Bahamut, can you comment on the performance of the N-1? e of pi has extensive training and lots of experience running spacecraft performance numbers. I have a lot less knowledge, but running the basics as I understand them and using figures from Mark Wade's Encyclopedia Astronautica for the N-1 stages, I get mass figures that are compatible with the claims this timeline makes.
That is, I find the target of 75 tonnes to orbit (presumably at 185 km altitude or so, more or less circular, presumably inclined 51 degrees to the equator as per normal Soviet/Russian practice OTL) pretty reasonable. To get that I find the Ghe stage must burn a bit, mainly because if it doesn't and the Veh stage is sufficient to get into orbit by itself, the resulting payload is greater than 75 tons! (And the accumulated delta-V, naively ignoring both gravity loss and air loss, is a bit less than the 10 km/sec that is my rule of thumb for typical naive delta-V for a successful launch; the amount of burning the Ghe stage must do to bring the total orbited mass to exactly 75 tons just about brings it to that magic number, so...)
Then in turn the Ghe stage alone does not have enough propellant to launch the De and Soyuz on to TLI, not quite, but if the De burns a bit, the resulting mass sent on that kind of orbit is greater than the 16 ton figure e of pi produces.
Some variables I can't narrow down without sheer guesswork are:
How much does the average ISP and thrust of the A stage engines get reduced by atmospheric pressure toward the sea level thrust and ISP?
How much does the Soyuz mass? Is it indeed intended to have enough propellant so that in case of a De stage failure, it can escape a low Lunar orbit with enough energy left over to achieve a return orbit to Earth and still retain some maneuvering margin, all on its own? For that matter, is the De stage meant to achieve both Lunar orbit insertion and TEI?
My figuring suggests it can indeed be done that way, or anyway almost! If it can than the cosmonauts can survive the failure of any of the upper stage engines including the Soyuz. If the Ghe stage fails it will presumably do so right off, as they are trying achieve parking orbit--then they abort to suborbital landing far downrange. If it fails during TLI the De and Soyuz together can possibly get them on a return to Earth orbit; if the De fails during TLI I presume the targeted orbit is quite near a free return, well within Soyuz margins. If it fails approaching Luna, perhaps even if they approach for a polar orbit the Soyuz can maneuver into a return orbit. If it fails to fire for TEI, the Soyuz alone can perhaps manage a slow but feasible Earth return--and if all the other engines work but the Soyuz doesn't, the first time they learn that will be during midcourse corrections headed home, and perhaps the auxiliary thrusters can manage well enough to guide them to a safe return. Especially if these thrusters are fed from the same fuel supply that feeds the main engine.
Here is the data and figuring I've done based on Mark Wade's figures for the 5 stages and a guess as to Soyuz mass, based on the idea that the Soyuz has emergency return from Lunar orbit capability:
Block A
(30 engines as given here; 24 ITTL)
Gross mass: 1,880,000 kg (4,140,000 lb).
Unfuelled mass: 130,000 kg (280,000 lb). (delete 6*1250 kg engines. 7500 kg)
Gross mass: 1,872,500 kg
Unfuelled mass: 122,500 kg
Height: 30.10 m (98.70 ft).
Diameter: 10.30 m (33.70 ft).
Span: 16.90 m (55.40 ft).
(OTL, 30 engine)Thrust: 50,300.00 kN (11,307,800 lbf). vacuum thrust.
ITTL, replace with 39,214 kN
Specific impulse: 330 s.
Specific impulse sea level: 284 s.
This implies
37,091 sea level thrust--note that is a whole lot more than the weight of the stack!
Burn time: 125 s. (156.25)
Block B
No Engines: 8.
Gross mass: 560,700 kg (1,236,100 lb).
Unfuelled mass: 55,700 kg (122,700 lb).
Height: 20.50 m (67.20 ft).
Diameter: 6.80 m (22.30 ft).
Span: 9.80 m (32.10 ft).
Thrust: 14,039.98 kN (3,156,313 lbf).
Specific impulse: 346 s.
Burn time: 120 s.
Block V
Gross mass: 188,700 kg (416,000 lb).
Unfuelled mass: 13,700 kg (30,200 lb).
Height: 14.10 m (46.20 ft).
Diameter: 4.80 m (15.70 ft).
Span: 6.40 m (20.90 ft).
Thrust: 1,608.00 kN (361,492 lbf).
Specific impulse: 353 s.
Burn time: 370 s.
Block G
Gross mass: 61,800 kg (136,200 lb).
Unfuelled mass: 6,000 kg (13,200 lb).
Height: 9.10 m (29.80 ft).
Diameter: 4.40 m (14.40 ft).
Span: 4.40 m (14.40 ft).
Thrust: 446.00 kN (100,264 lbf).
Specific impulse: 353 s.
Burn time: 443 s.
Block D
Gross mass: 18,200 kg (40,100 lb).
Unfuelled mass: 3,500 kg (7,700 lb).
Height: 5.70 m (18.70 ft).
Diameter: 2.90 m (9.50 ft).
Span: 2.90 m (9.50 ft).
Thrust: 83.30 kN (18,727 lbf).
Specific impulse: 349 s.
Burn time: 600 s.
1,872,500+560,700+188,700+61,800+18,200
assume 7 tonne Soyuz (dry) that has delta-V budget of 1000 m/sec with isp of 319, this masses 2640 more in fuel or 9640. Allow 4500 for SAS/fairing. (based on
this site)
To be sure a suitable escape system from the N-1 stack might need to mass a lot more, to get the capsule much farther away from a much bigger fireball than the Soyuz rocket could produce.
On the other hand, I've often wondered if the Soviets could have been more economical with their fairing masses--you two showed an illustration of a Vostok that was enclosed in a fairing and there were vast amounts of empty space above the orbital craft in the fairing!
And anyway, even quite large masses don't deduct a whole lot from the performance of the massive first stage; I assumed the launch escape system and fairing were ejected after first stage burnout. Perhaps I should have kept it through the Be stage burn as well?
Anyway all up this gives us
2716 tons.
So thrust is some thousand tons greater; the whole thing should take off the pad at a brisk third of a G acceleration! I noticed much the same is true of the R-7 derived rockets; Soviet engineers seem to believe in quite high pad accelerations and pulling pretty high G's during launch.
First stage should achieve at least 1295.5 m/sec real velocity straight up, over 156 seconds. Perhaps less considering air drag, but this is based on sea level thrust and ISP applying all the way, so is probably too pessimistic.
Averaging with vacuum isp brings it to 1529.
Anyway the rocket will not go straight up, it will start to turn, so being more precise than this requires I have some clue what its turning schedule is!
From this point on I just note total ideal delta-V, figuring gravity loss and air drag are deducted from the traditional goal of 10,000 m/sec.
Vacuum-no grav impulse is 3346.5
2nd stage 3126, total 6472.6
3rd 3431.14, total 9903.74
burning 14640 kg of Ghe stage fuel brings orbited mass to precisely 75 tons, gains 617.5 more m/sec--well over 10,000!
The remaining delta-V from the Ghe stage takes us to 2755.95 toward TLI.
Assume a 180 km parking orbit, speed is 7800.7 m/sec
To reach a transfer orbit that reaches out to 500,000 km, we need 403.5402 more m/sec.
That requires 3095.412 kg from De block, leaving a gross mass of
15105+9640=24,745
So there is 11,605 kg of fuel in the De block still.
Allowing 1100 for Lunar orbit capture and escape, we'd need just a bit more. Going back over the sequence with a higher Soyuz mass is beyond me for the moment.!
Plugging these figures for stage, fuel, thrust and ISP into the Silverbird Calculator and assuming launch from Baikonaur, to a 185 altitude orbit and 51 degree inclination, tend to endorse your claims of performance--only by putting in the sea level values for the first stage and selecting the Earth escape velocity option did the lower range of the bracket of masses given go as low as e of pi's 16 tons to TLI.
But I believe the Silverbird calculator wants vacuum figures and automatically figures the sea level loss of thrust for you.
Can you confirm or deny that the stage figures Wade gives, suitably modified as I did to deduct 6 engines from the A stage, match the ones you are using?