# Burnsim numbers fiasco – What are C*, Isp*, Isp, and Ve?

So I’ve solved the ‘crazy numbers in BurnSim’ problem that I was having. This particular problem resulted in a crazy claim of a 38mm K motor – from a 76% solids formulation. This has since been corrected.

The origin of this issue comes from the thrust equation (1):

where the left hand term in the equation represents the integral of the pressure forces (the resultant force) acting on the chamber and nozzle.

According to this equation, total impulse of the motor is proportional to a term in the right hand side of the equation, Vₑ, the effective gas exit velocity of the motor. This term is directly proportional to the C* of the motor, a term for the characteristic gas velocity of the propellant when combusted at a specific pressure value with no nozzle expansion (typically 1000 psi chamber/14.7 psi ambient). The Isp* value that BurnSim uses is this C* value divided by the gravitational constant (in this case, 32.2 f/s), so gas velocity (dist/time) becomes just time, and C* becomes Isp*. Confusing, right? What makes it even more confusing is that Burnsim refers to this Isp* value as “Char. Isp” even though it is not the characterized Isp at all.

In reality, the characterized/delivered Isp should almost always be higher than the Isp*, since rocket motor nozzles should have an expansion section, increasing velocity of the gas flow, in turn increasing efficiency. This expanded gas flow velocity is Vₑ, and if divided by the gravitational constant, we get the motor’s effective delivered Isp. So C* is related to Vₑ by how much the expansion of the nozzle increases efficiency. This value is known as the thrust coefficient (Cf). In short, Vₑ > C* and Isp > Isp*.

The issue that I was having came from using a delivered Isp value for the Isp* input in BurnSim. Because the characterized/delivered Isp was around 210 seconds, the program output a new delivered Isp of 278 seconds. In reality, Isp* values should be around 150-165 seconds (or C* = 4800-5280 feet/second).

So the moral of the story is to correctly calculate your C* before trying to run BurnSim calculations on a motor. Having the wrong Isp* or C* value can lead to wildly inaccurate outputs of thrust, total impulse, and mass flux. Garbage in, garbage out.

Note: this was originally published in September 2013, however I decided to edit it and republish it because I felt that it did not adequately explain the problem I was having and how I came to understand it and solve it.

# Lost Content

So, my friend that had hosted this site for two years is MIA and nowhere to be found. As such, I am missing a couple posts (two I think?). It’s a good thing I don’t ever update this blog, otherwise I would have actually lost some work! This is just another reason to backup your data as often as you can. Don’t trust that everything will be around forever. I may have only lost a couple posts on a wordpress blog this time, but I could have easily lost a year’s worth of email if I was not being careful. I suppose I should say I learned my lesson about placing absolute trust in one entity.

Anyways, despite losing a bit of content, I’m gonna try to kick off the 3rd year of this blog with a bang and explain what I’ve been up to lately. Stay tuned.

# New Webhost

Hey all,

I’ve had some issues with uptime on the previous webhost that I was using, aka “a friend hosts it for free no I’m not kidding no you can’t have free hosting too”. So I decided to purchase hosting. I lost a bit of content but we will try to contact said friend and get it all sorted out. Should be no more issues. I also had to change the theme but to be honest the old was was garbage anyways.

# An Editorial on Stability

So you want to design the most high performing rocket that you can. Great, but is it stable? Dynamic stability is tricky, as no hobbyist level programs have a very accurate Cp calculation system for dynamic stability (see “Rasero v. OpenRocket“) .

However, xCp isn’t the only thing that garners dynamic stability. A very important aspect of dynamic stability is the amplitude of how much your rocket can correct it’s path from a disturbance, known as the Corrective Moment Coefficient. I recommend reading the Apogee Rockets Newsletter on the topic, Tim has a very good explanation of the concept.

I have firsthand experience with a low corrective moment. My 54mm Guardian went unstable due to a very low correctional moment, had my fins been larger, they would have been able to force the rocket back onto a straight path much more effectively.

Another important note is that stability “calibers” is basically a “fudge factor” in the first place. Designing for efficiency at 1.00 calibers is missing the point of stability calibers in the first place. Theoretically, if the Cp is aft of the CG relative to the nose, the rocket is stable. This is why trying to maximize your performance based on stability margin optimization is going in circles.

Instead, find a fin shape that fits your flight profile. Change the dimensions, making the fin bigger and bigger until the apogee altitude starts going down – you’ve reached the theoretical limit for optimization. Then, make the fin bigger again. At some point in this region is the sweet spot for higher corrective moment without trading too much altitude.

Use this handy chart to visualize the effects of different fin sizes.

-Fins are too small. There isn’t enough force of lift or corrective force for the rocket to be stable.

-Slightly small fins. If the fins are large enough for the rocket to be stable, but not quite, your apogee altitude will be reduced due to coning or other dynamic instabilities that cannot be cancelled by the small corrective moment.

-The theoretical maximum altitude. If the fins were any bigger, apogee altitude goes down. Any smaller, the rocket isn’t stable enough. However, due to many unknown circumstances such as wind shear, the corrective moment can prove to not be large enough, causing the rocket to be unstable. Success chances are low.  (Guardian fits here).

-Larger corrective moment. The tradeoff in possible success is worth the reduced potential altitude. Success chances are high. (Colossus fits here).

-Fins start to get too big, increasing drag force and reducing altitude far too much. (Most rockets fit into this category due to lack of optimization)

-Fins are too large! The material fails due to large aerodynamic loads on the surface area.

In summary, make your fins bigger than you think they should be. You’ll be happy if you do.

# Stability Analysis – OpenRocket vs. RasAero vs. Aerolab

I’ve always been distrustful of RasAero’s stability analysis. And when my RasAero designed 54mm Minimum Diameter went unstable at Mach 2.5, this distrust was confirmed.

Keep in mind that I am only testing free programs here, so analyses from programs such as Solidworks CFD and Aero/HyperCFD are not included.

While OpenRocket predicted this instability, it predicted that my rocket was unstable at around Mach 1. In the flight, this proved to be untrue, as it powered through Mach 1 and went unstable right at the end of the burn, at around mach 2.5 – While RasAero claimed I was stable until Mach 4.

OR was far too pessimistic with it’s stability analysis, while RasAero was far too optimistic. RockSim included no Velocity-based CP predictions, which means that it’s essentially useless for this purpose. My next goal was to find some middle ground between RasAero’s extremely optimistic predictions and OpenRocket’s extremely pessimistic ones.

This is the predicted CP for my 75mm MD using three different programs. As you can see, OR is the most pessimistic of the simulations while RasAero is the most optimistic. Both are wrong – RasAero thinks this rocket is stable until Mach ~4.5, no matter the Angle of Attack, while OpenRocket claims the rocket goes unstable at Mach ~2.3. Aerolab is a fairly unknown program but it seems to be the best middle ground between the two. I will do more tests with more data in the future.

# Computational Fluid Dynamics flow simulation of a Von Karman Nose Cone

I’ve been working on getting SolidWorks CFD to work for future projects. The first test was getting a simulation of the flow of a Von Karman Nose Cone. At Mach 4, the air is forced away from the cone at the tip and never rebounds. This means that there is a relatively low pressure zone about 2/3rds of the length of the cone from the tip. It is therefore probably okay to put Baro relief holes in that part of the cone, since according to SW, the pressure there is about what it would be in a conventional spot (about 5-6″ from the base of the cone, or in a vent band directly below the cone)

# Guardian 54 Final Paint designs

My design is a four color fade on the separating upper section. The booster with the fincan on it will have no paint whatsoever.

The fade is based on the fade design for gun/knife skins in CS:GO.

This rendering was done using SolidWorks 3D CAD software, where I have also done the majority of the design work on Guardian

# Rx Testing Weekend and Homemade Test Stand

This week, my dad and I built a test stand for testing Rx motors. It’s made of 3/4″ and 1/2″ EMT Conduit and a few assorted bolts and rods. It’s adjustable for motors 38mm to 75mm, at any length. It can withstand 5000N (~1100 Lbs) of downward thrusting force without bending.

The test stand is based on Richard Nakka’s design. We currently don’t have any data acquisition equipment, but this test stand will be useful for static burning for the sake of reassurance.

This upcoming weekend, we will be testing two motors: a 6 Grain 38mm and a 6 Grain 54mm.

The 38mm is around a 65% J670, and the 54mm is an ~8% L890. Both utilize a stepped core geometry with my favorite “Soylent Green” propellant.

The 54mm L

The 38mm J

# Guardian 54 Construction Continuing

I’ve been working hard on Guardian 54.

I did all 3 sets of Fillets using Cotronics Duralco 4525. This stuff is very expensive, but I was lucky to have some “donated” to me by a friend who was no longer using it.

Duralco 4525 is useful because of its very high tensile strength (10.8 ksi) and it’s very high heat distortion temperature of around 500F. For this high performance rocket, I decided to bond the fins with the best epoxy that I can get in small quantities.

I used a 5/8″ wooden dowel to shape the fillets. I also terminated the fillets at the length of the bevel of the fin.

After pulling the tape, the fillets looked great!

Here is the fully assembled rocket so far – Parachute and Electronics bay are included as they are completed too.

You can see that I also coated the nose cone with Cotronics Epoxy. Three layers have been applied, with minor sanding between coats. I now need to sand it to smooth, but this epoxy is extremely difficult to sand.

The rocket can be seen here in a Solidworks 3D model that I made. The model includes every component that will actually fly in the rocket. Note the parachute (yellow ellipsoid with a gray band around it) and it’s line cutter, as well as the BigRedBee GPS transceiver for GPS altitude verification and tracking, and finally the Raven Altimeter Bay. It’s a pretty tight fit in that nose cone! Hopefully everything will fit in there in reality just like my model.

This model also includes the internals of the motor such as the nozzle and forward bulkhead, and the propellant grains.

Next up is the tip to tip reinforcement. I will be doing two layers of bidirectional plain weave, vacuum bagged.