Bill,
Keep in mind that the Wikipedia Starship dry mass and propellant mass
data I worked from was all labelled "needs updating". In fact, the
remarkably close agreement between my 1111 tons of propellant needed for
a LEO-lunar mission and the Wiki listing of 1100 tons capacity leads me
to suspect the possibility that someone may have backfigured those Wiki
numbers from SpaceX's statements that Starship would be capable of such
missions.
I might guess from the utter public lack of hard data that final stage
masses and overall delta V split of that two-stage system have not in
fact yet been set by SpaceX. I would not be surprised if they're
waiting till they have more flight data from the various prototypes (and
possibly more data as to who the most likely customers are) before they
finally pin all that down.
Which makes perfect sense to me. The more data you have when you
attempt to optimize a system, the better your chances are of actually
arriving at something close enough to optimum to be economically viable.
That said, it occurs to me they may well make the decision to include
enough additional tankage on their upper stage to allow it to fly lunar
surface missions even if that extra capacity isn't used on routine LEO
launches, accepting the additional dry mass penalty for the extra utility.
In fact, some such extra capacity is implicit in the idea of being able
to deliver to LEO either 100 tons dry payload or 100 tons propellant...
Henry
On 8/28/2019 7:16 AM, William Claybaugh wrote:
Jim, et al:
Help me out here: SpaceX’s vehicle is a two stage system. If they have optimally splint delta-v then the upper stage is good for about Mach 15, flying on it’s own. That is not enough energy to get to the lunar surface and return.
It looks to me like the upper stage is probably capable of a circum-lunar mission if fully refueled but is going to require a second refueling to get to the surface and return. Is that not correct?
Bill
On Wed, Aug 28, 2019 at 7:38 AM James Fackert <jimfackert@xxxxxxxxx <mailto:jimfackert@xxxxxxxxx>> wrote:
Henry is the king of analysis on a table napkin!
So about 10 tanker flights to refuel a Starship to head for the
moon. Still no need for a permanent fuel depot.
First tanker parks in refueling position optimal for the mission,
9 (?) more tanker flights meet it, dump their payloads and go back
for more.
Mission Starship meets it, tanks up and heads out, and the prime
tanker heads home for the next mission.
As has been pointed out, there is no optimal position for a depot
and no need to develop a specialized depot until the traffic on
the lunar rail line warrants it.
jim fackert
On 8/27/2019 8:51 AM, Henry Vanderbilt wrote:
RE the commonly-assumed one tanker flight per Starship Lunar mission... When in doubt, run the numbers. Delta V = LN(MR) x Vexh isn't just a good idea, it's the law. (That's natural logarithm of the ratio of the ship's pre-all-burns-mass/post-all-burns-mass, time the rocket motor's exhaust velocity, equals the overall ship's velocity change. All you need is a calculator with an Ln key and you too can play rocket scientist on the internet!)
That said, ahem, I believe SpaceX's proposed LEO-Lunar missions for refueled Starship will require multiple tanker flights.
LEO-Lunar surface requires delta V in the neighborhood of 5.5 km/s, the return roughly 3 km/s less with aerobraked reentry. Ship data: Wikipedia figures (all of which are labeled "needs updating") say Starship dry mass is 85 tons, full propellant load 1100 tons, LEO payload 100 tons. And a good LOX-CH4 engine should manage a vacuum Isp around 360 seconds, AKA exhaust velocity around 3.5 km/s.
So let's assume we're delivering the max 100 ton payload to Luna and coming back empty. So we break the trip down into two parts.
We'll calculate coming back first, because the propellant we'll need to carry for that has to be part of the outbound leg number.
With 3.5 km/s exhaust velocity, the rocket equation says to reach 2.5 km/s delta V to return from Luna to Earth reentry, you need mass ratio 2. So for an 85 ton Starship, that's 85 tons of propellant. Not bad so far, less than one 100-ton Starship payload earth-to-LEO.
But for the outbound LEO-to-Lunar-surface leg, our total ship mass at landing on Luna has to be 85 tons of Starship plus 100 tons of payload plus 85 tons of return propellant, 270 tons. And for the outbound delta V of 5.5 km/s, we need a mass ratio of 4.8. (Propellant+delivered-mass/delivered-mass) So, 3.8 times 270 tons equals 1026 tons of additional propellant in LEO. With the 85 tons return propellant, 1111 total tons of propellant in LEO at the start of our Lunar trip. Given we're using ballpark numbers, that's remarkably close to Starship's listed max propellant load of 1100 tons.
So, that's 11 Starship tanker flights at 100 tons propellant each to support one full-load Starship flight to Luna. You might cut that to 9 or 10 flights by using a stripped-down version of Starship as tanker, but at 85 tons dry for that capability there's not a lot to strip.)
My take, mentioned earlier, is that SpaceX is skipping a LEO propellant depot for these missions not because it wouldn't make sense for them - having a loaded crewed Starship hanging around in LEO through ~10 tanker arrivals is both a cost and a risk - but because a tanker version of Starship is less current load on their already highly-loaded engineering (and likely also fiscal) bandwidth than a separate depot.
I think this is a good business decision, mind - time enough to spend resources on a LEO propellant depot when they get to the point where the costs of ~10 tanker rendezvous per Lunar flight start becoming obvious.
Henry
On 8/27/2019 7:48 AM, James Fackert wrote:
Maybe the orbiting fuel depot as a separate entity is not optimal. The fuel depot implies that there is a requirement for a much larger supply of fuel than a single tanker can bring up.
SpaceX's plan seems to be to launch a big tanker to an appropriate orbit, then launch the ship that needs refueling to meet it, tank up and move along to whatever destination it is headed.
Tanker returns home, to load up to supply the next mission.
When you have a big ship with lots of supplies and living space and stuff for a real long term mission rather than a touch and go, you also have a ship capable of being a tanker that can bring enough fuel in one flight to refuel that ship for an extended lunar or interplanetary mission and return.
Now all you need is a nice big reusable booster to loft those guys. Sound like a plan?
