revolutions per minute debate

[goodgrouper]

Yes. I see your point.
Can anyone find some more data on this and provide a link?

[Richard338]

GG, I'm surprised to hear that you found conflicting info. Classical physics is well understood. The best book I've found is McCoy's book on Modern exterior ballistics. I work in science, not in this area, so this doesn't make me an expert, but I was able to read and understand McCoys book as well as the next guy.
Your original question was "will the bullet spin more or less than 4 1/2 times in the 786th yard". The answer is MORE. I think it is easy to imagine the translational velocity decaying more quickly than the rotational. The reason that they call 6 DOF calculations six degrees of freedom is because there ARE 6 degrees of freedom. This means that one component of the velocity doesn't have to be fixed by one component of the rotational freedom.

[Buffalobob]

RPM

We will shoot a 50 gr bullet with a BC of .251 from a 220 Swift with a 1:8 twist 36 inch barrel at two different velocities 4000 fps and 3000 fps. These bullet will be sprinkled with magic faery dust to prevent them from going subsonic and getting 4fkdHrn upset with us.

At time T=-0.??? and X=-1 the bullet is at rest in the chamber. The trigger is pulled and the bullet begins to accelerate down the barrel. At Time T= 0.0 and X=0.0 the bullet reaches the end of the barrel where it is now traveling at V=4000fps and has an RPM of 360,000 and a RPD of 1.5 Revs per foot

Quickly we do this again and shoot the downloaded round and at Time T=0 and X=0 it exits the barrel with V= 3000 fps and a RPM of 270,000and a RPD of 1.5Revs per foot.

We quickly run down range and observe the rounds as they go by at 100 yards

The first round now has a velocity of 3532 fps, Rpm is 360,000 = 6000RPsec, RPD =6000RPS /3532 fps= 1.698 Rev per foot
The second round has a velocity of 2615 fps, RPM is 270,000 = 4500RPS, RPD =4500/2615 = 1.72 Revs per foot.

Having recorded our data we turn and sprint down to 200 yards and observe the two bullets going by

First bullet has a velocity of 3112fps, RPM is 6000 RPS RPD = 6000RPS/3112 FPS = 1.92 Revs per ft

Second bullet has a velocity of 2247fps, RPM is 4500 RPS, RPD = 2.00RpFt

Like roadrunner with Wiley Coyote in pursuit we swiftly relocate ourselves at 300yds and record our data.

First bullet V= 2726fps, RPS = 6000 and thus RPD = 6000RPS/ 2726 fps = 2.2RpFt
Second bullet V= 1910fps RPS = 4500 and thus RPD = 4500Rps/ 1910 fps = 2.356revs per foot

Hustling on down to 400 yds we observe
First bullet V = 2349 fps RPS = 6000RPS and RPD = 6000rps/2349fps = 2.55 revs per ft
Second bullet V = 1589 fps, RPS = 4500RPS and RPD = 4500rps/ 1589fps = 2.83rev per ft

From here we head for the next observation point but have to make a slight detour around the rattlesnake.

500 yards

First bullet V= 2003fps, RPM = 6000rps and RPD = 6000rps/2003fps = 2.99 Rev per ft
Second bullet V= 1313fps, RPM = 4500 rps, and RPD = 4500rps/1313fps = 3.43 Rev per ft

Just like superman, we are faster than a speeding bullet so we head on down range

At 600 yards

First bullet V= 1679fps, RPM = 6000rps,and RPD = 6000rps/1679fps = 3.57Rev per ft
Second bullet V =1114fps, RPm = 4500rps and RPD = 4500rps/1114fps = 4.04Rev per ft

Now then because we have been drinking a lot of beer, we stop and pee on a bush and the bullets get to a 1000 yards before we can get zipped up and on down range.

At 1000 yards we observe the following

The first bullet has a velocity of 934fps and RPM is still 6000RPS thus the RPD = 6000RPS/943fps = 6.36Revs per foot

After waiting awhile the second bullet finally comes by and it has a velocity of 796 fps and a RPM of 4500RPS thus the RPD = 4500RPS / 796fps = 5.65revs per foot traveled.

We are very perturbed because we note that somewhere between 600 yards and 1000 yards the faster bullet is now turning more revs per foot than the slower bullet. We suspect that GoodGrouper has set us up with a trick question. Somewhere in the vicinity of 800 yards the two bullets will actually have the same revs .

We are also mad because we are a long way away from our beer.


Now then we are hot and tired from all that running so we drag ourselves back to our 429SCJ mustang and get some more beer. It occurs to us that maybe the spin decays with time and distance so we can make a few crude calculations to see what might happen. Being as we are now semi drunk we will assume spin decay is related to the time bullet spins. So at 1000yards
First bullet time of travel = 1.5 seconds and it has turned 1.5 X6000Rps = 9000 revs

Second bullet time of travel = 2.13sec and has turned 2.13sX 4500 rps = 9585 revs.

So we see the slower bullet would have more decay by the time it reached 1000 yards and would therefore be turning even fewer revs per foot than the faster bullet assuming friction acts on each rev the same for both bullets.

Having solved this weighty problem we decide to call it a day when we notice the dark puddle under the engine and bending down we perceive we have knocked a hole in our oil pan by driving off road with our mustang. Taking out our cell phone we see that there is no reception. Going to the cooler we find we are out of beer and the dam ole rattle snake has crawled under it and bites us on the leg. We decide to take a leak and get ourselves hung in the zipper. Some times it just doesn’t pay to get out of bed.

[ricka0]

GG writes: [ QUOTE ]
It seems that there are several reputable sites that give conflicting info on this subject. I believe that it is all theory and no one has actually devised a way to "capture" a bullet at long range on slow mo video to see if it is still spinning the same rpd's as it was when it left the muzzle!
I found this:
RPD increases
Scroll down to where it says, "some caveats"


[/ QUOTE ]

My background is MS in applied math specializing in numerical solution of PDEs. I used this in CFD (computational fluid dynamics) as an applied mathematician at Boeing. I can't say I'm an expert on supersonic calculations as all the work I did was commercial airliner (sub-sonic). I could check with my pdh pals who do super-sonic/boundy layeer/turblent flow work, but I don't see where there is any difference in opinion. The ref you site looks very accurate to me
[ QUOTE ]
Now consider a bullet chronographed at about 3000 f/s muzzle velocity fired from a rifle with say a 10" twist. It is rotating at around 3600 revolutions per second (216,000 rpm). Let the flight velocity decay to 2000 f/s. Now what is the bullet rotational speed? It doesn't fall off much because the only things slowing it down are inertia and skin friction drag which is pretty low, so the rotational velocity is only slightly slower than 3600 rps

[/ QUOTE ]

The statement could be made more precise.
For axial symmetric projectiles with angular laminar flow (smooth bullets), the ratio of rotational drag to translational drag is > 10^n ( I don't know, maybe 100,000) in the supersonic range.

Even with pulled bullets with surface marks (that have fairly high turbulent skin friction, the ratio is still very high)

If you provide references to conflicting sites I would be happy to review them.

[LB]

The only thing I see that has not been nailed down is the imprinted rifling marks on the bullet, necessary to impart the spin in the first place, but they appear to be a mechanical brake, of sorts; in free air. I would think that the muzzle RPS would actually degrade enough at a thousand yards, so that, perhaps.....

[ QUOTE ]
It doesn't fall off much because the only things slowing it down are inertia and skin friction drag which is pretty low, so the rotational velocity is only slightly slower than 3600 rps


[/ QUOTE ]

....the above may not be perfectly true?

Am I way off base? Skin friction drag, wise?

Good hunting. LB

[4ked Horn]

We all seem to know how much I love supersonic bullets. [img]/ubbthreads/images/graemlins/wink.gif[/img]

During the time the bullet is supersonic the shock wave coming off the bullets point will cause an area of reduced air density near a bullet body ( which is why a boat tail gives very little benefit to bullets in SS flight) so the drag of the rifling groves would still be quite small (nearly 0) untill the fairy dust was all blown away and the bullet came back from the "spirit world" and flew subsonic again.

[ricka0]

Maybe that's what changes the RPF. I thought buffalobob was pulling our legs with his data, so a quick check with Shoot V3 and excell shows he's not. I posted the excell data at Buf Bob's 220 Swift RPF

Sorry about the inconvient format, this was just a 15 minute Excel upload to one of my sites. RPF tab (bottom) gives Rev Per Foot vs. Velocity and is what we would expect. Sheet1 is just the boring data you can review (differs somewhat from BB's) Sheet2 shows the counter-intuitive transtions to lower RPF - probably due to going sub-sonic

If somebody will post Kirbys 7mm with a good (projected) wildCatCullets.com pill I'll post that data to 1000 yards.