If you scale up a bullet to another calibre, the ballistic coefficient goes up.
Is there a formula for working it out, or a computer program/astrological guessing method available to do it?

Karl.

[ 12-06-2003, 10:55: Message edited by: Karl ]

When you scale up a bullet, you scale up both diameter and length to have the same shape on a bigger scale...You multiply by the difference in the diameters squared; and the length by the difference in calibers to get the scaled up weight...Example-- 150 gr 30 cal up to 50 cal--
.3 squared is .09--.5 squared is .25--so 150 times
.25 over .9 = 416---416 times .5 over .3 =
694 gr bullet in scaling up a 150 gr 30 cal to
50 cal...This gives you the same shape in the length..Ed.

Ed I was wondering though if it is possible to have a stab at what the new Ballistic coefficient might be.
For eample the 50BMG bullet has a much higher BC than the 30 it was scaled off.
Is there anything to work this out or is that real tricky engineering maths?

Karl.

Karl-The ballistic coefficient of a 150 gr
30 cal compared to a 700 gr 50 cal would be almost double.A 30 cal spitzer 150 gr will be
.360 coeffient and a 700 gr 50 cal is .660. Both
flat based.

Coefficient is found by following math.it is the
sectional density times the form factor(that is
a term for its nose shape).From Powleys chart the 150 gr form factor is 1.6.For 50 cal scaled up it will about 1.72.
Math on these is as follows--Secional Density
times 1.6 on 30 cal and times 1.72 on 50 cal.. Sec Density is bullet weight divided by diameter squared.

For 30 cal--150 gr divided by 7000 grs/lb, divided
by .308 squared , all times 1.6 = .360

For 50 cal--700 gr divided by 7000 gr/lb,divided
by .510 squared, all times 1.72 = .660.

Now you add a boattail and a 100 grains to that 50
cal, and BC is about .950...Ed.

Thanks Ed.I have been playing around with numbers for big lathe turned solids.

Karl.

i dont know what this add's over what Ed said.

I recall that in windtunnel tests, and then powered MODEL test, that scaled up/down aircraft reacted very differently than expected. For instance, there is a minimum surface area that the control surfaces had to have to be remotely effiecent.

If you look at some of the serious f-18 or other fighterjet flying RCs, you'll see outsized control surfaces. This is not to create extra control, but to maintain flight characteristics, roll/clib aspects, etc, in relation to, i guess, weight.

and now I have exhausted my knowledge of aerodymanics

jeffe

jeffe

A problem with scaling "up or down" is that the ratio of surface area and volume change.....hence a grain of sand blows about in the the wind but a large piece of sandstone does not move.

Consider a cube with 2 inch sides. It presents a side of 4 square inches and has a volume of 2 X 2 X 2...8 cubic inches.

Now let us scale it up to a cube with sides that are 10 inches.

It now presents a side that is 100 square inches, that is, 25 times greater than the cube with 2 inch sides.

However, its volume is 10 X 10 X 10 = 1000 cubic inches which is 125 times greater than the 2 inch cube.

What this means in terms of bullets, which I think Ed has already mentioned, is that when we scale a bullet up we have a bigger sectional density........as is the case with the 10 inch cube as compared to the 2 inch cube.

To go two steps further:

1) If all else is equal the bigger bore can always use a bullet of higher sectional density.

2) If all else is equal the smaller bore can always use a bullet of lower sectional density.

If we try and use bullets in a 2 inch gun with the same sectional density as 50 grain 224 we finish up with a bullet that is like a disk.

If we try and use bullets in a .224 gun with the same sectional density as 3 pound (or whatever) 2 inch gun we finish up with a bullet that is like a piece of wire.

Mike

Extremely interesting and informative. Thanks, gents.