[Self] Total delta-v of Saturn V rocket including Apollo Spacecraft

When searching for this I found an old post with exactly the same question. There was a similar (but not identical) question which was linked as "good enough" on StackExchange.

When looking at the answer given at StackExchange I noticed the rocket was calculated as having no payload, nothing on the third stage (see: emtpy mass 10 t).

I couldn't find a source where the Apollo Spacecraft was included so I gathered all the numbers and threw them together myself.

Combinded delta-v (m/s)	delta-v of stage	fuel mass (kg)	gross mass	specific impulse (s)	notes
3403	3403	2150000	2934154	263	using sea level Isp. Vacuum Isp would yield 3934 m/s.
8087	4684	443800	654154	421
12178	4091	109500	174154	421	after 3rd stage burnout: discarding LES and SLA (adapter) and docking CSM zu LM
13793	1615	18410	45114	314	using the CSM engine until depletion, then discarding CSM
16198	3050	8200	15034	311	using decent engine, then discarding descent module
18316	2118	2353	4700	311	depleted ascend engine

So the answer should be 18.3 km/s. Assuming 9.5 km/s is needed to reach low earth orbit this is an excess of 8.8 km/s, which is not enough to leave the solar system (without gravity assist) but should be barely enough to crash into Titan.

I'm surprised this is pretty close to the calculated answer for the delta-v up to the third stage without any further stages/paylod at all (17.9 km/s), and the CSM adds the smallest amount with just above 1.6 km/s.

There are 3 possible sequences for the last 3 burns:

• 1. CSM 2. LM acent 3. LM descent
• 1. LM ascent 2. LM descent 3. CSM
• 1. LM ascent 2. CSM 3. LM descent

The option that burns the most fuel first was used because that should produce the highest delta-v overall.

The rocket equation was used. The gross masses for some stages slightly differ from explicit sources as these are also calculated adding together the individual parts, for example you can find the mass of the LM as being 28,800 kg but adding together the ascent module and descent module yields 30,080 kg. This is to be expected as slightly different versions were used for the different missions.