The Lunar Dog Project was not just fun and games. The interns designing the experiments had to utilize math and science to determine exactly how much helium would be required per pound of dog to provide a lunar gravity simulation. Below are the equations and procedures used to determine such diverse aspects of the project as lift potentials and diffusion rates.

Helium lift capacity: ~24g/mol at 1 atmosphere (14.21 psi) and standard temperature (273 K)

Mass of object: 451g/lb

Amount of helium required (n): 18.79 mol/lb

Volume of balloon: (4/3)*(pi)*(r^3)

Ideal gas law: PV = nRT (R=.0821 (l*atm)/(mol*K))

Put them all together, and you get: V = (3/4)*((18.79*weight)*R*T)/((pi)*(r^3)*P)!

For diffusion, it requires a bit of advanced differential calculus, but I'll make it simple. Basically, to determine the time it takes for a balloon to lose a certain amount of a fluid, in this case helium (measured in the change in internal pressure), it is necessary to know the pore size of the balloon material, the thickness when expanded fully, the starting pressure and temperature of the fluid, and the viscosity of the fluid. Since we're dealing with helium, the viscosity is close to zero. However, all of the other variables need to be addressed. Our mentor did the derivations on a white-board for no particular reason one day, and I copied down the final result.

t ~ (mu/dP)*(1/(1+((D*mu)/((L^2)*dP)))

Where mu is the viscosity, dP is the change in pressure, D is a combination of the pore size and distance between pores, L is the thickness of the balloon, and "t" is the amount of time that passes during diffusion.

Also, for those of you getting tired of math, we did a little test on the maximum possible radius of the balloon (yes, I know I implied that there would be no math, but bear with me.) To do this, we basically had Erik put on some cool sunglasses/safetyglasses and earphones and inflate a balloon with helium until it exploded. The video of the explosion was then analyzed to determine the maximum width, using Erik as the reference object. It turns out that the balloon was 3.5 feet across, 50% larger than designed! The resulting explosion was probably in excess of 140 dB, as it gave Erik shell shock from merely standing next to it (with ear protection, even.) From a 90 psi regulator, it took 2 minutes and 24 seconds to inflate the balloon to that size. Wow.

And, as the last test before the actual video, Max's center-of-gravity, or CG, had to be determined. To do this, David just picked him up at different points until his weight in front was equal to his weight in back. A very scientific measurement, if you would ask me.