Monday, March 6, 2017

Reverse-Engineered "Dragon" Data

Reverse-Engineering What the Versions of “Dragon” Can Do       
GWJ       2-17-17                 updated 3-5-17

Sources:  Spacex’s website and the Wikipedia articles on cargo Dragon,  crewed Dragon,  and Red Dragon.  There is also DragonLab,  which is a very close variant of cargo Dragon.  These give dry weights for the spacecraft that seem to include the associated trunks,  except in the case of Red Dragon,  which is listed in a very sparse article as “6.5 ton plus payload up to 1 ton”.   Comments made in public by Spacex have indicated the possibility of more than 2 metric tons payload to Mars for some time now. 

Cargo Dragon:  The Wikipedia article lists dry mass as 4200 kg,  and speaks of a chute drop test at 5400 kg that includes a max cargo weight of 2500 kg.  Propellant quantity for the Draco thrusters is no longer on Spacex’s site,  but was once listed as just about 1290 kg.  The capsule has a jettisoned nose cone fairing for ascent,  for which a wild guess is 50 kg. 

The ocean landing test configuration would be capsule dry mass plus max rated cargo,  plus some propellant residual if not jettisoned after entry and chute deployment.  Being toxic,  they should be jettisoned before recovery is attempted by humans.  I assumed zero propellant residuals,  so that the actual capsule and trunk dry masses could be determined in this way:

Both the website and the Wikipedia article list max cargo “up” as 6000 kg,  with at most 3000 kg in the capsule,  and with 3000 kg unpressurized in the trunk.  Max “down” cargo is listed as 2500 kg in the capsule,  with up to 3000 kg of waste in the trunk to be destroyed on entry.  Max cargo available to be carried to the ISS is listed in the Wikipedia article as 3310 kg,  presumably a max of 3000 kg in the capsule,  and the rest in the trunk.   The station’s arm is used to unload items in the trunk.

Weight statements for cargo Dragon can now be estimated to the accuracy that trunk dry mass estimate is accurate,  and that the nose cone mass can be guessed.  For three possible cargo loadouts these are:

Compare the launch weights above with Falcon-9 capability to LEO from Spacex’s website.  If flown as an all-expendable launcher,  the rocket can send 22.8 metric tons to LEO,  and only as a guess probably something close to perhaps 15-17 metric tons to ISS.  All the cargo Dragon estimates shown above fall well within that capability,  at none over 11.5 metric tons.  Whether the booster core is recoverable at 11.5 tons is just not determinable (the website does not list those reduced payload limitations).

One of the things in the weight statement is the set of ignition and burnout weights for the capsule-only,  no trunk.  Cargo Dragon is not operated that way,  however!  It retains the trunk until after the reentry burn.  So it is capsule-plus-trunk ignition and burnout weights that we are really interested in. 

To get those ignition and burnout weights,  you add the capsule-only ignition weight and the total loaded trunk weight for capsule-plus-trunk ignition weight,  from which you delete the propellant for burnout weight.  This leaves out the nose cap,  which was already jettisoned during ascent.  

The cargo Dragon has 18 Draco thrusters arranged in two pods of 4 and two pods of 5 within the outer mold line.  These provide attitude control and maneuvering delta-vee,  plus re-entry delta-vee.  Each Draco is about 90 lb thrust (400 N).  These burn NTO-MMH,  for which one might assume Isp = 335 sec for a “good vacuum” engine design,  meaning a long bell for high expansion ratio.  The corresponding mass ratios (MR) and max theoretical delta-vee capabilities for capsule-plus-trunk are:

Crewed Dragon (Dragon v2):  This is the same basic capsule pressure shell and mold line,  modified for four protruding pods,  each pod containing two Super Draco thruster engines and four Draco thrusters for attitude control and minor maneuver.  The Super Dracos are listed on the Wikipedia article as 16,000 lb thrust (71 KN) each.  They use the same propellants as the Dracos.  Spacex’s website lists the eight total Super Dracos as having 200,000 lb axially-directed thrust (890 KN).  Older versions of the site listed the propellant load as just about 1890 kg.

The Wikipedia article lists dry weight as 6400 kg,  which apparently includes an empty trunk.  This capsule has the same chutes,  a retained reusable nose cap,  crew life support,  crewed interior seats and fitments,  and landing legs.  The trunk is of similar size,  but arranged with conformal surface solar panels instead of folding solar panel wings.  It does have four aerodynamic fin surfaces for aerodynamic stability during crew escape situations.  There is no information available anywhere I can find by which to separate the trunk dry mass from the capsule-plus-trunk dry mass. 

Crewed Dragon operates in space as capsule-plus-trunk,  until after the reentry burn,  when the trunk is jettisoned.  The Wikipedia article lists exactly the same cargo masses and volumes as for cargo dragon.  Unlike cargo Dragon,  crewed Dragon uses the chutes only as a safety backup landing method,  or for landing in the ocean.  Its intended mode is a propulsive landing on dry land with the Super Draco engines,  no chutes at all.  Because of this,  both the capsule-only and capsule-with-trunk max theoretical delta-vees are of interest.  Note however that you cannot achieve both simultaneously,  because there is only one propellant supply to be used for both purposes! 

The best I could do was to simply assume the two trunks were comparable mass in spite of the design differences.  The uncertainty in the resulting data is dominated by that assumption.  Again,  I assumed Isp = 335 sec for an exhaust velocity of 3.285 km/s.  Using cargo Dragon’s trunk mass, the crewed dragon capsule dry mass (which includes the reusable nosecone) is:

This capsule-only dry mass is slightly more than 2 tons higher than cargo Dragon,  but there are the eight Super Draco engines,  an uprated heat shield,  landing legs,  life support,  and crew seats and fitments to consider,  so it is “reasonable”.  From this, one can estimate the same sort of weight statement breakout already reported for cargo Dragon,  including both capsule-only and capsule-plus-trunk ignition and burnout weights.  I did this for only one crew/cargo value,  chosen to approximate a capsule-only delta-vee of 0.7 km/s to compare with Red Dragon.

These figures show comparable values of capsule-plus-trunk delta-vee to cargo Dragon’s ~0.5 km/s,  which is realistic,  considering crewed Dragon is a derivative design,  operating in the same capsule-plus-trunk configuration.  The slightly-higher capsule-only figure is to compare with crewed Dragon’s unmanned derivative Red Dragon (for one-way probes to Mars).  Note that this would vary significantly as crew/cargo is adjusted.  Under the assumptions of 100 kg person,  100 kg suit,  50 kg air and water,  we are talking about 7 crew plus 1050 kg cargo in this 2800 kg loadout.  The weight to launch falls well within the Falcon-9’s LEO capability,  being just about like the heaviest cargo Dragon presented above.

Red Dragon:  This is the crewed Dragon with the crew seats and fitments,  life support,  and chutes removed,  and some equipment racks installed.  The heat shield is reduced in thickness as well.  Since the vehicle is not to be reused,  a jettisonable nose cap like that of cargo Dragon is assumed.  It will need some sort of trunk for launch and for electricity during the trip,  but this is jettisoned before Mars entry.  Course correction burn is assumed trivial,  so that essentially the entire propellant load is available for powered landing on Mars. 

There are no available data for the masses of any of the change items just discussed.  All that is available are wild guesses and educated guesses.  The lighter heat shield I estimated as a reduction from 8 cm thick to 6 cm thick,  on a flat circle 3.7 m diameter,  and a specific gravity of ~0.3 for PICA-X.  I just rounded off to the nearest 10 kg.  It’s just too rough not to round off like that.    

I have just assumed the same trunk mass as I used for cargo and crewed Dragons.  Trunk mass dominates the uncertainty,  being the largest item.  I simply took the crewed Dragon estimated dry mass,  and subtracted things.  Those guesses are listed in this estimate for Red Dragon dry mass:

If I load this vehicle with 1 ton of cargo and 1890 kg propellant,  then mass at entry is 7640 kg,  which is not far at all from the 7500 kg indicated the Wikipedia article!  1 ton of cargo is what is indicated as deliverable to Mars in that same article.  (Some public announcements indicate that 2-4 tons are actually under consideration at Spacex.)

Using these figures,  the weight statement for Red Dragon can be roughly estimated.  What is of interest here is the capsule-only delta-vee,  as a function of cargo delivered to the surface of Mars.  Bear in mind that an utter minimum delta-vee capability for powered landing will be near 0.7 km/s,  the Mach 3 point coming out of atmospheric entry hypersonics.  There’s very little in the way of gravity and drag losses to correct the theoretical delta-vee in this scenario.  The error is less than the uncertainty in the basic requirement.

The 0.7 km/s figure is pretty rough,  that being 3 times the nominal speed of sound in the Martian atmosphere at something like 5 km altitudes.  This could vary quite a bit.  In order to successfully land reliably,  you actually need a little more delta-vee to cover final maneuvering around obstacles. 

The Mach 3 point is also a bit arbitrary,  that being only the definition of min-hypersonic for blunt objects.  Prior probes deployed chutes at local Mach 2 to 2.5,  although they did this much higher up (15-25 km altitudes or more).  Waiting to lower speeds lets you penetrate to lower altitudes,  while heavier items also penetrate to lower altitudes,  simply because of higher ballistic coefficients. 

The 0.7 km/s “requirement” I use here is thus just a figure of merit,  although it is actually in the ballpark of the true requirement.  

These numbers are too rough to judge “for sure”, but it looks like 1 or 2 metric tons should be easily deliverable to Mars with Red Dragon,  just like Spacex has indicated.  These numbers say 3.2 tons is getting to be quite marginal,  but that would actually depend upon what the true landing delta-vee requirement really is.  Note that the requirement would vary with location and season across Mars,  as that atmosphere is much more variable in its density than is Earth’s. 

Spacex’s website lists Falcon-Heavy as able to send 13.6 metric tons to Mars,  flown fully-expendably.  All these configurations fall within that capability.  Even at 4 tons cargo,  the weight to launch would be just about 12 tons,  which still falls within the launch capability.  Therefore,  it will be landing delta-vee that sets the payload deliverable to Mars!  That may explain the “extra propellant” remark found in the Wikipedia article.  Whether 11 tons at launch is small enough to recover the booster cores is unknown. 

DragonLab:  this is cargo Dragon with an instrument bay between the pressure shell and the outer mold line.  The door on this bay opens to space,  and recloses before entry.  It is otherwise the same as cargo Dragon,  so no separate analysis is done here.    Use my figures for cargo Dragon to represent DragonLab.

Using variants of Red Dragon as unmanned one-way probes elsewhere:  This depends on the delta-vee requirement to land,  relative to the vehicle capability.  For airless destinations with direct landings from the interplanetary trajectory,  several-to-many percent above the body’s escape speed is a figure of merit.  Example:  Mars escape 5 km/s,  typical direct entry speed 6 to 7 km/s.  Call it 1.5 Vesc as a typical figure of merit.  Remember that this is only a very crude estimate,  unlikely to be correct!

Potential destinations include the moons of Jupiter and Saturn,  the asteroids,  and our own moon.  Mars and Venus have atmospheres that allow aerobraking to a propulsive landing,  as does Titan at Saturn.  Mercury requires all-propulsive landing,  as does the moon.  Values of escape speed and surface gravity strength follow.  I did not include Venus because landed vehicle lifetime would be too short,  if it made it down to the surface at all.  I also did not include Earth itself.

The first thing apparent from the list is that any of the asteroids,  Titan,  and Mars all seem to be within reach of Red Dragon on a Falcon-Heavy,  just as it is.  The significant atmospheres of Mars and Titan make aerobraking feasible,  the rest are airless or so tenuous as to make aerobraking infeasible.  Like the Earth’s moon,  the moons of Jupiter seem out-of-reach,  due to escape speeds that are too high.

As a one-way probe destination,  Earth’s moon is interesting on its own.  Key here is getting into lunar orbit using the upper stage of the launch rocket,  without using any of the Dragon’s propellant.  As it turns out,  that delta-vee requirement for the launch rocket (no more than 12.4 km/s) is very similar to that for sending things to Mars (at least 12.1 km/s).   Those figures include 5% gravity/drag losses on the first 8 km/s of that delta-vee.   From there it takes 1.68 km/s to make a powered landing.  That’s out-of-reach for Red Dragon without considerable extra propellant. 

It might be more desirable to instead enter lunar orbit with a crewed Dragon,  and let them rendezvous in lunar orbit with a separately-sent lunar lander.    

The lander must descend and ascend to a delta-vee of essentially the orbit velocity each way, for an utter minimum of something like 3.36 km/s plus a tad for gravity losses.  At the moon,  the crew needs a minimal place to ride,  not a full capsule,  but the stage does need landing legs.  It needs to carry surface stay gear and a rover,  as well.  That design is not explored here.

As for the missions to the outer moons,  there needs to be a fairly-large propulsion stage added to the Red Dragon.  It seems like the Dragon probe assembly could be sent to Earth orbit on a Falcon-9,  and the propulsion stage sent there with a Falcon-Heavy,  to be docked together in orbit,  and launched on its mission from there.  Very much better information on velocity requirements is needed to size such an exploration stage design.  That is not addressed here. 

Conclusions:  Red Dragon as presently envisioned works for Mars,  Titan,  and any of the asteroids.  The other outer planet moons require a fairly large powered stage added to the Red Dragon to achieve the necessary delta-vee for capture and landing.  The combined weight exceeds Falcon-Heavy capabilities for direct interplanetary trajectories,  so that something other than direct launch to interplanetary travel is required.  Falcon-Heavy is able to fling 13.6 metric tons to Mars,  perhaps 12-13 tons into lunar orbit.

For Apollo-like lunar missions,  crewed Dragon with extra propellant in the trunk (yielding near 1.6 km/s capability) fits one Falcon-Heavy,  and a lander not based on a Dragon fits another Falcon-Heavy.  These need to weigh under 12-13 metric tons to be successfully launched direct from Earth’s surface,  and must rendezvous in lunar orbit.   Red Dragon itself,  as it currently is envisioned,  seems unattractive for one-way missions to the moon,  with a direct landing delta-vee near 2.4 km/s.  However,  whatever added propulsive stage works for the outer planet moons would work at Earth’s moon. 

Addendum 3-4-17:

I looked very crudely at how much propellant to carry in the trunk to enable a crew Dragon to depart from lunar orbit and still have propulsive landing capability at Earth.  This would be for a crew of only two,  with their suits,  and about 500 kg of supplies and samples.  I did actually add propellant tank inert mass to the trunk (about 147 kg),  which requires iterations.  One needs the trunk for electrical power during the trip home to Earth,  so it is capsule-plus-trunk mass ratio and delta-vee that are pertinent. 

Results are given in the Figure just below.  It is slightly over 12 metric tons as launched.  Falcon-Heavy just might be able to deliver this to lunar orbit with a delta-vee of no more than 12.4 km/s,  because Spacex’s website says it can send 13.6 metric tons to Mars (with an estimated delta vee no less than 12.1 km/s).  Those delta vee estimates are my calculations made using Hohmann min-energy transfer ellipses at orbital semi-major axes that produce the largest delta-vee requirements,  and for which I applied 5% gravity and drag loss to the first 8 km/s getting off the surface of the Earth. 

The capsule-plus-trunk needs about 0.8 km/s sec to depart lunar orbit onto a free-fall homeward trajectory to an aerobraking entry.  It perhaps needs about 0.7 km/s capability to cover a propulsive landing on land,  per the basic design of the crewed Dragon.  The total is 1.5 km/s,  for which a few percent margin gets you quickly to 1.6 km/s capability.  The configuration shown in the figure has such capability by adding some 2800 kg pf propellants to the trunk,  in tankage weighing about 147 kg.  That total is 2947 kg,  within the 3000 kg cargo rating of the trunk.  It is the capsule that is lightly loaded at only 2 suited persons plus modest supplies.  Adding a third crew person pushes the total closer to 13 metric tons,  just about the limit that Falcon Heavy could possibly deliver to lunar orbit.  

Addendum 3-5-17:

The same sort of added propellant in the trunk could also be done with Red Dragon.  Note that I have already pretty much defined the maximum propellant already at about 2800 kg.  Red Dragon being similar to crew Dragon,  the capsule-plus-trunk delta-vees will fall far short of what is needed to capture and land on the outer planet moons (1.6 km/s or thereabouts versus 2.5+ km/s).  The capsule-only value indicated in the figure is wrong,  because most of that propellant must be in the trunk.  

I’m not at all convinced that a capsule is the best vehicle by which to send probes to the airless bodies,  including the asteroids,  which Red Dragon could certainly reach.  But Red Dragon should serve very well for probes to Mars,  and maybe Titan.  With aerobraking entry,  a capsule and heat shield are necessary. 

Crewed Dragon could easily become part of a system to send men back to the moon with very few changes from what will start flying this year.  Flyby missions need no changes,  and orbit missions require some extra propellant in the trunk for the Super Dracos.  Landings will require a separate lander sent ahead to lunar orbit unmanned,  for the crew to rendezvous with and utilize.  If such a lander totals under 12-13 metric tons,  Falcon-Heavy could fling it to lunar orbit launched directly from Earth’s surface. 

Final Comments as of Posting 3-6-17:

Enjoy!  These figures may not be exactly right,  but they are pretty close.  I suggest you create spreadsheets to calculate delta-vee in capsule-plus-trunk configurations for cargo Dragon and for crewed Dragon,  and for both capsule-plus-trunk and capsule-only Red Dragon.

Then,  given real delta-vee data to reach a destination,  you can compute for yourself whether the corresponding Dragon configuration can reach it.  Be sure to factor-up astronomical values for gravity and drag losses where those apply.  This is required before you size mass ratios and weight statements.

There's no information out there about it,  but I would hazard the guess that Spacex is already looking at versions of crew Dragon and Red Dragon that have extra propellants in the trunk.  That just makes too much sense for them not to be doing that.


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