Need to confirm some numbers...

[GoSlash27]

I'm working on a spreadsheet to plan interplanetary missions and need to verify that the numbers I'm getting are correct. Could you folks please look this over and make sure it's close to correct?

Kerbin to Duna:

A Hohmann transfer window opens once every 909 days, 3 hrs.

Duna should be 44° prograde Kerbin at injection burn.

Injection burn from LKO is 1,078 m/sec

Elapsed time of Hohmann transfer is 302 days.

Kerbin should be 75° prograde Duna upon arrival

Circularization burn at LDO is 616 m/sec (if I don't aerobrake).

Kerbin should be 75° retrograde Duna at departure.

Duration of stay to Hohmann transfer window home is 529 days 4 hrs

Injection burn home is 616 m/sec from LDO.

Elapsed time of Hohmann transfer home is another 302 days.

Retroburn at LKO is 1,078 m/sec (if I don't aerobrake).

Total mission duration 1,133 days, 4 hrs.

Kerbin to Eve:

A Hohmann transfer window opens once every 680 days.

Eve should be 54° retrograde Kerbin at injection burn.

Injection burn from LKO is 1,043 m/sec

Elapsed time of Hohmann transfer is 170 days 2 hrs.

Kerbin should be 36° retrograde Eve upon arrival

Circularization burn at LEO is 1,402 m/sec (if I don't aerobrake).

Kerbin should be 36° prograde Eve at departure.

Duration of stay to Hohmann transfer window home is 543 days 4 hours.

Injection burn home is 1,402 m/sec from LEO.

Elapsed time of Hohmann transfer home is another 170 days 2 hrs.

Retroburn at LKO is 1,043 m/sec (if I don't aerobrake).

Total mission duration 714 days, 1 hour.

Thanks,

-Slashy

Edited October 17, 2015 by GoSlash27

[Gaarst]

While these values seem correct overall, you don't need that kind precision. The numbers for two different launch windows will always be slightly different, but if you do your burn and corrections correctly, you should not spend over a few tens m/s dV more than planned.

You could also use Alexmoon and Olex's Window Planners; even if you wish to get the values yourself, they can be useful to check them. Alexmoon's is more detailed, but Olex's shows angles between planets.

[FancyMouse]

^^ this.

I almost never do exact Hohmann transfer for interplanetary. Just 100~200m/s more dV and I can choose my departure/arrival date from a much, much wider range. I also suggest studying the porkchop graph from transfer planners. If you care about arrival time, make sure you scale x and y axes identically. You'll find something interesting for sure.

[GoSlash27]

Gaarst and FancyMouse,

Thanks and I appreciate that, but I'm just looking for confirmation of the model or (more importantly) glaring inaccuracies. Especially the phase angles and durations.

The idea is that this model is supposed to be used for mission planning for ship design purposes.

I need to make sure it's acceptable so ships designed with it will perform as expected. Either that, or I need to know that it's incorrect so I'm not designing stages that can't perform in the actual mission.

Thanks,

-Slashy

[FancyMouse]

OK we thought you're just interested in the number itself, and that's why we said no need for this precision. Since the intention is design-related I take a closer look and here's my comment.

1. Delta-V. No problem for Duna. Eve might have a problem - because of its inclination, the optimal delta-V for each window has a non-trivial variation. Transfer window planner shows a variation up to 300m/s between different windows. You might want to double check that.

2. Mission duration - not too big a problem for Duna or Eve, but for other planets where the orbit period differ a lot (e.g. Jool), there might be a non-optimal transfer that costs just extra 200m/s but catch up one or even more earlier returning transfer windows.

[mdkendall]

Kerbin to Duna:

A Hohmann transfer window opens once every 909 days, 3 hrs.

Duna should be 44° prograde Kerbin at injection burn.

Injection burn from LKO is 1,078 m/sec

I think your model must use the simplifying assumption that the orbits are circular. I believe this same assumption is made by Kerbal Alarm Clock if you choose Formula Based calculation of windows, and by Olex's online window planner. This gives you a fixed time between windows based on an average value for the correct phase angle.

The orbits of the planets are actually slightly elliptical, so the optimum phase angle (and hence also time between windows) varies slightly from window to window. I know of no closed-form solution that will produce the optimum phase angles, but it is possible to solve numerically. I know this was done by Matti Eiden in ksp-toolkit and the resulting table of values for the first 100 years is I think what Kerbal Alarm Clock uses if you select Modeled Data for the calculation type.

[FancyMouse]

In fact, closed form exists if only one burn is executed. The math background for it is Lambert solver, the same thing that all those transfer window planners use at their core. A Lambert solver can tell, given the data of the gravity source (Sun in the case of interplanetary), a departure location (with time) and an arrival location (also with time), what is the orbit that carries you from departure to arrival. Input location can be derived from departure planet/date and arrival planet/date. Once the solar orbit is computed, it then just needs to compute the burn needed for ejecting to/inserting from the solar orbit.

Although - it has too many intermediate steps so no one really bother to actually write the full expression out. But it does have a closed form and the computation can be done in O(1) time. Otherwise the planner can't ever plot the porkchop this fast.

[GoSlash27]

I think your model must use the simplifying assumption that the orbits are circular. I believe this same assumption is made by Kerbal Alarm Clock if you choose Formula Based calculation of windows, and by Olex's online window planner. This gives you a fixed time between windows based on an average value for the correct phase angle.

MKendall,

Yeah, that's what I did. Perhaps I need to also work out a worst case DV to account for eccentricity and inclination...

A precise time- based model wouldn't really work for what I'm trying to do.

*edit* it looks like my prediction of transfer window intervals is completely wrong. The table you linked has much shorter intervals. *'nuther edit* these tables are in Earth days, not Kerbin days. Looks like it's okay after all...

Thanks,

-Slashy

Edited October 17, 2015 by GoSlash27

[FancyMouse]

*edit* it looks like my prediction of transfer window intervals is completely wrong. The table you linked has much shorter intervals.

Keep in mind some of those are old calculations based on Earth days (when Kerbin day wasn't a thing). You need to multiply by 4 to get modern Kerbin days.

[GoSlash27]

Keep in mind some of those are old calculations based on Earth days (when Kerbin day wasn't a thing). You need to multiply by 4 to get modern Kerbin days.

FancyMouse,

Thanks, I had just noticed that myself

Best,

-Slashy

[OhioBob]

Kerbin to Duna:

A Hohmann transfer window opens once every 909 days, 3 hrs.

Duna should be 44° prograde Kerbin at injection burn.

Injection burn from LKO is 1,078 m/sec

Elapsed time of Hohmann transfer is 302 days.

Kerbin should be 75° prograde Duna upon arrival

Circularization burn at LDO is 616 m/sec (if I don't aerobrake).

Kerbin should be 75° retrograde Duna at departure.

Duration of stay to Hohmann transfer window home is 529 days 4 hrs

Injection burn home is 616 m/sec from LDO.

Elapsed time of Hohmann transfer home is another 302 days.

Retroburn at LKO is 1,078 m/sec (if I don't aerobrake).

Total mission duration 1,133 days, 4 hrs.

Kerbin to Eve:

A Hohmann transfer window opens once every 680 days.

Eve should be 54° retrograde Kerbin at injection burn.

Injection burn from LKO is 1,043 m/sec

Elapsed time of Hohmann transfer is 170 days 2 hrs.

Kerbin should be 36° retrograde Eve upon arrival

Circularization burn at LEO is 1,402 m/sec (if I don't aerobrake).

Kerbin should be 36° prograde Eve at departure.

Duration of stay to Hohmann transfer window home is 543 days 4 hours.

Injection burn home is 1,402 m/sec from LEO.

Elapsed time of Hohmann transfer home is another 170 days 2 hrs.

Retroburn at LKO is 1,043 m/sec (if I don't aerobrake).

Total mission duration 714 days, 1 hour.

Slashy,

I ran through all the calculations myself and I get the exact same numbers as you, with one exception. For the total duration of the Eve mission, it looks like you added only one of the Hohmann transfer times. I get a total mission duration of 884 days 2½ hours.

Of course the ÃŽâ€v is going to depend on the altitudes of the orbits. For the ÃŽâ€v at Kerbin, I concur with your numbers when I set the orbit to 70 km (i.e. the top of the atmosphere). At Duna and Eve I get slightly higher ÃŽâ€v numbers when I set the orbit equal to the atmosphere height – 618 m/s and 1410 m/s respectively. To get your ÃŽâ€v numbers, I had to make the orbits 58 km and 100 km (± depending on rounding). I'm not sure what you used.

[GoSlash27]

Ohio Bob,

If your numbers line up, then that's *definitely* confirmation.

Yes, I used 60km for Duna and 100 km for Eve.

This confirms that the model is working properly.

Thanks,

-Slashy

Edited October 17, 2015 by GoSlash27