## Benchrest Barrel Weight Calculation Program

### By: Daniel Lilja

Download the program free.

A problem frequently encountered by the benchrest gunsmith when building a new rifle or rebarreling a rifle is determining where to trim the new barrel blank to make the barrel and rifle the correct weight. Usually the other components of the rifle are weighed and the difference in weight from the class weight limit is the weight of the new barrel. The barrel for a ten and a half pound rifle usually will weigh from about four and three quarter pounds to five and a half pounds. A barrel blank will usually weigh six to seven pounds or so. The problem will be further compounded if a specific barrel length is desired as well as a specific weight. It may become necessary to use a fluted barrel.

The weight of a given barrel can be determined beforehand by calculating the volume of the barrel taper and multiplying that figure by a density value for the type of steel being used. In the January-February 1981 issue of RIFLE magazine, author Stuart Otteson wrote an article describing how to calculate the volumes of typical benchrest tapers and their weights.

Two basic formulas are used in calculating the volumes of benchrest barrels. The first is the volume of a cylinder, which is: Volume = .7854 x diameter^2 x cylinder length. The second is the volume of the frustum of a cone, being: volume = .2618 x (larger diameter^2 + larger diameter x smaller diameter + smaller diameter^2). With these two equations the volume of a barrel can be determined. The volume of the cylinder portion of the barrel is added to the volume of the tapered portion (frustum of a cone) and the volume of a cylinder (barrel groove diameter multiplied by barrel length) is subtracted. The final volume is then multiplied by the weight of one cubic inch of the steel. In our case with benchrest barrels the weight is for 416-type stainless steel.

In his article Otteson used the weight value of .28 pounds per cubic inch. In checking with our supplier of stainless steel it was found that the value of .276 pounds per cubic inch is a little more accurate for the 416 stainless steel we use in barrels. This corresponds to a specific gravity of 7.64. In a five pound barrel this difference in the multiplier would change the calculated weight by about an ounce. For 4142 chrome-moly steel the weight for a cubic inch is .283 pounds.

Fluted barrels have steadily become more popular with benchrest shooters. The weight removed by fluting can also be calculated prior to the actual machining.

If the flutes are milled so that the depth of the flutes are parallel with the outside of the barrel and the milling cutter used is of convex geometry, the calculations are fairly simple. There are two formulas for calculating the volume of a flute. The first is used if the depth of the flute is equal to or greater than the radius of the milling cutter. The second is used only if the depth is less than the radius.

The formula for a flute depth of cutter radius or greater follows. The area of a circle of radius R is calculated as 3.1416 x R^2. This number is then divided in half and multiplied by the length of the flutes and the number of flutes to be milled. We now have the volume, in cubic inches, for flutes of a depth of cutter radius. For any depth over cutter radius, the additional depth is multiplied by the cutter width and then multiplied by the length and number of flutes and this volume added to the volume of the semi circle. The total flute volume is then subtracted from the total barrel volume and the weight calculated.

For an example let’s calculate the volume of six flutes, 20 inches long, milled with a 7/32″ convex milling cutter, .150″ deep. The radius of the cutter is .219/2 = .109″. The area of the semi circle is then (3.1416 x .109^2)/2 = .0187 square inches. This multiplied by the number and length of flutes is .0187 x 6 x 20 = 2.2395 cubic inches. The additional volume for the depth over cutter radius is .150 – .109 = .041″. This depth multiplied by the width of the flute, length and number of flutes is .041 x .219 x 6 x 20 = 1.0775 cubic inches. To determine the weight removed by the fluting these two volumes are added together and multiplied by the weight of one cubic inch of 416 stainless steel. The weight is (2.2395 + 1.0775) x .276 = .915 pounds or 14.6 ounces.

If the depth of the flute is less than cutter radius, a second formula is used and it is a little more involved. The actual width of the flute will be less than cutter diameter in this case. The area of the circular segment must be calculated and as above, is multiplied by the length and number of flutes to determine the volume. First the angle subtended by the arc segment must be calculated. The angle equals 2 x[arccosine (inverse cosine on most hand calculators) of 1 – (depth of cut/radius of cutter)]. The width of the cut is 2 x square root of [depth of cut x (cutter diameter – depth of cut)]. The length of the arc segment is .01745 x cutter radius x angle of arc segment. The area of the circular segment is .5 x[cutter radius x arc length – width of cut x(cutter radius – depth of cut)]. The volume of the flutes are the area times the length and number of flutes. This multiplied by .276 pounds per cubic inch is the weight.

As an example let’s calculate the weight for flutes machined with a .250″ wide convex cutter, a length of 20″, and a depth of .100″ for six flutes. The angle of the arc segment = 2 x[arccosine(1-.100/.125)] = 156.92 degrees. The width of the cut is 2 x SQR[.100 x (.250 – .100)] = .245″. The length of the arc segment is .01745 x .125 x 156.92 = .342″. The area of the circular segment then is .5 x[.125 x .342 – .245 x(.125 – .100)] = .0183 square inches. This figure multiplied by the number of flutes and their length and the value of .276 pounds per cubic inch is the total weight. It is .0183 x 6 x 20 x .276 = .606 pounds or 9.7 ounces.

There are two minor discrepancies in determining the volume of flutes in this manner. One is that in calculating the volume the equations assume that the two ends of the flute stop abruptly with a 90 degree corner instead of a compound radius. The second assumption is that the flute is being milled into a flat surface and not into a cylindrical shape like a barrel. In weighing barrels before and after fluting and comparing the weights to calculated weights from the above formulas, there is no noticeable difference. The difference is only a small fraction of an ounce.

Although the above formulas for calculating barrel and flute weights are fairly simple and straightforward, they are quite time consuming and there is the possibility for mistakes. They lend themselves very well to calculating on a personal computer.

To simplify the calculations, a computer program was written that will perform all of the above functions from the required data. Pre-programmed into it are the dimensions for the maximum diameter NBRSA heavy varmint and hunter class tapers in addition to what we call a 1.200 HV taper. A 1.200 HV taper is the same taper per inch as a maximum HV barrel, but it is .050″ smaller in diameter throughout its length. It makes a good choice for 10.5 pound rifles. Besides these three pre-programmed tapers, the program will calculate the weights for any diameter straight cylinder unlimited-type barrel and a straight taper barrel of non-standard dimensions.

The program will first allow you to choose one of the above five barrel tapers. If you choose one of the pre-programmed tapers, it will ask if you would like to trim the barrel from the muzzle end or the cylinder end. For example, you may want to trim 5 inches from the chamber end and trim the muzzle end of a maximum HV blank to make a barrel for a light varmint rifle. If you want to include them, the barrel thread shank length and diameter can be entered. It will ask for the barrel groove diameter and if you would like to add flutes.

If there are no flutes, the program will calculate and print on the screen the total barrel weight in pounds and ounces, the muzzle diameter, barrel cylinder diameter, cylinder length, overall barrel length, thread shank diameter and length, and the groove diameter. The user then has the choice of printing a hard copy, making changes to the barrel or starting over with a new barrel contour. The allowable changes include changing the barrel length (from either end), the groove diameter, adding or changing thread shank dimensions, adding or removing flutes, or changing any flute dimension.

If flutes are chosen, the screen or printer will print the above data as well as the total weight removed by the flutes in pounds and ounces, their length, width of the cutter, width of the flute if the depth is less than cutter radius, the flute depth, and the number of flutes.

The program has some built-in safety devices. If the barrel cylinder diameter is no more than .1″ over thread shank diameter, a warning will be printed. If the length of the flutes is within 2″ of the overall barrel length, you will be told. For flutes machined to within .100″ of the groove diameter, you will be warned. When using the pre-programmed barrel tapers, you will be notified if too much length has been trimmed from the chamber end and the overall barrel length would exceed a 29″ blank length.

As of January, 2000 we’ve added a copy of the computer code, written in GWBASIC, to the end of the article in this section entitled “A LOOK AT THE RIGIDITY OF BENCHREST BARRELS”. The code was modified since this article was first written and published in NBRSA News. The change included the addition of formulas that calculate values for the relative stiffness of individual barrel tapers as well as their weight.

For an article about calculating the weights of contoured barrels, like our standard #1 – #7 contours, Click Here.