driftrider

Well, I can certainly say one thing for certain...

Nomercy must have really paid attention during his math classes!!

I actually feel smarter after reading that!

Mike

Bilge

This is good stuff, especially the web site you included. I'm still digesting the info they have. I think the problem arises in the fact that, using your example, a 3000 fps projectile is encountering a 2045 mph head wind. I would think this GREATLY reduces the Magnus Moment. If my thinking is correct, the 2045 mph head wind combined with a 15 mph cross wind would create an effective yaw against the wind of only about 1.3 degrees versus 90 degrees (perpendicular air flow). And as the site says, "The Magnus force vanishes in the absence of rotation and in the absence of a yaw angle." I believe your calcutlations only account for perpendicular air flow. To quote the site further, "The Magnus force is usually very small and mainly depends on bullet geometry, spin rate, velocity and the angle of yaw." This leads me to believe that the head wind (especially in super-sonic flight) nearly negates the Magnus Moment.

The curve ball and the golf ball are spinning on an axis nearly perpendicular to their direction and hence a head wind aproximately equal to their velocity. That's why they encounter a noticable effect. The bullet on the other hand is spinning on an axis parallel to the head wind.

This does raise an interesting question though. In the case of an overstabilized bullet that maintains it's orientation in relation to the plane of the barrel, as the bullet starts to decend toward it's target the effective yaw in relation to the "head wind" would become greater and greater and the Magnus Moment might besome great enough to move the bullet left or right depending on the direction of the rifling.

By the way what number did you use for p? I might have missed it, it's late and I'm tired.

eldeguello

This guy is wrong, of course! BUT, there are a LOT of people who believe this!

A lot of people selling gun stuff are totally ignorant about the subject. For example, the other day I was at the local DICK'S "sporting goods" store looking for a couple of scope mount bases.. (Yeah, I know!) Well, I told the genius behind the counter that I wasnted a specific pair of bases. He started lookijng through his assortment of RINGS!!

I said, "those are RINGS. I need bases." I then had to lead him to the portion of the pegboard where the bases were hung up in little plastic bags. "Oh yeah." says he. "Bases." Believe it or not, he did find the right ones. there were two bases in the little bag, but he tried to sell me FOUR because "it says right here on the envelop that you need two." So I said "but there are two in this envelope, and that's how many I need." he says "Well, it's your gun. If you need another envelope of them, I guess you'll just have to come back." I just laughed and said "yes, I guess so! har, har!!"

eldeguello

Well, a bullet DOES actually drop faster in cold air vs warm air. The reason is that cold air is denser, and therefore provides more resistance to the bullet's passage, thus slowing it down faster. (Think of it as lowering the bullet's B.C. a little.) This means that the trajectory curve will be a little steeper when fired in cold air vs warm air. This is one of the reasons artillery firing calculations include both air temperature and local atmospheric pressure in the variables.

Bilge

After a little sleep and more reading here's what I've come up with:

We've both over looked the fact that the Magnus Moment acts on the Center of Pressure and not the center of gravity. I'm still standing pat on the fact that you don't have a 15 mph perpendicular flowfield but rather a 2000+ mph flowfield that is nearly parallel to the bullet path. As the bullet yaws in respect to the flowfield the Magnus Moment grows in magnitude and changes the yaw because it is acting on the CPM rather than the CG. And to quote another site(http://www.nennstiel-ruprecht.de/bullfly/fig11.htm), "However, the gyroscopic effect also applies for the Magnus moment and the bullet’s axis will be shifted into the direction of the moment. Thus, as far as the conditions of the figure above are valid, the Magnus moment will have a stabilizing effect as it tends to decrease the angle of yaw d." If the CPM is rearward of the CG then the MM will have a destabilizing effect because it will actually increase yaw, eventually causing the bullet to tumble.

Simply put, in the face of the actual flowfield, the Magnus Moment direction is constantly changing in response to yaw and hence is a very important factor in bullet stabilization. So, at no time will Magnus effect lift the entire bullet unless the CPM is behind the CG and the yaw approaches 90 degrees (the point where the MM is at it's greatest magnitude) but at this point the bullet is tumbling out of control and it's time to consider using a new bullet design. Even then the MM is still acting on the CPM and will probably just continue to spin the bullet around the CG in a plane perpendicular to the axis of symmetry.

ColoradoElk

WOW, you guys are pretty smart about this stuff. I just wanted to clarify something. I think the original post asked if the fired bullet actually rises, and the general opinion is that it does not, which I agree with. However, I have read in several long range shooting manuals that explains the rifling of a barrel does affect the point of imact, but does not impart enough force to make the bullet rise, and for a short period of time, offset gravity. What the books clearly say is that over longe ranges, rifling will impart enough "spin" so that the bullet path is a slight arc (left or right) depending on the orientation of the rifling, so it drops from gravity and also drifts (although very slightly) at the same time. Does this make sense???

Thanks,
CE

Bilge

Good point, that plus what DM brought up:

This means if you sighted-in in July in 90 deg weather you'd better check your point of impact at the range closer to hunting season when you might be shooting in 10 degree weather!

Now I'm curious, has anyone got any chronograph logs? What I'm wondering is if the chamber temperature (heating up as the gun gets fired over and over) has a noticable effect on velocity and there by affecting the point of impact. This may also be a factor for sighting in for hunting season because your deer is not going to wait there patiently while you fire off a few rounds to warm up the gun to the same temp it was when you put that final adjustment on your scope...LOL!

Bilge

ColoradoELK, yes it can happen even without a crosswind. The yaw of reprose is most likely the factor when this is obseved.
See:
http://www.snipersparadise.com/wound....htm#yawrepose

Hope this helps.

Nomercy

You are correct that the overall flow field is nearly parallel to the line of flight, however, because it is NOT parallel, I can chose whatever coordinate system I like and apply additive vectors to get the net flow direction (i.e. I take one step forward and one left, I end up moving 1.41steps at 45degrees). So, instead of saying I'm in a 2046mph I can say I'm in a 2045mph head wind with a 15mph cross wind, and have the same effect. In either case, the magnus effect would be virtually the same, because the perpendicular component of the angular flow field is ALWAYS 15mph, whether I say it's 2045.5mph at .46 Seconds of angle or I say it's 2045.45mph head on and 15mph side on.

Accounting for yaw angle isn't necessary if you do this addition. The advantage of it, however, is the ability then to account for the boundary layer buffering and shedding, which I've not yet seen a formula for that doesn't take more calculus to do than I can do in 5min sitting at the computer, and constants for directional drag coefficients or magnus coefficients that would be specific to each individual case.

Also, if I'm reading the figure and text you pointed out correctly (which I think is the same exact figure as one on the site I pointed out above), then the following will happen in my hypothetical 150grn .30-06 bullet...in which the center of pressure WILL be behind the center of gravity, as the relatively large cylindrical body will draw the center of pressure to it, while the center of gravity is shifted slightly forward because of the mass of the tip (assuming that you neglect the density difference in the copper jacket and the lead core, which would shift the Cg rearwards).

This also explains why the magnus force would only temporarily lift a bullet...

The magnus forces would start working, it would lift the bullet, but also turn it to become parallel to the overall flow field (turning your bullet into the wind), this would reduce the magnus lift force considerably...However, it would also be turning your bullet tip INTO the wind, which won't have a net positive effect because of the mass-mass impact of the x-wind and the bullet bluff body...Honeslty, I think there would be no net force in that direction, but more of a torque, so your bullet would become unstable because of the wind and start to gyrate.

So, basically what that figure shows, projectiles will be turned tip wise by a cross wind in addition to their lift, both caused by the magnus effect...this would have a LOT of results, drawing your bullet into the wind (negated by the wind PUSHING back), pointing your bullet into the wind (destabilizing it's flight), and reducing the lift force created by the rotation.

Like I said, no, it's not likely you'll ever see any net positive LIFT due to it, but the force is real, and given the right combination of oddities-which COULD be possible in a hunting environment-it could happen that the magnus force overcome the force of gravity momentarily.

Cut-throat (eldeguello) is correct about the bullets dropping SOONER (fall per foot traveled) in cold air vs. dense air, but I don't really agree with how he said it...

Bullets don't drop FASTER (per time) in cold air than hot, they just don't fly as fast so they drop SOONER (per distance traveled)...Meaning, the rate of fall isn't any FASTER, it's just that they don't travel as far horizontally per second as they would in less resistive hot air...The rate of fall is constant, the gravitational constant, 32.174ft/s.

Truth be told, the rate of fall would be SLOWER in cold air than hot (miniscule amounts) because of the density change...the more dense the air, the more bouyant force it exerts on the bullet...but this is a very small change, so it is over shadowed by the huge increase in drag force which slows the bullet and makes it fall sooner (in feet).

People miscommunicate that because they see their groups hitting lower at 100yrds in December than they did in June...they assume this means their bullet is dropping faster, but this is impossible, since the gravitational constant is a CONSTANT.

It's like the figure Bilge posted earlier, the dropped bullet and the fired bullet---no matter the speed--hit the ground at the same time.....it's just that the bullet in cold air isn't going to fly as far as the bullet in hot air.

Which I'd imagine is often also exaggerated by the fact that many modern powders are temperature sensitive, and will burn more efficiently at higher temps (giving higher pressure and muzzle velocity)...so you've got less resistive air and higher muzzle velocity, cold air shooting sucks.

BarnesX.308

If the guy at the gun shop is reading this, he's scratching his head and going "huh?". He's talking about the picture on the back of the old boxes of shotgun slugs and trying to justify that it's really what the bullet does.