Author Topic: Lunar Liftoff Delta V Calculations Q&A  (Read 10764 times)

Offline joertexas

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Lunar Liftoff Delta V Calculations Q&A
« on: 06/20/2012 04:18 am »
I've noticed that most references state that a lunar liftoff requires somewhere around 1.8 - 2.1 km/s Dv to achieve orbit. As an example:

http://en.wikipedia.org/wiki/Delta-v_budget#Launch.2Flanding

However, I think that calculation assumes an accel of somewhere around 15 m/s2. Lower thrust liftoffs would consume much more fuel due to gravity drag, making the Dv more like 2.5 - 2.6 km/s.

Is this correct, or am I missing something?

Thanks.

JR

Offline sdsds

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Re: Lunar Liftoff Delta V Calculations Q&A
« Reply #1 on: 06/20/2012 06:28 am »
Most sources are probably implicitly or explicitly covering the Apollo lunar ascents. For those, this looks reasonably authoritative:
http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19790072468_1979072468.pdf

It asserts for Apollo 14 the theoretical minimum would have been 6045.3 fps (1842.6 m/s) over ~430 seconds of flight time.

As regards your question: yes, fighting gravity will eat into your performance. How much depends on the pitch angle required during the ascent. As a chart in the paper shows, after an 10 second vertical ascent the Apollo lunar module quickly pitched over ~50 degrees and by the end of its burn was essentially horizontal.
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Offline joertexas

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Re: Lunar Liftoff Delta V Calculations Q&A
« Reply #2 on: 06/20/2012 05:11 pm »
Thanks. So, the quoted Delta V figures are correct, assuming that the vehicle in question can fly approximately the same profile as the Apollo module, right?


JR

Offline Warren Platts

Re: Lunar Liftoff Delta V Calculations Q&A
« Reply #3 on: 12/20/2012 06:03 pm »
How do you calculate suborbital delta v's on the Moon? It would be nice if there was a simple formula that would give the delta v as function of distance or latitudinal degree equivalents....
"When once you have tasted flight, you will forever walk the earth with your eyes turned skyward, for there you have been, and there you will always long to return."--Leonardo Da Vinci

Offline Andrew_W

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Re: Lunar Liftoff Delta V Calculations Q&A
« Reply #4 on: 12/21/2012 05:03 am »
LLO velocity is about 1.6km/s.
If we assume a vehicle takes off from the Moon's with an average acceleration of 16m/s, the time of the powered ascent would only be 100 seconds, assuming no gravitational losses, but even if we assume 100% possible gravitational loss during the boost, the maximum loss would only be 160m/s, so in practice the required delta v to LLO shouldn't be more than 1600m/s + 160m/s = 1760m/s

The Apollo LM ascent stage had a thrust-to-weight ratio at liftoff of 2.124 (in lunar gravity), which means an initial vertical acceleration of only about 1.7m/s, lower acceleration means far higher gravitational losses.
« Last Edit: 12/21/2012 05:26 am by Andrew_W »
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Offline sdsds

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Re: Lunar Liftoff Delta V Calculations Q&A
« Reply #5 on: 12/21/2012 05:20 am »
LLO velocity is about 1.6km/s.
If we assume a vehicle takes off from the Moon's with an average acceleration of 16m/s, the time of the powered ascent would only be 100 seconds, assuming no gravitational losses, but even if we assume 100% possible gravitational loss during the boost, the maximum loss would only be 160m/s, so in practice the required delta v to LLO shouldn't be more than 1600m/s + 160m/s = 1760m/s

So Apollo took 430 seconds of flight time to reach LLO; you're proposing doing it in 100 seconds. Assuming the same specific impulse, doing it in 100 seconds will take 4.3 times the thrust (to expend the same total propellant mass).

I could point to some side effects of that thrust requirement. But perhaps a better approach is to suggest a different sizing technique, i.e. a lift-off thrust to weight ratio of about 2. That would give the vehicle an upwards acceleration of 1.6 m/s^2, which is about what a vehicle on Earth would get with a T/W ratio of 1.15. I think it's the case (but double-check!) that the engine then doesn't have any need to throttle; constant thrust even against the reduced mass at the end of the burn still won't push the vehicle beyond what structure, cargo or crew could tolerate.
« Last Edit: 12/21/2012 05:44 am by sdsds »
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Offline Andrew_W

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Re: Lunar Liftoff Delta V Calculations Q&A
« Reply #6 on: 12/21/2012 05:31 am »
Yep, but I think engine throttling (which the ascent stage could not do) is more likely in the future, the savings in propellant would surely (OK, haven't done the math!) be worth while.
I confess that in 1901 I said to my brother Orville that man would not fly for fifty years.
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Offline Warren Platts

Re: Lunar Liftoff Delta V Calculations Q&A
« Reply #7 on: 12/21/2012 07:48 am »
How do you calculate suborbital delta v's on the Moon? It would be nice if there was a simple formula that would give the delta v as function of distance or latitudinal degree equivalents....

Use the technique described in Bate, Mueller, and White (for ballistic missiles at Earth) except use the moon's gravitational parameter and rotation rate, and double the answer (since you need to slow down propulsively at the end rather than letting the atmosphere do it).

Wow thanks Jorge! I see that the entire book is readily available as in free pdf form. Will check it out! Very interesting history of the ballistic missile as well. :)

http://www.fgg.uni-lj.si/~/mkuhar/Zalozba/Fundamentals_of_Astrodynamics-Bate_Mueller&White-1971.pdf
"When once you have tasted flight, you will forever walk the earth with your eyes turned skyward, for there you have been, and there you will always long to return."--Leonardo Da Vinci

Offline MP99

Re: Lunar Liftoff Delta V Calculations Q&A
« Reply #8 on: 12/21/2012 11:33 am »
LLO velocity is about 1.6km/s.
If we assume a vehicle takes off from the Moon's with an average acceleration of 16m/s, the time of the powered ascent would only be 100 seconds, assuming no gravitational losses, but even if we assume 100% possible gravitational loss during the boost, the maximum loss would only be 160m/s, so in practice the required delta v to LLO shouldn't be more than 1600m/s + 160m/s = 1760m/sy

So Apollo took 430 seconds of flight time to reach LLO; you're proposing doing it in 100 seconds. Assuming the same specific impulse, doing it in 100 seconds will take 4.3 times the thrust (to expend the same total propellant mass).

I could point to some side effects of that thrust requirement. But perhaps a better approach is to suggest a different sizing technique, i.e. a lift-off thrust to weight ratio of about 2. That would give the vehicle an upwards acceleration of 1.6 m/s^2, which is about what a vehicle on Earth would get with a T/W ratio of 1.15. I think it's the case (but double-check!) that the engine then doesn't have any need to throttle; constant thrust even against the reduced mass at the end of the burn still won't push the vehicle beyond what structure, cargo or crew could tolerate.

The lander needs to hold itself together during launch - 3-5g.

Engine burn will be a different thrust path, but would 1.6g be a big problem? Heavier engine, of course.

Cheers, Martin

Offline sdsds

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Re: Lunar Liftoff Delta V Calculations Q&A
« Reply #9 on: 12/01/2016 04:50 am »
As a reference (linked from https://www.hq.nasa.gov/alsj/alsj-descent.html):
NASA TM X-58040 (8.6Mb PDF) NASA Technical Memorandum, "Apollo Lunar Descent and Ascent Trajectories" by Floyd V. Bennett, presented at the AIAA 8th Aerospace Sciences Meeting, NYC, 19-21 January 1970. Planning and post-flight analysis for Apollo 11. Scan by Gary Neff.

For ascent:
6056 Foot per second = 1845.869 Meter per second
(page 16 of 33 scanned)

So 1846 m/s is a reasonable number to reach 17 km x 83 km orbit.
(EDIT: I calculate a Hohmann 2 burn elliptical transfer requires and additional 23 m/s to reach 100 x 100 km.
1846 + 23 ~= 1870.)
« Last Edit: 12/01/2016 05:56 am by sdsds »
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Offline sdsds

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Re: Lunar Liftoff Delta V Calculations Q&A
« Reply #10 on: 12/01/2016 05:00 am »
Years later Altair planners thought they needed a nominal ascent delta-V of 1833 m/s to reach a 15.24 km (50,000 ft) x 75 km orbit.
https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20080009584.pdf (page 4)
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