All serious long range shooters are aware that bullets have a ballistic coefficient, and that it’s somehow related to how much the bullet will drop and drift in the wind. Shooters place various degrees of importance on knowing the exact BC of their bullets, and shooting bullets with high BC’s. In this paper, I want to explore some of the benefits of knowing precisely what the BC of their bullet is, and also, the different methods available to determine the BC of a bullet. The main point of this writing is to show that BC’s can be measured from firing tests more easily, and with less error than is commonly thought.
First, why is it important to know the precise BC of your bullets?
Well, for many shooters, it isn’t. Those who shoot targets at known distances with sighter shots allowed don’t necessarily care about calculating drop and drift precisely. We just take a couple sighters, and adjust from there. Good chance we use the sighters to foul our barrel after a cleaning anyway. So to long range target shooters, knowing BC is only important as a means to compare bullets to see which has the higher BC.
However, not all long range shooting is done at known distances. Long range hunters and snipers care a great deal about knowing the exact BC of their bullets, because they use that information to calculate drop and wind drift for the all important first shot kill. Most live targets don’t allow many sighter shots. Now there are a lot of things that have to be calculated in order to predict the drop of a bullet at long range. The BC of the bullet is at the top of a long list of variables including: atmospheric conditions, muzzle velocity, range to target. Even the inherent potential accuracy of the program you’re using to calculate the trajectory can be a limiting factor (see How External Ballistics Programs Work).
In the following paragraphs, I’ll explain the pros and cons of the options available for determining BC. Note, these are different than the methods available for calculating trajectories. The methods below figure out BC, then the BC is entered into another program that calculates trajectories, based on BC.
1. There are analytical aerodynamic prediction methods. With such methods, you use the shape of the bullet to calculate the various components of drag and other aero forces, add them all up, and arrive at an answer. McDrag, and the JBM online drag calculator are examples of analytic aero prediction codes.
2. There are semi-
that rely on Reynolds number (like Magnus coefficients) may be effected by the lack of Reynolds number match. I've only recently become aware of this Reynolds number problem, and am looking into how to make Reynolds number corrections for smaller diameter projectiles.
3. CFD, or Computational Fluid Dynamics. CFD is an intense computational method that has the potential to be very good, but requires a large amount of experience by the user. In particular, CFD has problems modeling turbulence and viscous phenomena like flow separation (as do all aero codes). CFD codes are also more expensive, and can take many hours, or even days to converge on solutions even on supercomputers.
4. Wind tunnel is close to experimental, but you still have test fixtures to deal with. Base drag is the bane of wind tunnel testing for projectile shaped objects because of the sting's (supporting arm) interference with the flow at the base of the projectile model. Wind tunnel testing, especially supersonic wind tunnel testing is extremely expensive.
5. Actual test firing in spark photography ranges stands the highest chance of producing the most accurate drag data, but other coefficients can be hard to extract from the observed motion. For example, dynamic derivatives like pitch rate damping and alpha_dot damping cannot be resolved into separate components based on spark range data reduction. In the end, both factors are combined into a single pitch damping coefficient.
6. Instrumented range (doppler, multiple chronographs, etc) can also be used to measure velocity decay and provide very accurate drag data. Again, the other aero coefficients are hard to get.
So you see, with all of the available methods to calculate cd (let alone other aero coefficients), there are many considerations to be made. And each method is good at some things, poor at others. Some require much more knowledge and resources from the user.
Even when each method is used properly, you will have variation in the predictions
for Cd and other aero coefficients (BC relates directly to Cd). Cd may be within
+/-
Bottom line is, when it comes to BC, test firing is the best way to go if your goal is accuracy. Some people worry about the 'pitching and yawing' motion induced to different degrees by individual rifles. I've modeled this effect and have concluded the following:
Drag does go up when the bullet is pitching and yawing. However, the levels of pitch and yaw that are NORMAL for modern rifles is TOO SMALL to effect the measured drag.
