Bullet Design and Drag Calculator

I was looking around the Border Barrels website tonight, where they have an excellent calculator for figuring out the optimum Twist for a known bullet....

http://www.border-barrels.com/barrel_twist.htm

It turns out that they also have a fabulous Bullet Designer as well.... You can input various dimensions, the material specific gravity (eg. it uses 11.4 for lead), and it will calculate the bullet weight, draw a diagram of the bullet shape, show a graph of the Drag Coefficient, and give you the Ballistics Coefficient at every 0.5 Mach, up to Mach 3.... If the bullet weight is known, you can use that as well.... It will even give you the optimum twist rate for the bullet at each Mach number....

http://www.border-barrels.com/drag.htm

Here is an example of the drag curve for a .22LR bullet.... The Coefficient of Drag is plotted against the Mach Number.... Notice what happens to the drag at about Mach 0.8 (900 fps).... Between there and about Mach 1.05 (1200 fps) the drag increases by about a factor of four....

http://i378.photobucket.com/albums/o...psa6aa78e3.png

The calculator also gives the Ballistics Coefficient, expressed as the G1 model.... For that bullet, it is 0.11 at Mach 0.5, 0.08 at Mach 1-2, and 0.07 at over Mach 2.... Changing the shape of the bullet significantly changes the shape of the drag curve.... Here is the graph for a 63 gr. bullet in .224 cal, with a .11" Meplat....

http://i378.photobucket.com/albums/o...psc3225ac9.png

Note that the Drag Coefficient is roughly the same as the first example in the subsonic region (~0.23), but the inflection point where the drag increases is moved up to about Mach 0.9 (~1020 fps).... In addition, the supersonic drag is much less than for the round nosed .22LR bullet.... The G1 BCs for this bullet are 0.16 at Mach 0.5, 0.21 at Mach 1, 0.18 at Mach 1.5, and 0.17 from Mach 2 and up.... In other words, this shape is MUCH better at supersonic velocities, even though it has a flat nose....

You may wonder why the two bullets have such a large difference in BC when subsonic, even though the Drag Coefficient is similar at 0.23.... The answer lies in the Sectional Density.... They are the same diameter, but the 63 gr. bullet is 54% heavier, and has an SD of 0.179, compared to 0.118 for the 41 gr.... The drag is the same, but the heavier bullet has 54% more weight preventing it from slowing down.... and so the BC is also about the same amount higher....

Now for the interesting part.... I ran a whole bunch of cast bullets through this calculator, Round Nosed, Hollow Points, and those with varying sizes of Meplats, short dumpy bullets and long skinny ones.... The graphs showed the range of the Drag Coefficient at subsonic velocities was VERY small.... Most of the bullets by far had a subsonic Cd of ~0.23, and the range was between 0.22 and 0.25 for all the ones I looked at.... and they all showed minimum drag at Mach 0.5 or just below (~500 fps) In addition, all the bullets had a huge increase in drag at between Mach 0.8 and 0.9 (900-1020 fps).... Round Nosed bullets tended to get draggy at 900 fps, and the bigger the Meplat (in cailbers) the faster they could be driven before the big increase in drag started.... Short bullets (again, measured in calibers) tended to get draggy at 900 fps, and long ones more towards 1000.... which makes perfect sense as short bullets are lighter, and have a lower SD.... However, ALL the bullets showed a HUGE increase in drag at between 900-1000 fps.... one more reason to limit the velocity to that range....

If you are curious about how changing the shape of a bullet affects the drag, and want to get a good idea of the Ballistics Coefficient for a given design and weight.... this is an excellent website.... One more thing.... There is a button on the results page that says "Ballistics".... Click on that and you can put in the velocity and range and it will print out a drop and windage chart for you.... I don't think it gets any better....

Bob

I've been playing around with the Bullet Designer on the Border Barrels website, looking at the data for Mach 0.5, which is right in the middle of the plateau for the subsonic part of the bullet drag curve.... The Cd is relatively constant right up to the transonic region, as I noted above.... Not only that, but it is in a very narrow range over a wide variety of bullet shapes.... As you are probalby aware, the Ballistics Coefficient of a bullet is closely tied to its Sectional Density.... In fact if you divide the SD by a "Form Factor" you will get the BC.... For a Roundball, the FF is 1.55.... As bullets become more streamlined, the FF decreases, and so the BC increases....

I made up a simple spreadsheet where I could vary the nose shape of the bullet, and also change the length.... If you keep the caliber constant, the SD increases with the length, and so does the BC.... I used four different bullet shapes.... a round nose (hemisperical nose, 1/2 caliber radius), a radiused nose (nose length is 1 caliber, coming to a point), a radiused nose with a 1/2 caliber meplat, and a spire point where the nose is 1/2 the bullet length.... I ran each shape for a bullet length of 1.5 to 4.0 calibers and graphed the results, for both .25 cal and .50 cal bullets.... For the 1 caliber long bullet I used a roundball.... Here are the results....

http://i378.photobucket.com/albums/o...psa0f6ea31.jpg

http://i378.photobucket.com/albums/o...ps65248823.jpg

The Form Factors were calculated by dividing the SD by the BC produced by the Border Barrels program.... It only gives the BC to 2 decimal places, and that is part of the cause of the wavy lines in the curves.... However, one thing is apparent immediately.... For bullets about 2 calibers long and over, the FF is basically a constant.... and there is little difference in the value of that constant between .25 and .50 cal.... Virtually all of the data points are between 1.10 and 1.20, averaging a Form Factor of 1.15.... That means that for virtually all normal shaped cast bullets, if you divide the Sectional Density by 1.15 you will get a very close estimate of the Ballistics Coefficient.... within about 4%....

The other thing you will notice is that once the length drops below about 2 calibers, the FF increases, until it reaches 1.55 for a roundball.... If we average the 8 values for a bullet length of 1.5 calibers, we get a Form Factor of 1.30.... If you divide the SD by 1.30 for bullets that are 1.5 calibers long, you would get the BC within about 8%....

BC = SD / 1.15 for bullets 2 calibers long or over

BC = SD / 1.30 for bullets about 1.5 calibers long

BC = SD / 1.55 for roundball

Where SD = Wt.(gr.) / Cal ^2 / 7000

Note that all of these bullets had parallel sections from the nose back, and no driving bands, and a full diameter base.... I did not explore boat-tails at all, as they are unusual for a cast bullet.... The BCs derived by this method should be valid below the transonic drag increase which takes place between 900-1000 fps depending on bullet shape.... I did have a brief look at full wadcutters (cylinders), and they have much more drag, and consqeuently higher Form Factors and lower Ballistics Coefficients.... This method would not work for them, but for most traditional round nose bullets, or those with a radiused nose, spire point, or one ending in a meplat they should be valid estimates....

Bob

There'd be scant little point to a boat-tail in your a/g application- you won't be driving them anywhere near fast enough to take advantage of the design.

Nonte did a fine write up as a series on boat-tails- well worth looking up through the old Gun Digest annuals.

Lyman's Cast Bullet Handbook is an excellent resource, especially if you are "rolling your own". There's plenty out there as custom cast as well, that should be of interest...

Regards,

Doc Sharptail

Actually, from the data I've been seeing lately, boattails DO work at subsonic velocities.... reducing the drag by up to 50%.... That surprised me too.... I'm working on some testing of the numbers right now and will post in this thread when I have something interesting....

Bob

I've been looking at the idea of using a Boattail design for subsonic use.... I've heard that there is little point, that they are intended for supersonic use, but generally they are used on long spire point bullets which already have high BCs at Mach 2 plus.... I was wondering what would happen if you use one on a bullet that is more suitable for airgun use, one that is optimized for Mach 0.9 (1000 fps) and below.... The Border Barrels Drag Calculator had the ability to explore this, so I chose a design which makes sense as a starting point, and then tried various sizes of Boattails and put the values for Ballistics Coefficient and Twist into an Excel spreadsheet for Mach 0.5 (~550 fps, in the middle of the subsonic low drag bucket), Mach 1.0, and then also looked at the twist at 1000 fps using the Border Barrels Twist Calculator, which gave more detailed results for the 800-1000 fps range that interested me.... One other reason I want to examine the boattail is that I have a feeling that moving the corner of the base away from the bore may make any irregularities caused by the sprue cutter when casting bullets less important to accuracy.... The part of the bullet that is released from the crown of the muzzle is where the boattail starts, not at the base.... I'm not certain that will make a big difference in accuracy.... but my view is that it very well may.... and it can't hurt.... First of all, here is the basic bullet shape I was working with....

http://i378.photobucket.com/albums/o...psd3c24018.jpg

The basic bullet is .25 cal, 2 calibers long (0.50"), has a nose with a 2 ogive radius (0.25" long), and a meplat of half the caliber (0.125").... Because it incorporates a meplat, it could also be made with a hollowpoint without changing the profile.... I examined three lengths of boattail, and various diameters down to 64% of the bullet diameter (ie 0.16").... The reason I didn't go smaller is that the Border Barrels Calculator flags a warning when the boattail is less than 65% of the caliber, stating that the transonic and supersonic drag may be incorrect.... Anyway, here are the results of an afternoon of plugging numbers into the Border Barrels Drag Calculator....

http://i378.photobucket.com/albums/o...ps3b90118d.jpg


The basic flat base design (in pure lead) weighs 59 gr. as a solid, and likely about 53 gr. as a hollowpoint (depending on cavity size).... The thinner and longer the boattail, the lighter the bullet would be, of course.... For the shortest boattail (0.05" long) a solid would be between 57-59 gr. depending on the diameter of the base.... For a 0.10" long boattail a solid would be 55-59 gr.... and for the longest boattail (0.15" long) a solid bullet would be between 53-59 gr.... The corresponding hollowpoint would be about 10% (~6 gr.) lighter....

What does the above graph tell me?.... Well, for a start, boattails DO reduce the drag at subsonic velocities (in blue), in fact by as much as a factor of 3.... The length of the boattail has little effect on the resulting subsonic BC, but the diameter of the base has a large effect.... At supersonic velocities (in red), however, with these relatively short, blunt bullets, the boattail actually INCREASES the drag as you make the tail thinner.... A long boattail postpones the drag increase as the angle of the boattail for a given base diameter is less.... The point where the BC @ Mach 1.0 drops to 0.12 occurs at about 11 degrees for all the boattail shapes I looked at.... As the base diameter decreases, the stability decreases as well, and a faster twist rate is required.... The graph above shows the twist required for a Stability Factor of 1.5 at Mach 0.5, at just below Mach 1.0 (worst case), and an additional line for 1000 fps (Mach 0.9, shown in black) which is about as fast as it makes sense to drive a bullet of this shape, as the drag is already rising sharply by that time.... Here is a graph of the Drag Coefficient of the basic bullet, without the boattail....

http://i378.photobucket.com/albums/o...ps18a2f182.png

Here is a graph of the Drag Coefficient for the same bullet, using a boattail that is 0.10" long and 0.20" diameter at the base....

http://i378.photobucket.com/albums/o...pse6d67c67.png

Note that the Cd in the subsonic range is only about 0.13, compared to 0.24 without the boattail.... and that the subsonic BC has increased from about 0.11 to about 0.21.... in other words below Mach 0.85 (950 fps) the bullet has about 45% less drag.... There is a price you pay, however, you need a faster twist rate to stabilize the boattailed design.... Here is the twist rate for a SF of 1.5 for the basic bullet, without boattail....

http://i378.photobucket.com/albums/o...psff00c5ea.png

Compare that to the twist rate required for the same bullet with a boattail 0.10" long and 0.20" diameter, also for an SF of 1.5....

http://i378.photobucket.com/albums/o...ps64b17771.png

At just below Mach 1 (the worst case), the boattailed design needs a twist rate of about 12.5", compared to about 17.5" for the flat-based bullet.... Having said that, at 1000 fps, the required twist rate for a 57 gr. solid bullet would be about 14.5", and for a hollowpoint (which at about 51 gr. effectively has a lower Specific Gravity and hence less stabilty) would be just under 14".... It just so happens that a TJ's .25 ACP liner has a 14" twist, which is why I find that number significant....

I offer this design as a proposed starting point if any of you are interested in developing an optimized bullet for subsonic use in airguns.... Please feel free to discuss it, modify it, and ultimately I hope that somebody gets a custom bullet mold made and tries it.... Note that the design should be "scalable" to any other caliber, and it could also be "stretched" or "shrunk" in length to change the weight, or how it fits into a magazine (this one is too long for an MRod .25 cal magazine, for example, they accept a maximum length of only about 0.48").... I chose the dimensions as a starting point only.... For those who like a larger diameter meplat, that can be done as well, but it will change the BCs, twist rates, and possibly the optimum dimensions.... Here are what this bullet, scaled to other calibers, would weigh as a solid.... Deduct about 10% for a hollowpoint version....

.177 cal: 20 gr.
.217 cal: 37 gr. (.22 airgun size)
.224 cal: 41 gr.
.25 cal: 57 gr. (.25 airgun size)
.257 cal: 62 gr.
.308 cal: 107 gr.
.357 cal: 164 gr.
.40 cal: 235 gr.
.452 cal: 339 gr.
.457 cal: 346 gr.
.50 cal: 459 gr.
.58 cal: 717 gr.

You will note that the weigh in .22 cal is very similar to a .22LR bullet.... That is not a coincidence, as the proportions of that bullet make sense for a lot of reasons for high subsonic velocities.... Incidently, the twist rate will scale in proportion to the caliber.... double the caliber, double the twist in inches required for stability....

Bob

I'd be much interested in what is found in an actual trial... Drag is not the complete stability picture.

The rebated base of the .22 lr bullet has much to do with it's accuracy- and it's an actual step around the bullet base.

IIRC, the boat tail design arose out of efforts to make a jacket for the early pre-production hornet. I'd have to read up on my Woody, Wotkyns, and Whelen in order to recall how they ended up shaping the LR brass that they used as an experimental jacket into a boat tail....

Regards,

Doc Sharptail

With what I have learned over the past few days about bullet design and the fact the boattails will in fact work to reduce drag at subsonic velocities.... I decided to develop a design for a .25 cal boattail airgun bullet.... There were several criteria to be met....

1. It had to fit a standard airgun bore with 0.250" groove diameter....
2. It had to be stable in a 14" twist barrel at 1000 fps and less....
3. It had to fit in a stock .25 cal MRod magazine....
4. It had to have a Meplat of about 1/2 the caliber....
5. It had to be convertable to a HollowPoint design....

In addition to the above, I wanted the highest subsonic Ballistics Coefficient that I could achieve.... I wanted to use a Tangent Ogive design with the longest nose radius that I could.... and yet maintain the longest driving band length for bore alignment (conflicting requirements).... I did quite a bit of research on Rebated (stepped) Boattails, and found the Corbin website very helpful in explaining why they made sense, and how much of a step worked.... The advantages are a cleaner release from the crown, less blowby, and on average 15% smaller groups than a conventional Boattail (where the tail meets the body at an angle).... but there is a slight increase in drag, primarily when supersonic.... One additional advantage I came up with is that since the step is not at the base of the bullet, any slight base imperfection from the casting process (eg. the sprue cutter) won't affect the area that releases from the muzzle crown, ie the base is further back and less likely to cause accuracy problems.... The part that releases from the muzzle crown is the back point of the rear driving band....

I played around with a variety of dimensions, changing the proportions and seeing what affect they had on the BC and Stability.... I consulted with Erik at HollowPoint Mold Services in regards to the HP cavity dimensions.... and I eventually settled on the following design....

http://i378.photobucket.com/albums/o...ps8f3ceb36.jpg

The subsonic Drag Coefficient is half that of a flat base bullet of the same dimensions, giving a BC of 0.20 for the HP and 0.22 for the RF design.... The Solid (RF) weighs 51 gr. (in pure lead), and the HollowPoint should be about 46 gr.... The Stability Factor is just over 1.5 at 1000 fps, and is 2.2 at 500 fps in a 14" Twist.... If launched at 90 FPE, it would have about 80 FPE remaining at 100 yards, assuming the BC lives up to expectations....

I showed the design to Sean Pero, he pondered it for a while, and then offered to make a Cherry cutter and make me a single cavity mold to find out how it works.... I know Sean is a busy guy, but with Winter coming, maybe, just maybe, he'll find the time and I'll be able to test the theories....

Bob

Sean just sent me this photo of the blank for the Cherry for the new bullet....

http://i378.photobucket.com/albums/o...ps6ee7bea3.jpg

I can't believe he did this so quickly.... WOW!!!

Bob