A Look at Bullet Ogives and Chamber Throat Angles
By: Daniel Lilja
After ordering a new set of bullet dies recently, I began to wonder how the new ogive shape that I had decided on would compare to the throat angle of my chamber reamer. Typically the reamer makers will grind a one and a half degree angle on the throat (or leade, as it is sometimes referred to) for cartridges intended for target shooting.
The SAAMI specifications for some cartridges designed for hunting call for a steeper throat angle, often up to 3 degrees or so. For example, the 222 Remington has an angle of 3 degrees, 10 minutes and 36 seconds. The 7mm Remington Magnum has a throat angle of 3 degrees, and the 308 Winchester has a standard leade of 1.75 degrees. A few cartridges, but not many, have a more shallow angle. For example, the 270 Winchester has an angle of 47 minutes and 33 seconds. The NRA book Handloading by William C. Davis has a reference section that has SAAMI chamber drawings for many of the popular commercial cartridges, including throat angles.
Why there are so many angles, I am not sure. As mentioned above though, target chambers often have a 1.5 degree throat angle. That brings up the question, why 1.5 degrees? I asked one of our long established and knowledgeable reamer makers that question. His reply was that angle was most often requested and just seemed to work. We can’t argue with success and as the saying goes, if it works don’t fix it.
The bullet swage die that I ordered, though, was not typical of common 7 caliber radius, tangent ogive bullets used in benchrest shooting. It was a 13 caliber secant ogive.
It seemed as though the “best” throat angle, if there is such a thing, would be one that is tangent to the bullet ogive radius at that point on the bullet which would be engraved by the rifling. Put another way, if we opened a pair of calipers to rifle barrel bore diameter (nominally .237″ for a 6mm) and slid it along the nose of the bullet until both jaws of the caliper touched the bullet nose, we would have found that point on the ogive where the lands of the barrel would begin contact with the bullet. If we were to then draw an imaginary line from that point to the point on the bullet where the ogive and the bullet bearing surface meet, we would have the throat angle as described above. In the case of a 6mm bullet, the angle would be measured between the diameters of .243″ and .237″. The axial distance between these two diameters will vary with changes in the ogive radius. (See illustration.)
There are several ways in which this angle could be found for a specific bullet. The bullet could be physically measured on an optical comparator or a tool maker’s microscope. There are also machines called coordinate measuring machines that are capable of making such measurements and computing angles and radii. Another method is to determine the throat angle mathematically, and this is the technique I used.
To use the mathematics method, certain physical dimensions of the bullet must be known, such as the diameter of the bullet and the rifle barrel bore diameter. The type of ogive, tangent or secant, must be known, and its radius. In the case of a secant bullet, the meplat diameter also must be known, as well as the ogive length. The ogive length is determined mathematically with a tangent radius. Its length depends on the radius of the ogive and the meplat diameter.
From this information, the location of the ogive radius center can be determined. Then, using calculus the axial distance can be determined between the point where the ogive and bearing surface meet and the point on the ogive where the diameter is bore diameter. Knowing this distance and the barrel land height, then it is a simple trigonometry calculation to determine the throat angle.
Computer Program to Calculate Throat Angle
10 CLEAR:CLS:PRINT”CODE -THROAT’ WRITTEN IN GWBASIC BY DANIEL
LILJA 1990″
20 INPUT”ENTER BULLET DIAMETER (INCHES):”;BD
30 INPUT”ENTER MEPLAT DIAMETER (INCHES):”;MD
40 INPUT”WHAT TYPE OF OGIVE DOES THIS BULLET HAVE (1=TANGENT
2=SECANT):”;QO
50 IF QO=2 THEN INPUT”ENTER THE LENGTH OF THE OGIVE INCHES):”;NL
60 INPUT”ENTER THE OGIVE RADIUS (CALIBERS):”;RC
70 INPUT”ENTER THE BORE DIAMETER OF THE RIFLE BARREL
(INCHES):”;RBD
80 C=(BD-MD)/2
90 R=RC*BD:REM OGIVE RADIUS IN INCHES
100 IF QO=2 THEN GOTO 140
110 REM COMPUTE NOSE LENGTH AND THROAT ANGLE LENGTH FOR
TANGENT OGIVE
120 NL=SQR(R*2*C-C^2):REM FIND NOSE LENGTH
130 CC=(BD-RBD)/2:XX=SQR(R*2*CC-CC^2):GOTO 230:REM CALC AXIAL
DISTANCE BETWEEN 0GIVE TANGENCY POINT WITH BEARING SURFACE
AND BORE DIAMETER ON OGIVE
140 REM COMPUTE X-Y COORD OF OGIVE RADIUS CENTER FOR SECANT
OGIVE
150 HYP=SQR(NL^2+C^2):REM HYPOTENUSE OF TRIANGLE IN OGIVE
160 H=R-.5*SQR(4*R^2-HYP^2):REM HEIGHT OF CIRCULAR SEGMENT
170 A=ATN(C/NL):REM FIND ANGLE OF OGIVE SLOPE
180 HX=H/COS(A):REM HYPOTENUSE OF RIGHT TRIANGLE IN CIRCULAR
SEGMENT
190 X=R*SIN(A):REM FIND AXIAL LENGTH OF X COORD FROM MIDPOINT OF
OGIVE CHORD
200 B=SQR(R^2-X^2):REM FIND LENGTH OF Y COORD
210 YC=(B-HX-(BD+MD)/4):REM FIND Y COORD FOR OGIVE RADIUS CENTER
FROM AXIS
220 XC=BL-(NL/2+X):REM FIND X COORD FOR OGIVE RADIUS CENTER FROM
BASE (BL=bullet overall length)
230 REM:CALCULATE THROAT ANGLE AND THROAT LENGTH
240 LHT=(BD-RBD)/2:IF QO=l THEN GOTO 350:REM HEIGHT OF LAND
250 BDY=(BD/2)-LHT:REM Y COORD OF BORE DIAMETER
260 XSEC=BL-NL-XC
270 XX=NL/10000+XSEC:REM START FIRST DISC AT ONE HALF THICKNESS
280 DIM Y(5000),XX(5000):REM CALCULUS ROUTINE TO FIND LENGTH OF
THROAT ANGLE FOR SECANT OGIVE
290 FOR D=l TO 5000:REM 5000 DISCS
300 Y(D)=SQR(R^2-XX^2)-YC:REM EQUATION OF CIRCLE = X^2+Y^2=R^2
310 XX=XX+NL/5000
320 IF Y(D)<=BDY THEN GOTO 340
330 NEXT D
340 XX=XX-XSEC
350 ANG=ATN(LHT/XX)*57.3:REM ANGLE OF OGIVE SLOPE AT THROAT
CONTACT POINT IN DEGREES
360 PRINT””:PRINT “THE THROAT ANGLE IS (DEGREES PER SIDE):”;:PRINT
USING”##.##”; ANG
In the table is a listing of various ogive shapes and their corresponding throat angles. To make a general conclusion from the information, a 7 caliber tangent ogive has an angle of 1.7 degrees. An 8 caliber tangent ogive has an angle of 1.6 degrees, and a 9 caliber tangent ogive, an angle of 1.5 degrees. There is some variation in these values according to the caliber. The reason for this is due to the difference in barrel land height in the various calibers. For example, using the nominal dimensions for a 22 caliber barrel of .219″ and .224″, there is a land height of .0025″. With a 6mm barrel having dimensions of .237″ and .243″, there is a land height of .003″. With a 30 caliber barrel, the diameters are .300″ and .308″. This results in a land height of .004″. The reason the throat angle changes with differences in land height is simple. As was stated earlier, the throat angle is determined by the triangle formed by the land height and the distance between the two diameters mentioned. In the example of the 6mm barrel, these diameters are .237″ and.243″.
As can be seen in the table, a streamlined secant ogive has a throat angle considerably steeper than the tangent ogives. The 6mm secant ogive listed is similar to the 105 grain bullet that Walt Berger is making.
Another factor is throat erosion. Does a throat that starts out at 1.5 degrees maintain that angle as erosion from firing advances the throat ahead? As I said above, I am not proposing that there is a “best” throat angle. It does seem reasonable, though, that some bullets may perform better with an angle more closely matched to their shape. The somewhat standard throat angle of 1.5 degrees for target chambers is quite close to the calculated angles for 7-9 caliber tangent ogives. It would take a great deal of testing with a number of bullet shapes, fired in a number of barrels with different throats, to prove that one angle is superior to another. The bottom line is performance on the target.
THROAT ANGLES FOR VARIOUS OGIVES
OGIVE TYPE | THROAT ANGLE IN DEGREES |
.22 CALIBER: (.219″ BORE DIAMETER .224″ GROOVE DIAMETER) | |
6 CALIBER TANGENT | 1.74 |
7 CALIBER TANGENT | 1.62 |
8 CALIBER TANGENT | 1.51 |
9 CALIBER TANGENT | 1.43 |
10 CAL SECANT .55″ LONG X .046″ MEPLAT | 2.50 |
6MM CALIBER: (.237″ BORE DIAMETER .243″ GROOVE DIAMETER) | |
7 CALIBER TANGENT | 1.70 |
8 CALIBER TANGENT | 1.59 |
9 CALIBER TANGENT | 1.50 |
15 CAL SECANT .65″ LONG X .07″ MEPLAT | 2.77 |
30 CALIBER: (.300″ BORE DIAMETER .308″ GROOVE DIAMETER) | |
7 CALIBER TANGENT | 1.74 |
8 CALIBER TANGENT | 1.63 |
9 CALIBER TANGENT | 1.54 |
12 CAL SECANT .75″ LONG X .07″ MEPLAT | 3.40 |