Improving shooting accuracy with CFD

The firing tests were performed by Bryan Litz who is a ballistician at Berger Bullets, an Aerospace Engineer, and an accomplished U.S. rifle team shooter and coach.

Accurate drag coefficient data improves the shooter's accuracy of hitting smaller targets at longer ranges. The drag coefficient is an indicator of the amount of aerodynamic resistance that a bullet faces while in the projectile. A small miscalculation in the drag coefficient may lead the bullet off-target, especially in windy conditions.

Still, most bullet manufacturers use simple, and often inaccurate, computer programs to estimate drag coefficients. In this article, I propose CFD (Computational Fluid Dynamics) modeling as a way to accurately estimate drag coefficients, and, as a complement to the firing tests for a better understanding of the bullet ballistics. I will compare the CFD results with field firing tests data on drag coefficients for a Berger bullet.

The Berger bullet

A 0.308 caliber 155 grain VLD Berger bullet is used for this case study. This bullet is one of the flattest (low drag) bullets that can be used for hunting or target shooting. The images below show the original photo of a 0.308 caliber 155 grain VLD Berger hunting bullet and a schematic with the dimensions (inches).

1 grain = 1/7000th of a pound = 0.065 grams

Source: Berger Bullets and Applied Ballistics

CFD Simulations

OpenFOAM CFD software was used to perform CFD simulations on the bullet. Specifically, a density-based compressible flow solver, called rhoCentralFoam, based on central-upwind schemes was used. Unstructured meshes with 0.18 million cells (medium) and 0.26 million cells (fine) were used. Four simulations were run, for four different supersonic flow conditions or Mach numbers. An additional fifth simulation was run with the fine mesh to see if the results improve with refinement.

The velocity contours around the Berger bullet for a Mach number of 2.5 are shown above.

Comparison of CFD data with firing tests data

The resulting drag coefficient values for each of the four Mach numbers are plotted on the original plot generated from firing tests followed by a table containing the error quantification. It is observed that the medium mesh provides a fast and reasonably accurate prediction (within 6% error) of the drag coefficient (Cd) and correctly predicts the drop in drag coefficient with increasing Mach number. The fine mesh takes longer to run but gives very accurate drag coefficient predictions (within 2% error).

The blue dots represent medium-mesh CFD results and the pink dot represents fine mesh CFD results. The black dots represent the values measured by Bryan Litz in the firing tests.

The future of ballistics with CFD simulations

The drag coefficient is an important parameter to understand the ballistics of small ammunition. This validation shows that the CFD software OpenFOAM can be successfully used to very accurately calculate the drag coefficient of Berger 0.308 caliber 155 grain VLD bullets.

As an extension, it is reasonable to say that OpenFOAM can be used to accurately calculate the drag coefficients of other similar ammunition as well. CFD will play an increasingly important role in designing low drag bullets for recreational and professional shooting in the coming years.

Do you want to improve your ammunition designs, reliability, and customer experience? Leave a comment and Follow Paanduv Applications on LinkedIn.