by **BigBang** » Wed Nov 01, 2006 5:50 pm

Jimmy, I truly appreciate your thoughtful comments. Without a bit of controversy science is just no fun. I also agree that more data is necessary before we can close the case on this one. Nevertheless, let me throw some further considerations into the discussion.

In separate correspondence Freefall has pointed out to me that there is a problem with your accounting of recoil. There is, instead, a momentum balance which must be preserved; i.e., M1*V1=M2*V2.

Recalling that kinetic energy is 0.5*M*V^2, after a bit of algebra we can derive the following relationship:

KEgb*Mgb = KEsg*Msg (1),

where KEgb and KEsg are the kinetic energies of the golfball and spudgun, respectively, and where Mgb and Msg are the respective masses.

Next we recall that

KEgb+KEsg=(eta)*(Total energy released during combustion) (2),

where eta is the effencieny you have mentioned previously. Using equation (1) in equation (2) and rearranging we then find

KEgb = eta*(Energy Released)*Msg/(Msg + Mgb).

In most cases the mass of the spudgun will be much much greater than that of its projectile. (In my case, the Crusader weighs in at about 10lb, while the golfball comes in at a measly 46g.) Therefore virtually all of the energy goes to the projectile, or

KEgb ~ eta*(Energy Released).

Now, the total energy ET released is

ET = (Chamber Volume)*(fuel volume fraction)*(heat of combustion)

For my gun, I used a 1X stoichiometric MAPP mixture in a chamber with a volume of 3728ml, yielding ET=(3728)*(0.05)*(154.45)= 27.8kJ.

I teach probability and statistics and regularly tell my students that a single data point does not constitute a trend. I am perfectly willing to accept that the Mach 2 shot was potentially erroneous. Focusing then on the median velocity of 1679fps (511.76 mps) - which is less influenced by outliers than is the mean value - we find that the effeciency of the process comes in at a perfectly acceptable 21%. That is...

eta = (0.5)*(0.046)*(511.76^2)/27.8 = 0.21

If we instead we assume that the efficiency was 30% then we find a maximum expected speed of ~2006fps (611.34 mps).

Based on these calculations my measurred speeds are not only well within reason, they are in fact quite plausible. Why others have not achieved similar results prior to this is a mystery to me too.

I'm not tying to throw fuel on the fire, or ruffle feathers. I too am interested in getting to the bottom of this. It just fascinates me.

Have a nice evening,

BigBang