Apollo return fuel requirements?

[Trebor]

Hi all,
Anyone know how much fuel the Apollo missions required to return from the Moon and what the delta-v necessary was?
A good analysis of the orbit would be superb as well.... is seems the new hoax theory is that the return was 'impossible' due to insufficient fuel, or more precisely a lack of knowledge of basic orbital mechanics.

[Luke Pemberton]

Hi all,
Anyone know how much fuel the Apollo missions required to return from the Moon and what the delta-v necessary was?
A good analysis of the orbit would be superb as well.... is seems the new hoax theory is that the return was 'impossible' due to insufficient fuel, or more precisely a lack of knowledge of basic orbital mechanics.

This link to Bob's page is most useful

http://www.braeunig.us/apollo/hybrid-profile.htm

ETA: Specs for CSM are also at Bob's place:

http://www.braeunig.us/space/specs/apollo.htm

[Trebor]

Hi all,
Anyone know how much fuel the Apollo missions required to return from the Moon and what the delta-v necessary was?
A good analysis of the orbit would be superb as well.... is seems the new hoax theory is that the return was 'impossible' due to insufficient fuel, or more precisely a lack of knowledge of basic orbital mechanics.

This link to Bob's page is most useful

http://www.braeunig.us/apollo/hybrid-profile.htm

ETA: Specs for CSM are also at Bob's place:

http://www.braeunig.us/space/specs/apollo.htm

That's perfect, thanks.
I should have known that Bob B had already done the work

[Luke Pemberton]

I should have known that Bob B had already done the work

Yup, he is a Supreme Jedi Master when it comes to the documentation of the orbital aspects of Apollo. I usually follow the following flow when I have a question.

(1) Check Bob's site.
(2) Check Clavius.
(3) Google said keywords and Apollo Lunar Surface Journal in the same search bar.
(4) Search the forum
(5) Post a question here.

I knew this info was on Bob's site, but forgot where, so I went straight for 3 and Google popped up Bob's site.

[Bob B.]

Anyone know how much fuel the Apollo missions required to return from the Moon and what the delta-v necessary was?

Yes.  The average transearth injection ∆v for the six lunar landing missions was 978 m/s.  The average mass of the CSM immediately following LM jettison was 16,582 kg.  The specific impulse of the SPS engine was 314 seconds.  Therefore, using Tsiolkovsky rocket equation, the required fuel mass was

∆v = I_sp * g_o * LN( m_o / (m_o - m_p) )

978 = 314 * 9.80665 * LN( 16582 / (16582 - m_p) )

m_p = 4508 kg

The dry mass of the CSM was about 11,900 kg, therefore the approximate amount of propellant available was

16582 - 11900 = 4682 kg

which was more than enough to get the job done.

A good analysis of the orbit would be superb as well

See link provided by Luke

.... seems the new hoax theory is that the return was 'impossible' due to insufficient fuel

So in other words, they're making stuff up again.

These silly "not enough fuel" arguments have been around in some form or another for many years.  I've personally performed the math on all the Apollo manuevers to verify that (1) the ∆v shown in the Apollo reports is correct, and (2) there was enough propellant to produce the required ∆v.  I've done this for the Saturn V, the CSM and the LM.  In all cases everything has checked out perfectly.  The hoax claims are pure nonsense.

or more precisely a lack of knowledge of basic orbital mechanics.

It is the hoax theorists that lack a knowledge of basic orbital mechanics.  NASA and I understand it just fine.

[Luke Pemberton]

There was extra propellant then... but not much.   

Does anybody know the mass of the fuel burned in mid-course corrections? I knew some of the margins were fine, but this drives home just how fine they played with the margins.

There is always something that makes me think it was even more remarkable than how remarkable I thought it was before. I never understand the CTs, when one thinks of all the engineering issues that had to come together they honestly think a hoax could be kept under wraps on such a complex project?

[Bob B.]

Does anybody know the mass of the fuel burned in mid-course corrections?

On the return trip, almost nothing.  The transearth course corrections were usually only about 5 ft/s (<2 m/s), and were were typically performed using the RCS.  The biggest MCC was the one Apollo 13 performed using the LM DPS, though this was over dramatized in the movie.  It was only a 7.8 ft/s burn that lasted 14 seconds.

The course corrections on the outbound trip were typically larger.  This was partially because some of the missions were initially launched on a free return trajectory.  About halfway through the trip they had to perform a burn to change from the free return to the planned mission trajectory.  This was called a "hybrid trajectory".  The largest of these burns was 71.1 ft/s (21.7 m/s) on Apollo 14.

[Bob B.]

Anyone know ... what the delta-v necessary was?

I’d like to elaborate a little bit on my previous answer.  Determining an accurate number is complicated 3-body problem; however, it’s not too hard to come up with a ballpark approximation. 

TEI was typically initiated from a 60 nautical mile orbit, or about 111 km.  At this altitude, orbital velocity is 1628 m/s and escape velocity is 2303 m/s.  Therefore, escaping lunar gravity requires a burn of 2303 – 1628 = 675 m/s.  This would place the spacecraft into an Earth orbit approximately equal to the orbit of the Moon.  The spacecraft’s velocity relative to the Moon would be 0 and relative to Earth about 1010 m/s.  To reach Earth, the spacecraft would have to perform another burn to lower its perigee until it intersects Earth’s atmosphere.  Doing so requires the spacecraft to slow down to 182 m/s.  After slowing down the spacecraft’s velocity relative to the Moon is 182 – 1010 = –828 m/s.

Fortunately we don’t have to perform two burns as described above.  When we burn to escape lunar orbit we don’t have to stop at escape velocity.  We can give our spacecraft enough velocity that it will have some speed left over after escaping the Moon’s gravity.  The amount of excess velocity that we want the spacecraft to have is the 828 m/s.  If we burn in the correct direction, after leaving lunar space the spacecraft will already be going –828 m/s relative to the moon and 182 m/s relative to Earth.

This extra velocity is called excess hyperbolic velocity, and is given by the formula

V∞² = V_bo² – V_esc²

where V∞ is the excess hyperbolic velocity, V_bo is the burnout velocity, and V_esc is the escape velocity.

We what V∞ to equal 828 m/s and we already know that V_esc is 2303 m/s, therefore

V_bo = (828² + 2303²)^1/2 = 2447 m/s

Since our initial orbital velocity is 1628 m/s, the required ∆v is simply the burnout velocity minus the orbital velocity,

∆v = 2447 – 1628 = 819 m/s

This is approximately the minimum ∆v required to get back to Earth, putting the spacecraft on a trajectory that would take about 5 days to reach Earth.  The reason the actual Apollo TEI burns were closer to 1000 m/s was to reduce the travel time to about 3 days.

[gwiz]

I've personally performed the math on all the Apollo manuevers to verify that (1) the ∆v shown in the Apollo reports is correct, and (2) there was enough propellant to produce the required ∆v.  I've done this for the Saturn V, the CSM and the LM.  In all cases everything has checked out perfectly.  The hoax claims are pure nonsense.

Apollo examples frequently turn up in aerospace engineering textbooks.  An awful lot of engineering students over the years have also personally checked the Apollo numbers.

[bknight]

Looking at the drawing on Bob' web page http://www.braeunig.us/space/specs/drwgs/apollo.htm
It looks like there was a covering/containment "tubes" around all the volatiles in the CSM.  Is this a correct depiction?  I remember looking at the Damaged CSM on AS13 http://www.hq.nasa.gov/alsj/a13/AS13-59-8500.jpg
I don't see any  tubes, but they may have been destroyed when the oxygen tank ruptured.

[Bob B.]

Looking at the drawing on Bob' web page http://www.braeunig.us/space/specs/drwgs/apollo.htm
It looks like there was a covering/containment "tubes" around all the volatiles in the CSM.  Is this a correct depiction?

I'm not sure what you are looking at, but could you be referring to the space radiators?  Portions of the service module's exterior were covered with radiators consisting of tubes through which coolant was circulated.  The coolant would radiate its excess heat to space.

I remember looking at the Damaged CSM on AS13 http://www.hq.nasa.gov/alsj/a13/AS13-59-8500.jpg
I don't see any  tubes, but they may have been destroyed when the oxygen tank ruptured.

The tubes aren't visible in that photo, but the radiators are the lighter colored areas on the exterior of the SM.

[bknight]

No I am referring to the interior cut-out view showing two of these "tubes".  One of the tubes has a cut-out toward the bottom and one toward the top both showing interior equipment.  I'm not sure of the correct terminology of the pieces.
http://www.braeunig.us/space/specs/drwgs/apollo.htm

[Bob B.]

No I am referring to the interior cut-out view showing two of these "tubes".  One of the tubes has a cut-out toward the bottom and one toward the top both showing interior equipment.  I'm not sure of the correct terminology of the pieces.
http://www.braeunig.us/space/specs/drwgs/apollo.htm

Could you be referring to the fuel tanks?  The fuel tanks are to two primary structures shown inside the SM, one horizontally across the top and one horizontally across the bottom.  The top tank has a cut-out showing what I think is the bladder system.  The cut-out on the bottom tank is to show equipment behind the tank in the adjacent bay, which looks to me to be the oxygen and hydrogen tanks.

[bknight]

We're getting closer, the lower cut-out I contains a spherical tank, that I believed is one of the oxygen tanks, but you are probably correct it is a "behind the tanks".  The other (upper) cut-out with a cylinder in the cut-out.  I assume that is the bladder you refer.

[Bob B.]

We're getting closer, the lower cut-out I contains a spherical tank, that I believed is one of the oxygen tanks, but you are probably correct it is a "behind the tanks".  The other (upper) cut-out with a cylinder in the cut-out.  I assume that is the bladder you refer.

The spherical tank behind the bottom fuel tank looks like an oxygen tank.  To the 4 o'clock position of the oxygen tank you can see the dome of another tank, which should be a hydrogen tank.  I'm quite certain those are behind the fuel tank because you can see that both walls of the fuel tank are cut out.  The top fuel tank shows only one wall cut out, so the cylindrical device we see is probably inside the fuel tank.  I'm not certain what that is, but it does look somewhat like a diagram I've seen of a tank bladder system.  It could be something else, however.  I've read documents that refer to a tank "sump", so perhaps that's it.