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Looking at data from today's NS-10 launch, I estimated the acceleration early on in the flight between the 10 and 15 sec marks; from about 43 ft/s to 110 ft/s in 5 seconds, which gives roughly 13.4 ft/sec^2.

The Blue Origin site claims that the New Shepard produces 110,000 lbf of thrust, so

110,000 lbf - m x 32ft/s^2 = m x 13.4 ft/s^2.

Solving for m, I get 77,533 lbs.

That seems light for a fully fueled ship like that...no? Thats only like the legal weight of an 18 wheeler. Is it that light?

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    $\begingroup$ What's your question? $\endgroup$ Jan 25, 2019 at 3:22
  • $\begingroup$ @ChrisAdams your other posts have been well-written but this one was a little disorganized. I've cleaned it up a bit and answered. Next time try to do some proof reading before posting? $\endgroup$
    – uhoh
    Jan 25, 2019 at 10:45
  • $\begingroup$ If New Shepard is 3.66 m (12 ft) in diameter and 14.8 m (48.6 ft) in length (Reddit guesses: reddit.com/r/BlueOrigin/comments/3u8m2h/…), you get a propellant volume of 54 m3. Propellant is liquid hydrogen (70 kg/m3) and liquid oxygen (1141 kg/m3) and ideal combustion ratio is 6 LOX/LH by mass. Total mass is then 7x LH mass, and LH mass is V_Tot * (rho_O * rho_H) / (rho_O + rho_H), where V_Tot is total tank volume and rho is mass density. This comes to 25,000 kg or 55,000 lbm, and with your numbers dry mass = 77,500 - 55,000 = 22,500 lbm. $\endgroup$
    – user39728
    May 6, 2021 at 15:57
  • $\begingroup$ 22,500 lbm is 10 metric tons, which is between the 4 tons of a Falcon 9 V1.1 stage 2 and the 20 tons of a Falcon 9 V1.1 stage 1. Old numbers but enough for comparison. Both Falcon 9 V1.1 stages have the 3.66 m diameter given for New Shepard, with stage 2 being 5 m shorter than New Shepard and stage 1 being 25 m longer, so all things being equal you'd expect New Shepard to be closer to Falcon 9 V1.1 stage-2 dry mass---which it is, even though New Shepard has systems the Falcon 9 stage 2 doesn't---like steering fins and spoilers (drag fins), which would add mass. $\endgroup$
    – user39728
    May 6, 2021 at 16:09
  • $\begingroup$ So the 77,000 lbm in your calculation shouldn't be too far off, it seems? $\endgroup$
    – user39728
    May 6, 2021 at 16:10

2 Answers 2

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Using the OP's numbers:

  • average acceleration (between T+ 00:10 and T+ 00:15): 13.4 ft/s^2
  • thrust: 110,000 lb force
  • g: 32 ft/s^2

solve for the approximate average mass between T+ 00:10 and T+ 00:15.

$$ ma = F_{thrust} - F_{grav} $$

$$ F_{grav} = mg $$

$$ ma = F_{thrust} - mg $$

$$ m(a+g) = F_{thrust} $$

$$ m = \frac{F_{thrust}}{a+g} $$

Wait! First lets convert to metric units just in case...

  • average acceleration (between T+ 00:10 and T+ 00:15): 4.06 m/s^2
  • thrust: 489,280 Newtons
  • g: 9.81 m/s^2

$$ m = \frac{489,280 \text{N}}{13.9 m/s^2} \approx 35,000 \text{kg}.$$

Multiply by 2.2 and you get 77,000 lbs, same as in the question.

Congratulations, you are right

In other words, using your numbers, I get the same thing, and it is around the max weight of a 18-wheeler.


Petersen's Data On Class 8 Tractor-Trailer Combination Weights:

Data On Class 8 Tractor-Trailer Combination Weights

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New Shepard is a suborbital launcher: it can get into space, but it can't stay there. As discussed in this oft-linked What If, the major challenge of orbit isn't reaching space, but going fast enough horizontally -- 7800 m/s or so -- that you don't fall back to Earth.

New Shepard doesn't have to reach those very high speeds, so it doesn't need the huge amount of fuel that orbital rockets do.

It's lighter than you might guess by looking at it because its fuel is liquid hydrogen, which is extremely light: about 1/14 as dense as water. About 3/4 of the interior volume of the first stage is consumed by the hydrogen tank. The liquid oxygen tank is much smaller than the hydrogen tank, but carries about 6 times the mass.

Blue Origin doesn't seem to publish a lot of figures, but with more data it would be possible to cross-check your mass estimate in at least a couple of ways:

  • Using the rocket equation, work out the mass ratio needed to achieve the suborbital trajectory (needs trajectory information and mass of the crew capsule);

  • Given the dimensions of the stage, work out the actual propellant tankage volume and from there the mass of fuel and oxidizer (needs stage diameter and height, and engine oxidizer-to-fuel mixture ratio) -- this one should be easy to estimate even without firm specs.

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