## Monday, August 6, 2018

### Exploring Mars Lander Configurations

I have corresponded on-line with many people who want to explore what might be feasible as a Mars lander vehicle.  I worked out a configuration sizing and performance analysis,  and coded it into a spreadsheet.   This uses nothing more than algebra and the rocket equation.  I used it to get these results in this article.  If you want a copy of this spreadsheet,  email me.  I would be happy to forward it to you.  This article,  among other things,  is a user's manual for that spreadsheet.  It addresses one-stage,  two-way,  reusable vehicles;  and two-stage,  two-way,  non-reusable vehicles.

There are 4 worksheets in the spreadsheet.  One ("misc"),  is where among other things,  you can guess realistic estimates of vehicle inert mass fraction,  by stage if multi-stage.  Two other worksheets address one-stage and two-stage vehicles.  If two-stage,  all of the descent is handled by one stage,  and all of the ascent by the other.  In all cases,  the same max payload is used for both ascent and descent calculations.

The fourth worksheet is an exploration of re-engining a vehicle with a different propellant combination,  at the same propellant total volume.  That proved not very practical,  because the oxidizer and fuel tank volumes must also change.  That is a core rebuild,  not just a re-engine effort.

If instead,  you want to know what the now-cancelled Red Dragon might have done at Mars,  I worked out a reverse-engineering analysis with minimal but realistic assumptions some time ago,  based on posted Spacex data.  It covers cargo Dragon,  crewed Dragon,  and Red Dragon.  That article is posted at http://exrocketman.blogspot.com as the article dated 3-6-17 and titled "Reverse-Engineered Dragon Data".

"Mars Landers My Way"

Here is a crude but well-in-the-ballpark way to estimate the size and performance of aerobrake/retropropulsion-type Mars landers from the payload masses they must carry.  These would be large vehicles operating between low Mars orbit and the surface.  End-of-aerobraking would be too low for using chutes.

Flight requirement conditions are 3.55 km/s orbital velocity,  0.70 km/s remaining velocity about 45 degrees downward at around 3-5 km altitude for heavy vehicles coming out of aerobraking entry,  about a 2% empirical "kitty" for gravity and drag losses applied to ideal delta-vee,  and a factor 1.5-to-2 scaleup on the min landing delta-vee,  for direct retropropulsive landing without chutes. That's about 1.05-to-1.4 km/s min to land.  An on-orbit rendezvous and maneuver "kitty" is modeled as a user input factor Frm (greater than 1) applied to the ascent delta-vee. This is only slightly greater than one,  if no orbital plane change is required.

Vehicle design requirements depend upon whether the vehicle is one stage or two.  If one stage,  for design purposes, the ascent and descent payloads are assumed the same at the user-input design maximum value.  If two stage,  the same payload assumptions are true,  plus stage 1 is sized for the descent delta-vee,  while stage 2 is designed for the ascent delta-vee.

The inert mass fractions for each stage are user-input values.  Caution should be applied to select reasonable values for designs that must include landing legs,  heat shields,  enough structural robustness to handle rough landings and whatever degree of reusability that the user intends,  and excess vehicle volume to enclose bulky,  low-density payload during aerobraking.  This volume may require pressurization,  and may even need to be compartmentalized under pressure.  It is recommended that these inert fractions be 10% or greater,  even for a simple 1-shot design.

The propulsion model is very simple:  a user-input value for the average delivered Isp out of the engines.  This should be a realistic value factored for real efficiencies and any off-angle mounting effects.  The effective exhaust velocity model is Isp x gc, for use in the rocket equation. Metric gc = 9.807 m/s^2.

Descent engine thrust sizing is based upon 0.7 km/s to be "killed",  along a slant path about 7 km long (assuming a 5 km altitude at 45 degrees),  at the vehicle descent ignition mass,  and Mars gravity (0.384 gee). This is for the total of the descent engines at near full thrust.  It is effectively a 3.6 standard-gee initial deceleration requirement applied to the max descent mass.  (This velocity change is factored-up for losses and maneuvering effects.)

Ascent engine thrust sizing is based upon a force ratio factor (3) applied to the local weight of the ascent ignition mass at Mars gravity (0.384 gee) to achieve about 2 Mars gravity's net upward acceleration.  It works out to about a 3 standard-gee requirement. Rapid accelerations ease control problems by taking advantage of pitch and yaw inertia.  If accelerated rapidly,  the vehicle does not have time to change attitude significantly.

For single stage designs,  the greater thrust requirement of the two,  is actually used.  For two-stage designs,  the thrust requirement (and user-input Isp) can be different for each stage.  Throttle-down capabilities and number of engines making up the thrust are not specified in this sizing procedure.

One-Stage Vehicle Sizing:

User inputs are max payload mass Wpay (kg),  specific impulse Isp (sec),  inert mass fraction Win/Wig,  landing velocity scale-up factor RV (min 1.5,  max 2),  and ascent rendezvous and manuever "kitty" Frm (recommend a number between 1.05 and 1.10 as long as no plane changes are required). This Frm factor applies to delta-vee,  not sized propellant mass.  A summary of results takes the form of an overall weight statement with overall mass ratio and total delta-vee shown.

Exhaust velocity Vex (km/s) = Isp (sec) x 9.807 / 1000
Required delta-vee capability dV (km/s) = 0.7 * RV + 3.55 * 1.02 * Frm (first term descent delta-vee,  second term ascent delta-vee)
Mass Ratio MR = exp(DV/Vex)
Propellant fraction Wp/Wig = 1 - 1/MR
Payload fraction Wpay/Wig = 1 - Win/Wig - Wp/Wig (infeasible if negative or zero)
Ignition Mass Wig (kg) = Wpay/(Wpay/Wig)
Propellant Mass Wp (kg) = Wig*(Wp/Wig)
Burnout mass Wbo (kg) = Wig - Wp
Thrust requirement Fth (KN) = larger of {Wig * 3 * 9.807 / 1000 or 3.6 * 9.807 * Wig / 1000} pending number of engines and which are used

Two-Stage Vehicle Sizing (stage 1 descent,  stage 2 ascent):

User input max payload mass Wpay (kg),  specific impulses Isp1 and Isp2 (sec) for stages 1 and 2,  inert mass fractions Win1/Wig and Win2/Wig for stages 1 and 2,  landing velocity scale-up factor RV (min 1.5,  max 2),  and ascent rendezvous and maneuver "kitty" Frm. A summary of results takes the form of descent and ascent weight statements,  with stage mass ratios and delta-vees shown.

Exhaust velocities Vex1 and Vex2 (km/s) = Isp (sec) x 9.807 / 1000 for stages 1 and 2

For the ascent stage required delta-vee capability dV2 (km/s) = 3.55 * 1.02 * Frm
Ascent stage mass ratio MR2 = exp(dV2/Vex2)
Ascent propellant fraction Wp2/Wig2 = 1 - 1/MR2
Ascent payload fraction Wpay/Wig2 = 1 - Win2/Wig2 - Wp2/Wig2
Ascent ignition mass Wig2 (kg) = descent payload mass = Wpay/(Wpay/Wig2)
Ascent propellant mass Wp2 (kg) = Wig2*(Wp2/Wig2)
Ascent burnout mass Wbo2 (kg) = Wig2 - Wp2
Ascent thust requirement Fth2 (KN) = Wig2 * 3 * 9.807 / 1000

For the descent stage required delta-vee capability dV1 (km/s) = 0.7 * RV
Descent stage mass ratio MR1 = exp(dV1/Vex1)
Descent propellant fraction Wp1/Wig1 = 1 - 1/MR1
Descent payload fraction Wpay/Wig1 = 1 - Win1/Wig1 - Wp1/Wig1
Descent ignition mass Wig1 (kg) = Wig2/(Wpay/Wig1)  recall that the ascent stage ignition mass is the payload for the descent stage
Descent propellant mass Wp1 (kg) = Wig1*(Wp1/Wig1)
Descent burnout mass Wbo1 (kg) = Wig1 - Wp1
Descent thrust requirement Fth1 (KN) = Wig1 * 3.6 * 9.807 / 1000

User inputs include the average bulk density of the payload materials,  and an effective packing fraction for how tightly-together the individual items are spaced.  A minimum value of the payload bay volume is then based on the sized max payload mass:  vol (cu.m) = Wpay (kg) / (1000 * specific gravity * packing fraction).  This is true for any design.  The vehicle dimensions depend upon what specific configurations are to be analyzed. That is beyond scope here.

One-Stage Vehicle Performance Estimates

The nominal design performance estimates presume the same max payload in ascent as in descent.  The vehicle is presumed to be fueled on-orbit about Mars,  and must return to orbit for any refueling.  The descent and ascent delta-vees are used separately to determinine mass ratios,  to define the individual descent and ascent propellant masses,  and thus the ascent ignition mass.  Results take the form of a two-burn weight statement,  with two mass ratios and two delta-vees shown,  and an overall payload fraction.  Also shown are the mass percentages of propellant capacity used in each burn.  Because thrust is defined from initial descent ignition mass,  this ignition mass value is taken to be a design limit.  Because the propellant tankage is of fixed size,  the design total propellant mass is taken to be another design limit.

If used for a one-way descent,  there is no need to carry the ascent propellant,  and its mass equivalence may be added directly to max payload.  This stays within both the ignition mass and propellant mass design limits.  The results are reported as a one-burn mass ratio and delta-vee,  with percent of propellant capacity that is actually loaded also shown,  plus an overall payload fraction.  This payload is very much larger than the nominal design value for two-way operation.  To recover and re-use the vehicle,  there must be propellant refueling capability on the Martian surface. Using user inputs for payload mean density and packing fraction,  a min payload containment volume is also defined and shown.  This payload is the largest for the one-way descent scenario.

If propellant refueling capability is available on the surface,  then a one-way ascent also becomes possible at somewhat-increased payload.  One will hit the max ignition weight limit before hitting the design propellant capacity limit,  for any properly-sized design.  Using the ascent delta-vee and max ignition mass,  the burnout mass can be determined,  and with it,  plus the inert mass of the design,  can also be determined the ascent propellant mass,  and the total payload that can be carried,  which will exceed the two-way design value.  These results are presented as a one-burn weight statement,  with mass ratio,  delta-vee,  and percent of propellant capacity actually loaded.  Payload mass fraction is also shown. Such a vehicle could be refuelled on-orbit,  and re-used.

Overall,  the nominal one-stage two-way vehicle configuration design result is a very large vehicle that carries a rather small payload on the design two-way mission.  This very same design can carry enormous descent cargo if used one-way,  then refueled on the surface.  It also gets a significantly improved ascent cargo,  if operated one-way from the surface,  having been fueled there.

Typical One-Stage,  Two-Way,  Reusable Results

Figure 1 shows where some of the numbers used in the analysis came from.  The 3 ton payload presumes a man with suit and spares,  and a month's open-cycle food, water,  and oxygen,  all masses half a ton.  A crew of 3,  plus half a ton of instruments and equipment,  and a one-ton rover car,  totals to 3 tons of payload.

Figure 1 -- Design Analysis Assumptions for One-Stage Two-Way Vehicle

This figure includes a result from a semi-organized way to guess a ballpark inert mass fraction for the vehicle structure.  That figure also shows the basic assumptions made about the lander configuration.  There is a center cylindrical core containing the propellant tanks,  a sealed engine compartment,  and a crew control cabin that could also be an abort-to-surface escape capsule,  somewhat similar to the Red Dragon concept from Spacex.

Around this core is a conical volume containing the ascent or descent cargo.  There are a heat shield and extendible landing legs attached to the cargo deck,  that in turn is the frame tying the vehicle together.  The conical cargo volume is pressurizable in a compartmented sense,  and can serve as considerable crew habitation volume.  It is deliberately sized to contain a large amount of low density cargo at low packing fraction.  The overall shape resembles the old Gemini capsule.

Because the engine compartment is otherwise sealed,  the engines can fire through openings in the heat shield without any closures during aerobraking,  since there is no through-flow into a dead-end passage.  A static gas column is the best insulator of all.

Figure 2 shows the sized results at 330 sec specific impulse (a typical figure for a fairly large expansion bell,  using storables like MMH-NTO).  The most notable result item is the low payload mass fraction,  because of the high inert fraction more-or-less inherent with this kind of design.  A higher-specific impulse propellant combination (such as liquid methane - LOX) would offset the inert mass fraction effect some,  and push the vehicle to a higher payload fraction. Liquid methane - LOX is thought to be producible on Mars,  given an adequate source of water ice. At 330 sec (storables) and 0.2 inert fraction,  payload is just over 2.1% of ignition weight.  At 360 sec Isp (more like liquid methane-LOX),  this rises to just over 8.0%.

Figure 2 -- Sizing and Nominal Performance Results for One-Stage Two-Way Vehicle

Figure 3 shows the descent and ascent performance possibilities obtained with surface refueling of this very same vehicle,  using the sized ignition mass and sized propellant quantity as hard limits.  Ignition mass sized the engine thrust,  which requires a thrust increase if it grows.  The propellant tanks are of fixed volume,  which renders max loaded propellant mass a constant. Note the remarkably-large payload mass fraction available in this vehicle if operated one-way in descent,  assuming surface refueling for re-use.  The effect during ascent is much smaller,  but still considerable,  for a surface-fueled,  one-way ascent. For 330 sec and 0.2 inert,  the descent payload fraction rises from 2.1% to over 52%,  and the ascent payload fraction rises from that 2.1% to about 9.2%.

Figure 3 -- Performance of One-Stage Two-Way Vehicle Operated with Surface Refuelling

Overall, the conclusion here is that,  given the "right" propellants compatible with surface refueling, this rather limited two-way payload capability dramatically grows into a very versatile one-way capability,  made reusable in that mode with that surface refueling. This kind of design approach offers great promise of long and versatile service life without any need to develop new vehicles.

One final observation:  it might be wise to upsize the design thrust per engine in a multi-engine cluster,  in order to cover an engine-out situation.  This requires increasing further the engine turndown ratio,  plus shutting down even more engines later in the trajectory, in order to stay within a nominal 3-4 gee ride limitation.

Two-Stage Vehicle Performance Estimates

These estimates are easier and less extensive.  The vehicle is fundamentally non-reusable.  The ascent stage and mission payload are together the payload of the first stage (descent stage).  Each stage is already a one-way,  one-use item.  There is only nominal design performance at max payload to evaluate for each stage.  You do the ascent stage first at the ascent delta-vee,  then use its ignition weight as the effective payload for a descent stage evaluated at its delta-vee.  These numbers are computed as part of the sizing process.  They get reported as a two-stage combined weight statement,  with mass ratios and delta-vees for the two flight segments.  Overall payload fraction is also shown.  Propellant tanks are always filled to capacity in a vehicle delivered to low Mars orbit.

The only variation would be to replace the ascent stage with a simple payload pod of equivalent total mass to the ascent stage.  This is the only way available to increase the payload mass deliverable by a descent stage to the surface.  The disadvantage is that this delivery of increased cargo delivers no ascent stage at all.

Typical Two-Stage,  Two-Way,  One-Shot Results

The assumptions and configuration approaches for the two-stage,  two-way,  one-shot design are given in Figure 4.  Note that there is no backshell for the hypersonic entry.  Instead,  exposed structures need a thin coat of an ablative,  perhaps Avcoat.  The plasma is quite hot,  but the flow velocity and its heat transfer scrubbing action are much reduced,  compared to the windward side of the heat shield.  The descent stage propellant tanks are tapered,  so as to be out of direct windblast,  even at fairly high pitch or yaw angles during hypersonic entry.

Figure 4 -- Assumptions and Source Data for Two-Stage One-Shot Vehicle Design

What obtained was a very much smaller lander-and-ascent vehicle,  as described in Figure 5,  which gives sized data and nominal performance,  plus a max cargo delivery variant without an ascent stage. Replacing the ascent stage with a cargo pod significantly increases the deliverable payload mass.  I used a 10% inert fraction for this cargo pod,  on the assumption that it be designed as pressurizable and compartmentalizable.  That way,  additional habitable space could be brought down by this variant.  The "standard" form with the ascent vehicle has a pressurizable cargo bay,  but it is quite small,  too small for an extended visit without some augmentation sent down by other means.

Figure 5 -- Nominal and Max-Cargo Variant Performance for the Two-Stage One-Shot Lander

There is one design possibility here that could possibly reduce inert weight further,  something that directly increases payload fraction in any scenario.  That would be to use the ascent engines as part of the descent engine count.  That would reduce the number of engines to be incorporated in the design,  but it would require a switchable propellant interconnection between the two stages,  one that must be disconnected entirely,  before the ascent stage can lift off.  Whether the engine count reduction reduces inert weight more than the propellant interconnection hardware increases it,  is an unknown that remains to be seen. That level of detail requires real detail design,  which this configuration study is not.

One-Shot Versus Reusable Effects

The one-shot,  two-stage vehicle carries the same payload as the one-stage reusable vehicle,  but is very,  very much smaller overall.  In part,  this is the staging effect,  which for this application is going to be inherently non-reusable.  When required delta-vee is high,  the propellant mass fraction is also very high,  with an exponential dependence.  Since propellant mass fraction,  inert mass fraction,  and payload mass fraction must add linearly to unity,  then for a demanding delta-vee,  often the payload fraction is quite tiny,  or even infeasible as a negative number. Staging is a way to reduce the required delta-vee on each portion of the vehicle,  so that feasible payload fractions result.

With staging and inherent non-reusability,  there is no need to build the structures capable of withstanding the rigors more than once.  That leads to lower inert fractions,  reflecting the more fragile structure.  That is why the stage inert fractions in the two-stage non-reusable vehicle are lower than the inert fractions in the one-stage vehicle that is intended to be reusable.  Lower inert fractions also lead to larger payload fractions,  for any given delta-vee and its corresponding propellant fraction.  The two effects together produce the great disparity in ignition masses for the two designs.

Propellant Selection Effects

The propellant combination assumed for both configuration designs was the well-known storable combination MMH-NTO.  Storables require simple,  lightweight tankage,  and are good for long times between firings (days,  months,  even years).  Cryogenics can only use simple,  lightweight tankage if the time between loading propellant and its use is relatively short (hours-to-days only).  Otherwise,  they need insulated tanks or Dewar flasks,  and perhaps powered cryocooler rigs.  This increases inert mass fractions,  a choice which has since been added to the spreadsheet's "guess-the-inert-fraction" feature.

For nozzles firing into vacuum, or near-vacuum as is the Martian atmosphere,  expansion bells can be large,  and the specific impulse higher than at sea level on Earth.  That is where the 330 sec value used in the design study came from.  This value of specific impulse is easily converted to a good approximation of the exhaust velocity,  for the purpose of doing configuration studies with the rocket equation.  For a real detailed design,  you need to do real engine-nozzle ballistics with a real engine design. That is out-of-scope here.

Higher specific impulse is higher exhaust velocity,  leading to smaller propellant fraction for a given delta-vee demand. The one-stage reusable vehicle configuration is right at the "hairy edge" of feasibility with 330 sec of specifc impulse,  with the result of a very low payload fraction.  For a given payload requirement,  that makes the vehicle ignition weight very large.

MMH-NTO is not a combination currently contemplated as a possible thing to manufacture on Mars from local resources.  The mild cryogen combination liquid methane-LOX is a good candidate for local manufacture on Mars.  Its vacuum-bell specific impulse will be nearer 360 sec.  That is a significant increase in specific impulse and effective exhaust velocity over the storables,  leading to a significant decrease in required propellant mass fractions.  For the same inerts otherwise,  this could be a significant increase in payload mass fractions.

The first inclination is to try this higher specific impulse in both designs.  However,  mission practicalities say otherwise.  The two-stage one-shot lander is sent from Earth to Mars orbit,  or to a direct entry.  The journey there is months long.  That is fine for the storables,  but not for the mild cryogens.  Inert mass fraction must increase for the insulated Dewar tankage and cryocoolers required for the months-long voyage to Mars.  Plus,  the design is inherently one-shot.  It will never be refueled for any reuse,  precisely because it is two-stage.  Thus the storable design is simply the better choice for that application.

The one-stage reusable design is similar,  in that at least initially,  the right choice is storables,  because of the months-long journey to Mars.  The design as it is,  simply cannot afford the weight of insulated Dewars and cryocoolers,  even with the higher specific impulse.  When I plug in 25% inert and 360 sec specific impulse,  payload fraction drops to zero.  Such a vehicle would have to be shipped empty to Mars,  and its propellant supply shipped separately,  until propellant production is established on the surface of Mars.  That is just not very practical.  An empty vehicle is no good for direct entry,  and cannot maneuver itself,  even if separately braked into Mars orbit.

However,  once propellant production is actually established on Mars,  vehicles with simple lightweight tankage,  previously operating on storables based from Mars orbit,  could be landed and re-engined with liquid methane-LOX engines,  and operated for relatively short flights from the surface of Mars reusably,  and locally refuelled.  In that case,  the specific impulse is now 360 sec,  with the inert fraction still only about 20%.   Unfortunately,  the fuel to oxidixer volume ratios are wrong for this,  being about 2-to-2.7 by mass for the storables,  and in the vicinity of 3.25 for the mild cryogens.  What that really says is that you design the thing to use liquid methane-LOX from the outset,  or else you design it to use MMH-NTO storables from the outset.  Re-engining is not really an option.

Not only the engines,  but also the tankage volume ratio in the center core,  must be substantially altered to allow the use of mild cryogen propellants made on Mars.  That is a major structural design change.  This is not a very practical thing to attempt.

Overall Conclusions

Either design approach will work.

If one-shot,  use a two-stage vehicle using storable propellants.  It can land about 3 tons for a 22.2 ton vehicle,  using those storable propellants,  from either low Mars orbit or direct entry.  Replacing the ascent stage with a cargo pod,  it can land 12.4 tons in that same 22.2 ton vehicle.  The ascent stage can take that same 3 tons back to Mars orbit.  Available cargo volume convertable to habitation space is quite limited,  being around 20 cubic meters nomimal,  and only 82.9 cubic meters if the ascent stage is replaced by a cargo pod.

If one-stage and reusable,  and refuelled in Mars orbit from a storable propellant supply kept there,  the vehicle can land about 3 tons in each flight,  in a vehicle massing 269 tons at ignition.  It can carry the same 3 ton payload back to Mars orbit.  These are the same storable propellants as the two-stage non-reusable configuration.

Replacing the ascent propellant with cargo as a one-way descent trip,  means that 140.7 tons can be landed without the possibility of reuse. Similarly,  if refuelled with storables on the surface somehow,  it can bring 24.7 tons of payload back to Mars orbit.  The same 269 ton ignition mass limit applies to the two-way and one-way cases.  Cargo volume potentially habitable is over 469 cubic meters,  based on the cargo descent with no ascent.

There is no scenario where re-engining the two-stage one-shot vehicle to use liquid methane-LOX produced on Mars makes any sense.  That is because nothing about this design is reusable in any way.  That eliminates the point of any surface refuelling.

Re-engining the one-stage reusable vehicle to use liquid methane-LOX produced on Mars also makes no sense,  because the oxidizer and fuel tank volumes are all wrong in the very core of the vehicle.  This is a major redesign and rebuild problem,  not just an engine replacement problem.

Finally,  it makes no sense to design the vehicles from the outset to use liquid methane-LOX propellants,  because of the increases in inert fractions to counter boil-off losses during the months-long transit to Mars,  plus the fact that,  initially,  such propellants are simply not available at Mars.  Those increases in inert fraction negate the gains in propellant fraction at the higher specific impulse.  In point of fact,  payload fraction gets zeroed.

Whichever approach you choose,  go with storable propellants such as MMH-NTO.  Personally,  I like the one-stage reusable design,  because of what it can do if used as a one-way descent vehicle.  The tankage is just twice as lightweight.  I also like two-way reusability based from Mars orbit,  if sufficient propellant can be shipped there from Earth.