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I would like to find out why there is a straight hole down the middle in all solid rocket engine motors.

The hole is shown here

I thought it only makes sense in hybrid engines where pure oxygen needs to be blown down the tube.

And why isn't there a hole down the middle in model rocket engines?

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    $\begingroup$ One other reason that isn't mentioned in any of the other answers here, but isn't necessarily large enough to warrant its own answer, is center of mass control. A SRB that burns from the bottom up will have its center of mass shift forwards as it burns. $\endgroup$ – TLW Nov 3 '15 at 22:52
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    $\begingroup$ @TLW If you perhaps include that a 3D bore will also reduce residual grain loss, improve viscoelastic damping reducing resonant vibrations and might improve combustion stability, that should warrant writing a new answer IMHO. Tho, perhaps, that's a bit over the scope of this particular question. $\endgroup$ – TildalWave Nov 4 '15 at 0:09
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A bore in the solid propellant grain increases exposed surface area and allows for a higher burn rate to increase thrust. There might be several grain geometries used, to meet launch vehicle's ascent profile needs through grain regression and with it control flow rate as the solid propellant core burns. From Wikipedia on Solid-fuel rocket - Grain geometry:

Solid rocket fuel deflagrates from the surface of exposed propellant in the combustion chamber. In this fashion, the geometry of the propellant inside the rocket motor plays an important role in the overall motor performance. As the surface of the propellant burns, the shape evolves (a subject of study in internal ballistics), most often changing the propellant surface area exposed to the combustion gases. The mass flow rate (kg/s) [and, therefore, pressure] of combustion gases generated is a function of the instantaneous surface area $A_s$, (m2), and linear burn rate $b_r$ (m/s):

$$\dot{m} = \rho \cdot A_s \cdot b_r$$

  • $\dot{m}$ is here a mass flow rate in kg/s,
  • $\rho$ is mass density of the fluid,
  • $A_s$ instantaneous surface area and
  • $b_r$ linear burn rate

Some of the grain geometries and their corresponding thrust curves might look like below examples:

           enter image description here

     Common solid propellant core cross-sections of grain geometries, including circular, finocyl and non-circular bores.

Other profiles in use are a C-slot (wedge cut out at the side of the core), Moon burner (off-center circular bore), and so on. Grain geometry can also use three-dimensional cross-sections, usually achieved by stacking two-dimensional cross-section bored core segments one atop the other. E.g. Ariane 5 SRBs (EAP P238 and P241) use such stacked segments to achieve a three-dimensional grain profile, but there are other launch vehicles that use that, too.

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It depends on the particular engine.

Thrust from a solid rocket is approximately proportional to the burning surface area of the fuel (also called the grain). A long solid rocket motor with a channel along its length is burning more surface area than an "end-burning" motor, so produces more thrust. Typically solid rocket boosters are used to provide very high levels of thrust at liftoff, so the long channel in the grain is needed.

If the channel is a simple circular bore, the area increases as fuel burns away, making thrust increase over time. This generally isn't what you want, because mass is decreasing as the fuel is spent, so the rocket accelerates too fast. For this reason, other grain profiles are used as described in TildalWave's answer to control the thrust-versus-time curve.

Model rockets usually fly with a much higher thrust-to-weight ratio than full-sized orbital rockets - higher than 5:1 TWRs are common for model rockets, while large rockets are often below 1.5:1 at ignition. End-burning grain, therefore, is more than sufficient for them.

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    $\begingroup$ Does that also make it burn quicker? $\endgroup$ – user2990508 Nov 3 '15 at 18:14
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    $\begingroup$ Yes. For a given volume of solid rocket fuel, thrust times time is approximately constant. $\endgroup$ – Russell Borogove Nov 3 '15 at 18:36
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    $\begingroup$ @AdamDavis I think the opposite is true. A crack in a solid grain can suddenly and dramatically increase the burning area when the flame reaches it. A crack in a motor with an intentionally large burn area will not produce as significant an overpressure. The safety of model rocket engines comes from the fact that they contain a very small amount of propellant and, in the unlikely event they do explode, their cardboard cases and soft clay nozzles are unlikely to produce dangerous shrapnel. $\endgroup$ – Kevin Krumwiede Nov 4 '15 at 19:08
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    $\begingroup$ @AdamDavis I'm not a rocket engineer, either. The source of my understanding is a book about building your own rocket motors that I repeatedly checked out from the library as a kid. One of those books that the DHS has probably confiscated from libraries now... $\endgroup$ – Kevin Krumwiede Nov 4 '15 at 20:29
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And why isn't there a hole down the middle in model rocket engines?

Model rocket engines are available in many "sizes"--varying thrust and duration. One configuration has the hole down the middle. They do make a lot of thrust for a short time. These were designed to be used for booster stages.

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Fwoosh instead of boom.

Others noted that the model engines may or may not have a bore, and that bores may or may not be round. To that I'll point out that some of the bores aren't actually cylindrical, either. Various tapers are used, too.

It's to maximize thrust, certainly, but that's not just burn rate.

You have to toss mass away from (as in separate and remove, creating a reactive force) or smack mass into the mass you want to move. Gases wandering about don't help, excepting as they increase the efficiency of the parts that are. (or happen to hit the mass appropriately)

Thus, the other biggie is shaping the flume. With a naked burning cylinder end, you do get thrust, but the lateral expansion is almost utterly wasted. With burning from the center out (or plugged with appropriate nozzle) that lateral expansion increases the pressure of the main body of the flume and, thus, the thrust. (Any nozzle used needs to be fitted to this purpose correctly or it will get popped right off.)

Check out "shaped charge" for further edification. See also why guns have a chamber. These are all linked.

(Ed.: My friend pointed out that insulation against the burn is quite important, as well, to prevent the destruction of the shaft and also reduce the benefit of the nozzle.)

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    $\begingroup$ All model rocket motors I've ever seen have nozzles. Can you explain why their cylinder-on burn fails to capture lateral expansion? $\endgroup$ – Nathan Tuggy Nov 4 '15 at 21:47
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    $\begingroup$ The nozzle is there specifically to permit the harnessing of (some of) the lateral expansion. Are you asking how losing it causes a loss of thrust? $\endgroup$ – The Nate Nov 6 '15 at 5:03
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    $\begingroup$ No, I was asking why you're conflating the central bore with the use of a nozzle, since (most) model rocket motors have no central bore, and always use a nozzle. The edit clarifies that a little, but it's still a bit muddy. $\endgroup$ – Nathan Tuggy Nov 6 '15 at 5:08
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    $\begingroup$ I'm not conflating the two. I simply pointed out that these are two common ways of accomplishing the stated goal: a concentration of mass flow opposite the desired thrust vector. Without doing this, you just get a burn or explosion rather than thrust. Hence the first line. $\endgroup$ – The Nate Nov 7 '15 at 15:26
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    $\begingroup$ It bears noting that it would be a perfectly serviceable mental model to think of the shaped combustion effect as a fluid form of a nozzle. If that helps, go for it. The "walls," in this case, are generated by expanding gases, but they do accomplish a similar effect. Personally, I don't think of it that way, since I consider a nozzle to be solid as part of its definition, but I'm not a stickler for terms. If it walks like a duck it could be a monotreme, and all that. $\endgroup$ – The Nate Nov 10 '15 at 17:57

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