I don't know if you ever watched the old balloon race event, but in that event it often turned out that air movement in the room played a much bigger factor in the outcome then anything the competitors could calculate. The PV=nRT equation describes the physics very well but it tells you nothing about the aerodynamics of the balloon and what effect even a slight up or downdraft will have on the flight of the balloon. It is even entirely possible to mathematically model the aerodynamics of the balloon, but if you have no way to measure, or more importantly, control the wind then you have no way to calculate how much positive (or negative) buoyancy you will need to get the balloon task to work successfully and with the most possible points. In the old Balloon race many competitors were surprised to find that their balloon would actually start rising but then a wind would blow it back down again., or a team that didn't even know what they were doing would accidentally add too much mass yet the balloon would rise anyway due to an updraft from someone walking by at just the right time (or the A/C blowing just right).There's actually a couple other factors, but they're hard to take into account. Use the ideal gas law, PV=nRT. (If you're not familiar, pressure x volume = number of moles x gas constant x temperature.) Balloons float for the same reason that people can swim; the weight of the balloon is less than the weight of the air it displaces. This buoyancy force is determined by ρVg, density of displaced fluid x volume x gravitational acceleration.
Manipulating the equations, you find that the weight you can lift is equal to ρgnRT/P - mg (of balloon). Disregard the gas constant, the gravitational force, and the weight of the latex for simplicity's sake, and you're left with ρnT/P. This is where you realize you're screwed. Air density itself varies based on pressure, humidity, and temperature, yet so does the volume of your balloon. If you could somehow regulate the number of moles so that nT/P was constant for your current location, you'd be all set. Show up with a calculator and lots of paper, bring your barometer, pressure gauge, and thermometer, and you'd know exactly how many moles of helium to add to provide the proper lifting force.
Or, on the day of competition, you could fill up a balloon all the way, and just add weight until it stops going up.
Isn't that to be expected at a national level competition? Sporting competitions often have "photo" finishes where the top places separated by very small differences in time/score. It's not uncommon for random environmental differences to affect their outcome. This is accepted an part of the competition.at Nationals the difference between the top 10-15 teams is often quite small
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