Science a GoGo's Home Page Forums General Discussion Physics Forum How does Balsa Wood's weight change with altitude?

Hi all,

I'm in a bit of a pickle here and need help figuring out a problem. In 10 days I will be traveling to a National competition to race CO2 powered dragsters. Some fellow students have warned me that because of the change of altitude(341 feet above sea level to 5280 feet above sea level) that the mass of my balsa dragster will change. This is important becuase there is a minimum weight the dragster must be(45g). I've been told that the difference will be 1.5g-2g below what my car weighs now.

The problem is that my dragster currently weighs 45.25 grams and I have been trying to calculate the exact diffenrence to avoid be disqualified or putting on too much weight. F=ma and the fastest car wins.

Using a change in air density and a change in gravitational energy I've come up with a difference of only .10g!

Does anyone have any further insite into how to calculate a accurate value?

I appreciate anone's help,
Alpha

If you need info here is some:

Volume of Balsa: 244 cubic cm
Mass of balsa used: approx 15.5g
Balsa Density: 4 Lbs/Ft3
Balsa's % of air content: 92%
initail altitude: 341 Ft above sea-level
final altitude: 5280 Ft above altitude

Volume of wood in balsa ~ 15.5 ml per 15,5 g of balsa wood (cellulose has a density cca 1g/ccm)
Density of air ~ 1.2 mg/1 ml at 300 m above sea level and 1.05 at 1600 m a.s.l. (15 % difference)
Buoyancy, i.e. weight of air expelled by 15 g of balsa 1.2 x 15.5 = 18.6 mg << 100 mg limit.
The altitude difference would remain bellow 18.6 x 0.15 = 2,8 mg limit. In real case portion of air remains trapped in wood pores, so that the difference in car mass with attitude can be higher (max cca 30 mg difference) - but still bellow 100 mg limit safely.

A more relevant for your balsa car disqualification can become moisture content (a humidity) of air, which can increase its weight due the absorption of watter in wood pores significantly. I'd recommend to keep your car at elevated temperature before race and store it in plastic bag until weighted. There are chemicals, which absorbs moisture from air, for example silica-gel. Try to dry your car overnight at 45°C (113 F) and compare the weight of car before and after drying to estimate moisture content.

the air pressure is what will change , not the gravity.

there is apx 14.7 lbs sq/in of pressure pressing down on your desk right now.

your desk if located at an altitude of 5280 ft above sea level , would weigh less on a weight scale.

only because the air pressure that surrounds it has lowered and there is less pressure pressing down on each sq inch.

the downward pull due to gravity has not changed.

on an aircraft that is flying at 20,000 ft above sea level you can still boil water at 212 F in a few minutes and make coffee with it.

this is because the aircraft is pressurized.

if you were to try and boil water on a mountain such as everest 29,028 FT above sea level, at a altitude of 20,000 ft above sea level with 212 F
it would probably never get hot enought to make coffee , but the water would all boil away much quicker.

your main concerns should be the difference in the opposing air pressure that the power plant will see.

ie 14.7 psi vs altitude pressure.

you should see quite a bit of excess power from your power plant , so the F in the F=ma will increase.

the m will decrease due to the lower air pressure.

the a will increase due to the F and the m changes.

.......

you could build a vacume box to simulate the decreased pressures with , given that you know the apx pressures
at the higher altitude.

place a set of scales in the box with your car on it , then pump out the pressure until the pressure is at the race pressure.

this should give you a very close apx of the cars weight at altitude , it could also provide acclimatization to the race pressures.

you might even be able to increase your power output from the CO2 by fabricating a aerodynamic low pressure exhaust nozzel .

I know you will already be in a lowered air pressure , but by creating a lower air pressure for the CO2 to exit will boost the performance of the power plant.

as the car accelerates through the surrounding atmosphere a well designed nozzel could lower the pressure that surrounds the exhaust gasses , thus increasing the power that the CO2 can provide.

you could even supercharge the power plant by directing the CO2 exhaust into a vacuumed container momentarily.

hope this helps , there may be something I forgot.

There's a mean decrease in acceleration due to gravity of only 0.3086 x 10-3 cm/s2 per meter of altitude. That's minute, and means that your overall figure of 0.1g is probably right. If we're being that technically precise, gravity varies from place to place due not only to altitude, but also to subsurface mass distribution; and centrifugal force varies with latitude.

Then again, what method is used for the weighing? A 45g pan weight would obviate any such problem. If in doubt, why not simply take emergency add-on material (e.g. a pin).

To Zephir,
Yes I totaly forgot about moisture content and humidity. How would I go about calculating the mass lost from the change in humidity? I'm afraid I would ruing the paint( i.e. cracking and splitting) if I "bake" my car.

To Paul,
Good point and I wish I could construct the items mentioned in time but there isn't enough time. Also the power plant used is simply a seltzer bottle CO2 cartridge and those are unable to be modified in any such way.

To redewenur
The .1g was a combonation of both air mass lost and loss of gravitational field strength. Added a pin or any other weights is illegal. I can only place decals, paint, wheels, axels, and bushings on the car.

To all,
How would I calculate the loss of moisture content?

Alpha, the fact that participants are considering the gravity issue suggests that the weighing method is something other than a balance with a standard 45g weight. Are you quite sure that this is the case? Given the essentially scientific nature of the event, it is incongruous.

Alpha: "How would I calculate the loss of moisture content?"

I don't have a clue. That said, I do suspect that under normal atmospheric conditions changes are only significant over long periods of time - weeks at least - because (a) the permeability of balsa wood may be low, except in the case of pressure impregnation (and if you oil painted the whole car, it would be effectively sealed) (b) the mean moisture gradient over time is unlikely to be very great. As I said, I don't know, but they are factors to think about.

Paul: "the m will decrease due to the lower air pressure."

Sorry to be dense (! ), but could you explain how decreased air pressure causes decreased mass? The volume and density may change, but not the mass.

Well I do know that the way the judges weigh the models is by using a digital scale, not a balance. I beleive then the weight would change at a higher elevation becuase gravity is less. I did calculations and at 341' g=9.82m/s/s and at 5280' g=9.815m/s/s giving a loss of approx. .045grams

Also doesn't absolute humidity change with elevation? Doing some research I found that relative humidity is only a ratio of (water mass)/(air mass). This ratio is also equal to (relative humidity)/(barametric pressure). spelling? Given that the balsa contains 92% air shouldn't I be able to calculate the diferences in water mass of the air contained in the balsa?

what I was referring to is that the (m) is the object that the (F) is acting against.

and the decrease in weight due to (g) is outweighed by the decrease in air pressure when considering (a)

in a (race) it is (a) that is important.

if I have a container that is pressurized with 100 lbs of CO2 , and I place a CO2 cartridge charged with 100lb CO2 in it , and release the CO2 in the cartridge , nothing will leave the cartridge.

if I release the 100 lb cartridge in a 14.7 psi (sea level)atmosphere I would get less thrust than if I released the 100 lb cartridge in a 12.2 psi (1 mile high)
atmosphere.

this extra thrust would be more readily available if the CO2 were acting against a solid surface such as a turbine or piston.

I did a similar calculation and got even less than that Either way, it's trivial, and since they choose to use digital scales, I guess they're aware of that.

Yes, since there's a drop in air temperature of 1C per 1000ft, and cool air can contain less vapour than warm air, I would think that humidity generally decreases with altitude. I'm not sure why you're anticipating a difference in mass - are you expecting the balsa to dry out to a significant degree?

I am infact anticipating the balsa to dry out a bit. My teacher has in the past seen drops of 1.5g-2g. I want to see what the exact loss would be of my car so I could prepare to add mass to it to acheive 45g, the legal minimum weight. I take this competition seriously as it will be my last year competing, only grades 6-12 are eligable.

I've been doing some experiments to backup my theories. So far I've vacumed pieces of balsa and have dried out a test car in the oven. SO far these little experiments have helped me narrow down a number of how much mass my car will loose.

To all,
If you want more info on the type of CO2 I am talking about visit www.science-of-speed.com The website has great information and photos of the cometition and cars.

Presumably the 1.5-2g loss is from an original weight of 45g, i.e. 3-4%, right?
A few questions:
- Over what time period is that?
- How does that time period compare with the time you expect your car to be exposed to lower humidity?
- Have you been able to reproduce that loss in your experiments?

Jeeepers! a finicky sod like you, obsessed with every possible miniscule affect on every detail. You either should win or learn the lesson that cost benefit analysis of how you alocate your time is worth considering.

The balsa could change weight by loss of absorbed moisture. this seems to be the biggest factor, but is very difficult to quantify precisely. 6% of wood mass is common at sealevel as equilibrium moisture content. Will reduce at altitude and reduceed temp but slowly. Density of air displaced over the total volume of vehicle is a very small reduction in mass, slightly exaggerated by a difficult to estimate and reducing over time by expansion of air trapped in microcellularstructure of the balsa . Altitude would reduce gravity, this is unlikely to be significant. Its interesting that the mass of the mountains is offset by lower density subcrustal bodies and usually does not make for gravitational anomalies. So simple estimates based on global figures are probably close to real.

I'd doubt that moisture content would change much in a week if your balsa is painted at all well. Balsa has a very closed cell structure as compared with other woods. If you want to eliminate any measurable variation there, just keep it in a sealed plastic bag except when unleashed.

If you are losing sleep over this, just take your own digital scales. Check before qualification tests. 0.1g digital scales are inexpensive.
The extra power and reduced aerodynamic drag are big bonuses to performance. Unlikely that a gram of excess weight would be anywhere as important as your exhaust systems resonant frequency behaviour (could double your harvested power easily) or the aerodynamics (simular 2x performance differentials probably in the comp.)
And if you are a smidgen under at the weigh in they will let you schmooze them into failing to notice it probably and fixing it definately. (just rave about all the calcs and factors discussed here that you've tried to pin down and they'll probably tick the box just to shut you up LOL's)

Just focus on those acoustic resonances in the exhaust system. Tuned pipes for rpm and cone/header geometry for width of powerband. (standard 2-stroke IC engine chamber analysis). And aerodynamics. You'll blitz 'em!

Yes I do like detail! That discription is spot on! I just get so detailed becuase it is a challenge and a great learing expereince.

btw These dragster are a foot long and powered by a standard CO2 setlzer bottls cartridge. No way is is possible to contruct an exaust nozzle saddly. WOuld love to make a CD choke flow nozzle but all cartridges are the same for fairness.

Having a car with a mass of 45.05g will be faster than a car with 45.25g of mass. so that is why I needed to find out the mass my car would be loosing to make sure I'm not dissqualified for going below 45.00g of mass and have a car very close to it.

I have however run CFD computations to design the car. took 12 trials but I got an awsome design.

redewenur,

The teacher saw the change imediatly when he got there. All cars are turned in the day the competition starts. The races last about 4 days.

As for the experiment I could not reproduce the results. Using a similar car I was only able to pull .7 grams out of it by drying it in an oven at 135F for 12 hours. This is why I am so confused. I actually did calculate this number by using my mixing ratio equation I stated a few days ago. A teacher say 1.5-2 grams lost. A judge has said 4 grams lost. It is inconsistant and gets me worried.

For four years I've wanted to win at nationals so please bear with me if I'm paranoid as it is my last chance and I'm so close! Even if I don't win I'm still very proud of how well I've done so it is a 50/50 situation.

Yes, I can see it's confusing. Maybe others have done the experiment differently: more heat, or time, or both. But from all that you've said, it does look as though you can ill afford to reduce the car's weight to less than 47grams before the competition date - unless you can be ready to with some legal means of adjusting the weight at the 11th hour.

But what about the question of a sealant? Paint has been suggested. How about gloss lacquer? Wouldn't that obviate the humidity problem? Then you could shave the weight close to 45gm. And the gloss finish would also reduce drag. Some of these questions may seem stupid, but you have the advantage of being on the spot and knowing what's what, so to speak

P.S. Good Luck!

Thanks redewenur. The car is infact painted and sealed except for the actual hole the cartirdge fits in. I do have a plan on how to legally added weight so I can only hope for the best.

my final plan:
Construct different size and material washers and axles to have many possible combinations of mass. Once I get to denver I will mass the car with the combonation then assemble it there.

I leave sunday early so thank you for the luck I'll be sure to let everyone know how well the dragster did.

Well I want to thank everyone for their help! It sure was a learning experience!

As far as the dragster, it lost exactly .20g of mass after three days. That Denver air sure is something!

Also 4th in the Nation isn't a bad finish! Finally after 4 years of work it paid off!

In the next 3-6 months the results should be posted on www.science-of-speed.com if any are interested.

Thanks once again!
Alpha

Well done, alpha! Does no harm to bounce your ideas off people, even if they aren't versed in the subject