This is a study Shawn LeBaron and I did on how bullet shape effects the drag a bullet experiences. I hope you find it enlightening!

1. Effects of Bullet Shape
on Drag
Shawn LeBaron and Sterling Swift

2. Purpose
Bullets exit muzzle at max speed, quickly lose speed due to drag effects.
Especially over long distances, drag has great effect on range.
Analysis of the effects of the shape of a bullet on the drag effects helps to predict
trajectory, maximize effectiveness

3. Drag
Drag is the effect that air has of resisting things moving through it
The object’s shape affects the way the air has to move around it as it moves
through the air. Shapes that make the air go way out of its way as it flows around
them have much more drag than streamlined shapes.

4. Basic Bullet Terms and Definitions
Nose-Front section of bullet
Ogive-Rounded, tapered section, usually a nose section
Caliber-Maximum diameter of the bullet, sometimes used as a unit to
describe proportions (ex. a the G1 standard has an ogive that is 1.3
Calibers long with a radius of 2 calibers)
Boat Tail- tapering of rear portion of bullet to reduce drag

5. History
● There are a couple of ways that people look at drag on bullets. Some use the
coefficient of drag, others use the ballistic coefficient or use the shape factor.
● The ballistics coefficient is a measure of how well a bullet can overcome drag.
The higher the ballistics coefficient the better the bullet can overcome the
drag. (This is the number they use in industry)
● The shape factor (i) is ratio of the drag coefficient for a test bullet to the drag
coefficient of a standard/known bullet. (G1 or G7)
http://www.frfrogspad.com/extbal.htm -list of known bullet shapes
http://www.frfrogspad.com/drgshape.htm -list of known bullet shapes

6. Experiment Discussion
● We designed an experiment that will allow us to calculate the drag on bullets
of different shapes.
● Because of the limitations of our wind tunnel analyzed bullets that travel at
subsonic speeds.
● We created a scale model that is 6x bigger than the original, this allowed us to
decrease the speed of airflow in the wind tunnel from 1000 ft/s to about 160
ft/s, because we were only worried with matching Reynolds number.
● The following slides will use math equations to show how we were able to
calculate the Cd, BC, and shape factor. There will be an explanation for the
subsonic case, which we were able to test, and the supersonic case.
● We also compared these results to a CFD model, an online BC calculator and
to similar shaped bullets found in industry.

7. Hand Calculations
-density
V- Velocity
L-Length (we used diameter)
- dynamic viscosity
D-Drag (lbf)
A-cross sectional area
M-mass
CG-coefficient of drag of some
known bullet (G1 or G7)
CT-coefficient of drag of the
bullet you’re measuring
These are the main equations that we used to
calculate drag, BC and shape factor

8. Subsonic Case
● For the subsonic case we will
focus on matching Reynolds
number only. This is because the
main component of drag is the
parasitic drag. Compressibility
effects and wave drag don’t affect
the overall drag coefficient that
much until you reach Mach 1.
● The picture to the right illustrates
this point that Cd isn’t affected as
much by speed until you reach
Mach 1 (1116 ft/s).
● For the subsonic case we will
assume that the Cd is the same
for similar shapes despite the
difference in speed.

9. Subsonic Case

10. Subsonic Case

11. Supersonic Case
For the supersonic case it was important to
match both Reynolds number and Mach
number. This is because at supersonic speeds
compressibility of the air and the wave drag
does become important. Also, as a result the
Cd becomes much more dependent on
velocity. So we wouldn’t be able to use the
same equations that we used in the subsonic
case

12. Supersonic Case

13. Supersonic Case

14. Discussion
For the supersonic bullet the Drag is proportional to the difference in size. So, if you have a
model bullet that is 6x bigger than the real bullet, then the bigger bullet will have 6x the drag
of the smaller bullet. This make sense because the compressibility of the air becomes
important at supersonic speeds. Because air is compressible at high speeds, there is an
increase of pressure in front of the bullet. If the bullet is bigger, it will have higher pressure in
front of it due to the increase in cross sectional area.
For the subsonic case the the drag of the smaller and larger bullets about equal. This is
because the other components of drag such as wave drag and lift drag are negligible. They
aren’t exactly equal because the coefficient of drag will be slightly different due to the
difference in speed, but they’re close.

15. Experiment
● We desired to analyze the drag on bullets of various shapes.
● In order to do this we designed an experiment that would allow us to calculate
the drag. Then using the drag we calculated the drag coefficient, ballistic
coefficient and shape factor.
● In this experiment we had to scale up the size of the bullets, because our
wind tunnel maxed out at 161.3 ft/s. We also decided to use subsonic bullets
so that we didn’t have to worry about matching Mach number.

16. Experiment cont.
Created geometry based on a 5.56mm round
Included designs with pointed nose, straight and
boat tailed end.
Scaled to greatest speed achieved by wind tunnel
matching Reynolds number.
Neglected viscous effects
*due to time constraints only the pointed models were created. However, we
still performed cfd and comparisons with the blunt models.

17. Experiment cont.
3D printed both pointed nose examples
We measured the drag of the bullets in a wind
tunnel at 161.3 ft/s (110mph) using a sting
sensor.

18. Results from Experiment
Type Cd BC Shape
Factor(i)
Pointed Boat tailed .2485 .3219(G1);
.1378 (G7)
.7289(iG1),
1.7024(iG7)
Pointed no Boat tail .3262 .2453(G1);
.1050(G7)
.9566(iG1);
2.2343(iG7)
Boat tailed bullet showed improvement over straight tail

19. Computational Fluid Dynamics
Simulated flow around each round using Star-CCM+

20. Results from CFD
Type Cd BC Shape factor (i)
Pointed Boat tailed k 0.2721;
k 0.3178
k 0.2940 (G1)
0.1259 (G7);
k 0.218 (G1) 0.1078 (G7)
k 0.7979(G1) 1.8636(G7)
k 0.9319 (G1) 2.1766 (G7);
Pointed no Boat tail k 0.3231 k
.3677
k 0.2476 (G1); 0.1060 (G7)
k 0.2176 (G1); 0.0932(G7)
k 0.9475 (G1); 2.2130 (G7)
k 1.0782 (G1); 2.5182 (G7)
Blunt Boat tailed k 0.1729;
k 0.17
k 0.4627 (G1)
0.1981 (G7);
k 0.4703 (G1) 0.2013 (G7)
k 0.507(G1) 1.1842(G7)
k 0.4981 (G1) 1.1653 (G7);
Blunt no Boat tail k 0.3349;
k 0.3677
k 0.2389 (G1)
0.1023 (G7);
k 0.2176 (G1) 0.0932
(G7)
k 0.9822(G1) 2.2939(G7)
k 1.0784 (G1) 2.5187 (G7);

21. Online Calculator
Calculated from http://www.geoffrey-kolbe.com/drag.htm
Pointed, Boattailed Pointed, Straight Blunt, Boattailed Blunt, Straight

22. Data from Industry
● Here you can see that this
company uses the technique of
listing their ballistic coefficient to
tell buyers what the effects of drag
are on these bullets.
http://www.sierrabullets.
com/documents/BallisticCoefficient-rifle.
pdf

23. Ballistic Coefficient Comparison
Pointed nose, Boat tailed
Pointed nose, Straight
Calculated Online Calculator CFD Industry Provided
0.329 (G1), 0.1378(G7) .33 (G1), 0.19(G7) K .2518 (G1), .1078 (G7);
K .2940(G1), .1259(G7)
.393
(.22 CALIBER (.224) 80 GR.
HPBT MATCHKING)
Calculated Online Calculator CFD Industry Provided
0.2453 (G1),0.1050(G7) .16 (G1), 0.09(G7) k 0.2176 (G1); 0.0932(G7)
K 0.2476 (G1), 0.1060(G7)
.181
(.22 CALIBER (.224) 45 GR.
SPITZER)

24. Ballistic Coefficient Comparison
Blunt nose, Boat tailed
Blunt nose, Straight
Online Calculator CFD Industry Provided
0.37 (G1), 0.21 (G7) K 0.4703(G1), 0.2013(G7);
K .4627(G1), 0.1981(G7)
Couldn’t find
Online Calculator CFD Industry Provided
0.19 (G1), 0.11(G7) K 0.2176(G1), 0.0932(G7);
K 0.2389(G1), 0.1023(G7)
.180 (9 MM (.355) 125 GR. FMJ)

25. Existing Data

26. Existing Data
● One of the parameters that affect the drag is the length of the ogive.
● This becomes especially important when the bullets are supersonic
because the sharper the point the less compression drag there is.

27. Existing Data
Nose effects
From NACA study of aerodynamic effects nose shapes at various Mach numbers
Sharper noses bring the shockwave closer to the nose, so there’s less pressure
building up in front

28. Existing Data
Tail Effects
According to the US Army’s Ballistic Research
Laboratory, increasing boattail angle
decreases drag monotonically in subsonic for
reasonable angles/lengths. In supersonic
regime, optimal angle is 7.9 degrees

29. Conclusion
Shape of a bullet has a great bearing on performance, but the effects depend strongly on size and speed of the bullet.
Remember, the lower the drag, the farther the bullet can fly.
At subsonic speeds, boattail length and angle improve drag up to practical limit. This is because they reduce the pressure
drag, because it creates a smaller wake. The ogive shape doesn’t have too much of an effect at subsonic speeds. This is
because the main component of drag is the pressure drag, which is affected mostly by the size of the wake. The shape of
the ogive doesn’t change the size of the wake. However, the boat tail shape does affect the size of the wake.
At supersonic speeds, the shape of the ogive (how pointy it is) affects the drag. This is because at these speeds the
compressibility/shock wave drag becomes a huge factor. The sharpness of the point plays a far greater role, because it
cuts the air and creates a oblique shock wave. Because the tip is pointed there is far less pressure that accumulates in front
of the bullet than if the bullet was blunt. Blunt bullets have a normal bow shock in front which greatly increases the drag.
This is due to the high pressure that forms on the front of the bullet, that results from the air being compressed. To see how
the shapes of these shockwaves compare, see the images on slides 19 and 25.

30. Sources
B.G. Karpov, The Effect of various Boattail Shapes on Base Pressure and Other Aerodynamic Characteristics, U.S Army
Materiel Command, Ballistic Research Laboratories, August 1965
Alvin Seiff, Carl Sandahl, The Effect of Nose Shape on the Drag of Bodies of Revolution at Zero Angle of Attack, NACA
Conference on Aerodynamic Design Problems of Supersonic Guided Missiles; 2-3 Oct. 1951
R.M. Cummings, H.T. Yang, Y.H. Oh Supersonic, Turbulent Flow Computation and Optimization for Axisymmetric
Afterbodies, Computers & Fluids, Volume 24, Issue 4 May 1995
A Short Course in External Ballistics, http://www.frfrogspad.com/extbal.htm, 9 September 2014
Bullet Drag Calculator, http://www.geoffrey-kolbe.com/drag.htm
Helpful list of Ballistic Coefficients, http://www.sierrabullets.com/documents/BallisticCoefficient-rifle.pdf
Certain equations for the BC,http://www.bergerbullets.com/form-factors-a-useful-analysis-tool/ and https://en.wikipedia.
org/wiki/Ballistic_coefficient, and (book) Bruce R. Munson (2013). Fundamentals of Fluid Mechanics. Jefferson City: Don Fowley.
513. (slide 6)

31. Images
http://www.123rf.com/photo_7856482_bullet-holes-easy-to-place-on-different-color-or-background.html bullet hole background
http://www.aerospaceweb.org/question/aerodynamics/q0094b.shtml streamlined shape example
https://i.ytimg.com/vi/gjzs79kDr6E/maxresdefault.jpg G1,G7 standard models
http://www.cruffler.com/Features/JAN-02/trivia-January02.html bullet characteristics diagram
http://www.frfrogspad.com/extbal.htm G series drag coefficient plot
CAD models via NX10
CFD simulations via STAR-CCM+
Bullet shockwave images:https://en.wikipedia.org/wiki/Bullet_bow_shockwave; https://www.shootersforum.com/ballistics-internal-external/81381-bullet-acceleration-sound-barrier.html
http://www.dtic.mil/dtic/tr/fulltext/u2/474352.pdf Bullet shockwave photo, boattail vs drag coefficient graph
http://tmtpages.com/calcbc/coxe-bugless.htm Ogive length vs diameter graphic
http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20030067331.pdf Nose effect study images
https://www.sierrabullets.com/store/product.cfm/sn/9390/224-dia-80-gr-HPBT-MatchKing bullet image and industry ballistic coefficient example