Long Duration Burns and ∆v

[Clipperride]

I'm used to my trips to Minmus from LKO costing something over 800m/s in ∆v. I was somewhat surprised when testing out different engine options on my Space Plane and found the following;

After reaching a 99x101km orbit, I set the SAS to hold prograde and fired up just the nuclear engines. I noted down my orbital velocity on starting the engines and ran them until fuel depletion and noted the final velocity. Taking the final from the starting velocity gave a difference of 588m/s (indicated speed went from 2234m/s to 2822m/ss) When I switched to the map, I was surprised to see my trajectory left Kerbins SOI. No sling shot from the Mun or Minmus was involved. I was so surprised I've repeated the rest a couple of times with the same result. How is this possible?

Being a low TWR vechile, the burn took ~7 or 8 minutes in total. I've obviously made an error in my calculations somewhere, but where? Please help as it's driving me nuts!

Edited September 21, 2015 by Clipperride

[UmbralRaptor]

Could we see the vehicle? Notably fuel state before/after the burn would be helpful for checking on how much ÃŽâ€V was actually expended.

Keep in mind that given the long burn (8 minutes is a quarter of an orbit at 100 km), the craft will drift upwards significantly (trading kinetic for potential energy). The 2822 m/s you mention is escape speed at 287 km altitude, so was that where you were upon switching off the engines?

[mhoram]

You measured the two velocities at different altitudes, you you can not simply substract them.

At the higher altitude (end of the burn) you are traveling slower than at the Periapsis which is normal for Kepler orbits.

So you burned more than the 588 m/s dV.

And as a small side note: in a 99x101 km orbit your minimal velocity (at apoapsis) is 2242 m/s which is higher than your measurement of 2234 m/s.

[UnusualAttitude]

In low Kerbin orbit, you are still well within Kerbin's gravity well. As you expend fuel to accelerate into a higher orbit, or escape, gravity is still pulling you back all the time. So your final speed will be very different from your intitial velocity + dV expended. This will be more noticeable with low TWR vehicles: since the burn lasts longer, gravity has more time to affect your final velocity.

Do the same test and keep watching your orbital velocity after the end of the burn: it will continue to decrease until you reach the limit of Kerbin's SOI.

[Clipperride]

Thank you for the explanations. I'll repeat my experiment later to see how much the altitude changes over the burn. I know its quite a lot as Kerbin looked a fair bit smaller at the end of the burn! I'll also get a screenshot of the current set up UmbralRaptor.

Mhoram - It's possible I transposed the last two digits when making notes and my original velocity was 2243m/s rather than 2234m/s.

UnusualAttitude - Now you explain it, it's obvious from my trips to the Mun and Minmus. Thinking about it late last night, it was far from obvious

Which raises the next question; How can you measure the ∆v of a craft with low TWR in stock KSP (I fear the answer involves a lot of Maths)?

[UmbralRaptor]

Which raises the next question; How can you measure the ∆v of a craft with low TWR in stock KSP (I fear the answer involves a lot of Maths)?

Onboard ÃŽâ€V for a stage is always 9.80665*Isp*ln(M_initial/M_final). The amount needed for a given burn will vary somewhat if you can't usefully use impulsive approximations. I think that kicks you out into numeric solution territory, but one might be able to simply throw a correction factor at it and get good enough values.

[UnusualAttitude]

Which raises the next question; How can you measure the ∆v of a craft with low TWR in stock KSP (I fear the answer involves a lot of Maths)?

I would add that, as you can see from the rocket equation, TWR and delta V are unrelated. However, a craft with a very low TWR will not be able to take full advantage of the Oberth Effect (https://en.wikipedia.org/wiki/Oberth_effect), so you won't get as much bang for your... delta V. Remember that when you create a maneuver node in KSP, it assumes an instant change in velocity at the point in your orbit you set the node at, which is of course not actually possible. If your burn lasts more than a couple of minutes, the difference will be noticeable.

To summarize: you won't get as far in a craft that has 800m/s dV and a TWR of 0.1 than with a craft that has 800m/s a TWR of 1. There may be a way to calculate just how much dV is wasted by having a low TWR, but it is probably very complicated .

Sorry if this is obvious to you, but it sounds like what you were asking.

Regards, UA.

[Chaos_Klaus]

To summarize: you won't get as far in a craft that has 800m/s dV and a TWR of 0.1 than with a craft that has 800m/s a TWR of 1. There may be a way to calculate just how much dV is wasted by having a low TWR, but it is probably very complicated .

While I know what you mean, I have to point out that this conclusion is phrased completely wrong. Delta V is independant of TWR! The only reason why low TWR vehicles use up more delta v is due to the oberth effect. If there was no gravitational well involved, low TWR vehicles would use just the same amount of delta v as high TWR vehicles. Oberth makes the difference.

But there is something else to consider. Although a high TWR craft will make better use of the Oberth effect and therefor will use up less delta v, it might not be the most efficient craft. High TWR usually requires heavier and less fuel efficient engines. They will need more fuel to get the same delta v budget. This means you need to bring more fuel and more engine. Both of which means more weight, which in turn means a bigger launcher.

So, the conclusion is. Build very light upperstages to keep your lower stages small. If you have to sacrifice TWR to do that, so be it. It's not thaaaat important.

[UnusualAttitude]

From my post above: "TWR and delta V are unrelated. However, a craft with a very low TWR will not be able to take full advantage of the Oberth Effect".

I have to point out that this conclusion is phrased completely wrong. Delta V is independant of TWR! The only reason why low TWR vehicles use up more delta v is due to the oberth effect. If there was no gravitational well involved, low TWR vehicles would use just the same amount of delta v as high TWR vehicles. Oberth makes the difference.

C'mon man, read posts carefully before saying they are completely wrong

To clarify my completely wrong conclusion: try doing a transfer to Mun from LKO in a single burn with a TWR of 0.1 and 800m/s dV. While it might be possible, it certainly won't be practical.

Edited September 21, 2015 by UnusualAttitude

[Clipperride]

As promises, here are the numbers from another test flight of my STTO experimental creation.

Mass = 112.2t including the 8.8t payload. Only engines used after reaching orbit were 2 x LV-N Atomic Rocket Motors

Prior to Burn

Initial Orbit: 109,187m x 107,448m (relative to Kerbin)

LF / OX: 1968 / 1365

Burn started at: Alt 107,800m, Velocity 2234m/s, Time: T+ 20' 12''

Figures at engine cut off:

Final Orbit: 15,652,209,304m x 11,572,366,920m (relative to Sun)

LF / OX: 0 / 1339

Burn finished at: Alt 545,131m, Velocity 2821m/s, Time T+ 30' 51''

Notes:

The difference in OX is due to vernier engines firing due to holding prograde heading.

The picture showing the "Work GDU Test III b 2" (I was frustrated when I chose the original names and its been through quite a few iterations!) was taken on a different flight so the figures won't match what's found above. The final two pictures were taken on the above flight. As you can see I underestimated the burn time. It was actually 10 minutes 39 seconds.

I guess the only way to use such a craft is by making multiple, short burns each time I pass periapsis to raise the apoapsis in stages. Although I'm not sure how that translates into a Mun or Minmus encounter? Also, what is the longest practical burn time for such a Space Plane? I'm guessing around 1 minute starting 30 seconds before periapsis/maneuvere node?

Thanks for your help

Now for the pictures........

Rear view of plane

View after burn

Map after burn

Edited September 21, 2015 by Clipperride
I can't spot errors until I hit Save

[UnusualAttitude]

Yes, your initial TWR is about 0.11, so you will have to raise your apoapsis gradually. How you do this depends on how much dV you have to begin with, which I can't really tell from your screenshots.

I would kick up my apoapsis to 2,000 or 3,000km in three or four short burns, then wait for Mun to come round (place your node close to where the Mun rises over the horizon) and do a final longer burn to get as close as possible to an encounter. You will probably have to make an additional course correction after this last burn to nail the Mun's SOI.

For Minmus, remember that you can make significant course changes to get the encounter later on (out beyond the Mun's orbit) for a reasonable cost in fuel.

If you are intent on flying low TWR ships like this one, I would definitely recommend an informational mod such as KER to calculate TWR, dV, etc.

Good luck!

[Clipperride]

Cheers for all your answers.

It's not so much a desire for very low TWR craft as my experimenting with different combinations of engines. I've only be playing KSP a few months and I've been concentrating on rockets. As I'm a bit of an Apollo buff, I've read a lot about the Space race which stood me in good sted in the VAB. The space plane hanger, on the other hand has been a trial. Thanks to these forums I managed to get a Mk2 and now Mk3 based plane into space and now I'm looking for that "perfect combination" of propulsion

[Laie]

Which raises the next question; How can you measure the ∆v of a craft with low TWR in stock KSP (I fear the answer involves a lot of Maths)?

Insufficient data for a meaningful answer. It depends on so many things that you need to state the question much more precisely before you can even begin to tackle it with maths. But here's a few ballpark figures from experience, in the hope that they might be useful:

Maneuver nodes are magic, they update and compensate for errors as you go. This works well until it breaks down.The extra expenditure for a single maneuver depends mostly on how much your trajectory bends while you are doing the burn. In a Kerbin-like orbit around the sun, burns may last a few hours and the extra expenditure for low TWR will be barely measureable. In LKO, a five-minute burn means only about 1-2% extra dV, but fifteen minutes will cost like 15% extra (and you'll need a sizeable correction after the maneuver, easily another 5%). If your departure burn takes even longer, this will quickly become ruinous/impossible.

Someone has posted a "long burn calculator" a while ago. It could only deal with prograde burns (iow, you had to fix your inclination before the burn), the actual maneuver was "lock sas to prograde, start engines at just the right time, prepare dinner". With that approach, I could go to Jool on 0.1g at an extra dV expenditure of only 10%, including the correction burn.

[OhioBob]

The following is something I posted months ago that I think is relevant to the discussion here. This was done prior to v1.0, though that really shouldn't matter.

I just performed an experiment in which I simulated an interplanetary injection from low Kerbin orbit using different thrust-to-weight ratios. I assumed starting from a 70 km circular orbit and maintained the thrust vector pointed in the prograde direction throughout the duration of the burn. I stopped the burn when the hyperbolic excess velocity reached 1,000 m/s, which is about the median for a trip to Duna or Eve (a little less for Duna and a little more for Eve). I assumed a specific impulse of 390 seconds, though Isp really doesn't make that much difference. Below are the results:

[TABLE=width: 300]

[TR]

[TD=align: center]TWR[/TD]

[TD=align: center]ÃŽâ€v (m/s)[/TD]

[/TR]

[TR]

[TD=align: center]∞[/TD]

[TD=align: center]1101.5[/TD]

[/TR]

[TR]

[TD=align: center]2.00[/TD]

[TD=align: center]1102.6[/TD]

[/TR]

[TR]

[TD=align: center]1.50[/TD]

[TD=align: center]1103.2[/TD]

[/TR]

[TR]

[TD=align: center]1.00[/TD]

[TD=align: center]1104.9[/TD]

[/TR]

[TR]

[TD=align: center]0.75[/TD]

[TD=align: center]1107.3[/TD]

[/TR]

[TR]

[TD=align: center]0.50[/TD]

[TD=align: center]1113.8[/TD]

[/TR]

[TR]

[TD=align: center]0.30[/TD]

[TD=align: center]1133.6[/TD]

[/TR]

[TR]

[TD=align: center]0.20[/TD]

[TD=align: center]1167.9[/TD]

[/TR]

[TR]

[TD=align: center]0.15[/TD]

[TD=align: center]1209.2[/TD]

[/TR]

[TR]

[TD=align: center]0.10[/TD]

[TD=align: center]1301.7[/TD]

[/TR]

[/TABLE]

A TWR of ∞ is, of course, a theoretical instantaneous burn. As you can see, for TWRs greater than about 0.50, the losses are very small. However, for extremely small TWRs, the losses start to become significant.

[Clipperride]

That's make for interesting reading thanks OhioBob. I'm enjoying experimenting with different configurations (with a quick trip to the Mun by way of a change last night )

A couple more pictures of two different engine combinations I'm currently using.

Edited September 22, 2015 by Clipperride

[Yakky]

I guess the only way to use such a craft is by making multiple, short burns each time I pass periapsis to raise the apoapsis in stages. Although I'm not sure how that translates into a Mun or Minmus encounter? Also, what is the longest practical burn time for such a Space Plane? I'm guessing around 1 minute starting 30 seconds before periapsis/maneuvere node?

Well, maybe not the "only way", but definitely the most efficient way. It is always most efficient to do your burn as low as possible in the gravity well when you are moving fastest. This is the Oberth Effect. Consequently, short repeated burns near periapsis are the way to go when using low-TWR craft. The price you pay is that it's that more tedious to complete a multi-lap burn than a single high-thrust burn.

Roughly speaking, I think your estimate of 1:30 burn time per lap is a reasonable one, although other people will have their own views. Your burn efficiency is a function of orbital velocity, so one way to judge how far out to extend your burns is to note how your speed changes (when coasting) as you approach periapsis, and decide for yourself how much inefficiency you can tolerate. To a first approximation, the Oberth Effect says that if you are traveling only 90% as fast (for example) as at periapsis, burning at that point is only 90% as efficient as would be a burn at periapsis.

But there's another inefficiency as well: assuming you are using maneuver nodes and pointing at them during your entire burn, your maneuver noed won't always be aligned with your prograde marker. This means you have to add in the cosine losses from burning in a direction that is not totally aligned with your prograde direction all the time. This obviously gets more severe the farther away you get from periapsis.

If you want to use repeated short periapsis burns for a Mun/Minmus encounter, you need to plan how many orbital laps this process is going to take you, and orient your apoapsis to take that into account. This adds to the complexity and tedium, but it isn't difficult as long as you don't mind a little math.

Edited September 22, 2015 by Yakky