  It's not a matter of updating the table with new values for Eve:  general values simply don't exist.

On 1/31/2024 at 9:26 PM, rogerawong said:

So, what would the equivalent of this be in modern times?  I'd like to add this back to the wiki. I found it useful for Kerbin. It would likely be helpful for Eve.

An atmospheric density table would be nice, but density varies with temperature, which varies a lot with latitude and time of day, as well as altitude, so a table probably doesn't make much sense compared to an equation, or at least an algorithm.

More pragmatically useful would be a list of good landing locations that combine high-altitude plateaus for launch with proximity to multiple biomes for research.  Eve's rotation period is nearly four (Kerbin) days, so there isn't much to be gained from landing at the equator (55 ^m/_s of eastwards rotational velocity instead of Kerbin's 175 ^m/_s), but landing four kilometres above sea level is useful to avoid both the density and the heat of Eve's lower atmosphere.

There is the idea that, given Eve's greater and more constraining challenges, the kinds of rockets needed to ascend from Eve's surface will be much more generally similar than the many and varied vehicles that come from Kerbin.  In such a situation, you can make simplifying assumptions about the nature of these rockets to get a generally applicable range of solutions to the optimal ascent problem.  However, those solutions are still dependent on the type of rocket, not on the planet itself, and so still wouldn't really fit on the wiki.

But if you wanted to make a tutorial thread, however, then that would be a fantastic idea.

Edited February 15 by Zhetaan

[rogerawong]

Zhetaan, still absorbing the breadth and depth of what you wrote, but quick note that I really appreciate the time you put into this knowledge transfer. Thank you.