How to calculate dV for other planets?

[fozba]

Hello guys. I am an amateur Kerbonaut and I want to start to calculate dV by hand since it is so nice and fancy to do. When I looked up, I came across this formula:

dV = Isp * gravity * ln(m0 - mf)

Everything is fine, but when I utilize this equation and check the results with VAB, I get HUGE differences for other planets. Currently I am trying to visit Eve and comeback. My lander should have God knows how much dV. So, for a stage (mid), I put:

Rockomax 32 (x1)

FL-A215(x1)

FL-A151S(x1)

Skipper

The upper payload is 4.090t. Therefore, according to the equation:

Isp = 280

Gravity = 16.7 

m0 = 32.740t

mf = 9.940t

and dV should be 280 * 16.7 * ln(32.74/9.94)= 5579.9 m/s but VAB says it is 666m/s. What I am doing wrong?

Good luck in your space journeys  

[OHara]

You are correct to be surprised at the strength of gravity making a difference.

The 'gravity' factor is due to convention about how rocket engines are specified, and is the gravity at the surface of Earth.

In Physics, impulse would be in [Newtons×seconds] and specific impulse would be the impulse per mass of the propellant, in [Newtons×seconds/kg = m/s].  In rocket engineering, traditionally we divide by the weight of the propellant instead of the mass, which depends on the force of gravity where the rocket designers live.  Under that tradition, we get a specific impulse in units of seconds, and have to multiply back in the value of 'gravity' at the location of the designers in order to use the number in a physics equation.

KSP uses the traditional convention; then people can compare I_sp in these units to real-world engines that they know.

[Rhomphaia]

Another thing to note is that the listed value for I_sp is at sea level on Kerbin, as pressure increases I_sp decreases so at Eves surface the value for the skipper will be much lower than listed.

[Streetwind]

1 hour ago, fozba said:

When I looked up, I came across this formula:

dV = Isp * gravity * ln(m0 - mf)

There is a very subtle mistake in there, which is not easy to spot for someone new to the world of physics.

The notation is not just a "g" for "gravity". It is very specifically "g0", or written out, "standard gravity". That means this is not actually a variable where you put whatever gravity is for the place you are examining. No, it is a constant. Simply a number with a fixed value. It has the same value anywhere - the average value of the force of gravity at the surface of the planet Earth.

You see, the so-called Tsiolkovski rocket equation originally read: dV = Ve * ln(m0/m1). Where "Ve" is "effective exhaust velocity" - describing the speed at which the jet exits the engine.

Now, enter a bunch of rocket scientists. Some live in Europe, where they work in metric units. Some live in the US, where they use imperial units. They meet and want to compare notes. And suddenly, they notice that some of them measure this exhaust velocity in feet per second, and others measure it in meters per second. Confusion ensues. If only there was some way of measuring this that works out to be the same in both of these systems!

So they decided to split off the offending component that has the non-uniform unit into a known, well-defined constant, leaving all the variables to have units that are identical in both metric and imperial systems. By dividing a speed (something per second) by an acceleration (something per second per second), only seconds are left as a unit. This is specific impulse. It is a measurement artificially created by math in order to unify two disparate unit systems that (thankfully) could both agree on the definition of a second.

And the acceleration they chose to divide by? Standard gravity. Both sides knew this number. It is different in each measuring system. But if you have an effective exhaust velocity in imperial units, and you divide it by standard gravity in imperial units, you get specific impulse. If you have an effective exhaust velocity in metric units, and divide it by standard gravity in metric units, you again get specific impulse. Problem solved!

Thus, Ve * ln(m0/m1) = Isp * g0 * ln(m0/m1).

As KSP usually works in metric units, your go-to value for g0 is 9.80665 m/s².

Edited June 15, 2020 by Streetwind

[fozba]

Thank you for very detailed answers. What a great community!

I totally understood the concept now. However, then how people can determine certain dV s for various interplanetary actions? For example, people say that "You need xxx m/s dV to escape Duna". Is this dV given in terms of vacuum? Or another way to ask, when I calculate if my rocket meets the dV requirement, do I use vacuum constants&parameters?

Again, thank you so much for brief explanations.

Edited June 15, 2020 by fozba
wrong word :)

[FleshJeb]

@fozba Here's a portal into the rabbit hole: https://en.wikipedia.org/wiki/Vis-viva_equation

Basically, you subtract your starting state from your desired end state. Even sitting on a planet, you're in an orbit--It's just been paused by the ground.

dV is almost always in vacuum. There's some rounding and error factor built into the community dV maps.

Edited June 16, 2020 by FleshJeb

[Streetwind]

Yeah, vacuum dV is the community standard, as it eliminates the differences between individual environments, which allows you to plan ahead with ease. This of course took some experimentation by players, to figure out how much vacuum dV is lost to environmental factors during launches. For example, orbital speed in low Kerbin orbit is about 2200 m/s, and typical dV requirements for launching into LKO are 3400-3500 m/s. That means between 1200 and 1300 m/s are typically lost due to lower engine efficiency under atmospheric pressure, aerodynamic drag, gravity drag, and steering losses. And that had to be determined empirically - you cannot really calculate it by hand. Even the vis-viva equation assumes vacuum only.

Edited June 16, 2020 by Streetwind

[king of nowhere]

even with the error for gravity, though, the difference between the calculated 5600 m/s and the VAB nominal 666 is way too big. using the correct value the answer should be around 3000 m/s. which, by rule of thumb, is what i would expect from such a setup anyway. two thirds of this rocket is fuel, it ought to be much more than 5600 m/s.

so, there is still some problem here. probably with the rocket, maybe there is no fuel transfer somewhere or something like that.

 

by the way, here i see another mention of delta-V maps. So far I just started to dabble in outer planets exploration, and i don't really know how much fuel i need to get to the other planets (my solution is just to pack a lot of deltaV in the transfer stage). it would be useful. where do i find such maps?

[Streetwind]

1 hour ago, king of nowhere said:

even with the error for gravity, though, the difference between the calculated 5600 m/s and the VAB nominal 666 is way too big. using the correct value the answer should be around 3000 m/s. which, by rule of thumb, is what i would expect from such a setup anyway. two thirds of this rocket is fuel, it ought to be much more than 5600 m/s.

so, there is still some problem here. probably with the rocket, maybe there is no fuel transfer somewhere or something like that.

Unlikely something is wrong with the rocket, as it's just a single stage with a single engine, that's pretty hard to screw up. More likely is that he selected Eve in the dV comparison tool and got the sea level atmospheric dV for Eve, which is extremely low because of how much the thick atmosphere chokes the Skipper engine (which is a sustainer engine for lower pressure environments to begin with). I'd believe a result of 600-odd m/s for this setup in such a case.

 

1 hour ago, king of nowhere said:

by the way, here i see another mention of delta-V maps. So far I just started to dabble in outer planets exploration, and i don't really know how much fuel i need to get to the other planets (my solution is just to pack a lot of deltaV in the transfer stage). it would be useful. where do i find such maps?

To read it, simply start from Kerbin and move node by node towards your intended target, adding all numbers you come across, except those where you intend to aerobrake. It works backwards that way, too - but note that aerobraking arrows are unidirectional. However, this map does not work for trips from one non-Kerbin body to another, and it does not tell you transfer windows. For those, you're better served with a proper porkchop plotter.

[Zhetaan]

4 hours ago, king of nowhere said:

by the way, here i see another mention of delta-V maps. So far I just started to dabble in outer planets exploration, and i don't really know how much fuel i need to get to the other planets (my solution is just to pack a lot of deltaV in the transfer stage). it would be useful. where do i find such maps?

It's in Tutorials:

4 hours ago, king of nowhere said:

even with the error for gravity, though, the difference between the calculated 5600 m/s and the VAB nominal 666 is way too big. using the correct value the answer should be around 3000 m/s. which, by rule of thumb, is what i would expect from such a setup anyway. two thirds of this rocket is fuel, it ought to be much more than 5600 m/s.

so, there is still some problem here. probably with the rocket, maybe there is no fuel transfer somewhere or something like that.

The problem is the location.  With the correct value for g₀, the delta-V for this rocket is 3273.2 m/s.  With the correct values for both g₀ and I_sp, the delta-V is 3740.7 m/s.

On Eve's surface, the specific impulse is about 57 seconds, and the delta-V is thus 666 m/s.  Don't forget that Eve's sea-level pressure is five atmospheres, not one.

I guessed 60 seconds from the curve in the part.cfg, (and that yields 701 m/s), but the important part is that the Skipper has no thrust at just six atmospheres.  Eve is pushing past the limits of sanity for the Skipper's service range.

@fozba:  I strongly suggest that you choose a different engine in addition to redesigning your rocket.  Alternatively, land on a mountain; the pressure drops quickly with altitude.  If this is a second stage for a sea-level lifter, then I still suggest a redesign because the Skipper is better-suited to third-stage or even vacuum operations at Eve.  Eve is a challenge planet and that is something that you will absolutely come to respect, one way or another.

 

Edit:  Ninja'd by @Streetwind

 

Edited June 16, 2020 by Zhetaan

[king of nowhere]

i always considered the skipper a good atmosphere engine. its isp is only a few % lower than others, and there is nothing else suitable in its weight category, if the "reliable" is too small but the "vector" or "mainsail" are too big. didn't account that the efficiency drop in eve would be much worse. doesn't leave many engines viable

[Grogs]

1 hour ago, king of nowhere said:

i always considered the skipper a good atmosphere engine. its isp is only a few % lower than others, and there is nothing else suitable in its weight category, if the "reliable" is too small but the "vector" or "mainsail" are too big. didn't account that the efficiency drop in eve would be much worse. doesn't leave many engines viable

That's exactly right. There are only a few engines capable of producing enough thrust at Eve sea level. The Vector (Mammoth)  and Dart are the kings, the Mainsail, Twin Boar, and Thud might work but not very efficiently, and most of the others won't even get you off the ground. The Eve atmosphere doesn't drop to a pressure less than Kerbin sea level until 15,000 meters so you need one of those three at least that far. I would try to build a design that used vectors/darts to at least 15,000 meters, then you can go to a good Kerbin-ASL rated engine for a second stage and then a good vacuum engine like a Terrier above 30-40,000 meters.

Also, note that you can't really fly a gravity turn on Eve the way you do on Kerbin. If you do, the ship will heat up too fast in the thick atmosphere. The most common launch trajectory I've seen is to go straight up until about 20,000 meters and then start gradually turning. Watch your Ap and throttle down once it gets above say 100 km, then when you get through most of the atmosphere you can point the ship horizontal and burn until you achieve orbit.

Edit: See this post for a table on how the various engines work at Eve sea level:

 

Edited June 16, 2020 by Grogs
Fixed engine list

[Zhetaan]

2 hours ago, king of nowhere said:

i always considered the skipper a good atmosphere engine. its isp is only a few % lower than others, and there is nothing else suitable in its weight category, if the "reliable" is too small but the "vector" or "mainsail" are too big.

That is the exact definition of a sustainer engine, as @Streetwind mentioned above.  It's best suited to upper atmosphere and vacuum operations where there's no need for a monster like the Mammoth but where you'd like to have more thrust than a Poodle.  You're right in that it's really the only thing in its service region:  there are seven LFO engines with thrust under 100 kN, six engines with thrust between 100 and 250 kN, five with thrust at or over 1000 kN, but between 250 and 1000 kN, there is exactly one:  the Skipper.

On the other hand, the Thumper and the Kickback also operate in this thrust region, which suggests a potential pairing with SRBs for rockets too heavy for Skippers alone, but too light to justify Mainsails.  There's also the option of clustering, which may be worth a look anyway since there is a size change when going from Reliants and Swivels to Skippers and Mainsails:  two Reliants and a Swivel offer comparable performance to one Skipper, but the Skipper offers much less mass.  Also, the lack of sustainer engines in general may have more to do with Kerbin's toylike size than any other particular oversight on the developers' part; you can reach orbit quickly enough that there's a reasonable argument against the need for a variety of upper-atmosphere engines.  I will look at Real Solar system and Realism Overhaul to see what solutions they have.

On the gripping hand, one of the Skipper's best qualities is its price.  At 5300 Funds, it provides more than half of a Vector's thrust for less than a third of the Vector's cost, and for very comparable I_sp values.

2 hours ago, Grogs said:

Edit: See this post for a table on how the various engines work at Eve sea level:

[Table]

I was wondering where that was; I knew that I'd answered this question before.  Anyway, yes, the Skipper's Eve ASL specific impulse is 57.4 seconds.

... Also, I have achieved inception.

Edited June 16, 2020 by Zhetaan

[Streetwind]

2 hours ago, Zhetaan said:

but between 250 and 1000 kN, there is exactly one:  the Skipper.

...Two, actually, assuming you have Making History The Skiff is a 2.5m sustainer putting out 300 kN at an Isp of 265s/330s. It is, admittedly, rather similar to the Poodle, and in many cases an inferior choice due to lacking 25s of specific impulse once out of the atmosphere. But it does feature a much better TWR (19.1 versus the Poodle's 14.6) and simply that bit more thrust - both in absolute terms, as well as what you get out of it in atmosphere. I actually used it just the other day when the second stage of my Mun rocket was a little too anemic for a smooth ascent with just a Poodle. Also, in contrast to the Poodle, the Skiff can be toggled to a 1.875m profile, where it then acts basically like the Skipper does for 2.5m.

And finally, of course, it's a kerbalified J-2 for replica building. I suppose that's its main raison d'etre....

Edited June 16, 2020 by Streetwind