Effects of Caliber on Ballistics Coefficient

I've posted a thread about this before, but I've cleaned up the graph and table so I though I would post it again for those who missed it the last time.... The Ballistics Coefficient of a bullet is calculated by the Sectional Density divided by a "Form Factor".... For most bullets it is very complex, but for a sphere it is 1.55.... Therefore, all we need to know is the caliber to calculate the BC.... Here is a graph showing what happens to the BC as you increase the caliber....

http://i378.photobucket.com/albums/o...ps7161580b.jpg

And here is the same information in a table....

http://i378.photobucket.com/albums/o...ps951918a6.jpg

The weight of a roundball is proportional to the cube of the diameter.... The Sectional Density is the weight (in lbs.) divided by the bore squared.... Therefore the SD is directly proportional to the caliber.... and the BC is directly proportional to the caliber as well.... If you double the bore, you can expect to double the BC.... When you look at the value of the BCs in the table, you will note that they are actually very close to what we get with a good quality, round nosed, diablo pellet such as the JSB Exact series.... 0.024 in .177 cal, 0.030 in .22 cal, and 0.035 in .25 cal.... From this we might expect that the new Big Bore Exacts in .30 cal and 9mm (.357) will have BCs of approximately 0.043 and 0.049 respectively....

Just some food for thought.... and something to explain why the larger calibers tend to buck the wind much better....

Bob

I've been researching the Ballistics Coefficients for .22LR 40 gr. bullets.... Depending on manufacturer and velocity, I've found values from a low of about 0.092 to a high of 0.158 for the subsonic, and from a low of 0.104 to a high of 0.141 for the supersonic rounds.... Then we have the Sierra chart, which looks more mathematically calculated than measured, which says subsonic 40 gr. has a BC of 0.169, and supersonic is 0.145.... If I throw out the few high and low ones, the range is a lot narrower, subsonic runs about 0.125 to 0.150, and supersonic from 0.120 to 0.140.... When you consider how similar in shape the .22LR bullet is from brand to brand, I'm surprised the variation is that wide.... In any case, I'm interested in Subsonic, and I'll choose the lowest value from that range of 0.125.... Now, using the theory from the previous post, let's see what happens if we scale that .22LR bullet up and down to the other calibers.... Since the SD and BC are proportional to caliber, this is what we get....

http://i378.photobucket.com/albums/o...ps75583096.jpg

Again, in tabular form, here is the same information....

http://i378.photobucket.com/albums/o...psc8116c9b.jpg

How do these values compare with some known designs that are somewhat similar in weight and shape?.... Well, the 158 gr. Lee RN in .357 has a BC of 0.207.... Their 120 gr. RN in .308 cal has a BC of 0.163.... The 340 gr. in .45 cal is only 0.211, but it has a flat nose.... I think those are enough examples to show that the method is valid.... One other cool thing about the chart is that you can tell at a glance what weight a .22LR bullet would be when scaled up to other calibers.... For me that is an interesting piece of information when I'm wondering what bullet weights might be worth trying in various calibers.... It is interesting how many of the common bullet weights gravitate towards being similar in proportions to the .22LR bullet....

Bob

Just another quick post to give you an idea of the minimum twist rate required to stabilize bullets of the same shape and proportions as a .22LR bullet in other calibers.... One thing most people don't realize is that for a given shape, the required twist rate is the same, measured in CALIBERS.... Therefore in inches, the length required for one revolution doubles if the calliber doubles.... I started with a 16" twist for the .22LR as we know that is the industry standard, and it works well, both subsonic and supersonic.... Just to be sure, I ran it through the Border Barrels Twist Calculator, and the minimum value for the stability is 1.33, and that is just below Mach 1.... Here is the graph showing the stability factor of a .22LR bullet in a 16" twist....

http://i378.photobucket.com/albums/o...l39_5gr16T.jpg

If we scale the bullet up or down for different calibers, we can expect the same stability as that exhibited by the .22LR bullet above.... Here is a table of the bullet length, weight and minimum twist rate for each caliber....

http://i378.photobucket.com/albums/o...psbb26dd56.jpg

Twist rates slightly faster than shown in the table are unlikely to hurt the accuracy.... but if they are slower, bullet stability, particularly just under Mach 1, may be a problem.... If your bullet is longer than shown in the table, it will likely require a faster (ie shorter) twist to stabilze properly....

Bob