I did the very best I could, reverse-engineering what the 2018 version of the BFS second stage might be able to do. This is based on the Musk presentation of a paying moon passenger, at Spacex, and posted on their website in Sept. 2018. I had to use the 2017 rocket engine data at 250 bar chamber pressures, as the 300 bar performance figures for 2018 are not yet available. I did not revisit the first stage BFR (see ref. 1). Things begin with a best-cut guess at the 2018 weight statement:
All metric ton 2017 2018
Payload 150 100
Inerts 85 135
Burnout 235 235
Propellants 1100 1100
Ignition 1335 1335
Note: payload reduced by 50 tons while inerts are increased by that same 50 tons, due to fins and the longer payload section. The 3 fins are heavier than the old 4 landing legs, but inherently span wider.
Mass ratio 5.6809 5.6809
Propellant fraction 0.82397 0.82397
Payload fraction 0.11236 0.07491
Inert fraction 0.06367 0.10112
Sum fraction 1.00 1.00
About the Engines:
Engines 6 7
SL 2 7(nom.) to 0
Vac 4 0(nom.) to 7
Pc, bar 250 300
Throttle, % 20-100 xxx
SL Fth @ SL, KN 1700 xxx
SL Isp @ SL, s 330 xxx
SL Isp @vac, s 356 xxx
SL De, m 1.3 xxx
Vac Fth @ vac, KN 1900 xxx
Vac Isp, s 375 xxx (380?)
Vac De, m 2.4 xxx
“Xxx” means actual data hinted at, but not available yet
BFS weights more-or-less determine SL-vac mix of engines:
Scenario M, ton 1-g KN .384-g KN
Landing 235 2305 885
Takeoff 1335 13,092 5027
To land on Earth with SL engine design (250 bar): use 3 engines at 45+%, if 1 lost, remaining 2 at 68+%
To land on Mars with vac engine design (250 bar): use 2 engines at 23+%, if 1 lost, remaining 1 at 47+%
To land on Mars with SL engine design (250 bar): use 2 engines at 26+%, if 1 lost, remaining 1 at 52+%
To take off fully loaded on Earth with SL design (250 bar): use all 7 engines at 110% (fully loaded takeoff not feasible)
To take off fully loaded on Mars with vac design (250 bar): Use 4 engines at 66+%, if 1 lost, remaining 3 at 88+%
To take off fully loaded on Mars with SL design (250 bar): Use 4 engines at 74+%, if 1 lost, remaining 3 at 99+%
Engine-Mix Conclusions (for 250 bar designs):
#1. BFS used only at Earth could use all SL engines, or use 3 SL engines to land, and 4 vac engines for better Isp to LEO. Requires BFR first stage with 31 SL engines.
#2. BFS used at Mars and returning to Earth must use 3 sea level engines for Earth landing, and 4 vac engines for best takeoff from Mars, as well as powering to LEO. Requires BFR first stage with 31 SL engines.
For Figuring Performance:
3 SL engines for Earth landing: Isp = 330 s, Vex ~ 3.236 km/s
4 Vac engines for Mars landing, or for powering to LEO: Isp = 375 s, Vex ~ 3.677 km/s
Test flight BFS-only takeoff 7 SL engines: Isp = 330 s, Vex ~ 3.236 km/s, max TO mass (to hover only) 1213 metric tons vs 1335 tons fully loaded
Estimating BFS Performance:
These are jigger-factored rocket equation estimates, per the methods of ref. 2. The orbital mechanics delta vee requirements come from ref. 3. For landing at Mars, retro-burn starts near end of hypersonics at very low altitude, near 0.7 km/s flight velocity (see landing estimates below). For landing on Earth, the “skydiver” descent rate at low altitude appears from Musk’s presentation to be ~ 0.2 km/s. For getting to LEO from the stage point from BFR, a slightly-factored delta-vee is orbit velocity minus stage velocity. Staging velocity is presumed to be ~ 3 km/s.
Powering to LEO on 4 Vac engines (250 bar design):
Stage velocity 3 km/s, orbit velocity 7.9 km/s, theo. dV = 4.9 km/s. Apply 5% grav-drag loss: dV = 5.1 km/s. Req’d MR = exp(5.1/3.677) = 4.00; Wp/Wig = 1 – 1/MR = 0.75, vs 0.82 available (8.5% margin). Margin is 3% at 2.5 km/s staging velocity. Therefore, the presumption of 3 km/s staging velocity, or perhaps slightly lower, is thus verified.
Departing LEO and landing upon Mars, using 4 vac engines (250 bar design):
Depart LEO dV = 3.9 km/s, land on Mars dV = 1.0 km/s (factored from 0.7 km/s by 1.4), total = 4.9 km/s.
Req’d MR = exp(4.9/3.677) = 3.791; Wp/Wig = 1 – 1/MR = 0.736, add 10% for boiloff to 0.810, with only 0.823 available (1.5% margin implies, at full payload, Hohmann min energy transfer only!!!!).
Departing Mars on 4 vac engines, and landing upon Earth on 3 SL engines (250 bar design):
Earth free fall = theo. min dV to land = 0.2 km/s, factor by 1.5 to 0.3 km/s; req’d MR = exp(0.3/3.236) = 1.0971 (figured from SL perf.); dWp/Wig = 1 – 1/MR = 0.089; add 10% for boiloff: dWp/Wig = 0.098.
Loaded Mars takeoff on 4 vac engines direct to min energy Hohmann interplanetary trajectory: min theo. dV = 5.35 km/s, factor up 2% for gravity and drag, dV = 5.46 km/s; req’d MR = exp(5.35/3.677) = 4.284 (figured for vac perf.); dWp/Wig = 1 – 1/MR = 0.767; total Wp/Wig = 0.865, with only 0.823 available at full rated payload! Therefore, payload must reduce!
Estimate takeoff Wig = 1100 tons propellants/.865 = 1272 tons. The difference 1335-1272 = 63 tons is the required payload reduction for the return trip, with no propellant margin at all. Max return payload = 100 – 63 = 37 tons, and that is for a min-energy Hohmann transfer trip!!!
There is not much change, if any, to the 31-engine first stage (BFR). The real changes are a lengthened payload section and 3 large fins, for the second stage (BFS). The vertical fin is fixed (and termed more of a landing leg than a fin by Musk), while the other two articulate about hinge lines for aerodynamic control during entry and landing. These 3 fins replace the four folding landing legs previously shown.
The articulation varies from roughly 45 degrees away from the vertical fin during entry and descent, to a 120 degree separation at landing, and during initial boost at launch. Per Musk, actuation forces for the articulated fins are “in the mega-Newton class”. See Figure 1 and Figure 2.
The best-estimated landing sequences are shown in Figure 3. Musk’s September 2018 presentation included a landing computer simulation video that he showed twice. It was clearly an Earth entry and landing, as effective deceleration to subsonic in the vertical-descent “skydiver” broadside-to-the-wind mode, would be impossible to achieve in the thin air on Mars.
For the Mars landing, the 2017 presentation’s computer simulation video is still the best guide, leading to a very low-altitude transonic pitch-up into a sort of tail-slide maneuver, to position the vehicle tail-first for its final touchdown. However, it is likely that thrust must be used to effect the pitch-up into the tail-slide, because lift equal to weight requires Mach 2-to-3 speed in such thin air.
That means landing thrust must start at end-of-hypersonics at about Mach 3 (about 0.7 km/s).
For those worried about the fin tips digging into the soil on Mars, here are some allowable soil bearing pressure data for selected Earth materials, which might be similar to some soils on Mars. Design practice requires static exerted pressures be less than these allowables. For dynamic events, design practice says stay under half these allowables. The ton in the data is the 2000 lb US ton.
Ton/sq.ft MPa type
1-2 0.1-0.2 fine loose sand
4-6 0.38-0.58 compact sand and gravel, requiring picking
8-10 0.76-0.96 hardpan, cemented sand and gravel, difficult to pick
10-15 0.96-1.43 sound shale or other medium rock, requiring blasting to remove
25-100 2.4-9.56 solid ledge of hard rock, such as granite, trap, etc.
Eyeballed Fin Dimensions, Etc.:
Looking at the BFS images in Figures 1 and 2, we might estimate fin dimension root-to-tip as about equal to basic body diameter, which is said to still be 9 m. That puts the fin tips about 13.5 m off of vehicle centerline. With articulation to 120 degree spacing, these tips form an equilateral triangle as the “footprint”.
That puts the shortest distance from the vehicle centerline to the adjacent footprint edge (halfway between two tips) at about 6.75 m. The “span” from there to the opposite fin tip is 6.75+13.5 = 20.25 m. The vehicle itself is over 50 m long, so the height to effective span ratio is about 2.5 to 3. For the 2017 design with 4 landing legs, this fell in the 3-4 range. Some slight improvement in rough-field landing stability may have been obtained, by going to the fin-as-landing-leg approach.
The rounded tips on the rear tips of the fins cannot be more than 1 m diameter, as eyeballed from the images. That puts the total supporting bearing area for 3 fins at about 2.35 sq.m. Exerted static bearing pressure at landing weight on Earth is 0.98 Mpa, and on Mars is 0.38 MPa. Exerted static bearing pressure at BFS-only takeoff weight on Earth is 5.6 MPa, and 2.1 MPa on Mars.
Mars regolith in many places looks like sand and gravel requiring picking, in other places like loose fine sand. It would appear the BFS could land on the sand and gravel requiring picking, but not the loose sand. However, it cannot take off from that sand and gravel, because the weight after refilling with propellant requires a medium rock to support it without sinking-in, and getting stuck, or possibly toppling over and exploding. Prepared hard-paved pads appear to be fundamentally necessary for this design, unless the fin tip landing pad area can be at least tripled.
Issues Not Fully Explored Here, But Still Quite Critical:
#1. Rough field landings: both soil bearing pressures and overturn stability on rough ground or because of obstacles under a landing pad. This requires serious attention!!!
#2. How to seal organic-binder carbon composite propellant tank structures against propellant leakage, and also have this sealing (and the basic structures) survive at cryogenic temperatures. None of this has been made public yet.
#3. How to keep hot slipstream gases from scrubbing the leeside windows and composite structure. These hot scrubbing flows result from the flow fields at high angle-of-attack, that are induced by vortices shed from the strong body crossflow component, and from the nose-mounted canard tips. See sketch in Figure 4! This can be a very serious issue for window failure. It was for the Space Shuttle.
#4. How much internal pressurization is required to resist broadside airloads during entry and descent?
#5. No designs have yet been presented for cargo and tanker versions. In particular, the tanker design affects how many tanker refilling flights are necessary for BFS to depart from LEO.
#6. Estimated costs per launch from Spacex are unavailable. Some things seen recently on the internet suggest ~ $300 million per launch. For 100-ton payloads, that is ~ $3 million per ton, for the one flight. Such figures are entirely unreliable as yet, and likely will remain so, until several flights into LEO have been made.
#1. Article dated 4-17-2018 and titled “Reverse-Engineering the 2017 Version of the Spacex BFR” located on this site at, authored by G. W. Johnson.
#2. Article dated 8-23-2018 and titled “Back-of-the-Envelope Rocket Propulsion Analysis” located on this site at, authored by G. W. Johnson.
#3. Article dated 9-11-2018 and titled “Velocity Requirements for Mars” located on this site at, authored by G. W. Johnson.
Figure 4 – How Crossflow Vortices Greatly Enhance Lee-Side Heating Rates