Falcon heavy to the moon

[Engineer817]

First off, I'm not entirely sure this is the right category so please move it if you feel the need to. I first want to point out that I work with computer hardware and rockets are not my thing. But I've been wondering if there are any good articles or areas to delve into that could give a general idea of what the falcon heavy can put onto the moon in either a polar or equatorial landing. I know there's a lot of variables, but I'm only looking for ball park figures to about a quarter ton. If any one knows of any good articles or can point me in the right direction to the materials I would need to learn the calculation methods myself, I would be greatly appreciative.

 

[Kyle]

It's been discussed, the answer is: it has enough Delta-v to reach the moon, and a Dragon spacecraft could do a free-return, but it would take something along the lines of the Falcon X to be able to launch a lander/Dragon duo and actually get into orbit around the moon and then land on the moon.

 

[Engineer817]

Manned mission denied

I wasn't thinking about a manned mission. More of a lunar probe mission. I remember astrobotic's mission outline and they were using a falcon 9 but would only land a rover and the lander itself and that would be half the payload fairing if I recall. I'm trying to figure the estimated landing weight for a paper that I am writing. Of course citation on this point is needed. any ideas?

 

[T.Neo]

It's been discussed, the answer is: it has enough Delta-v to reach the moon, and a Dragon spacecraft could do a free-return, but it would take something along the lines of the Falcon X to be able to launch a lander/Dragon duo and actually get into orbit around the moon and then land on the moon.

You do not need a Falcon X to do that; you could simply launch more than once, and perform orbital assembly.

 

[kamaz]

If any one knows of any good articles or can point me in the right direction to the materials I would need to learn the calculation methods myself, I would be greatly appreciative.

Back-of-the-envelope calculation is quite simple.

The trip is broken into 3 parts:

- injection to Low Earth Orbit
- transfer to Low Lunar Orbit (trans-lunar injection + lunar orbit injection)
- lunar landing

If you want to go back, then:
- ascent to Low Lunar Orbit
- trans-Earth injection

You need no propellant to land on Earth, because you can aerobrake.

The first thing you do, is get the delta-v values for each leg of your trip. Wikipedia has them: http://en.wikipedia.org/wiki/Delta-v_budget

Then, you have to calculate the corresponding mass ratio, using the rocket equation:

dV = v_e*log(m1/m0)

dV is delta-v value [m/s]

v_e is exit velocity of your propellant [m/s]. Also v_e [m/s] = Isp * 9.8 [m/s^2]. Engine Isp is about 450 for LH2/LOX, about 350 for LCH4/LOX and about 300 for hypergolics. Of course LH2/LOX is best, but since it boils off quickly, you will not be able to take it to the Moon.

m1 is wet mass of the spacecraft stage (with fuel)

m0 is dry mass of the spacecraft stage

Reasonable mass ratio for a kick stage itself (i.e. without payload) is about 10 (based on Centaur). Your lander is the payload of the kick stage. You'll probably arrive at m1/m0 of about 2 for the kick stage + lander + payload assembly.

Reasonable m1/m0 for a lunar lander is about 2 (based on Apollo LM). With about half of m0 being the payload, the other half being the spacecraft itself.

If you have any existing hardware you'd like to use, look up its dry/wet mass and delta-v budget.

A typical mission design would be like this:

0. Your stack is: payload (rover) riding on lander (LM, Morpheus) riding on kick stage (Centaur) riding on your launch vehicle.

1. The launch vehicle puts you into a 300 x 300km parking orbit. (OR, it puts you into a -180 x 300km orbit, and then your kick stage circularizes to 300 x 300 km). Look up how much mass your launch vehicle can put into the parking orbit, or use this calculator: http://www.silverbirdastronautics.com/LVperform.html

2. The kick-stage performs a trans-lunar injection and is discarded.

3. The lander performs a lunar orbital insertion and landing.

You look up how much delta-v each stage needs for its job and calculate the corresponding mass ratio.

Alternatively, if your kick stage has enough delta-v, you can try using it for both trans-lunar injection and lunar orbital insertion and (if you still have propellant) for powered descent, or at least part thereof (so-called crasher stage).

---------- Post added at 11:30 PM ---------- Previous post was at 07:02 PM ----------

You do not need a Falcon X to do that; you could simply launch more than once, and perform orbital assembly.

It's a bit counter-intuitive, but if you're doing two launches, the best idea is to rendez-vous in lunar orbit (dual LOR mode).

Launch 1: lunar lander to LLO.
Launch 2: crew in capsule (Orion/Dragon) to LLO.

Capsule does rendez-vous with lander in LLO, the crew transfers, the lander lands on the Moon.

Why: calculate mass of the kick stage needed to throw lander+capsule assembly past TLI, compared to the size of the kick stage needed to throw each of them.

 

[Engineer817]

If it wasn't for the TI89 I would be in real trouble

I hope I am getting my math right here: The ISP for LH2/LOX (I'm modeling after that because the lander may be reused as a hopper later on) is 450s I multiplied that by 9.8m/(s^2) and got 4410m/s for the Ve. Now what? I know the TLI DeltaV is 4100m/s but I'm not entirely sure how to proceed from there. Do I plug the starting mass in and find the "dry" mass? If that was what I was supposed to do, then I get 6231.2 kg from the original mass of 53000kg that I received from the data on the falcon heavy. Thats only TLI. Wikipedia had 16000kg down for TLI for the falcon heavy under: [ame="http://en.wikipedia.org/wiki/Comparison_of_orbital_launch_systems"]Comparison of orbital launch systems - Wikipedia, the free encyclopedia[/ame]
so what did I do wrong?

 

[RGClark]

I hope I am getting my math right here: The ISP for LH2/LOX (I'm modeling after that because the lander may be reused as a hopper later on) is 450s I multiplied that by 9.8m/(s^2) and got 4410m/s for the Ve. Now what? I know the TLI DeltaV is 4100m/s but I'm not entirely sure how to proceed from there. Do I plug the starting mass in and find the "dry" mass? If that was what I was supposed to do, then I get 6231.2 kg from the original mass of 53000kg that I received from the data on the falcon heavy. Thats only TLI. Wikipedia had 16000kg down for TLI for the falcon heavy under: Comparison of orbital launch systems - Wikipedia, the free encyclopedia
so what did I do wrong?

One problem is the number you're taking for TLI at 4,100 m/s. It's actually only in the range of 3,150 m/s. See:

http://en.m.wikipedia.org/wiki/Trans-lunar_injection

Remember this is only the number to meet up with the Moon, not to enter orbit. To enter orbit you'll need an additional 900 m/s delta-v. The total of 4,050 m/s is close to the number you cited so perhaps this is what you were thinking of.
I'm not sure how you were calculating using the rocket equation to get 6231.2 kg mass to TLI. The way it's done is e^(DeltaV/Ve) = (initial mass)/(final mass). So even if using your 4,100 m/s delta-v number this would give e^(4100/4410) = 2.53. If the initial mass is 53 metric tons(mT), this ratio results in 21 mT final mass. Note though this includes both the propulsive stage dry mass and the payload mass. However, the 16 mT number to TLI for the Falcon Heavy means only payload to TLI. And it is not using any additional stages, such as a Centaur, just the Falcon Heavy.

To calculate the complete flight use the delta-v numbers for the Earth-Moon system in the Wiki page cited by Kamaz: http://en.m.wikipedia.org/wiki/Delta-v_budget . It gives 4,040 m/s delta-v from LEO to lunar orbit, then 1,870 m/s from lunar orbit to lunar landing, for a total of 5,910 m/s. Then using a 4,410 m/s Ve, this gives a ratio of e^(5910/4410) = 3.82. For an initial mass of 53 mT, this requires a final mass of 14 mT. But this has to include both the propulsion stage dry mass and the payload.
The Centaurs get a 10 to 1 propellant mass to dry mass ratio. So scaling one up twice to 40 mT propellant mass and 4 mT dry mass, or using two together, we could get a 8 mT payload to the Moon:
the initial mass is 40 + 4 + 8 = 52 mT and the final mass is 4 + 8 = 12 mT, which amounts to a better mass ratio than needed.
This is by doing it by a single stage. By using two stages we could get even more payload to the lunar surface.


Bob Clark

 

[kamaz]

I hope I am getting my math right here: The ISP for LH2/LOX (I'm modeling after that because the lander may be reused as a hopper later on) is 450s I multiplied that by 9.8m/(s^2) and got 4410m/s for the Ve. Now what? I know the TLI DeltaV is 4100m/s but I'm not entirely sure how to proceed from there. Do I plug the starting mass in and find the "dry" mass? If that was what I was supposed to do, then I get 6231.2 kg from the original mass of 53000kg that I received from the data on the falcon heavy. Thats only TLI. Wikipedia had 16000kg down for TLI for the falcon heavy under: Comparison of orbital launch systems - Wikipedia, the free encyclopedia
so what did I do wrong?

First, 4.1 km/s is not TLI, it's TLI + LLO insertion. TLI itself is about 3km/s. This diagram has it all broken down nicely: http://en.wikipedia.org/wiki/File:ApolloEnergyRequirementsMSC1966.png ( and while we are at it, here is a program for recovering data from graphs: http://www.frantz.fi/software/g3data.php ). So with 55 tons IMLEO and LH2/LOX upper stage you get about 11 tons past TLI.

Second, it's enough to put the spacecraft in a transfer orbit with apoapsis beyond the EML1 point (i.e. about 300'000 km). Once it gets past EML1, the Moon's gravity will capture it, and it will enter a lunar orbit. Then, do a periapsis burn to lower apoapsis so you are not recaptured by Earth again This takes longer than a direct transfer, so not good for humans, but robots should be OK.

Third, there is saving related to using launch vehicle's upper stage for TLI, as opposed to using the two-stage vehicle to lift up your own kick stage into LEO and using that for TLI. So, keeping in mind the previous point, this is what I get from the calculator:

Launch Vehicle: Falcon Heavy w/standard fairing
Launch Site: Cape Canaveral / KSC
Destination Orbit: 185 x 300000 km, 31 deg
Estimated Payload: 15867 kg
95% Confidence Interval: 12988 - 19320 kg

Ta-dah! It seems that 16 tons past TLI is indeed true! (Inclination is critical. 31 deg is from Apollo 11.)

That greatly simplifies things. We'll simply put the lander directly atop Falcon. Per the above diagram, we'll need about 1 km/s dV for insertion and 2 km/s dV for landing. That's 3 km/s. Using LCH4/LOX, 16 tons wet mass works out to 2 6.5 tons dry mass. Payload is half that, so, you get 1 3.2 ton rover on the surface.

Since we have Orbiter and Delta-Glider has a nice delta-v indicator on the lower panel, I'd use that to check. Start in a 185 x 185 km orbit, raise apoapsis to 300'000 km, transfer to the Moon, lower apoapsis and land. Write down the delta-v actually expended in each step and use that for calculations.

Hope this helps

EDIT: *Facepalm* The rocket equation uses NATURAL logarithm, so, if you are using Excel to calculate this, the correct function to use is LN() not LOG(), which calculates decimal logarithm. (In most programming languages log() is the natural logarithm while log10() is decimal log.). Hence the striked out numbers above...


---------- Post added at 04:23 PM ---------- Previous post was at 03:27 PM ----------

If the initial mass is 53 metric tons(mT), this ratio results in 21 mT final mass. Note though this includes both the propulsive stage dry mass and the payload mass. However, the 16 mT number to TLI for the Falcon Heavy means only payload to TLI. And it is not using any additional stages, such as a Centaur, just the Falcon Heavy.

One thing to keep in mind is that Falcon Heavy uses a kerolox upper stage (342s Isp per wikipedia), while Centaur is LH2/LOX.

So, paradoxically, you get better performance by putting Centaur as a third stage on Falcon, then when using Falcon itself up to TLI. But, if I was engineering, I would probably NOT go with Centaur, because of the cost and hassle involved in integrating this. For a robotic mission, 16tons past TLI is plenty anyway.

Now, if SpaceX built a proper LH2/LOX upper stage, it would be sweet...

 

[RGClark]

EDIT: *Facepalm* The rocket equation uses NATURAL logarithm, so, if you are using Excel to calculate this, the correct function to use is LN() not LOG(), which calculates decimal logarithm. (In most programming languages log() is the natural logarithm while log10() is decimal log.). Hence the striked out numbers above...


---------- Post added at 04:23 PM ---------- Previous post was at 03:27 PM ----------

Yes, if he used the equation:

dV = v_e*log(m1/m0)

and took the "log" there to be common log on the calculator instead of natural log it would result in that number 6231.2 m/s he got. The correct button to use appears as "ln" on the calculator, for natural log.


Bob Clark

 

[Engineer817]

A few other questions

First off, I want to thank you very much for your help. I checked and double checked the numbers and if I'm correct its 13.8 mT land-able from the original 53mT using 3.15 +.9 +1.87 km/s for TLI to landing. What mass of this do you think the lander itself will take up?

There's quite a few other questions I have such as polar landing fuel consumption.

Also, you mentioned the LH2/LOX would boil off if taken to the moon. I wasn't quite sure if you meant on its way to the moon or left on the moon for a certain period of time. Also, any idea where I can find some links to different engines that can be used on landers or will their ISPs all be the same for the given fuel?
Again, thats for the support

 

[kamaz]

What mass of this do you think the lander itself will take up?

Two cargo landers, for you:

http://www.astronautix.com/craft/apotruck.htm
[ame="http://en.wikipedia.org/wiki/Project_Morpheus"]Project Morpheus - Wikipedia, the free encyclopedia[/ame]

There's quite a few other questions I have such as polar landing fuel consumption.

Polar landing mission is going to take much more delta-v -- plane change is needed probably...

Also, you mentioned the LH2/LOX would boil off if taken to the moon. I wasn't quite sure if you meant on its way to the moon or left on the moon for a certain period of time.

Both. LH2 simply evaporates from the tank at the rate of 17% per day: http://www.ulalaunch.com/site/docs/publications/CentaurExtensibilityForLongDuration20067270.pdf

Also, any idea where I can find some links to different engines that can be used on landers or will their ISPs all be the same for the given fuel?

Isp going to be about the same for given fuel.
You can look up engines on astronautix.

 

[Admiral_Ritt]

Hey, lets calculate the way a Space Agency does when it doesn't want to do
a particularly challenging mission.

Prepoderous Vehicle mass x Absurd Mission safety parameters x built each
component in 30 different with preffered suppliers = SORRY too expensive.


The Shuttle could have been used indirectly to get back to lunar exploration.

NASA, wanting to discourage these wild thoughts, decided to do a
study, of just using one Shuttle launch to facilitate some kind of mission to the moon.
Turns out the shuttle can only place a small vehicle with a mass of few tons on the moon. ONE WAY, unmanned.

They could have used One Shuttle Launch and One Delta heavyLaunch to do a 3- man Lunar Orbital and 2 man lunar Lander mission. AS FOLLOWS

PART 1)
Shuttle Launch containing Reg Crew of 3 Plus 3 Lunar mission Specialists.

In the cargo bay is a Lunar Orbital Vehicle and Lunar Lander.
Both WITHOUT Propulsion Modules.

The LOV, is designed to do limited aero braking, just enough to enter LEO.

PART 2
Delta Heavy Launch. Propulsion Module for TLI and back, assited with limited aerobraking.
A propulsion Module for the Lunar Lander.

Assembly in Space, Launch mission from LEO
Recover LOV from LEO with Shuttle,
De_orbit and land with shuttle.

The LEM of the apollo missions would fit nicely in cargo bay
THE LOV would need to be designed inexpensively (How about modifying a Bigelow inflatable module by adding a
heat shield and small thursters for LEO maneuvering minor course corrections, Leave the rest of the spaceship
systems needed attached to the propulsion modules)

 

[Engineer817]

2 part

This post is in 2 parts, the first is way off topic, but is a responce to Admiral_Ritt, the second part is a few other questions and concerns.

The shuttle's efficiency was under used over its service period. Aero capture was a concept I discussed indepth with others and there hasn't been much practice in that area. I'm not sure if I would risk men to try an aero capture with out at least testing it out with the equipment several times, but that's just me. I understand a lot of people like the idea of going to the moon and exploring and seeing those nice youtube videos with the inspirational music happen in their life times, but be honest. Can you really imagine this country jumping through all the political hoops with the international community, forwarding the funds towards such a mission, and sustaining that kind of mission all for lunar rocks? Politicians can't realize the scientific value, and they are the only ones that can actually allocate funds towards a manned presence on the moon. Stone aerospace, artimus, etc can all try but you are constantly seeing these project hitting the billion dollar brick wall. I will never support a manned presence on the moon before having an industrialized system in place before hand. I say this simply because industry can grow greatly from a seed to a great empire using ISRU technology and bootstrapping its capabilities. Many processes have been invented to produce materials from regolith with minimum to no reactants. Having missions that fit the realistic price tags are more likely to be successful than missions that are manned and there for expensive. I think we can all agree its all about the money, and I think if you are serious about human advancement, you'll stop thinking about putting up lunar bases and going to mars when it doesn't provide near term monetary returns to the investor(s).

My new questions are on planning out the entire launch to landing senerio more accuratly. The math that you showed me how to do is great, but if I am going to put anything on paper, I'd like it to be a bit more accurate and detailed then a couple of equations. Where would I begin to learn the more advanced concepts of designing a mission from launch to landing? Thanks

 

[Engineer817]

Just a continuation of my quest

I looked up Apollo's payload to weight of its fuel system ratio with 18394/(22783+10300) equating to about 55% of the landing propulsion system as fuel and engines. If the 13.8 Mt mentioned above is correct, then is it realistic to say that only 6.1 tons is landable payload? I know that's missing the framework and guidance, but I'm not sure how to proceed with taking that into account. Any advice?

 

[RGClark]

I looked up Apollo's payload to weight of its fuel system ratio with 18394/(22783+10300) equating to about 55% of the landing propulsion system as fuel and engines. If the 13.8 Mt mentioned above is correct, then is it realistic to say that only 6.1 tons is landable payload? I know that's missing the framework and guidance, but I'm not sure how to proceed with taking that into account. Any advice?

Remember that ratio is highly dependent on the propellant used. For the lunar lander, Apollo used hypergolics, which are highly reliable but have comparatively low Isp. This results in the payload portion out of the total mass landed being smaller than for hydrolox propellant.
I would consider in the Apollo case the gross weight of the ascent stage to be the useful payload, since you could replace it with a cargo container of the same weight and the descent stage could land it just as well. This would put the payload at 10,300 lbs.

Bob Clark

 

[RGClark]

...
Polar landing mission is going to take much more delta-v -- plane change is needed probably...

Anyone know what that delta-v would be to get to polar landing sites and back from LEO? I want to find out how much the new Falcon 9, version v.1.1, scheduled to test launch in June will be able to return from the permanently shadowed regions of the Moon.

Bob Clark