Sunday, May 7, 2017

Test flights of the Falcon Heavy for missions to the moons of Earth and Mars, Page 1.

Copyright 2017 Robert Clark

  The SpaceX Red Dragon lander mission to Mars on the Falcon Heavy has been pushed back to 2020, perhaps to return a Mars surface sample. SpaceX though plans for two Falcon Heavy test flights for the latter part of this year, 2017.

  Elon has discussed testing recovery of the stages on these first test flights which will reduce payload. He has also discussed putting a "fun" payload on one of them, like his cheese wheel on the first Dragon test flight.

  I suggest instead missions be undertaken of great scientific and practical importance, missions to the moons of Earth and Mars. 

Flight to a Permanently Shadowed Crater on the Moon.
 Abundant evidence suggest ice water deposits in the permanently shadowed craters on the Moon. This has been proposed to be used to produce orbital propellant depots. This would radically reduce the mass that would need to be launched to orbit for a Mars mission since most of this mass is just propellant. 

 There have also been some tantalizing indications from the LCROSS mission of valuable metals in the shadowed craters. Then the first space mining missions may be to the Moon rather than the asteroids.
 I'll estimate the delta-v to land on the Moon using this diagram:

 The delta-v to GTO (geosynchronous transfer orbit) is 2.5 km/sec. Then after that according to the delta-v diagram we need an additional 3.2 km/sec to land on the Moon. We wish to use the cargo version of the Dragon to land on the Moon. This weighs about 5.5 metric tons (mT) fueled with its own propellant, while the FH can get 26.7 mT to GTO. 

 So the idea would be to get extra delta-v by using the smaller mass of the Dragon capsule. To estimate this we'll need the specs for the upper stage of the Falcon Heavy, same as for the Falcon 9's upper stage, 348 s Isp for the Merlin 1D FT, approx. 107.5 mT propellant load, and approx. 4 mT dry mass. Then the delta-V this upper stage achieves with the 26.7 mT payload is 348*9.81*Ln(1 + 107.5/(4 + 26.7)) = 5,136 m/s.

 So by reducing the payload mass from 26.7 mT to 5.5 mT we want this upper stage to achieve a delta-v of:

5.1(to reach GTO) + 3.2(to land on the Moon) = 8.3 km/sec .

 And calculating the delta-v of the stage with the reduced payload we get:

348*9.81*Ln(1 + 107.5/(4 + 5.5)) = 8,572 m/s.

 This is above the needed 8.3 km/s, though close. Actually we'll get somewhat better than this because the lower stages having to loft a lighter payload will be able to provide more delta-v than before.

 Also, we actually will use the Draco thrusters on the Dragon to do the actual landing since the FH upper stage would put the capsule to high up if it were to land vertically, and it's thrust is so high achieving the stable landing is made difficult.

 That raises another difficulty because of the low thrust of the Draco thrusters. There are 18 Dracos of the cargo Dragon each of thrust level 400 N, for a total of 7,200 N. This can lift 7,200/9.81 =  734 kg in Earth's gravity. In the lunar gravity at 1/6th g, the Dracos could lift, 4,404 kg. But the fueled mass is 5,500 kg.

 There are a couple of things we can do to lighten the Dragon. We could remove both the parachute and thermal protection systems since the capsule won't be returning to Earth in this mission.  These weigh about 5% each of the landed mass, so about 10% all together. So this shaves 420 kg off the landed mass.

 Another possibility would be to replace the Dracos with Superdracos, which have many times greater thrust. But I'm not sure how well these would fit in the same housing for the Dracos.

 We could also remove most of the pressure vessel for landing on the airless Moon. From images of the Dragon's pressure vessel, this could be a significant mass:

 For the rover, we might use a copy of the Mars Pathfinder mission. NASA often makes two or more copies of its spacecraft for testing purposes. Then we could use one of these copies. This weighed only 264 kg for the lander plus 10.5 kg for the Sojourner rover.

 Other possibilities for a lightweight rover might be those being developed independently by entrants to the Google Lunar X-prize:

Flight to Phobos, the mysterious moon of Mars.
 A great scientific mystery also is the make-up of the Mars moon Phobos. Flyby missions showed it to have surprisingly low density. Serious scientific speculation included that it may actually be hollow. Current theories are though that it may be analogous to a "rubble-pile" type asteroid. This is not known for sure however. A lander mission may help to resolve the issue.

 Note also that key to Elon's plan for manned flights to Mars is getting the fuel for the return trip from Mars. Taking the fuel from the Martian moons instead would have advantages such as low gravity for getting the fuel to an orbiting propellant depot. Then these first flights to the Martian moons could serve as scout missions for water ice deposits.

  The Falcon Heavy test flights this year will be outside the optimal launch window in 2018. This means they will require higher delta-v to reach Mars, and higher delta-v to slow down on reaching the destination. This limits the mass that can be transported to and landed on Mars, in addition to the expense of the extra in-space stages required.

 Then I will suggest here a method that has long been proposed for arriving at Mars but never attempted, aerocapture. This slows down a craft arriving at Mars by plunging deep within the atmosphere so that minimal propellant burn is required. Note, that if these tests missions using aerocapture succeed then this will suggest it will work to solve the problem of landing large masses on Mars such as a crew habitat, a key enabling technology for manned flights to Mars.

 For the delta-v required to depart from Earth I'll use the orbital calculation program:

Trajectory Planner.

 This provides the delta-v's required for the Hohmann tranfer orbits between the various planets. The program provides pork-chop plots that allow you to estimate departure and arrival delta-v's dependent on departure time.

 The program though uses Modified Julian Date format, which can be converted to standard date format here:

 For a Dec. 23, 2017 departure, which is given in Modified Julian Date format of 58110 in the "Trajectory Planner", the delta-v Hohmann transfer delta-v is 6.155 km/s. We then need to calculate the delta-v needed on leaving Earth orbit. On the Orbiter-Forum discussion forum for the Orbiter space simulation program this formula was provided by member Dgatsoulis:

 \Delta V = \sqrt{V_{\infty}^2 + V_{esc}^2} - V_{orb}

where V_{\infty} is the hyperbolic excess velocity (departure deltaV from trajectory planner).

V_{esc} is the local escape velocity, aka the escape velocity for the parking orbit altitude.

V_{esc} = \sqrt{\frac{2GM_{planet}}{R_{planet}+alt}}

where G is the gravitational constant, M_{planet} is the planet's mass, R_{planet} is the planet's radius and alt is the altitude of the parking orbit.

V_{orb} is the parking orbit velocity.

V_{orb} = \frac{V_{esc}}{\sqrt{2}} 

 Same applies for arrival. If you want to simply calculate the periapsis velocity and not the orbit insertion/injection dV, then don't use the V_{orb} term.


 So the  delta-v on leaving Earth orbit is:
 This 1.11 km/sec more than the usual delta-v to make a Trans Mars Injection during the optimal departure windows of 3.8 km/s.

 We need to calculate how much mass the FH upper stage could get to this higher delta-v of 4.89 km/s. By the FH specs it can get 16.8 mT to Trans Mars Injection.This FH upper stage with the 16.8 mT payload mass can do 348*9.81Ln(1 + 107.5/(4 + 16.8)) =  6,211 m/s delta-v. So with a smaller mass we want to achieve 6,211 + 1,110 = 7,321 m/s delta-v. This can be done with a 10 mT payload:

338*9.81Ln(1 + 107.5/(4 + 10)) = 7,377 m/s.

 Now we have to calculate how much is the speed on arrival at Mars.  The Trajectory Planner gives the "arrival" speed as 4.275 km/s. However, again this is not the speed the spacecraft would have on entering Mars's atmosphere. This is instead the speed at which it arrives at Mars's position in its orbit around the Sun, i.e., the Hohmann orbit delta-v needed to be supplied to match Mars' solar orbital speed.

 To get the entry speed into Mars' atmosphere, use the Dgatsoulis formula above without the Vorb term. Using 5.0 km/s as the escape velocity for Mars we get:

 If all we wanted was to slow down to enter Mars orbit then we would subtract off from this by aerocapture to bring the speed down to Mars' orbital velocity of 3.56 km/s. However we also want to be put it on a trans Phobos insertion from Mars. By the delta-v chart above we need an additional .9 km/s, so to 4.46 km/s. So by the aerocapture we only need to slow it down by about 2.11 km/s.

 This should be well within the capabilities of aerocapture. However, the payload mass may be as high as 10 mT. The question is could the dragon's approx. 10 square meter base provide sufficient air drag to slow down that high mass, and would its heat shield be thick enough?

 In follow up posts I'll present some preliminary calculations that suggest that plunging deep into Mars atmosphere, skimming the tree-tops so to speak, should allow large masses such as this to be slowed at such high entry speeds.

 With the payload of the FH as high a 10 mT, the rovers and equipment that could be transported could be 4.5 mT above the 5.5 mT fueled weight of the cargo Dragon. But according to the delta-v chart we still need 0.5 km/s delta-v to land on Phobos. The cargo Dragon has a delta-v capability of about 600 m/s with its Draco thrusters for the Dragon capsule alone. So this should be sufficient, but it would not be if the extra cargo was several metric tons. So we could keep the cargo low as for a Mars Pathfinder sized rover or we could add additional propellant tanks to increase the landing capability.

 The possible cargo carried by the Dragon being as high as 4.5 mT suggests though we should try to make use of that cargo space. One possibility would be the processing equipment to produce ISRU (in situ resource utilization) propellant. Perhaps a rocket to do a sample return. Possibly orbiting imaging spacecraft for Phobos or Mars. Others?

    Bob Clark

Note: thanks to members of Keithth G and DGatsoulis for helpful discussions on this topic and member Piper, for writing the Trajectory Planner program.

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