Rocket launcher deliverable #2

Just like last week, you are basically free to do what you want during the lab work period, you just have to deliver to me the result I ask for by the end of the week. My impression so far is that you're all making very good progress, so this deliverable should be easy.

This week, I want you to tell me the following:

• Did you find that you need to use the same rocket and turret for reliable results, or did it not matter too much?
• Give an estimate of the variability in the launcher's range for at least 3 angles. For instance, if you do 5 launches at a given angle, what are the mean, maximum, and minimum ranges? 
• Given the variability you find, approximately what size target do you think you could hit reliably? Ballpark answer is fine.
• How does the actual range of the rocket compare to what you would predict without drag forces, evaluated for at least 2 angles?
• How much kinetic energy must be lost to drag forces for each of those angles (say, a % of the launch energy)?
• Using the example code I've given you (below), or code you've written, what drag coefficient makes your simulations match your measured data reasonably well?

Rocket launchers, first deliverables

From now on, our 'labs' will be characterizing the rocket launchers and figuring out how to predict their motion. Each lab session, you'll get your launcher and tell us what sensors or equipment you might need for that session. We will not have written procedures or detailed lists of tasks, just a final goal and a set of deliverables each week.

For example, next week (by Friday), your primary deliverable is to have figured out the muzzle velocity of the launcher as well as some estimate of its uncertainty. A secondary deliverable is to sketch out how you will proceed during the following week. How you choose to proceed is up to you, I will only give advice as to whether your plans are reasonable or not, and how you might alter them if they are not reasonable.

Your deliverables will take the form of a short memo (2 pages maximum), one per group, due by the end of the day Friday March 7. Any reasonable format is accepted (hard or soft copy). This memo should contain, at least, the following key points:

• What is the launch velocity, with an estimate of its uncertainty. Does it depend on which rocket and which turret you use?
• How did you determine the velocity, in brief? (E.g., what sensor did you use.) Define your measure of uncertainty, or how you quantified uncertainty.
• What are the appropriate equations of motion for your projectile, including drag? That is, what does the force depend on? (You do not need to solve the equations yet, just figure out what they are.) 
• At launch time, you will have the ability to measure the target coordinates. Besides that and the muzzle velocity, what else do you need to know to set up your launch to hit a target?
• What quantities can be determined experimentally ahead of time, and which will only be known once you know the target coordinates?
• What are your potential sources of uncertainty, and how could you characterize them? A detailed plan is not necessary, just an idea.

As the week progresses, we'll discuss the finer points of your memos. All you really need is a measure of the velocity, and a rough idea of what things you're going to need to figure out over the next weeks.

Tomorrow's lab

Tomorrow, we'll do one more 'regular' lab before starting with the rocket launchers. The main point is to learn how to use photogates for timing, which will be useful for characterizing your launchers. A secondary point is to verify conservation of momentum in 1D collisions.

Also: the rocket launchers just arrived yesterday, so tomorrow I'll show you what they look like and how they work. We'll need a couple of days to install the right software on the lab computers, but either this Friday or next Monday we'll get started with them.

Class for Wed 19 Feb / upcoming exam

We'll continue our discussion of momentum a little bit, time permitting, at least as far as figuring out how to handle collisions. A larger portion of the class will be related to homework problems, which are directly relevant for the exam, and another lab on programming.

For the homework, you should be a little bothered by #6, I'll outline 2 methods to solve this one. Number 7 should be quite mysterious, and that is OK - the technique you need to solve it is related to the experimental propagation of uncertainty - if you change one variable a little bit, how do the others change? This is related to how you move along surfaces in 3D, something you are learning or have learned in Cal III.

Number 8 requires some thought - the equilibrium spacing is where U(r) is minimum, or where dU/dr = -F = 0 and the net force is zero. Find this first. The breaking point of molecule is when you exceed the maximum restoring force implied by U(r). If you find F(r) = -dU/dr and look for its maximum, this will occur for a particular r, beyond which the force binding the atoms together is exceeded and the atoms will come apart. Mathematically, that means setting dF/dr = 0 to find the maximum, that's the radius beyond which you break the molecule. Using the result for the equilibrium spacing, you can write it in terms of only n, m, and the equilibrium radius. I might have asked this question before if you are willing to dig a little.

For the exam, the format is exactly like the last time. It will likely consist of 6 problems, of which you have to solve 4. The questions will only be on work, kinetic energy, potential energy, and conservation of energy - 2 chapters in the book. You'll have a formula sheet given like last time, and can bring 1 sheet of paper of your own. I will post HW3 solutions by Thursday morning, hopefully, to help you study.

Finally, the lab: we'll continue with coding. You have two basic tasks.

1) I assert that the sum of the first n cubes of integers (sum of i^3 from i=1 to i=n) is the square of the sum of the first n integers (square of the sum of i from i=1 to i=n). Write a program that can check this for specific values of n. Print out your code and results for n=10 and n=17. Basically: sum the integers, square the sum, and compare to the sum of the cubes of integers.

2) Write and evaluate a program to calculate the range of a projectile under only the influence of gravity (no drag forces). Verify that it gives the correct result (within a few percent numerical error) for a launch speed of 25 m/s and a launch angle of 45 degrees. (You already know how to calculate the range without a drag force ...) Note that links I gave previously, and specific folders here are highly useful. Print out your code and note your results for the conditions noted.

Starting with Python

For tomorrow's "lab", we'll start messing around with python. Nothing fancy, just a few simple examples so you can learn to do basic calculations (like multiply stuff) and display the answer. We'll work our way up to more complicated things. If you are interested enough to mess around on your own, try the excellent tutorial here. Don't feel bad if you haven't programmed before. It will be weird at first, but you'll pick up enough to do what you need to in no time.

Starting our project

As I mentioned on Friday, from now on we're going to stop with the usual labs and work on a project for the rest of the semester. The basic project is to characterize and simulate USB-controlled foam rocket launchers.

The ultimate goal will for you to be able to calculate numerically the flight of a realistic projectile and use this result to actually hit a target with the launcher. You will have to include drag forces and everything - using measured values of launch velocities, drag coefficients, etc. The experimental end of this will be measuring launch velocities, their variability, and trying to measure drag coefficients using the sensors we have. How to get a good measure of the drag coefficient will require some time and care. By the end, we should be able to specify a target, and you will perform the calculations and then actually hit the target.

The theoretical end of this is figuring out how to calculate things numerically. Projectile motion with drag can't be done analytically, so we'll need to learn how to simulate things. To start with, we can do this in pseudocode, as I did on Friday, just learning the appropriate algorithm for calculating trajectories numerically. Once you've got your head around how the process works, we can start with actual code. For those of you that can program, you're free to use any language you want and any methods you want. What you do has to make sense, and it has to work. For those of you that can't program, I'm going to teach you just enough Python to get the job done. We'll start learning basic python coding tomorrow; see the next post.

Lab for tomorrow

Work and energy.

Lab for 5 Feb

Tomorrow, we'll do a relatively simple lab on friction.

Additionally, we'll start to talk about work & energy, and figure out some better problem-solving methods that are less tedious than what you've dealt with so far. If there is time, I'll sketch out the solutions to the exam problems, but that may have to wait until Friday.

Given that I was out sick yesterday, and am not feeling great today, I am not sure when the exams will be graded. I'm hoping for Friday, but Monday at the latest.

Wednesday's lab

Here you go - just like one of the problems we worked out in class today.

Tomorrow's lab

Here is the background reading and procedure. Please read it before tomorrow's class. You can print it when you arrive, no need to print it at home. Depending on how the time goes, we may finish the prep questions and writeup on Friday.

You might also find this derivation of linear regression interesting, but it is not required reading.

Lab 1 / Wed 15 Jan

On Wednesday, we'll do a lab on uncertainty analysis.

You don't need to print this out, just read it before Wednesday's class. You can print what you need in the classroom when you arrive. Please just print one copy per group, you'll be working in groups of 3-4.

Rocket launcher progress

Before the end of tomorrow, I want you to write me a memo regarding your plans. About 2 pages (max), one per group, due by the end of tomorrow.

The details will become more clear after today's class, where we will spend a good amount of time on further characterizing the rockets.

Tomorrow's class

Thursday, we will devote about an hour to more measurements of the rockets and characterizing the launchers. This, as opposed to the rotational dynamics lab previously scheduled.

Remember your end goal: predicting, for a given angle of launch, where the thing is going to land. Keep in mind the target may not be at the same level as the launcher. Tomorrow or Friday we'll also discuss in more detail how to use your data to model the drag force empirically and use that in your trajectory calculations.

Thursday's lab

We will take two carts, and run them into each other.

Also: we will spend time setting up a few of the homework problems. You aren't putting them off, right?

Thursday's class

FYI: schedule change.

There are scheduling difficulties with the lab we had planned for today (nothing interesting, merely difficult), so we will instead focus on problem solving for a good chunk of the class. Part of that will be setting up this week's homework problems.

I will first go into some more detail on potential energy and conservation of energy, but will try to confine that to 45min or so ... such that most of the time will be spent figuring out how to use the new ideas.

Thursday's lab procedure

Tomorrow, we'll do a lab to verify Newton's second law. Please print one copy per group when you arrive. If you get time before class, have a look through the procedure.

Lab for Thursday 22 Jan

Here is a draft of tomorrow's lab procedure. Have a look through it before class if you can.

There is no need to print a copy before coming to class ... it will probably undergo some tweaks and reformatting before tomorrow's class. The basic procedure will not be affected, however, so it is still worth a read.

Today's lab

I apologize for this being a bit late, but the lab I originally had planned was fraught with difficulties, so I made a new version.

Here is the lab procedure for today. If you don't have time to read this before class, that is OK ... I will give some extra time in class for that.

This week

Today we'll review some math we'll need very soon, including basic calculus and vectors in some detail. For some of you, this may be a bit of review, but I suspect that much of the vector topics we cover will be substantially new for most of you. At the end of class, there will be a short quiz (15 min or so) based on what we have covered in the lecture.

For Thursday, three things need to happen.

First, there are three more problems due at the beginning of class. After tomorrow's lecture, you should have all the information you need to solve them. Chapter 3 in the text covers the necessary material.

Second, we will begin studying motion in one dimension. For this, you should read chapter 2 before class on Thursday. Really ... even if you only skim.

Third, there will be a lab. I will post the procedure here later by Wednesday, please have a look at it before Thursday's class as well (it will be short).