ladajo wrote:So why don't we do the back of the napkin, as I have been suggesting. Let's do it with what we know, and the goal of minimizing g stress on pax.
Since nothing about rockets makes sense until you run the delta-v numbers, here's the back of a slightly bigger napkin:
The BFR breaks down as follows:
Dry mass: 160 tonnes.
Prop mass: 2905 t.
Max Sea level thrust: 1700 kN * 31 = 52.7 MN
SL Isp = 330 s, so exhaust velocity = 3234 m/s
Max Vac thrust: 1830 kN (SWAG) * 31 = 56.7 MN
Vac Isp = 356 s = 3489 m/s
Dry mass 85 t.
Prop mass 1100 t.
Assuming only vac engines at going to orbit Max Vac thrust = 4 * 1900 kN = 7.6 MN
Vac Isp = 375 s = 3675 m/s
Let's assume about 10 tonnes of payload (i.e. 100 passengers at about 100 kg/passenger--enough for an average person and about 15 kg of luggage).
That makes gross liftoff mass = 4260 t.
T/W at launch is 1.36. Acceleration = T/W - 1 = 0.36 gee.
Acceleration (T/W doesn't make much sense now...) at BFB burnout = 4.3 gee. Throttle down to 45% to hit 2 gee.
Acceleration at second stage start = 0.6 gee (T/W doesn't make much sense now...)
Acceleration at second stage burnout = 8.2 gee. Throttle down to 24% to hit 2 gee.
Delta-v of BFR stack at 10 tonnes of payload:
BFB delta-v (assume the average of the SL and vac Isps) = 343 * 9.8 * ln (4260/1355) = 4210 m/s
BFS delta-v = 375 * 9.8 * ln (1195 / 95) = 9305 m/s
Total delta-v = 13,515 m/s
Note: delta-v doesn't really change if you throttle stuff down--especially if you're shutting down whole engines to do it. However, the big deal here is gravity drag, which is the loss of delta-v caused by the vehicle falling back toward Earth at 9.8 m/s^2 the whole time it's thrusting up
. Typically, launch to LEO requires about 9200 m/s of delta-v, to achieve an orbital velocity of about 7800 m/s. Aerodynamic drag usually doesn't lose more than 200 m/s of delta-v, so "normal" gravity drag is about 1200 m/s. That number will get higher as T/W goes down, because the rocket has to spend more time thrusting up (and therefore also falling in the gravity field).
You've got an extra 4315 m/s to fool around with here. If you need to throttle back to 45% to keep things under 2 gee during BFB boost, and to 24% during the BFS burn, it's going to be fine. And things are even better if all you're doing is a point-to-point suborbital.
The BFS without the BFB
is really close to being a viable suborbital point-to-point system. You'd have to launch on all 7 engines, and they'd probably have to be some kind of intermediate between the SL and vac expansion ratios (rather than 4 vac and 3 SL). Figure an average Isp = 355 s = 3479 m/s exhaust velocity and 1875 kN per engine = 13.1 MN
Liftoff T/W = 1.12
Delta-v = 3479 * ln (1195 / 95) = 8809 m/s.
Figure you'll need 500 m/s of delta-v to land, and you're down to 8309 m/s.
That ought to be good enough for a lot of suborbital destinations.
But now you really
need to worry about gravity drag, because you're launching at low T/W. Throttling back is probably OK above 4 gee, but not much before then.
On the other hand, the big problem I've had with this point-to-point stuff is that launch on top of a 31-engine BFB and 2905 tonnes of methalox with no possibility
of a launch escape system simply isn't going to (ahem) fly. So going the SSTO route ought to be very, very attractive.
If I were SpaceX, I'd be thinking about going with a special 9-engine BFS in an ocatweb. If I did the math right, you could fit a 1.9 m diameter engine (halfway between the current SL and Vac Raptors) in a 9 m vehicle with no problem. Assuming you're now at a dry mass of 89 t:
Thrust = 9 * 1870 kN = 16.8 MN
Liftoff T/W = 1.44
Delta-v = 3479 * ln ( 1199 / 99) = 8277 m/s with the landing reserve.
Whether that saves you more in gravity drag than it loses you in delta-v loss from the extra dry mass would require some serious simulation.