Spring Talk

[benos]

I got this in an email from a forum user in Paraguay. I know some of you will just love it - so here it is:

Hola Brian, I'm Ruben Nasser, a gun aficionado from Asuncion, Paraguay.  Congratulations for your excellent site, I'm not posting in the forums but I'm picking a lot of valuable information.

Regarding the discussions on "spring rates", apparently most people in the forum are very confused about what is a "spring rate".  In normal engineering terms it means the "spring constant" (force vs compression rate), but in "1911 world" a 16 lbs. spring is one that exerts 16 lbs. when fully compressed in the gun at the end of the slide1.6" rearward travel.

Constant rate springs are linear devices: the force a spring responds with is directly proportional to the amount (distance) it is compressed from its free length.  The distance and force are related by the spring constant which is a property of a given spring.

Since recoil spring manufacturers don't supply conventional spring data, it is useful to know how to calculate a spring constant.  The obvious way is to put a weight on the spring and measure the spring's deflection, and there are kits to do this (or you can make your own).

Theoretically the formula for light weight springs (thin wire compared to outside diameter) is k = (G*d^4)/(64 R^3*n). G is the modulus of rigidity;  its value is around 11.6*10^6 pounds per square inch for steel spring wire.

It is different for other materials, such as stainless steel.  d is the diameter of the spring wire.  R is the radius from the axis of the spring to the center of the spring wire; numerically, that would be half the quantity (outside diameter of the spring minus the diameter of the spring wire).  n is the number of active coils (...don't count coils  which are touching each other at the end of the spring).

In the case of any coil recoil spring of the 1911, there are three dimensions which are of prime importance other than the spring constant.  They are the free length, the installed length, and the fully-compressed length.  The difference between installed length and free length can be called X1 and the distance between fully compressed length and free length can be called X2.  When the action is closed, the force tending to keep it closed will be the recoil spring constant times X1. When the slide is drawn fully back, the force trying to return it will be the spring constant times X2.

The length of the spring does not affect the spring constant.  Making a spring with the same number of coils, wire diameter, and outside diameter but with a longer free lenght (or permanently stretching one) only changes X1; this causes the force at the installed length to be higher, but it does not change the spring constant.

If you cut a couple of active coils off any spring, you will lighten the maximum force since X1 and X2 will be smaller but you will also make the force curve peakier because the spring constant will be greater.

Work is force times distance or: integral F(s)ds.  If you plot the function of force versus distance the area under the curve will be this integral.  Since the spring is a linear device, the area under the curve is a triangle and the area of a triangle is one half the ordinate times the abscissa.  Since kx is the force of a spring, the potential energy of a spring (the work absorbed by it) is 1/2 k X^2.  

The work absorbed by a recoil spring when the slide moves from fully closed to fully open is = 1/2 k ((X2^2)- (X1^2)) .

This is equivalent to subtracting the area of the triangle associated with the installed compression of the spring from the area of the triangle associated with full compression of the spring.

Sorry for this long unsolicited explanation, all this is just basic theory but I always want to understand first the basics and then proceed to the complicated stuff.  Many gunsmiths and shooters are great artisans and have an amazing experience and "know how", but sometimes they miss these basics.

Saludos,

Ruben

Ruben,

Wow! Thanks for that great explanation. Of course I can't follow the formulas, but I do follow the principles. The way you described the variables involved with a coil spring contained at a fixed length, and compressed to a fixed length makes complete sense. I thought that was "what was going on" myself, but of course didn't have the expertise to put it into words. I'm going to post this on the forum, just to shut everyone up!

Again, thanks -

cheers,

brian

[benos]

As an addition to Ruben's informative post, I know have an approx 11 page Word doc, from the same, detailing most every aspect of the functioning of the 1911 pistol design. I should post it somewhere... maybe in the stock gun questions. OK, that's where it's going...

be