# Carbon dioxide rocket cars

Hi All

Hope this is the right forum, I am looking for an applied approach!

I am interested in modelling the behaviour of CO2 powered rocket cars. These small models are powered by releasing pressurised carbon dioxide from a “sparklet” cylinder. The model cars race along 24 metre long tracks. A typical time to cover 20 metres is about 1 second for a 55 gram car (mass not including mass of CO2 or cylinder) The cars are guided by a nylon line stretched tightly along the length of the track. The cars are launched by pricking the diaphragm that seals the rear of the sparklet cylinder.

We use computational flow dynamics to test the aerodynamics of the designs and this produces data about the aerodynamic forces acting on the car at a specified velocity as well as estimates of coefficients of drag.

There are lots of things we would like to understand about our designs, for example: How do the forces predicted by the CFD work relate to times on the track? The cylinder seems (visual observations) to run out about half way along the track so how do we factor in the coasting period as well as the acceleration phase. Since the cars are not accelerating all the way is there any difference between simple mass of the car versus rotating mass in the wheels. I suspect there is something important going on here as in some races a car that is well ahead in the first section of the race is overtaken in the second section.

Is the optimum mass of the car always going to be the minimum allowed (assuming structural integrity is maintained)?

Being practically minded, I would rather have graphical or spread sheet type models rather than have to go too deeply into differential calculus.

Bob

My daughter did this in high school, a few years ago.

Actually, as it turns out (and theory aside), the single most important variable with these CO2 cars is how big the hole is you punch in the membrane, how quickly you punch it, and what hold (or lack of it) the punching device has on the car before releasing it.

Of all mechanical effects, aerodynamics has the least impact. The angle of the exhaust, relative to horizontal, has some effect. Friction reduction as the car speeds along the guidewire has some impact too. Also, the kind of wheel-bearings one uses (hint: ball-bearing hubs aren't worth the weight penalty).

Hope that helps...

JF

I did an engineering simulation of the Estes Dragster over a 90 foot run:

http://www.hobbylinc.com/htm/est/est9114.htm

where to reduce elapsed time you clearly want to reduce mass, maximize thrust, reduce friction in the rolling axles and tether line, and finally reduce inertia in the wheels. Once these factors are optimized the air drag would become significant in the performance.

In my model I knew car mass and top speed from an EPA test report. Engine thrust is published by the National Association of Rocketry. In ideal surroundings top speed would be over 50 mph. I put in a worst case air drag model and it hardly slows down the car. So I dialed in a linear model of friction in the wheels/tether line and got top speed to 28 mph per the published test data with a reasonable looking run profile.

Thanks for the interest in my thread.

With regard to the effect of the size of the orifice I think this is quite controlled. A standard launch device is used which drives a spring loaded firing pin into the diaphragm so that variability has been minimized. Also the CO2 cylinders are stored at a standard 22 degrees Celsius in a thermostatically controlled environment prior to the contests. So both of these sources of variation are beyond our control and standardized.

The two factors we have identified as being important were the frontal area of the car and the quality of the wheels and bearings.

My guess is that at the most competitive stages of the contest (National level and above) things like the ratio of rotating mass to non-rotating mass and some aerodynamics give teams the edge as these teams already appreciate the importance of minimal frontal area and quality wheels and bearings.

One of our main difficulties is the lack of a test track so we must rely on simulations and modeling to test our designs prior to the event. Hence our interest in developing a mathematical model.

Bob

Bob,

Could you point me to a supplier of the firing mechanism and standard co2 tanks? Or provide a technical information link? I may wish to do some local activities with small rocket cars.

To run a good model you'd need the thrust-time curve, drag coefficient, frontal area, friction coefficient in the bearings, and estimate of wheel inertia. I might help with the simulation effort although I'm hoping to publish write-ups to my commercial web site for use in education or by the technology enthusiast. Most of my models would be college level but I'm hoping to push some of the dynamic system model understanding into the high school classroom.

Wow, sounds like fun. I did this in college, and totally obsessed with friction - to the point that I added bearings for the wheels. It turned out that the guys who stuck by F=ma where the winners - at least if their car didn't disintegrate at the end!

Since that time, I've obsessed about the problem (engineering mentality). What I would like to do, if I could do it over, would be to:

1. Buy two kits and use the front wheels from each to reduce the mass and moment of Inertia on the back wheel.
2. Machine away material from the wheels (most advanced cars had this)
3. Bore out the center line of the car, to reduce mass while maintaining strength
4. Fashion the body in a dart-like profile. Most cars that broke, did so towards the middle, where the bending moments got to them. The front only contributed weight and wasn't subject to such extreme bending.

We had a car that was about 1/2" thick along the front, and had F=ma for it's logo. It was the fastest, but broke midways. I think FEA will get you further than CFD.

Have Fun,

-Mike

Bob,

Could you point me to a supplier of the firing mechanism and standard co2 tanks? Or provide a technical information link? I may wish to do some local activities with small rocket cars.

To run a good model you'd need the thrust-time curve, drag coefficient, frontal area, friction coefficient in the bearings, and estimate of wheel inertia. I might help with the simulation effort although I'm hoping to publish write-ups to my commercial web site for use in education or by the technology enthusiast. Most of my models would be college level but I'm hoping to push some of the dynamic system model understanding into the high school classroom.

Hi

In the UK Denford run the competition and supply the bits and pieces. See their catalogue at http://www.denford.ltd.uk/cataloguemay09/index4.html [Broken] I think Pitsco supply similar in the US. See http://shop.pitsco.com/store/default.aspx?CategoryID=84&by=9&c=1&bhcp=1

The UK competition has a website http://www.f1inschools.co.uk/ and there is a global site http://www.f1inschools.com/ that may link you to your local organisation.

Thank you for your offer of help with the modelling. Our CFD package will give us estimates of the drag coefficients. We can measure the fontal area from the CAD designs and also use this to calculate the moment of inertia of the wheels. The thrust time curve might be more problematic, but I have seen a method we might try on the Bloodhound website http://www.bloodhoundssc.com/_db/_documents/Bloodhound_KS3and4_Static_testing_of_Estes_rocket.pdf [Broken] (You may need to register to access this link) I am unsure about how to measure the friction coefficient of the bearings. Any ideas would be welcome.

Best wishes

Bob

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Breaking due to bending moment is interesting. Is the thrust vector downward at the rear to keep the front wheels pushing down, thereby generating the bending moment? The Estes rocket cars practically fly down the tether line in some internet videos. Lots of things could happen depending on the details.

Bob,

Thanks for the links. This link includes a Macromedia flash animation showing 0.3 seconds of thrust:

http://www.science-of-speed.com/competition.asp?id=91

and mentions speeds up to 45 miles per hour which of course would be peak speed at the end of the thrust period. Ideally you'd need a force sensor on a test stand to measure average thrust, the way NAR does it, but we might be able to estimate the thrust from the physics of the fluid capacitor discharge.

I run basic differential equation solutions in Windows Vista using engineering and numerical tools. PM me if you're running XP or Vista.

Hi All

Mike, When you suggest Finite Element Analysis may be more informative than CFD could you give me a bit more of an idea how you would envision using it? My knowledge of the technique is very limited. I remember using it to simulate the decent of the lunar lander on a Teachers' course at Swansea university (1995 'ish) but nothing since then. Would we use it to analyse the bending of the car body? I am not sure if this is as big an issue in the UK formula as there is a minimum body diameter between the axles of 15 mm and the body must be solid. I have not seen cars snap in two as you describe. Most of the damage to our cars is caused by hitting the deceleration device (a loose pile of towels) at the end of the track.

I would like to be able to model the race millisecond by millisecond using a spreadsheet where each row represented a millisecond of time. In the model values from the previous row would be used to calculate the updated values in that row. I would guess that there might be some equations that would allow you to calculate the mass of CO2 passing through the orifice per millisecond and its velocity as it leaves. Knowing this it should be possible to deduce variables such as the change in momentum of the car during that millisecond and knowing its mass at the start of the millisecond the car's velocity during that millisecond. Other velocity dependent factors such as aerodynamic drag could be calculated using the starting conditions and applied to further update the model the model.

I may be looking at this the wrong way. Another thought would be to find (or collect) some thrust time data for actual CO2 cylinders. In the spreadsheet model this could be used in the form of a lookup table so avoiding the complications of modeling the flow of stuff through the orifice as I fear this is not at all simple having read a bit about the design of safety valves form model steam engine boilers.

Bob

My thoughts are based somewhat on my observations of the races and somewhat of my contemplations afterwords.

The case for CFD assumes that a significant measure of velocity is lost due to the opposing force due to air resistance. That is, the car will decelerate according to f=ma, where f is the force due to wind.

Now, the change in velocity of the car is to the integral of this deceleration over time. Given little time for the effect integration, there will be little effect in the velocity.

However, the peak velocity has everything to do with the mass of the car. Reduce the mass of the car, and the impulse of the CO2 cartridge will bring you to a higher velocity.

The problem I saw with the cars that were shaved away is that they broken upon impact with the cloth.

Striking head on the car would be in compression with the momentum from the heavy rear of the car along the body and into the point of impact. Compression isn't as big an issue as tension, so if the body bows, or the car rotates, then tension as it bows will determine where the break begins.

Hence the value of FEA. By maintaining uniform stress along the outer surfaces of the car, the mass can be reduced without creating weak points.

Thanks Mike

In the Bloodhound SSC class the rules are very simple, the cars must be machined from a single block of balsa wood. The wall thickness around the cylinder must be a minimum of 3 mm. The body between the from and rear axles must be a minimum of 15 mm diameter and the centre height of the CO2 cylinder is defined. Cars must have two guide eyelets at either end and the body must be between 170 and (200 mm I think) long. The full rules can be downloaded from the Denford website, but I think I have the main points here.

The 15 mm rod is quite rigid and seems to stand up to the impact with the towels OK. We found that the 2 mm silver steel axles got bent after a few runs and plan to replace these with 1.2 mm carbon fibre composite axles. Early CFD trials suggest that this will reduce the aerodynamic drag at 18 m/s from -1.05E-01 N to -8.14E-02 N a 22% reduction in aerodynamic drag. There will also be a lower mass with the CF axles

Now the real issue is in terms of all the drag forces acting on the car how much impact on the time to cover 20 m will this reduction in aerodynamic drag have?

Is the aerodynamic drag a significant factor for our cars? or are we just 'arranging the deckchairs on the Titanic' by fidlling around with CFD and tiny tweeks to the shape of the body?

Bob

Here's one simplified formula for acceleration:

$$a(t) = \frac{F(t) - cv^{2} - bv}{m_{R}}$$

where I define the equivalent rolling mass:

$$m_{R} = m + \frac{J}{r^{2}}$$

in which F(t) is thrust, c is quadratic drag coefficient, b is linear friction coefficient, m is the mass of the car, J is the inertia of all four wheels about the rolling axle, and r is the wheel radius.

The assumption B(v) = b*v means axle/tether line friction combined is zero at the start and increases linearly with velocity. This is purely for simplicity. The friction characteristic B(v) is the hardest parameter to measure/model in this system.

An inclined ramp of 2 or 3 meters length and an accurate timer might help you optimize the ratio of mass to inertia, reduce the axle friction, and pick a tire radius. These factors are linked, since if you reduce r to reduce inertia J, the angular velocity of the wheels goes up and could couple an increase in friction. In the design of the roll down test ramp one starts with the time to travel down a frictionless incline plane and then you might need a 1mS timer and good triggers to be able to detect meaningful changes in design parameters.

I found this equation to calculate the frictional torque in ball bearing races (http://www.smbbearings.com/SMBtechdata.htm)

Frictional torque (measured in Nmm or Newton millimetres)

The website also quotes various deratings for different lubrications. I am not too convinced by this model as there is no RPM term and common sense dictates that the faster the bearing runs the more torque is required to keep it running.

That being said it gives a starting point.

Bob

I only recently learned that Tribology is the study of rubbing/friction and the keyword appears to be Stribeck curve. Are you running ball bearings? I think a commercial plastic sleeve bearing is the proper choice to eliminate extra bearing inertia in these small machines but its just a hunch. Would you consider running 5spice as the model environment? I'm just starting to use it and by applying the torque-force-current analog and using controlled sources (as ideal transformers) you can model the whole mechanical system and solve the differential equations with feedback. It should have all the tools but as I said its something I just ran for the first time last night:

http://www.5spice.com/

Edit: 5spice may not be a good tool for this analysis after all. It is great for basic circuit interface but in terms of reading data files for the force-time curve and friction curve I must investigate further ...

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I only recently learned that Tribology is the study of rubbing/friction and the keyword appears to be Stribeck curve. Are you running ball bearings? I think a commercial plastic sleeve bearing is the proper choice to eliminate extra bearing inertia in these small machines but its just a hunch. Would you consider running 5spice as the model environment? I'm just starting to use it and by applying the torque-force-current analog and using controlled sources (as ideal transformers) you can model the whole mechanical system and solve the differential equations with feedback. It should have all the tools but as I said its something I just ran for the first time last night:

http://www.5spice.com/

Edit: 5spice may not be a good tool for this analysis after all. It is great for basic circuit interface but in terms of reading data files for the force-time curve and friction curve I must investigate further ...

I have come across SPICE as a circuit simulation tool, but not thought of it as a tool for analysing mechanical systems.

We use small shielded ball bearing races 2 mm ID 5 mm OD about 2 mm wide. These have enabled us to produce some very fast cars. I would be interested in knowing about the commercial plastic sleeve bearings. Some teams use ceramic bearings which cost about £50 each. I have yet to be convinced that they are any faster than ours, but I have not been able to do any controlled testing to be sure. I know that our cars with either 1 or 2 bearings in each wheel are amongst the fastest in the UK. I was talking to a chap that runs an injection moulding business last night and he mention a PTFE loaded delrin that sounds interesting. At present we use continuous cast delrin for the wheels.

Bob

I've seen small teflon and delrin flange bushings in catalogs, similar to this:

http://www.graphalloy.com/html/type_317.html

and it would reduce the inertia contributed by the ball bearings but might be worse in terms of friction at speed. I've been searching for some friction curves for small bearings with no success. Most engineering models are too complex for educational purposes.

I've used CircuitMaker Student Version SPICE in the past to model the Estes Rocket Car and the Mythbuster's JATO Powered '67 Chevy with simple models for driveline friction. Voltage at a grounded capacitor is velocity in the simulator. Current into the capacitor is force. And capacitance is mass. This solves the impulse-momentum integral by applying the force-current analog. The CM Student has an math integrator block to find position by integrating velocity, and ideal transformers can be used to couple the rotational load to the translational load. The 5Spice is a better interface for beginners, but it appears to have no integrator math block. If it has the integrator (still trying to figure that out), we could begin to study your drag reduction models to see how much time is saved coasting for say 0.7 seconds over a known distance. Without the integrator velocity and time are available but distance is unknown.

Since the cars are not accelerating all the way is there any difference between simple mass of the car versus rotating mass in the wheels. I suspect there is something important going on here as in some races a car that is well ahead in the first section of the race is overtaken in the second section.

Is the optimum mass of the car always going to be the minimum allowed (assuming structural integrity is maintained)?

So a less massive lower inertia car could accelerate faster due to a(t) = F(t)/mR. But then it would be less effective at pushing air and overcoming axle/tether friction due to have less equivalent rolling mass mR! In other words it would have a lower ballistic coefficient with regard to the pushing air part, which partly explains why a car wins part one (thrusting) but loses part two (coasting).

I've built the basic simulator model in 5Spice with a step force input F(t) = 3.3 Newton for 0.3 seconds. Mass m = 0.055 kilogram gives about 18 meter per second velocity at 0.3 seconds. Figured out how to integrate velocity using a clever trick where position change is less then 3 meters during this thrust model. Only problem here is acceleration is still hidden, but I think 5Spice is the first tool to use if it runs on your PC. I know it will handle the drag feedback model and may be able to handle a complex friction model eventually (not sure on that score). Graphical output from the Transient Analysis is rapid and clean.

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Hi and thanks for the pointer towards Graphalloy bearings. This could be very useful as long as we can achieve an excellent polished finish on the axles.

I agree with your thinking on the balance between rotating and non-rotating mass in the car. I remain convinced that this is significant in the heavier (minimum mass 55g) F1 class. I am beginning to think that the main factor in the less restricted Bloodhound SSC class will be minimising mass and rolling friction as long as the aerodynamics in not too stupid. Indeed, working towards a minimal mass will tend to produce a minimal frontal area the main factor in aerodynamic drag. My reasoning is that as these cars (bloodhound SSC) cover the course in 0.7 s compared to 1.1 s for the F1 class they are accelerating for most of the course assuming the thrust to last 0.5 s My estimate of 0.5 s thrust is just based on visual observation that the F1 class cars cover about half the track before the cylinder looks to have blown out. Of course, if they cover the first section very quickly so the 0.3 s thrust duration quoted earlier could be correct.

Bob

I think you've isolated the factors impacting performance. As to a computer model it is only as good as the assumptions and data. If you want a good model and know anyone with data acquisition equipment I suggest measuring (sampling) the force output from several co2 cylinders. I offer a couple of links to sensors (just to give an idea, haven't checked specs):

http://www.trossenrobotics.com/c/robot-force-sensor-fsr.aspx

http://www.tekscan.com/flexiforce/flexiforce.html

Also we could ask for assistance with a thrust model from the Classical Physics forum and compare with measured thrust. Depends how much effort you wish to put into making an accurate computer model ...