Good comments on the fins; the Mach cone angle at M3.5 is about 16 degrees. So these would need to have a really long root chord and short tip length. That alone will do wonders to reduce the flutter risk. Based on my experience with the 0.048" mostly-uni carbon fins, I think about 0.07" to 0.08" thick mostly-uni plate with a couple of layers of tip-to-tip unit carbon over that would have more than sufficient strength and stiffness. But I'd do some calculations first based on hitting some wind shear at M3.5. I'd also need to try to get my hands on some cotronics epoxy so I don't need to worry about the layup softening due to heating from the skin and motor. Anyone know what sort of motor case temperature to assume?
A 76mm booster to a 38mm sustainer would be an efficient way to get the M staged record, but the transition would be a pain to design and build. Staging 2 same-diameter birds with the motor as coupler (assuming a flush aft closure) makes it really simple. The two sections don't even need to be designed for multi-stage flight, as long as the sustainer motor can stick out the back and the booster is designed for recovery on a single airframe break. Besides, if you go with a little lower-impulse 75mm M, you have plenty of impulse left over for a decent 75mm K for the sustainer. When the sustainer starts its job at 40k, the drag lost to the extra diameter is not nearly as large as it is starting from the ground. For high-altitude sustainers, ISP becomes more important, just like it is in real launch vehicles.
Gosh, I go camping for a few days and you guys have it all figured out! 😀
Speaking for myself, I'm not interested in a multi-staged project. If this was recovered, then maybe stick a stage below or above it, but I'd (personally) have no interest in staging this from the get-go. But that is me.
Second issue - I have seen some rather elaborate fin cans that were done by highly reputable folks who vacuum bagged, used all the right materials, layers, epoxies, autoclaves, fin shapes, etc. -- and their can shredded like it was made out of toilet paper on an eerily similar project. (EX motor, BALLS, couple years ago). Again, speaking for myself - I do not believe we collectively have the skillset or the technology to hang fins on a MD rocket and expect them to stay there on a project like this. I've built perhaps 20+ MD rockets, and I've never lost a fin. I don't think I'd have a chance on this one. I think you'd have to go w/ an aluminum welded fin can (which could be below the airframe and as such, out of the airstream).
Anyone do any estimates on what the gees would be on a 3Kg rocket with that much horsepower? Remember, you have to keep a couple of batteries and a couple of sets of electronics intact.
Finally, the other issue with that many gees is propellant stripping away from the liner of the grains and falling into the core, which would be... spectacular (in a wretched sort of way). This is clearly a rocket that may benefit greatly by having more mass - the coast would be unreal, and you'd keep the speed and gees back. I don't think this is where you'd want to build as light as possible (ping pong ball vs. golf ball).
Sounds like a lot of challenges, but it would be cool to crack 50K. We'll know soon, I'm sure rockets are already being built to try this motor.
JW
Well, my rough single stage sim to 40k or so with a 3kg rocket would pull around 50G on its way to M3.2. The acceleration shouldn't be a problem - Adrian's I powered shot did fine with greater acceleration than that. As for the velocity - I still think that Adrian is right, and a couple of solid carbon plate fins would hold up just fine. I'll drag out the aerodynamics textbook though to see what kind of forces we could be talking about here, and that might give a better idea of what kind of fins would hold up best.
Well, after some calculations, it appears that 0.083" fins are all that is needed at a minimum, at least for my design. That is using the assumption of a launch at 4k ASL (black rock, roughly), and that max Q occurs at max velocity. That gives a max Q of roughly 86,400 PSI at Mach 3.3. I then calculated the lifting force on each fin based on a 150ft/s crosswind that is entered at exactly the worst time (at max Q), which gives an angle of attack of 2.4 degrees. Using published lift data from the SR-71 as a good approximation, that gives a lift coefficient of around 0.04, giving a fin force of 72,600 pounds. Assuming that the force acts at the midpoint of the fin (which is actually a worse scenario than what should actually occur), this means that with a fin 0.083" thick, the maximum stress at the root would be 145 ksi, which is a representative value for aerospace-grade carbon fiber that I could find. Of course, homemade CF would be somewhat weaker, but with 0.125" thick fins, I get a maximum stress of 97ksi for example. In addition, the maximum stress location is at the root of the fins, so if there were some fairly healthy fillets and T2T, that would significantly reduce the stress at that location, and increase the chance of success.
Also, keep in mind that this is a worst case scenario - specifically, that it hits a 150ft/s wind shear at exactly the point of greatest dynamic pressure. In all likelihood, this would not happen, and even if it did hit a wind shear, it would probably not be this strong. Because of that, I would think that 1/8" CF plate would be more than adequate to survive this, if it were attached solidly enough (it would probably be best to start with thinner CF plate, and then build it up with T2T). As for flutter? I doubt very much that flutter would be a problem with 1/8 CF plate in a fin with a 12" root and a 3" semi span (the design that I am currently running all of my numbers based on).
Great calculations, but if a layman like me understands the thoughts here, I think you are talking about stress on the fins - not the joints. The joints - not the fins - are what is worriesome. That is why I talked about a welded aluminum can.
I'd still be worried about gees. The toughest fins on earth aren't worth a song if the bottom grain in the motor collapses due to the weight of the other grains on top of it 😯
Interesting challenges indeed.
Just let me know when you guys get around to flying it... 😈
That's why I mentioned starting with relatively thin plate, and then adding quite a few layers of T2T. That in essence makes the entire fin can one piece of CF, and that should allow for these kinds of loads.
I'm with Chris on this - dadoed slots in the airframe with relatively thin, low mass cores properly glued in, then 8 maybe 10 or even more layers of tip to tip, vacuum bagged and with a proper cure process.
W
8 or 10 layers sounds like a bit much - you only need to build it up to roughly 1/8" plate. Anyone know how many layers there are in 1/8" plate CF?
On a related note - it's amazing how fast you forget things once you're out of school for the summer. Things like how to properly read the table in the back of the aerodynamics textbook. (apparently, 1.9270 and 1.9270*10^-3 are not the same number...)
All my numbers above are off by several orders of magnitude. The new value seems more reasonable (something seemed wrong when performing that calculation - now I know why). The side force on the fins is now just 72.6 pounds of force. Therefore, flutter becomes the main concern (and I still believe that the flutter would not be a problem with 0.1-0.125 inch CF). I also made an error in the required fin thickness to support the amount of force listed above, though it's irrelevant now that I've realized just how far off that value was.
😳
Well, after some calculations...
Ah, the cool refreshing sound of real engineering.
Very interesting results. 150 ft/sec of instant shear is a pretty conservative worst case, but it shows the margin we have here. What did you assume for the distribution of the fiber direction through the fin thickness? All uni, or just the outer layers? We would need some layers in the other direction to give it some resistance to handling and landing dings.
86,000 Kpsi dynamic pressure? Yikes. I think that the leading edges of the fins may not hold up to stagnation pressure that high. I have heard of other people getting some erosion /delamination of the leading edges for their high speed flights. Wrappng the leading edges with aluminum may be worthwhile to reduce the risk of delamination.
Next you should figure out how much bending moment gets generated in the tube by 76000 lbs of fin force. It would probably snap most tubes like a toothpick. Honestly it seems too high to be reasonable, but that probably goes back to the assumption of 2+ degrees angle of attack at max Q. Here again uni carbon in the tube will hel bail us out. But first, figure out the lateral forces on the part of the tube that is unsupported by the motor. start with calculating the angular acceleration. I think you'll find here that nose weight will make things somewhat worse by adding more pitch inertia. I would bet that the straight compressive load of the load from drag and inertia will be small compared to the bending load, but it would be interesting to see how it comes out.
Ok, 76 lbs is a lot more reasonable than stacking 10 SUVs on the end of the tube. I think i'll use rocksim to double check. It provides restoring torque as an optionin the graphs. I'll see if it let's me give it a super long tower that extends to max q.
What do your new calcs say about the necessary thickness?
New calculations:
(these ones are right, I promise)
New dynamic pressure: 86.4 PSI
New lifting force on a single fin: 72.6lbs
New thickness required (ignoring flutter): 0.019 inches of top, aerospace grade CF.
New peak stress within 1/8" thick fin in this scenario: 3500PSI (which also happens to be well within the maximum published specs by West System, Aeropoxy, and Pro-Set for bond strength, so bonding shouldn't be a problem). I'm now inclined to think that wind shear isn't as big of an issue as flutter.
My problem above was because my aerodynamics textbook uses a standard atmosphere table that has a multiplier at the top of each column. I looked at it, and saw that the density at 7000 feet was 1.9 slugs/ft^3 (ahh, the joy of english units 🙄 ). I missed the fact that every number in that column should be multiplied by 10^-3 to be accurate.
Well, I just ran it through rocksim, and rocksim seems to think the total force would peak at ~220lbf (that's not too far from my value of ~72lbs on a single fin, considering all of the assumptions that I had to make to get there). It's kind of a shame that you can't just graph or predict dynamic pressure in rocksim though.
Rocksim indeed lets you use a launch tower that is 5000 feet high, and enter 150 ft/sec of cross-wind. When I ran it, it predicted that such a situation would result in just under 300 N*m of torque when it left the tower at Mach 3 🙄 , given my fins with about 1.6 calibers of stability margin. With 3 fins, half of the torque would come from the fin perpendicular to line of action, so figure 150 N*m of torque, applied by one fin 16 inches (0.4m) behind the CG of the rocket. That makes about 375 lbs of side pressure on one fin.
If I ignore the center layers of the layup, and assume that the middle 6" of the fin is taking all the stress, then with a 0.01" thick layer of uni carbon on each side of the core, and 0.04" between the midpoints of the layers, (for a total thickness of 0.050") then I get 62500 psi stress at the root of the fins. The published strength data on the aircraft spruce & specialty website for a mostly-uni layer comes out to about 90 ksi. In other words, you could put a 430 lb weight 3" from the root a 6" long fin, and the fin would only have to be 60 mils thick, with 10 mil outer layers of uni-carbon, to withstand that force without breaking.
When I laid up my carbon plate for my fins, 10 plies resulted in about 36 mils thickness, so you could use just about anything to make a 0.035" core, put on 3 layers of unidirectional tip-to-tip carbon, and you can be assured that wind shear won't snap the fins off at the root. With a tip-to-tip layup, I think the only way the joint could be weaker than the fin itself might be with a debonding of the T2T layer from the fillet material. Even then though, I think the fin just above the fillet would be the weakest point.
For flutter, you'd need to calculate the resonant frequency for the bending/twisting mode shape you'd get with the flutter, and show that it's faster than the flutter frequency that can be generated by airflow at the given speed. Definitely more than a back-of-the-envelope calculation.
Latest Post: Hello World Our newest member: amiecannan4271 Recent Posts Unread Posts
