Sunday, January 18, 2015

Rocket Motor Basics - And Not So Basics (For N00bs)

I've been meaning, for some time, to write an introduction to motor basics for any rocket n00bs who check out this blog, but I've been putting it off. Well, I'm glad I did, because I've learned something new which will affect some of the information in this post.

That said, here are the basic basics of rocket motors for beginners.

Your basic model rocket motor has a solid propellant made of black powder, a combustible material invented in China in about the 9th century C.E., and was used for fireworks and military weapons.

An early Chinese rocket
In a model rocket motor, the black powder is formed into a solid and pressed into a thick paper casing. At one end, you see a clay or "ceramic" nozzle - a plug with a little hole in it. At the other, you see a clay cap.

The nozzle end

The clay cap
If you read my posts on launching your first rocket, you know that the motor (or "engine" as Estes calls it) is inserted in the base of the rocket with the nozzle pointing out the back. An igniter is inserted into the nozzle and held in place with a plug or some tape, and then you hook up your launch controller and shoot the thing into the sky.

But there are many sizes of rocket motors, and many levels of power.


Here's How They Work

Newton's Third Law of Motion states that for every action, there must be an equal and opposite reaction. The First Law states that an object at rest will stay at rest, and an object in motion will stay in motion, unless acted upon by an external force.

When the black powder motor is ignited, it combusts (it does not explode!), creating an expanding mass of gas inside the motor, which presses on the walls of the motor. Now, if the motor were a sealed chamber, the pressure would be equal on all sides, and with enough pressure, the motor would explode! But remember, you have a hole - a nozzle - in the rear of the motor. As the expanding gas presses on the interior of the motor, it presses against the forward wall of the motor, and the forward wall presses back. Because the pressure at the nozzle end is lower than at the forward end, the pressure is unbalanced. So the gas escapes out the rear nozzle, and the rocket motor flies forward - carrying the rocket with it!

All rocket motors and engines work this way.

A lot of sources say that the exhaust shooting out the back of the motor are what propel the rocket forward. This isn't exactly true. It's not the simple act of the rocket exhaust flying backwards which makes the rocket go forward. The reason the rocket goes upward is that the gas inside the motor is pushing forward on it, and the gas flies out the nozzle because the rocket is pushing backward on it. Consider two people on skates, standing together. If one skates off in one direction, the other one will stay put. It's if they push on each other that they go off in opposite directions. This is action and reaction - both skaters are acting, and both are reacting. You could consider one skater the rocket, and the other skater the expanding exhaust gas.

"Skaters showing newtons third law" by Benjamin Crowell
A typical black powder motor has three grains, or charges in it.

From the 2015 Estes Catalog


The first, of course, is the propellant grain. This makes up most of the mass inside the motor, and as it burns, it creates thrust, propelling the rocket upward. This phase of rocket flight is known as powered flight.

Once the propellant has burned out, the rocket continues coasting very far upward, and this is called the coasting phase of flight. At this time, the second grain, the delay grain or delay charge burns. It's a slow-burning chunk of black powder, which produces almost no thrust at all - certainly not enough to propel the rocket upward. While it creates no appreciable thrust, the delay grain does create a lot of smoke. This helps you to see the rocket (which can go very high and be hard to spot after a couple of seconds - especially a small rocket), so this phase is also sometimes called the tracking phase.

The delay grain burns for several seconds, and when it's done, it ignites the ejection charge. This is a bit of loose black powder contained in the top of the motor just under the clay cap. The ejection charge creates a tiny explosion inside the body of the rocket. This is what causes the nose cone and parachute to eject - the charge creates increased air pressure inside the rocket so that the nose pops off.

The parachute opens, the rocket floats gracefully to Earth, and you get to launch the rocket all over again with a new motor. You just remove the used one, pop a new one in, and do it all over again.

Why Do You Need the Delay Grain?

After the motor's thrust cuts out, the rocket will continue to coast upward for quite a ways. In fact, in most rockets, the coasting phase is much longer and gains much more altitude than the powered phase. Just think about throwing a ball straight up in the air - while it's in your hand, that's powered flight. But the ball doesn't stop when it leaves your hand - you can throw it much higher than your head.

An image from JollyLogic.com, a manufacturer of model rocket altimeters.
You can see from the illustration just how high a rocket can travel during the coasting phase alone.

You want the parachute to deploy at or near apogee, the highest point in the rocket's flight. At that point, the rocket will have slowed down due to gravity and aerodynamic drag. It will begin to arc over and start falling straight downward.

It's important for the recovery system to deploy when the rocket is going its slowest for two reasons. First, you want to get as much altitude out of a flight as possible. If the chute opens before the rocket is done coasting upward, the rocket will stop ascending and begin to descend, robbing you of altitude.

Second, and perhaps more important, is that if the rocket is going too fast when the chute deploys, the force of the shock cord against the end of the body tube can damage the rocket. It can cause a kink in the tube, or worse - a zipper. A zipper is when the cord rips straight down through the body tube, causing a jagged tear.

I've never had a zipper, but I have had the beginnings of one - on my first scratch built rocket, Janus I.


 Motor "Designations"

If you get a kit, you'll see listed on the packaging a number of appropriate motors for that rocket. You'll probably see a list like A8-3, B4-4, B6-4 C6-3, C6-5. What does that mean?


Well, this next part is going to get a little technical and a little long. But it's fascinating, and I'd encourage you to read it, but if you're a n00b and your eyes begin to glaze over, just think of it this way:
  • Each letter is twice as powerful as the previous letter (and four times as powerful as two letters back)
  • The first number is supposed to be the average thrust of the motor (but really isn't)
  • The second number is how long the delay lasts, in seconds

Rocket thrust is measured in newtons. A newton is a measure of force roughly equivalent to 0.10197 kilogram, or 0.2248 pound. Put another way, one pound of force is equal to about 4.448 newtons.

Rocket motors are designated with a letter indicating their approximate total impulse, measured in newton-seconds, which could* be stated "newtons per second." This will tell you how much total force the motor will exert on the rocket, which will affect how high and how fast the rocket will fly.

The total impulse is technically everything below the thrust curve. A thrust curve is a graphic illustration of the mathematical data describing the motor's performance.

A thrust curve for an AeroTech F20 composite motor. Image from ThrustCurve.org.
 But a good approximation is to think of total impulse as the average thrust of the motor multiplied by the total burn time of the propellant - the total time the motor is burning and producing thrust. There is a little data in the thrust curve that this calculation won't account for, but it will give us a pretty good approximation, and it's easier to understand.

Let's look at the motor data for the AeroTech F20:

The total impulse (in red) of this motor is 51.8 newton-seconds. The average thrust (in green) is 20.8 newtons. The burn time (in blue) for the motor is 2.5 seconds. If you multiply those, you get a total impulse of 52 newton-seconds - pretty close to the actual total impulse.

Furthermore, if you divide the total impulse by the burn time, you get approximately the average thrust:

51.8  ÷ 2.5 = 20.72 (approximate average thrust)

*Remember when I said "newton-seconds could be stated as newtons per second?" Well, the reason that's not exactly correct is obvious if you look at the actual thrust curve - it's not even. It's curved. The motor's thrust peaks early, then tapers off. But it does mean that you get about so many newtons over the course of so many seconds, and that's what is meant by "newton-seconds."

The Letter

The classification starts with A (it can go down to 1/2 A and 1/4 A, but let's keep this as simple as we can) and goes up from there.

Each successive letter class has a total impulse of up to twice that of the previous letter.

An A motor has a total impulse of up to 2.5 newton-seconds (or n-s). A B has up to 5 n-s total impulse. A C goes up to 10 n-s, and a D up to 20 n-s. So the quick and dirty way of explaining it is that if you go up a letter class, you get up to twice the power as before.

That's not all - if you have a cluster of two motors, or a multistage rocket, those motors add up - so a cluster of two B motors equal approximately 1 C motor. A multistage rocket with 2 C motors has the total impulse of a D motor.

64 A motors = 32 B = 16 C = 8 D = 4 E = 2 F = 1 G...

Model rockets (those not considered "high power" rockets, and therefore not restricted by the Federal Aviation Administration or the National Association of Rocketry) go up to G class (160 n-s of total impulse). Most F and G motors use composite propellant, which we'll discuss once I've had more experience with it.

So, if you get yourself a pack of C6-5 motors, those motors will have a total impulse of up to 10 n-s.

We'll come back to this point in a bit.

The First Number

OK, this is where it gets tricky, and where the books get it wrong. Stick with me - we'll get through this.

According to the rocketry literature, the letter indicates total impulse, the first number indicates average thrust of the motor, and the second number indicates the delay time. So, a C6-5 motor has a total impulse of 10 newton-seconds, an average thrust of 6 newtons, and a five second delay. Even Estes literature states this.

From the 2015 Estes Catalog. Note that the first number in the code is supposed
to be the average thrust of the motor. But hold on a sec...

That's so simple! But it isn't true.

First of all, above I wrote that a C motor has up to 10 n-s of total impulse. It could have anything from 5.01 n-s all the way up to 10. Most of the lower power motors are close to the top of the scale, but probably none of them are right there. This is fine - when you learn about the letter designation of motors, you learn that there is a scale - and when you get up to higher impulse motors - say, E or F and beyond - there's a lot of variation. High power rocketeers talk of flying with a "middle H" or "low K" motor. With a bigger scale comes bigger variation.

From the 2015 Estes Catalog. OK, this says that a C6 motor has a total impulse of 10 n-s. A bit
off the mark, but it's pretty close, as we'll see below. The first number, however, that's different.

So, the problem isn't with the letter. It's that first number.

Fortunately, we have a resource - ThrustCurve.org, created by master rocketeer John Coker. This website has thrust curve analyses of hundreds of motors - even the little black powder motors we as rocket n00bs use most.

If you look up the Estes C6 motor (the delay isn't counted in the thrust curve), you'll see that it has 8.8 n-s of total impulse. Not bad - pretty close to 10.

But if you look at the average thrust - that's where things go off the map. An Estes C6 motor has an average thrust of only 4.7 newtons - not close enough to 6 to say "about six."

4.7 does not equal 6. That's just basic math.

Now look at the info on the Quest C6 - 8.8 n-s of total impulse, but an average thrust of only 3.5 newtons! That's just over 50% of what you'd expect!


Because of this, a rocket with an Estes C6 will perform quite differently than with a Quest C6.


Thrust curves for the Estes and Quest C6 motors, respectively.
Even a cursory glance at these shows they're quite different.
When I first learned of all this, I found it a little frustrating, because the "official" meaning of the motor designation is so simple - 6 newtons of thrust. But the motors are in fact all over the map on this, making me wonder what the point of the first number even is.

Look around at other motors on ThrustCurve.org - AeroTech, Cesaroni (CTI), all the other composites. The first number is in fact much closer to the actual average thrust, but none are exactly there. Once you get up into double and triple digits, the margin of error is minor, so I suppose it doesn't matter much. But why doesn't The Handbook address this issue? Why don't Estes and Quest simply use a number which is more reflective of the actual performance of the motor? I have yet to find an answer to these questions. Motor designations seem to be partly informative, and partly a matter of convention.

As John Coker wrote on a thread I posted on The Rocketry Forum, "A motor name like 'C6' is just that; the name." Which makes me wonder why they bother using a number at all, if it doesn't mean anything? Why not CRobert-5? BMelissa-4 and BJames-4?



Now, there is one thing I'd consider to be an advantage to this. If the motor designations were straightforward, then a C6 motor would burn for about 1.666 seconds. In fact, an Estes C6 burns for 1.9 seconds, and a Quest for 2.5. That might seem like not much of a difference, when you're talking fractions of seconds, but powered flight is so quick that you do really notice a longer burn time. And powered flight is my favorite part of a launch. So, as long as the motor is strong enough to get the rocket off the pad safely, a longer flight with lower average thrust might actually be more fun to watch.

Why the discrepancy? I don't know. I think a lot of the higher power motors - your AeroTechs, your Cesaronis - are closer in average thrust to that second number. And perhaps earlier Estes and Quest motors were closer to it, and the motor designation is a holdover from an earlier time.

I want to be clear - I don't mean to disparage Estes or Quest here. I own a lot of Estes rockets and motors, and Quest rockets. And I love them, and will buy more. They work.

It's just that, if you read The Handbook and other sources, you're told that the motor designation means something very specific, but it's not the whole story.

OK, moving on...

The Second Number

I alluded to this above, but here it is. The second number (B4-4, C6-5) is the delay time, measured in seconds. This number is more or less accurate - it will vary slightly from motor to motor due to slight irregularities in the black powder mixture, but it's pretty close.

Most BP motors are sold with a number of delay times, and you want to select the ideal one for your rocket. Some rockets need a longer delay time than others, because once powered flight is over, they will coast further and for a longer period before reaching apogee and arcing over.

I fly most of my rockets on a C6-5 motor most of the time, and this works great for most of them. The Big Bertha, on the other hand, is heavier and experiences much more drag than others, so it arcs over quite soon after the propellant burns out. When I put a C6-5 in it, it starts to dive toward the ground before the parachute deploys - it can make you really nervous when that happens. So I've switched over to C6-3 motors for the Bertha. The motor performance is the same as a C6-5, but the parachute deploys closer to apogee.

The Quadrunner, on the other hand, will coast quite far after powered flight - those four C6 motors put a lot of thrust on that rocket! With too short a delay, as we've seen above, the rocket could be damaged - and I put a lot of work into that one, as you may have read in a previous post. With that rocket, I use four C6-7 motors - a nice, 7-second delay. That means the rocket will fly for about 9 full seconds before the parachute deploys - a nice, long ascent!

If you go with a kit, the proper motors with the proper delay times will be listed. If you need to pick one yourself, a rocket simulator such as OpenRocket or RockSim will help you.


In my OpenRocket simulation, you can see the recovery device (parachute) deploys right at apogee - perfect!

In the simulation I have an E9-6 (6-second delay) in the upper stage.
The Optimum Delay for this flight is 6.12 seconds - that's pretty close to perfect for this rocket!

What If the Second Number Is Zero?


A rocket motor with a 0 at the end - such as C6-0 - has no delay charge and no ejection charge. There's no clay cap on the end. These are only for the lower booster stages of multistage rockets. When the propellant charge burns through to the top, flaming propellant shoots forward into the nozzle of another motor in the upper stages.

On the left, a C6-0 motor. There's no delay charge and no clay cap, so you can see the
black powder propellant inside. On the right is a C6-5 motor, showing the clay cap end.
If you were to put a -0 motor into a single-stage rocket, the airframe would pressurize as soon as the propellant burned through, and you could get some severe damage to the rocket. So, save those motors for multistage use.

We'll talk about staging at another time.

Why Do I Need To Know All This??

Well, if you just by Estes kits and buy the motors recommended on the package, maybe you don't. But it's interesting. Learning new stuff is one of the fun parts of rocketry. And if you want to go further, it pays to know more.
If you get a kit from another vendor, or a more advanced kit - like a mid or high power rocket - or if you decide to design your own, you should know more about motors, because you may have to decide for yourself what motors to put into your rocket.

Looking at thrust curves will also show you what the peak thrust is, and when it happens. Peak thrust is that spike in the curve, and it's much stronger than the rest of the motor's thrust. This is often important for knowing if your rocket will be going fast enough when it leaves the launch pad to fly straight and true.

There are a few ways of determining what motors are appropriate for your rocket. One is to use a rocket simulator, such as OpenRocket or RockSim, and try running simulations with many different motors. Or you can go to ThrustCurve and input information about your rocket, such as diameter, weight, and motor mount size, and ThrustCurve will give you a list of motors that will probably work for your rocket.

Knowledge is power. Many newton-seconds of power.

Note: I really enjoyed writing this post, and it took me quite a long time. It helped me realize just how much I've learned since I started. And it made me brush up on my basic physics.

If any advanced rocketeers read this and notice I've left something out or made a huge mistake, please send me an email so I can edit the post and correct my mistakes! 

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3 comments:

  1. Daniel,
    This is a very informative post. I have been in and out of the hobby since I was a teenager (now 46). Along with my son have built and flown many of the Estes models. Your explanation and information provided is great. As you mentioned it must have taken hours to assemble the charts and data and then compile your thoughts. Very good! Thank you!
    Scott Stephenson

    ReplyDelete
    Replies
    1. Thank you, Scott! I'm particularly proud of this post. It took some work to get it done, but I think it's a pretty good introduction to the subject. I'm glad you appreciate it - that means a lot!

      Delete
  2. Daniel,

    Absolutely spectacular.

    Thanks for your contributions.

    ReplyDelete