Hola honderos, it was a time that I don´t came here and  I see that you are talking about interesting subjects. One of them is the determination of the speed of firing. I also am making some designs of apparatuses for his measurement, like this in that I am working, although am not very good with mechanics. He consists of a measurer of energy on the basis of two discs of friction that develop a constant resistance. A special sling is used, very simple, consisting in a single cord in whose end a special carved stone  of the desired weight is fixed . The measurer is near to the retention end and after it there is a knot that serve as release end. The mathematical principle is simple, the same showed by JeffH: all energy that takes the stone when leaving is absorbed in the work of friction in the measurer, which displacement  will measure it in an exact way. Some quick drawings will clarified better the idea. The advantage of the apparatus is that it can even be used in house -pay atention to de furniture-, as the stone remains tied to the sling. Also the measurer may be used with a conventional sling, as it is seen in the drawing 3.

Saludos a todos
Jesús




http://club.telepolis.com/gerar1/medidor.jpg

Great idea Jesús, It's simple, small and easy to use. It would be good to put the velocity scale. Does the jerk isn't too strong for the fingers after the release?

Jurek

OK, Yurek, in practice it can arise some problems of construction or handling and for that is necessary to experiment. The jerk I believe that  can be beared since the measurer will be progressive when absorbing the energy and to do as shock absorber. As far as scale of speeds, it is also relatively simple. Some formulas can clarify the subject:
Let us call "r" to the radius of the pulley where it goes coiled the cord of retention and "R" to the one of the small disc that rotate over the great one which it have the measurement scale. "F" is the weight that suspended is able to make rotate the disc surpassing the friction, and that calculates experimentally for the apparatus once finished. "M" and "V" will be the mass and speed of the stone. Finally, "d" and "D" will be the displaced distance in the pulley and in the circumference of the smaller disc that rotater over the scale.

d/D = r/ R        F x d = 1/2 ( M x V 2)      V2 = (2FD)/M    
V = square root of  (2FDr) / (MR)          

( using correspondent unities)  

So, each mark on the escale of D length (i.e.) will corresponde with an speed V, two marks with double speed, etc.

... is horrible to write formulas in a message...

Saludos
Jesús

Sorry, there is a mistake at the end of my message:

"each mark on the escale of D length (i.e.) will corresponde with an speed V, two marks with double speed, etc. "

It must say only:  "So, each mark on the escale of D length (i.e.) will corresponde with an speed V.

Jesús,

Your explanation was clear anyway. Thanks for your effort. I meditate about the practical and simple realization of your idea.
I love such experiments :)

Jurek