thrust at vacuum

[seyss]

Hello,

I have a spacecraft in a 100-km altitude (outside atmosphere) Kerbin orbit with an Atomic Engine on it.

The lighter the spacecraft, the faster it'll accelerate using the Atomic Engine?

Please clarify.

Thanks!

Edited April 13, 2015 by seyss

[Kerbart]

Google "Newton's second law of motion"

[Taki117]

Hello,

I have a spacecraft in a 100-km altitude (outside atmosphere) Kerbin orbit with an Atomic Engine on it.

The lighter the spacecraft, the faster it'll accelerate using the Atomic Engine?

Please clarify.

Thanks!

Newtons second law in a nutshell. The lighter the object being pushed the faster it accelerates. This is also known as Thrust-to-weight ratio.

[seyss]

thanks. it accelerates so slowly I can barely tell the difference...

[Taki117]

thanks. it accelerates so slowly I can barely tell the difference...

The maximum thrust is only 60kN, I suggest lightening your load, or getting Kerbal Engineer

[GoSlash27]

Minor diversion:

Did you know that you can actually get more DV out of less efficient and lighter engines if your payload is less than 10 tonnes?

It's true!

Best,

-Slashy

[Mister Dilsby]

One newton of thrust will change the velocity of a one kilogram object by one m/s in one second.

One kilonewton (kN) of thrust changes the velocity a one ton object by one m/s in one second.

So: if you have a 300t ship with a single LV-N engine (60kN thrust), it takes 5 seconds (300t/60kN) to add 1 m/s to your velocity. Intercepting Mun from LKO requires a change in velocity (delta V) of about 900 m/s. Not accounting for the change in mass as fuel depletes, this burn will take 900m/s * 5s/(m/s) = 4500s, or 75 minutes.

Your navball and other tools will do this calc for you when you're in orbit, but I find it's easy and very useful to scribble out something like the above when I'm considering a low thrust design.

[impyre]

Minor diversion:

Did you know that you can actually get more DV out of less efficient and lighter engines if your payload is less than 10 tonnes?

It's true!

Best,

-Slashy

Actually, you *always* get more dV out of a lighter engine (assuming ISP is the same), whether you get more dV out of a lighter engine that has a lower ISP actually depends on the ISP difference, and the weight ratios involved... not really on the total craft weight. (much less the "payload" weight).

dV=g*ISP*ln(mass_wet/mass_dry)=g*ISP*ln([fuel+vessel]/[vessel])

Divided both sides by g*ISP (aka exhaust velocity) gives dV/(g*ISP)=ln([fuel+vessel]/vessel).

Rewrite as an exponent of e to yield a more intuitive function: e^(dV/[g*ISP])=(fuel+vessel)/vessel.

On the left is a standard exponential function, as the exponent's base goes to infinity the left side goes to zero and as the exponent's base goes to zero the left side goes to infinity. dV basically sets the limit here.

On the right side is a plain old ratio. 1-(1/"the ratio") gives the percentage of the vessel's mass that must be comprised of fuel to attain a given dV at a given ISP.

For the following sections, I'll use a dV of 1000 for illustrative purposes, but changing dV requirements only affects the exponential function in a linear fashion.

If you look at the function on the left side more closely and take its derivative to solve for the slope, you'll find that the slope equals -1 at an ISP around 38... higher than this and the benefit of higher ISP engines trails off very quickly. In fact, at an ISP of 100 (well below most engines) the slope is merely -.03... which will almost always favor saving weight over ISP. For reference, if the dV required is upped to 2000, the point where slope is -1 moves up to an ISP of around 66.5 and at an ISP of 100, the slope is -.16 (considerably larger than before, but still pretty marginal).

Looking at the function on the right side, you can see that decreasing the mass of the vessel will have a similar effect on dV. I've actually created a 3-d plot with ISP on one axis, the weight ratio on another axis, and dV on a third axis. It's a pretty complex function, but generally speaking... saving weight is almost always more important than anything else. If you select by weight mainly, you may short yourself a couple m/s of dV here and there... but you'll generally come out far to the better than if you select by ISP alone. If anyone wants to see what this graph looks like, I'll try to post it here.

For me, I generally simply select the lightest engine that will provide the thrust I need for the mission at hand.

- - - Updated - - -

As an additional note, you really only need to be concerned with the ISP of engines for stages that are designed to have 8000+ dV, at these dV levels (and the associated weights that go with them, the types of ISP's typically found in KSP may have a significant impact).

Edited March 19, 2015 by impyre

[tsotha]

Rewrite as an exponent of e to yield a more intuitive function: e^(dV/[g*ISP])=(fuel+vessel)/vessel.

On the left is a standard exponential function, as the exponent goes to infinity the left side goes to zero and as the exponent goes to zero the left side goes to infinity.

Eh... it's been awhile since I took a math class, but I'm pretty sure back then e^0 = 1. And the limit as the exponent approaches positive infinity is infinity.

[worir4]

Force=mass x acceleration acceleration=fore /mass

Smaller the mass the higher acceleration up to the max force of the engine.

[impyre]

Eh... it's been awhile since I took a math class, but I'm pretty sure back then e^0 = 1. And the limit as the exponent approaches positive infinity is infinity.

Eh, I misspoke. I edited in the correction, thanks for catching it. I meant to say "the base of the exponent"... as the exponent is a fraction.

[Xannari Ferrows]

The nuclear engine is the pinnacle of engine-brought bossness in Kerbal space. Always love using it... getting silly amounts of Delta-V...

[jarmund]

RE: All references to Newton's 2nd law .

While it is correct and accurate, technical and/or mathematical explanations go nicely with an everyday example: Imagine slapping a baloon with your hand; The baloon, having its feeling hurt, jumps and bobs away. Apply the same slap to a bowling ball, and the bowling ball will barely move while it silently laughs at your puny human slap, and plots revenge.

[Xannari Ferrows]

RE: All references to Newton's 2nd law .

While it is correct and accurate, technical and/or mathematical explanations go nicely with an everyday example: Imagine slapping a baloon with your hand; The baloon, having its feeling hurt, jumps and bobs away. Apply the same slap to a bowling ball, and the bowling ball will barely move while it silently laughs at your puny human slap, and plots revenge.

And my day is already made^^

[Rematog]

After reading the claims that a light weight engine (say LV-909) beats ISP (LV-N), went to my spreadsheet for Rocket design.... "Those Damn Engineers", (Gen. Joachim Peiper about the 291st Combat Engineers at the Battle of the Bulge)

For my Atomic Powered Eagle lander, (LV-N, 60kN thrust, 800 isp, 2.25t) my base design has a gross weight of 9.21t (0.66 gee accel. at full fuel) and a mass ratio of 1.7. It has a dV of 4,143 m/s (and costs $23K, has 2 ea myst goo, Sci Jr & Thermo's) Yes it's a single seater, Jeb loves it!

Substituting the LV-909 (50kN, 390 isp, 0.5t), the design now has a gross weight of 7.46t (0.68 gee accel. at full fuel w/this motor) and a mass ratio of 2.0. It's dV drops to 2,701 m/s (for a cost of $15K). This is 2/3 the dV, so clearly not better.

By the way, I have a "stretch" version with an extra FL-T400 to get a mass ratio of 2 and a dV of 5,590 m/s (base design has a single FL-T800 fuel tank).

I use drop tanks (asparagus staging) to increase the "range" to a whooping 8,653 m/s using my single LV-N. This lander can get you there (it's a belly lander using four side mounted RM 24-77 to make the final drop after the atomic motor brings the ship to a hover at about 500-1000m. I return entire lander, LV-N and all, to Kerbin and soft land near KSP to recover most of the $23k cost. Don't need but two radial chutes to do this, between lander legs and a bit of thrust.

Yes, it's a low gee planet lander (>0.3) I'm going to try it on Duna soona, have to add an extra chute (Jeb's no Damn Engineer)

- - - Updated - - -

Hmmmm..... ISP........PB-ION with 4,200 isp. 2kN.....x40 = 80 kn..... hmmmm.... Damn Engineers!

Edited March 19, 2015 by Rematog

[undercoveryankee]

After reading the claims that a light weight engine (say LV-909) beats ISP (LV-N), went to my spreadsheet for Rocket design.... "Those Damn Engineers", (Gen. Joachim Peiper about the 291st Combat Engineers at the Battle of the Bulge)

For my Atomic Powered Eagle lander, (LV-N, 60kN thrust, 800 isp, 2.25t) my base design has a gross weight of 9.21t (0.66 gee accel. at full fuel) and a mass ratio of 1.7. It has a dV of 4,143 m/s (and costs $23K, has 2 ea myst goo, Sci Jr & Thermo's) Yes it's a single seater, Jeb loves it!

Substituting the LV-909 (50kN, 390 isp, 0.5t), the design now has a gross weight of 7.46t (0.68 gee accel. at full fuel w/this motor) and a mass ratio of 2.0. It's dV drops to 2,701 m/s (for a cost of $15K). This is 2/3 the dV, so clearly not better.

By the way, I have a "stretch" version with an extra FL-T400 to get a mass ratio of 2 and a dV of 5,590 m/s (base design has a single FL-T800 fuel tank).

I use drop tanks (asparagus staging) to increase the "range" to a whooping 8,653 m/s using my single LV-N. This lander can get you there (it's a belly lander using four side mounted RM 24-77 to make the final drop after the atomic motor brings the ship to a hover at about 500-1000m. I return entire lander, LV-N and all, to Kerbin and soft land near KSP to recover most of the $23k cost. Don't need but two radial chutes to do this, between lander legs and a bit of thrust.

Yes, it's a low gee planet lander (>0.3) I'm going to try it on Duna soona, have to add an extra chute (Jeb's no Damn Engineer)

- - - Updated - - -

Hmmmm..... ISP........PB-ION with 4,200 isp. 2kN.....x40 = 80 kn..... hmmmm.... Damn Engineers!

Chemical engines start to have the advantage once the stage gets small enough that one LV-N would be more mass than you have to spend on engines. The break-even point depends on your delta-v budget and required thrust, and in most cases where a 909 would outperform a nuke, a 48-7S cluster does even better.

[impyre]

Chemical engines start to have the advantage once the stage gets small enough that one LV-N would be more mass than you have to spend on engines. The break-even point depends on your delta-v budget and required thrust, and in most cases where a 909 would outperform a nuke, a 48-7S cluster does even better.

Precisely. If you've got a really heavy vehicle (such that changing from lv-909 to nuke doesn't change percentage of mass by very much) then favoring ISP will be more important... but this isn't always the case. Neither can it be said that swapping to a lighter engine over one with better ISP is not often beneficial, because in many cases it is. The problem with the nuke is that on really heavy vessels (where it's ISP is much more important and its weight less important) it doesn't have sufficient thrust to perform in a manner that most people will find satisfactory (I am *not* doing a 20 minute burn in three kicks); however, once you get to lighter vehicles where its thrust is more acceptable, it's weight becomes a big problem (and you'll probably get better dV out of a lighter engine). There are roles for which the nuclear engine are ideal, but it isn't always the most effective/efficient for a given build.

[Rematog]

Hell yes I'd like a Rock-o-max sized atomic motor, with say a thrust of 400 kNt and ISP of say 775 sec (they wouldn't be likely to give bigger thrust without taking away a little ISP...

But, I'm making my first run (Training mission to Mun & Minmus with 3 rookies to get them to Skill 3 in one go) in the "Kondor" lander, which has 2 LV-N's and a dV of 5,561 m/s. It's full fuel acceleration is 0.36 gee (0.66 gee for the last ton of fuel).

But, it's easy to add "Moar Nukes". With 3 LV-N's I get .55 gee & 5,113 m/s (0.99 gee for last ton of fuel) and if I go to 4 LV-N's the Kondor has 0.68 gee full fuel acceleration ( 1.18 gee for last ton) with a still respectable dV of 4,672.

Still, not going to land on Eve with it, but... good for all the small worlds..... and it's a Small World after All!

hmmm... never really thought about it. But guess by stated diameter of "Small" of 1.25 meters, which a single capsule fits, and IVA view showing Kerbanaught^TM fitting into the capsule in sitting position, so give sitting height of 1 meter, (get out tape, measure my head height to floor, 80% of my full height), so Kerbals are about 1.25 meter, or just over 4' tall, little green men, then.....

It's a Kerbal World, after All!