Tuesday, March 29, 2016

A Rocket Takes Shape

Today's update on the rocket won't be very long, since neither is our rocket. We have decided to only use one 18" body tube in conjunction with our 9" nosecone, resulting in a pretty stumpy looking rocket. The reason we did this was that the body tube and coupler were heavy, and with relatively modest fins, we can still maintain a stability of 1.3 calibers. So far, OpenRocket is predicting a 645 meter apogee and our ideal rocket scenario gives about 3,600 feet. The one test launch that has been conducted by someone to test OR's accuracy showed that it underestimated apogee by about 33%, so we are eyeballing a predicted altitude of 3,200 to 3,400 feet. This thing should really take off, assuming it holds together!

With the design completed and CADs submitted, we have begun assembly, which seems relatively simple. The engine mount assembly is in one piece with the shock chord (surprise! there's a shock chord we didn't know about!) attached. Our next step tomorrow will be to attached the engine mount assembly within the body tube, install the parachute and altimeter, and cut and attach our fins.

The last part is the only thing that has me a touch nervous. We need our fins straight and evenly spaced, and I think I know how to do this, but I need to find some scrap wood - even just one block will do. My plan is to make a guide with a cutout for the body that covers 90 degrees of arc and with sides normal to the curve's endpoints. This will let me use it initially to keep the fin straight for the first one, and then space the rest off of that fin, keeping them all straight. So our team's current task is to beg/scrounge/obtain about a 6" x 6" piece of wood and have the machine shop cut it to our specs for us. That or talk our project leader into letting us use the laser cutter for that, too...

Tuesday, March 22, 2016

No Plan Survives Contact with the Enemy

Field Marshall Helmuth Karl Bernhard Graf von Moltke once wrote that "no plan of operations extends with any certainty beyond the first contact with the main hostile force." I got to experience this firsthand today when I compared the model our team has drawn up with the parts we are actually to use. Oops. Bits were neither shaped nor fit together the way we were expecting. Needless to say that this is a setback. We are reassessing our design, and I think we may be able to maintain our predicted apogee of 3,200 feet. In the meantime, we assembled the parts that did adhere to our expectations - the motor mount.

Unfortunately, Helmuth's quote underscores an issue we have been encountering again and again throughout the entire project. The entire thing is horribly unorganized and poorly executed.

Through the first real meeting where we derived the idealized model I presented last time, everything looked great. But as we drew closer to and throughout the design phase, we found that the leads never provided sufficient information, and in the most infuriating moment, changed the entire design goal after we chose the parts we would be using. The lattermost was the worst, because where we were initially trying to get as close to 1,750 feet as possible - something that would require a lot of extra weights and inefficient fin design to hold back our motors, we are now expected to attain the highest possible apogee - something that requires as large a motor pushing as little weight as possible. As we were expecting to aim for a low target, we chose larger, heavier, more cumbersome parts and a weaker motor. Now we are scrambling to shed weight and hoping other teams are grossly inefficient.

While that has been the worst of it so far, the constant lack of information about parts and materials, even now as we redesign our rockets, hampers our attempts to build an accurate model. We are completely guessing at the density of the acrylic we will use to cut our fins. So as we are doing as a past employer of mine once said: "Control your controllables." I don't know the density of the acrylic, but the smaller the fins, the lighter they'll be regardless. And that is where things stand presently. I know we need a charge in the rocket to jettison the nose cone and deploy the parachute, but I don't know what it weighs. We need a surprise shock chord that we need to weigh and add into our model.

As frustrating and annoying as all of this is, I have to say it is probably a good representation of how things work in real life. I don't know how many times in previous jobs, I had a project that I'd start under a certain set of instructions and assumptions just to have them changed just before I finished. So really, this amateurish lack of organization is preparing all of us for real workplace conditions. That doesn't mean I like it. It just means that no plan of operations extends beyond first contact with the project leaders.

Thursday, March 17, 2016

Nymphs Part 2: Mountain Nymph

The crystal clear water of the icy pool shimmered and rippled in the still air of the morning. Gradually, the ripples grew in an upward undulation that formed shapely calves, then thighs, and eventually a fully formed woman of surpassing beauty.
Nymphs are loci geniuses that inhabit various natural places. While similar to what are sometimes called “fae”, they more closely resemble elementals of a specific locale. They are inherently tied to the location they inhabit; indeed, their very existence depends on the wellbeing of the environment. And they defend it vehemently.

All nymphs exercise a measure of control over their homes and use this, in combination with their preternatural beauty to ward off attacks. Their beauty is terrible and captivating, and they use this mercilessly to their advantage.

As dangerous as nymphs can be, they are excellent sources of information on the area in which they dwell, and if befriended, they make powerful allies. However, their legendary shyness makes this difficult, and their sadistic impulses make it doubly dangerous!

Mountain Nymph

CER 73 (OR 27 and PR 46)
Mountain nymphs are spirits of place who watch over mountainous areas.  They are closely attached to particular passes, grottos, peaks, etc., and may not stray more than a short distance from them without becoming seriously ill.  They defend their homes fiercely, employing magic to animate the mountain itself, often while dancing about high above.  All mountain nymphs command great knowledge about their environment.
ST: 9                                                       HP: 10                                                    Speed: 6.00
DX: 12                                                    Will: 10                                                  Ground Move: 6
IQ: 10                                                     Per: 11                                                   Climbing Move: 6
HT: 12                                                    FP: 12                                                     SM: 0

Dodge: 9                                                Parry: 10 (Unarmed)                           DR: 5

Punch (14): 1d-1 crushing. Reach C.
Quarterstaff (14): 1d+1 crushing (swing) or 1d crushing (thrust). Reach 1, 2*.
Animated Environment: Mountain nymphs can animate the environment around them to slide or knock intruders from their feet (target takes 3d crushing double knockback no wounding), strike at them (1d crushing or impaling) with rocks from above, or cause the ground to partially swallow a person – treat as Binding 10.
Difficult Terrain: A mountain nymph can cause anyone within their domain to have difficulty maintaining their balance or moving about.  The victim must roll a Quick Contest between his Will and the nymph's Will.  On a failure, the subject suffers a -2 penalty to DX and -2 penalty to Acrobatics, Jumping, Climbing, and Skiing lasting a number of minutes equal to his margin of failure.
Stunning Beauty: By striking even the slightest pose, anyone who sees her must make a Fright Check at -5 and roll on the Awe table.
Threshold Entity: This being doesn’t breathe, drink, eat, or sleep, is immune to metabolic hazards, and is either insubstantial and invisible or substantial and visible.

Traits: Acute Hearing 2; Appearance (Very Beautiful; Universal); Berserk (9) (Special Trigger, harming the wilderness); Callous; Can Be Turned by True Faith; Curious (15); Dependency (Home Mountain; Daily); Dislikes Loud Noises; Divine Curse (Keep to the letter of any promise); Fearlessness 2; Higher Purpose (Protect Home Mountain); Impulsive (12); Odious Personal Habit -1 (Capricious); Perfect Balance; Sadism (15); Sense of Duty (Home Mountain); Shyness (Mild); Super Jump 1; Terrain Adaptation (Mountain); Unaging; Vulnerability (Iron x2).
Features: Affected as Spirit.
Skills: Area Knowledge (Local)-12; Brawling-14; Climbing-16; Dancing-16; Intimidation-17; Jumping-16; Naturalist-12; Quarterstaff-14; Sex Appeal-12; Stealth-14.
Notes: Most nymphs won't negotiate because they are too shy.  Those who do are amiable enough, but dealing with such an astounding beauty is often disconcerting – especially while under the effect of her intoxicating beauty (see above).  Always scars from wounds inflicted by iron.

Monday, March 14, 2016

This Time It IS Rocket Science!

Last instalment, I discussed the parameters of the Rocket Design Project for this semester. This time, I’m going to get into how we make our predictions. Below is a derivation of the formulas necessary for predicting the apogee of a spherical bovine rocket undergoing air drag.

Warning: Math Ahead


So ultimately, we want to know how high the rocket will go. I am going to call this “y”, “displacement” or “apogee” interchangeably. I might even call it the height. Either way, this is what we are ultimately trying to solve for.

Anyone who has taken a basic calculus or physics class probably recognizes a few truths:
and
That is to say, the change in location of an object over a period of time is its velocity, and its change in velocity over a period of time is its acceleration. Thankfully, we can also say this in reverse:
and
This becomes important when we consider that the flight of any object is based on the sum of the forces acting on it. This is grounded in Newton’s Laws of Motion. Thus we know that the sum of our forces is

where F = force, m = mass, and a = acceleration. Thus,

Now we have a few terms here that we need to sort out: FThrust, FDrag, and FWeight. Of these, we can generally not worry about FThrust because that information is available based on our motor. Likewise, we know that FWeight = mg, where g is the acceleration due to gravity. This leaves FDrag for us to define:

where ρ = the density of air, CD = the coefficient of drag, A = the crossectional area of the rocket, and v = the velocity. This may seem like a lot of information, but much of it really doesn’t change with time for our purposes here. So I am going to combine a bunch of these into a constant. I will do this a few more times to clean up equations and put them in more easily recognizable forms, too.

Now we have a simpler looking equation:
Substituting this and the formula for FWeight, we get:
One more substitution, referring back to the beginning gives us
and we are ready to separate the variables and integrate.
But first, we are going to use some algebraic manipulations to get this looking like something we can integrate more easily:
Let
Thus
Now it’s time to integrate both sides:
Both m and k are constants, so we pull those out and integrate the right side:
We should now recognize the integral on the left as tanh-1 u:
By the definition of tanh-1, we can perform the following manipulations:
Therefore,
And define the constant
This lets us say:
Raising both sides to the e power gives:
Then we multiply both sides by the denominator:
Expanding the right side gives us:
Next, I need to isolate my v’s on one side:
Next, factor out v:
And divide both sides by (-ext-1):
Put more neatly:
And thankfully, we know that t = impulse divided by thrust, both of which are specifications provided by our motors. So now we know the final velocity when the motor finishes burning its fuel, but that doesn’t tell us either how high the rocket is at that point or how far it continues to coast. For that information, we need more integration.

We will begin by solving for yBurn, or how far the rocket travels while the motor is still providing thrust. For simplicity’s sake, we will assume the rocket’s weight does not change during this time (we are launching a frictionless spherical cow, aren’t we?), so m will continue to refer to the mass of the rocket while it is full of propellant.

Referring back to our original equation, we know that:
So we can say
By separating the variables and integrating both sides, we get:
Which becomes:
Now we know the rocket’s altitude when the motor cuts out, but the rocket won’t instantly stop; it will continue to coast. So let yCoast = the distance the rocket coasts on its momentum before beginning its descent. That is to say, how far will the rocket travel upward once FThrust = 0. Note that since the rocket has exhausted all of its fuel, we no longer use mFull – we are now use mEmpty.
This should all look a bit familiar, but not that because FThrust = 0, that term is simply missing:
By integrating both sides, we get:
Which becomes:
Now, we know the rocket’s apogee will be the sum of how high it goes while under power (yBurn) and how far it coasts before the acceleration due to gravity starts returning it to Earth (yCoast):
And there you have it! To summarize:








Where,
A = the area of the rocket’s cross-section normal to its velocity vector.
CD = the rocket’s coefficient of drag.
FThrust = the motor’s thrust in Newtons.
g = the acceleration due to gravity.
I = the motor’s impulse in seconds.
mEmpty = the mass of the rocket after burnout.
mFull = the mass of the rocket at liftoff.
ρ = the density of air.

Of course, the astute reader will notice that through all of that mess, there is one term still undefined- CD. This is the coefficient of drag, and determining it generally requires experimentation or running simulations. For our purposes, that is where OpenRocket and SolidWorks come in. Both are capable of determining CD.

Did you survive? I warned you there’d be math!


Monday, March 7, 2016

It's Not Rocket Science!

Today's post was going to be a derivation of the formulas we are using in the Rocket Design Project to predict our rocket's performance. It does get pretty math-intensive, and so I wrote it out ahead of time in word to more easily proof before pasting into here. This was a mistake. The formulas didn't transfer. Not only that, but I'm still looking for a good way to put them and any future math I may decide to include, in this blog. So instead of math, you're getting a llama.


Was this better than a few pages of integration?

Thursday, March 3, 2016

Building a Rocket (Part 1)

This semester, I am working with a team of students to design a model rocket as part of the Rocket Design Project for our local student chapter of the AIAA. And I figure I may as well write down my thoughts on the experience, as it progresses forward.

So What Is It?
This project requires teams of three to four students to design and build a model rocket with the goal of predicting and reaching as close as possible to specific target apogee – in our case, 1,750 feet. Points are awarded based on accuracy of our predictions, how close to the goal we get, and the overall aesthetic appeal of our rocket.

What Will We Use?
So far, we don’t have specific specs aside from knowing we are getting either G40-7W or G38-7FB motors. This means that the motors are the largest available without a license (G-motor), they both have a 7 second delay, and one has a specific impulse of 40 s and the other of 38 s. Basically, these are pretty big motors that should easily achieve an apogee of about 2,500 feet. The trick for us will be slowing them down, I suspect.

The rest of the parts are also given to us, excluding the fins – these we will design ourselves in SolidWorks and OpenRocket and cut from acrylic with our school’s laser cutter. This is really the only part we truly get to design; the rest are given to us.

So How Do Design It?
We will use a combination of SolidWorks and its fluid flow simulator and OpenRocket, an open source rocketry program that can also simulate flights. These can both be augmented by our own hand calculations, mostly likely solved with one of MATLAB, Mathcad, or Excel. Once we have a fin design that achieves an appropriate apogee, we will cut our fins and assemble our rocket.

So How Do You Launch It?
We will go to a sod farm where a local rocket club regularly launches. They will assist us in launching our rockets, which will hopefully perform according to our predictions. This will be done over the course of a weekend, at the end of the semester.

So What’s Next?

Next post will derive a set of simplistic two-dimensional equations for predicting apogee. It is worth noting that I have not achieved the level of knowledge needed to work out a 3D version of this or take into account things like changing propellant weight, wind speeds (let alone varying wind speeds with altitude), or varying thrust. Technically these should all be taken into account, but I also question to what degree these will affect our rockets, considering the slop in our own measurement and construction. Basically, I’m not sure if such an accurate model wouldn’t be invalidated by our manufacturing process or variations in the weather.

Tuesday, March 1, 2016

State of the Blog

Today is my birthday, and looking back over the last year, I recognize that while some aspects of my life have greatly improved - moving, getting accepted into a good university, and beginning work on my second degree - some areas have suffered, namely, this blog and writing in general. Part of that is due to the narrowness of the blog's focus; I just don't have the time I use to dedicate to worldbuilding or running games. In fact, Saturn Rising is no more. And while I continue to write for SJGames whenever I can, I am largely in the process of clearing my plate, so I can sort out just what I do have time for and focus accordingly.

So to keep the blog alive, I am expanding the scope to include pretty much anything I happen to be thinking about or working on. I will also begin restricting GURPS-related posts to Thursdays until I have a backlog (if that happens). Thus, I will be joining the GURPSday crowd as many weeks as possible.

So what sort of things can you expect to find here from now on?

  • Random GURPS content
  • Designer's Notes on my published material
  • Game or session reports
  • Various design project journals, such as the AIAA's Rocket Design Project
  • Random thoughts and ideas
  • Maps
  • World Building
  • Campaign Building
  • Conlangs
  • Anything else creative that springs to mind
I'm hoping with that list, I can hit the weekly output I really wanted to reach. Only time will tell, and honestly, if this falters, it is probably because I have other responsibilities in terms of classes, organizational commitments, and hopefully internships/jobs.