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This answer to How is New Shepard the first suborbital booster to successfully perform a powered vertical soft landing? discusses a potential differentiation between Falcon 9's first successful landing and New Shepard's.

Wikipedia's New Shepard begins:

New Shepard is a vertical-takeoff, vertical-landing (VTVL), crew-rated suborbital launch vehicle...

and I assume that includes both the booster and the capsule.

Question: Suppose a roughly capsule shaped payload fairing was put on top and a short 2nd stage based on a spherical SRB was added in an attempt to put a smallsat payload into orbit. Could this work without a substantial redesign of the booster?


This answer to New Shepard payload capacity to orbit? says:

As far as I know, there is no second stage that could reach orbit from a New Shepard, even disregarding the issue of size. It would need to very nearly be a SSTO. The Falcon 9 is well known for staging early, this being part of what makes it feasible to recover its booster, and for ASDS landings its booster is about 150 km downrange and moving at around 2 km/s when it crosses 100 km altitude, where New Shepard reaches a vertical peak at effectively zero velocity.

While it suggests that the payload capacity is low if at all, there are no numbers to support anything definitive, and the maximum horiziontal velocity of New Shephard when fully fueled and with a different second stage isn't addressed there at all.

Answers here should support conclusions with at least envelope-back level calculations. Thanks!

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    $\begingroup$ The first stage of a rocket could be arbitrarily low performance, the upper stages "just" need to have higher performance to compensate, the extreme being a "stage" that's just a launch pad fixture with a fully orbital rocket sitting on top. An upper stage that launched on New Shepard would need to very nearly be SSTO, however. $\endgroup$ – Christopher James Huff Apr 19 at 3:50
  • $\begingroup$ @ChristopherJamesHuff ya that seems to be the crux of the question; comparing the first stage maximum horizontal velocity at say 100 km. It seems to be something like 2200 to 2400 m/s at MECO for F9. $\endgroup$ – uhoh Apr 19 at 3:59
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    $\begingroup$ @OrganicMarble Thanks, I've differentiated this question from that one. $\endgroup$ – uhoh Apr 19 at 4:06
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    $\begingroup$ Do we have good specs on the vanilla New Sheppard? $\endgroup$ – BrendanLuke15 Jun 11 at 22:49
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    $\begingroup$ @BrendanLuke15 we'll find out'; that's sort-of the reason for asking the question. $\endgroup$ – uhoh Jun 11 at 23:00
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I think we can all agree that the crux of this question is in the New Shepard specifications, feel free to offer improvements to these. Here are the ones I arrived at (note: there is no recovery of the booster in this analysis):

Booster Masses: This reddit thread (that is now 5 yrs old) contains some estimates of tank volume and empty booster mass and I particularly like the comment from poster u/saabstory88:

https://i.imgur.com/i8BOXiu.jpg

We know two numbers for sure. The max thrust of the BE-3 is 489kn, and the minimum thrust is 90kn. Assuming that the stage and landing needs to be just a little heavier than the engine can lift at minimum throttle (to be able to hover), then 10,000kg seems like the reasonable base estimate

This other schematic from a less than convincing authority contains a scale: New Shep w/ scale The top of the tanks seems pretty concrete between the two diagrams (the curvature right below the grid ring unit). It is a bit more ambiguous for the bottom of the tanks. I used a frame from this test-fire video from 2013 and superimposed the exposed engine onto the scale-diagram: New Shep w/ engine 'x-ray' Which seems to place the bottom of the tanks a little higher than the previous diagram. Either way I approximated the tanks (bulk) as a cylinder with a 2.8317 m diameter and a height of 9.3607 m for a volume of 59$m^3$.

This was combined with this answer to Use of different fuels for stages of Saturn V:

while LH2/LOX (also known as hydrolox), has optimal mixture ratios ranging from 4.13 at sea level to 4.83 in vacuum. The STS ran with a ratio of about 6. At 4.12, the bulk density of hydrolox is 0.29g/cm³, at 4.83 its 0.32g/cm³. [emphasis added]

I used 300$\frac{kg}{m^3}$ to arrive at 17700 kg of propellant.

Second Stage: I chose the STAR48BV (TE-M-940-1, pg. 104) because it has thrust vector control capabilities and available specs (and successful history). This configuration looks something like this (proper relative scale): New Shep Orbital (the green payload box is ~70 cm x ~50 cm)

Launch Simulation: I built a very simple launch simulator to test the vehicle's capabilities. Some 'features' of the sim that are notable (for the inaccuracies they may introduce):

  • constant drag coefficient
  • atmospheric model from Braeunig Rocket and Space Technology
  • no throttle down for max-Q
  • non-rotating Earth, meaning the (prograde launching) rocket needs to achieve higher relative speeds (yields more conservative estimates which I don't mind)
  • constant specific impulses (value used would be somewhere between SL and Vac. value)
  • payload fairing jettison at stage separation
  • simple pitch program (literally just angle the thrust vector by 'x' until horizontal then maintain altitude)
  • 0.1 second time step
  • kills sim when permissible orbit reached (regardless of whether stage can actually shut down)

Here is a table of key inputs to the launch simulator that haven't already been mentioned:

Figure Value Justification
Fairing Mass 370.5 kg based on surface area of proposed fairing (red in above pic, 49.4$m^2$) and areal density of SpaceX fairing of ~7.5$\frac{kg}{m^2}$
Drag Coefficient 0.4 above mean value of this answer to How can I estimate the Coefficient of Drag on a Saturn V rocket, a simulator or some data would be pretty awesome
Cross-Sectional Area 9.71$m^2$ 3.516 m diameter circular cross-section
1st Stage Engine Isp 370 s near-ish RS-68 & RS-25 SL values
Thrust Vector Offset (Pitch Program) 1.7° iteratively determined to yield most circular final orbit
Coast period before 2nd stage burn 100 s iteratively determined to yield most circular final orbit
2nd Stage Propellant Mass 4431.2 lbm (2010 kg) STAR48BV (TE-M-940-1, pg. 104)
2nd Stage Total Mass (no payload) 4772 lbm (2164 kg) STAR48BV (TE-M-940-1, pg. 104)
2nd Stage ISP 292.1s STAR48BV (TE-M-940-1, pg. 104)
Initial Lift-off Mass 30260 kg includes payload, fairing, 2nd stage

Results: Yes! I was able to simulate putting a 25 kg payload into a 265 km x 188 km orbit. Here is a plot of the four key sim-state variables, the black vertical lines separate 1st stage burn, coast phase, and 2nd stage burn: Sim states

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    $\begingroup$ my goodness somebody is having fun! :-) This is a home-grown simulator? Was the 1st stage thrust vectored at 1.7 degrees throughout the entire burn? $\endgroup$ – uhoh Jun 13 at 17:44
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    $\begingroup$ @uhoh yes it is home-grown, and very crude :). No, there is a vertical profile for the first 2 km altitude. Here is a plot of the control modes over time $\endgroup$ – BrendanLuke15 Jun 13 at 18:10
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    $\begingroup$ Nice work! Your table isn't formatting correctly for display, though. A few points: a mix ratio of 5.5-6.0 is more typical in modern first-stage hydrolox engines (6:1 for RS-68, SSME, Vulcain 2; 5.3 for Vulcain 1). Worse specific impulse but much better propellant density. For specific impulse, a linear transition from sea level Isp to vacuum Isp as ambient pressure goes from 1 atm to 0 atm is pretty accurate. It's not difficult to incorporate launch site rotational velocity; take care to keep track of inertial velocity versus atmosphere-relative velocity. $\endgroup$ – Russell Borogove Jun 13 at 23:08
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    $\begingroup$ Table looks good now. Nice job! $\endgroup$ – Organic Marble Jun 14 at 17:30
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    $\begingroup$ Do you have a feeling why the performance is so bad? I mean, Electron weighs 1/3 but puts 10 times more payload into orbit. $\endgroup$ – asdfex Jun 14 at 17:34
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WEll my answer is yes, it- "could" be done

perhaps adding 2 Solid boosters in a C-Slot configuration on the sides to give it enough power to go sideways

then do the russian/titan hot staging technique with a high altitude/vacuum solid booster designed to burn for a long time to reach orbit and is adjustable as to meet the specific payload requirements

then we need a electron style in-house satellite platform to meet the specific orbital requirements

We then recover the new shepard stage by using leftover thrust from the side boosters to slow us down to a point where the shepherd's engines can kick in and slow the stage to a speed where parachutes can be used and either a helicopter or drone ship catches it

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    $\begingroup$ What's a "C-Slot configuration"? $\endgroup$ – Organic Marble Jun 11 at 18:23
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    $\begingroup$ My question specifies "... without a substantial redesign of the booster?" Of course a suborbital rocket might reach orbit by "perhaps adding... solid boosters" that's kind-of obvious as long as we include the magic "perhaps" but my question asks about an unmodified New Shepard. $\endgroup$ – uhoh Jun 11 at 23:04

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