External ballistics

WestKentucky · Jun 12, 2020

It is easily understood and accepted that a bullet exposed to wind resistance will gradually lose velocity, and at or about the point of becoming subsonic the bullet often destabilizes and accuracy falls apart. What I have never heard is any data on rotational force and if that force is maintained or gradually bled off as the bullet flies.

Maybe my explanation doesn’t make sense...
a bullet leaving a barrel at 3000 FPS from a barrel with 1-12 twist rotates at 18000 rpm at the end of the muzzle. At 200 yards down range, is is still at 18000 rpm or has it dropped? I would assume so. Is the loss of spin rate similar to the loss of linear velocity?

Walkalong · Jun 12, 2020

It has no other choice.

LoonWulf · Jun 12, 2020

From my understanding rotational velocity dosent drop as fast. Which is why changing launch velocity, to simulate distance, in bullet testing dosent work quite right.

I dont know much beyond that, but id GUESS that the rotational velocity wouldnt necessarily corelate to the bullets loss in travel velocity.

Allen One1 · Jun 12, 2020

The rotational rpm and velocity of the bullet would be slowing during the entire flight of the bullet. The bullet flight is not done after it goes subsonic there is a lot of turbulence during the transition from transonic to subsonic but after that the bullet will re-stabilize and becomes more predictable. That is how they are shooting a 6.5 Creedmoor 2 miles.

Texas10mm · Jun 12, 2020

You can't have one without the other.

To figure bullet rpm use this formula

(Velocityx720)/twist rate.

LoonWulf said:
From my understanding rotational velocity dosent drop as fast. Which is why changing launch velocity, to simulate distance, in bullet testing dosent work quite right.

I dont know much beyond that, but id GUESS that the rotational velocity wouldnt necessarily corelate to the bullets loss in travel velocity.

Ya must have failed both math and physics.

Kleanbore · Jun 12, 2020

Texas10mm said:
Ya must have failed both math and physics.

The question was about the relationship between the loss of angular velocity and the loss of linear velocity during flight, and how slowing through the transonic range might affect that.

Texas10mm · Jun 12, 2020

WestKentucky said:
It is easily understood and accepted that a bullet exposed to wind resistance will gradually lose velocity, and at or about the point of becoming subsonic the bullet often destabilizes and accuracy falls apart. What I have never heard is any data on rotational force and if that force is maintained or gradually bled off as the bullet flies.

Maybe my explanation doesn’t make sense...
a bullet leaving a barrel at 3000 FPS from a barrel with 1-12 twist rotates at 18000 rpm at the end of the muzzle. At 200 yards down range, is is still at 18000 rpm or has it dropped? I would assume so. Is the loss of spin rate similar to the loss of linear velocity?

Kleanbore said:
The question was about the relationship between the loss of angular velocity and the loss of linear velocity during flight, and how slowing through the transonic range might affect that.

Not as I read it. The question is does the bullet lose RPM when velocity drops. The answer is yes. The two go hand in hand.

Since the rotation speed is directly connected to the velocity. Of course we're assuming that nothing stops the forward velocity while leaving the rotational velocity.

The bullet can't have the velocity of the bullet drop by 1/3 without having the angular velocity drop by the same.

Middletown · Jun 12, 2020

I have wondered the same thing. By the way I calculate the rotational RPM's 3,000 FPS and 1/12 Twist would be 180,000 RPM's. Probably not a small thing. I had always heard that there is some turbulence introduced when going sub sonic which de-stabalized the bullet to some degree. Interesting subject and i would hope someone can give us some actual test data. Bullet design would have to have an effect one way or the other.

WestKentucky · Jun 12, 2020

Texas10mm said:
Since the rotation speed is directly connected to the velocity. Of course we're assuming that nothing stops the forward velocity while leaving the rotational velocity.

Well, is it? Linear velocity is being hampered by a head on resistance aka friction against the air it’s passing through. Rotational velocity is hitting that same wind, but the bullets aerodynamics are changing the shape and density of the air around it, but I don’t really know how that would effect rotational velocity loss. You can stop a bullets forward motion and it still be rotating, also seems as if you could stop rotation and it still be traveling forward. But in flight, does spin slow at the same rate as linear velocity. My guess is that no it doesn’t, but I don’t know the answer to that, and it would be really hard to figure it out as well... you can shoot through a chronograph, but how do you measure spin down range while still in flight??? Same question of physics works for footballs, golf balls, bullets, baseballs, but the aerodynamic profile seems like it would change things significantly, also the direction of rotational axis could easily change things a lot. Maybe we could do a large scale experiment which is easier to see and use the data to try and answer the question... who has a parrot gun, and who has a really really nice high speed camera.

Kleanbore · Jun 12, 2020

Texas10mm said:
Not as I read it. The question is does the bullet lose RPM when velocity drops. The answer is yes. The two go hand in hand.

The question was

WestKentucky said:
Is the loss of spin rate similar to the loss of linear velocity?

Texas10mm said:
Since the rotation speed is directly connected to the velocity.

In the barrel.

Texas10mm said:
The bullet can't have the velocity of the bullet drop by 1/3 without having the angular velocity drop by the same.

Do you have basis for that assertion?

Once the bullet has left the muzzle the linear velocity no longer controls the angular velocity. They are independent, and are acted upon by different forces.

You said something about math and physics....

Chaparral · Jun 12, 2020

WestKentucky said:
Well, is it? Linear velocity is being hampered by a head on resistance aka friction against the air it’s passing through. Rotational velocity is hitting that same wind, but the bullets aerodynamics are changing the shape and density of the air around it, but I don’t really know how that would effect rotational velocity loss. You can stop a bullets forward motion and it still be rotating, also seems as if you could stop rotation and it still be traveling forward. But in flight, does spin slow at the same rate as linear velocity. My guess is that no it doesn’t, but I don’t know the answer to that, and it would be really hard to figure it out as well... you can shoot through a chronograph, but how do you measure spin down range while still in flight??? Same question of physics works for footballs, golf balls, bullets, baseballs, but the aerodynamic profile seems like it would change things significantly, also the direction of rotational axis could easily change things a lot. Maybe we could do a large scale experiment which is easier to see and use the data to try and answer the question... who has a parrot gun, and who has a really really nice high speed camera.

I like this response. The formula above gives the velocity vs rpm at the muzzle, but after that the air resistance against, and its affect on, forward velocity and rotation are not necessarily proportional. I have seen a football thrown against a strong headwind - the ball’s forward motion stopped completely, but it was still rotating. I think the relationship between velocity and rotation, after leaving the muzzle, depend on the relative aerodynamic resistance to rotation and forward velocity, i.e., things like bullet length, diameter, density, and profile.

jmorris · Jun 12, 2020

and at or about the point of becoming subsonic the bullet often destabilizes and accuracy falls apart.

Transonic situations do odd things because the object might me moving below the speed of sound but the air moving out of its way is sped up to supersonic speeds.

If you want to see what it looks like on a bullet start around 4:40 in this video.

jbm · Jun 12, 2020

WestKentucky said:
It is easily understood and accepted that a bullet exposed to wind resistance will gradually lose velocity, and at or about the point of becoming subsonic the bullet often destabilizes and accuracy falls apart. What I have never heard is any data on rotational force and if that force is maintained or gradually bled off as the bullet flies.

Maybe my explanation doesn’t make sense...
a bullet leaving a barrel at 3000 FPS from a barrel with 1-12 twist rotates at 18000 rpm at the end of the muzzle. At 200 yards down range, is is still at 18000 rpm or has it dropped? I would assume so. Is the loss of spin rate similar to the loss of linear velocity?

(3000 ft/sec)*(60 sec/min)*(1 revolution/12 inches)*(12 inches/foot) = 180000 RPMs, not 18000.

Yes, the bullet rotation slows down as it goes down range. There is a coefficient for this (analogous to the drag coefficient) called the Spin Damping Moment Coefficient. McCoy's book lists it as Clp. I remember somewhere McCoy saying that a good approximation to Clp is the 1/4 of the component of skin friction to CD. The bullet does slow down faster in velocity than it does in rotation which is why bullets become more stable as they go down range.

Ed Ames · Jun 12, 2020

I think jbm’s answer is about as good as you can get in a paragraph.

I did want to emphasize, because a few people had linked velocity and spin: Linear velocity and spin are directly related only while in the rifled barrel.

Once the bullet leaves the barrel, the two are only loosely related. A supersonic bullet will have different drag that a subsonic bullet. However, a bullet can drop to zero linear velocity and still retain most of its spin. For example, if you shot a bullet straight up, at the top of the trajectory the bullet will have zero forward linear velocity but can easily still have enough spin to stay stabilized for at least part of the descent (and therefore retain a nose-up attitude).

jmorris · Jun 12, 2020

However, a bullet can drop to zero linear velocity and still retain most of its spin.

That’s no lie.

JumboJVT · Jun 13, 2020

Chaparral said:
I like this response. The formula above gives the velocity vs rpm at the muzzle, but after that the air resistance against, and its affect on, forward velocity and rotation are not necessarily proportional. I have seen a football thrown against a strong headwind - the ball’s forward motion stopped completely, but it was still rotating. I think the relationship between velocity and rotation, after leaving the muzzle, depend on the relative aerodynamic resistance to rotation and forward velocity, i.e., things like bullet length, diameter, density, and profile.

This. Angular velocity and linear velocity are only proportional when the two are mechanically tied together by the rifling within the barrel. Ain't necessarily so beyond the muzzle so the question seems valid to me.

JumboJVT · Jun 13, 2020

Texas10mm said:
Not as I read it. The question is does the bullet lose RPM when velocity drops. The answer is yes. The two go hand in hand.

Since the rotation speed is directly connected to the velocity. Of course we're assuming that nothing stops the forward velocity while leaving the rotational velocity.

The bullet can't have the velocity of the bullet drop by 1/3 without having the angular velocity drop by the same.

Why? The mechanical connection with the rifling is what imparts the rotation. After that connection has ended, why do you assert two still have the same relationship as determined by the twist? A top spins in place: lots of angular velocity, no linear velocity...but it still spins.

Aletheia · Jun 13, 2020

WestKentucky said:
I would assume so. Is the loss of spin rate similar to the loss of linear velocity?

No. The spin rate will, of course, slow gradually due to the friction of the air on the surface of the bullet as it spins, but the rate of velocity loss is very much higher than the rate of spin loss, as lots of videos of spinning bullets caught by ice will show you if you look for them. The "drag" that is slowing the spin rate is very weak compared to the resistance to forward motion the bullet experiences as soon as it leaves the rifle.

Bfh_auto · Jun 13, 2020

jmorris said:
That’s no lie.

I had know idea it worked like that. I thought the friction from the air would act like a brake to the rotational forces also. Kind of like dragging your foot on a merry go round.
I've only taken high school physics though and that was years ago.

Ed Ames · Jun 13, 2020

Bfh_auto said:
I had know idea it worked like that. I thought the friction from the air would act like a brake to the rotational forces also. Kind of like dragging your foot on a merry go round.
I've only taken high school physics though and that was years ago.

You are right, it does!

To give you another way of thinking about it: A bullet has kinetic energy in two ways. Linear velocity of the whole thing, and spin. You can stop either without necessarily affecting the other.

The “brake force” for linear velocity is based on factors like linear speed, frontal area, bullet shape, and the direction it is pointed compared to the direction of travel.

The “brake force“ that slows down spinning is based on factors such as RPM, bullet diameter, atmosphere, surface texture, and to some degree whether the bullet is supersonic....but not really to the bullet’s linear speed through the air.

I use “brake force” to go along with your foot on the merry go round analogy, but there are other terms like “drag” that mean basically the same thing and would be more common in this context.

CapnMac · Jun 13, 2020

We have to remember that angular momentum, in this case, spin, is going to be conserved, per Newton's 2nd.

Air becomes very laminate, there's not a lot of drag on the projectile's spin, compared to the drag, longitudinally, in flight. Which is especially true in supersonic flight, where there's a high-compression shockwave coupled to the projectile. Which lets the projectile spin in a lower-pressure area than if it were subsonic.

WestKentucky · Jun 13, 2020

jmorris said:
Transonic situations do odd things because the object might me moving below the speed of sound but the air moving out of its way is sped up to supersonic speeds.

View attachment 922856

If you want to see what it looks like on a bullet start around 4:40 in this video.

That video was pretty awesome. It also shows a whole lot at the end with the revolver which is just icing on the cake.

hdwhit · Jun 14, 2020

It is easily understood and accepted that a bullet exposed to wind resistance will gradually lose velocity, and at or about the point of becoming subsonic the bullet often destabilizes and accuracy falls apart. What I have never heard is any data on rotational force and if that force is maintained or gradually bled off as the bullet flies.

With respect to your question (i.e. retention of "rotational force" - whatever that means) you should ignore pretty much everything that has been posted so far.

"Wind resistance" and "Air resistance" are two different concepts as is the transition of a projectile from supersonic to sub-sonic velocity. You are mixing an elementary understanding of conventional dynamics with a very different understandings of aerodynamics (which is largely governed by differential equations). The difference, in the end, is whether or not simple Calculus or mere advanced mathematics are involved.

Mr. Zorg · Jun 14, 2020

Since all such relationships and equations that are used to describe and model them are time dependant with regard to motion and position, they are all differential equations. The complexity of such equations are not necessarily all the same. For example, acceleration and deceleration are functions of time to the minus two power, momentum and velocity ate functions of time to the minus one power.

At what point are the lines drawn between calculus, advanced mathematics, and basic mathematics?

jmorris · Jun 14, 2020

I had know idea it worked like that. I thought the friction from the air would act like a brake to the rotational forces also.

Oh, I didn’t say that, rather pointing out that the linear velocity could be completely stopped yet the bullet could still retain spin. It had very little exposure to friction from the air though.

External ballistics

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