SD’S, BC’S And The Science Of Flight.
Sectional density and ballistic coefficient relate roughly like flour and bread. If what I want is a slice of toast, I care about the quality of the bread, without giving much thought to flour. Similarly, sectional density alone isn’t very useful, but it is an important part of ballistic coefficient, and it doesn’t hurt to understand what it means.
Sectional density is the ratio of an object’s mass to its cross-sectional area. US bullet manufacturers calculate it by dividing bullet weight in pounds by the square of bullet diameter. Take for example a 180-grain .308 bullet. The formula is 180÷7000 to convert to pounds, divided by 0.308 squared, for an SD of 0.271.
The higher the SD, the deeper an object in motion tends to penetrate. To give an extreme example, a baseball has a sectional density of about 0.036. A vintage cedar-shafted broadhead arrow weighing 750 grains has an SD of about 0.830.
A few pitchers can throw a baseball 100 mph or a bit over. That’s about 150 fps. If we get hit in the ribs by the ball, it will certainly cause pain and it might even break a rib. But it will bounce off.
Likewise, a longbow with a 60-pound pull can launch that cedar arrow at around 150 fps. What happens if it hits us in the ribs? Most likely it will go right through the other side. It penetrates the target better than a baseball. It also penetrates the air better, meaning it will retain its velocity better.
All by itself though, sectional density doesn’t tell us much. We can’t compare bullets—or predict bullet path—knowing only their SD. Bullet shape also matters.
The 180-grain Hornady spirepoint (above, left) has an SD of .271, while the Speer 200-grain
RN has an SD of .301. However, the shape of the 180 gives it a higher BC (.425) than the 200
(.372). Bullet shapes continue to become more ballistically efficient. At left (below) is a
flat-base 100-grain .257 Hornady with a BC of .357. The more streamlined boattailed Hornady
.243 105-grain A-Max at right has a BC of .500.
Prior to 1900, rifle bullets were mostly round or flatnosed. When ballisticians began experimenting with sharp-pointed (spitzer) bullets, they found a substantial advantage in retained velocity, range and wind resistance. It was obvious spitzers would provide soldiers with a decisive advantage. So all major nations began adopting them.
But neither SD nor bullet shape alone helps much in predicting trajectory, retained velocity and resistance to wind drift. The solution is to combine them, dividing sectional density by a form factor to arrive at a ballistic coefficient (BC). The form factor comes from comparing the bullet to a standard projectile.
Most of the ballistic coefficients listed by manufacturers use as a standard a 1-pound, 1-inch diameter bullet with a flat base, a length of 3 inches and a 2-inch-radius tangential curve for the point. This “standard projectile” has an SD of exactly 1.0. The form factor of a specific bullet is the drag coefficient of the bullet divided by the drag coefficient of the standard projectile.
The mathematical calculations of a projectile traveling through a medium such as air get extremely complicated. Prior to computers they could take days or weeks. Today, we just enter numbers in a program such as the JBM app (my favorite) and get the results in seconds.
An extreme example of the differences SD and bullet shape make in ballistic efficiency.
These Hornady bullets (above) weigh roughly the same. Left, a .357 158-grain HP
(SD .177, BC .206). Right, .284 162-grain Match HP (SD .287, BC .534). Start both at
3,000 fps and at 600 yards the .357 is traveling 1,040 fps, drops 141 inches from a
100-yard zero, and drifts 70 inches in a 10 mph full-value wind. The numbers for the
.284 are 2,091 fps, 69-inch drop and 17.5-inch wind drift. Boattails (below) bump up
the ballistic coefficient. The BC of two otherwise identical .284 Speer Bullets
are .416 for the flat base, .472 for the boattail.
The French Connection
In 1829 the French military began to seriously study ballistics. Their primary interest was in artillery. They established research facilities at Gavre, a small fishing village on the coast of France connected to the mainland by an isthmus. The remote location and the long unoccupied stretches of sand made it ideal for their purpose.
Research would continue at Gavre for more than a century, conducted by military officers trained in mathematics (assisted on occasion by university scientists and mathematicians). It was an interesting melding of pure scientific inquiry and hardheaded practical utility. Ballisticians still use the letter “G” to describe drag functions, as a tribute to Gavre and its pioneering research.
The G1 model uses as a standard the projectile described earlier. For bullets with different shapes, results vary with velocity.
Manufacturers can show BC at a specific velocity, or averaged over a range of velocities, or they can show different BC’s for different velocity ranges. In the old days manufacturers could get a bit creative in their published BC. Back when 500 yards was considered extreme long-range shooting, the G1 BC was “close enough.”
Actually there are several “standard” projectile shapes. The G6 model, for example, has a flat base and 6-caliber secant ogive. For rifle shooters it’s enough to know the G1, which remains the industry standard, and the G7, used with very low drag (VLD) bullets.
Using the appropriate data in a well-designed ballistics program gives a good prediction of bullet trajectory and wind resistance. Remember, though, it is only a prediction.
The ballisticians at Gavre operated under an important principle—all theoretical models had to be tested by actual firing—something the modern long-range rifleman would be wise to adopt.
By Dave Anderson