Dot Physics

I have been wanting to look at this whole curved bullet thing, but I wasn’t sure how to approach it. In case you are familiar with the myth, this is from the movie WANTED (which I did not see). Apparently, some people learn how to make bullets curve by moving their gun. Here is a shot of a bullet curving in front of someone.

i-7d7c3292ea9bd42721ccf166ab28604d-you_tube_wanted_fun.jpg

Maybe the picture doesn’t do the clip justice, but it is enough for you to get an idea. Before I do an analysis, this reminds me of a great educational activity. In the activity, you give groups of students a full sheet of paper with lines that look something like this:

i-a6f787429e6dc907d67929992bc9cee5-paper_curves.jpg

You also give the students a ball, like a racquet ball or something. The goal for the students is to make the ball roll through the curve without hitting the lines. This CAN BE DONE. Students then proceed to try a whole bunch of different things, none of them work. It shows the common idea students have that an object can somehow “remember” motion. Give it some curving motion and it will kind of continue with that.

But I said it could happen! That you can get the ball through the curve without hitting the lines. Yes, there is a trick. Maybe you know the answer, but I am not going to give it away. I don’t know where this activity originally came from, but I first saw it done by Bob Beichner as part of the SCALE-UP project.

Ok, back to the bullet. So, why would a bullet curve? For something to change direction of motion, there must be a force acting on it. Instead of calculating the motion of a spinning bullet or something, I am just going to determine the force needed to make a bullet curve. That force can then be compared to other forces like gravity and air resistance.

How does a force make an object curve? If you want to think about it in terms of force and acceleration, the acceleration of an object moving in a circle is:

i-f68a2d7ff870197c8831cc7f29d01e1c-a_circular.jpg

The negative and the r-hat indicate that the acceleration is towards the center of the circle. So, what do I need to calculate this force to move in a circle?

  • The radius of the circle. I will talk about this in a moment.
  • The speed of the bullet
  • The mass of the bullet
  • Maybe the cross sectional area of the bullet and the coefficient of drag if I want to compare this force to air resistance.

i-0037c3cb16f1bcb33d8639f6bdad42fe-curve_path_12.jpgFor the circle, first I am using a circular path just because it is a little easier. I know the bullet might be able to do something else weird, but I am ok with that. How do I estimate the radius for a bullet? Well, in the WANTED scene, the bullet actually does two things. First it curves away from the person in the middle and then curves back to the target behind her. If I just look at the first curve, I can estimate the distance from the person and the deflection. From this, I can calculate the radius of the circle. Here is a picture.

So, if I estimate d and s I can get the radius of the circle. Here is the location of the two points on a circle that is centered at the origin.

i-7963c9dc369920a632f1ddb41809f0c2-circle_size_.jpg

So, the coordinates of the two points would be:

i-2b3fa7718dc1c37bb946f9b77224dc7b-points.jpg

And these would have to satisfy the equation for a circle:

i-e39f3b8bb3e626b9ba82d6810cd80927-circle_eq.jpg

The first point clearly works. Plugging in the second point for x and y:

i-ad68cdec3cd0b3e86a5182a8ac6b383e-solve_for_r.jpg

Now, what about the speed and mass of the bullet? There are so many different types of guns and bullets, I will just pick something. I will just use the info from the bullet in a barrel

post. In that, there was a 9mm fired into a barrel. The round has a mass of 8 grams and a velocity of 358 m/s. If you want to use different numbers, you can enter what you like in the embedded spreadsheet. The other two estimates are for d and s. Let me say d = 5 meters and s = 0.15 meters.

So, from my estimations the force needed to be exerted on the bullet is significantly larger than either the gravitational force or the air resistance force. But, clearly it was fake from the beginning.

Comments

  1. #1 Uncle Al
    June 19, 2009

    http://en.wikipedia.org/wiki/Magnus_effect

    OK for fuzzy tennis balls hit with English, rough-surfaced baseball (seams) traveling 59 feet from pitcher’s mound to home plate, sliced golf balls. Silly for a transsonic bullet flying a few yards. There isn’t enough time.

    Musket balls substantially wander during long flight. The US military has programmable exploding bullets that in demonstrations do controlled aerial maneuvers – XM25 rifle – notable for their absence from battlefields.

  2. #2 Rob
    June 20, 2009

    It’s been a while since I saw that movie. They use their minds to make bullets do all sorts of strange things.

  3. #3 Rob
    June 20, 2009

    There was a mythbusters where the used magnets to deflect a bullet. I don’t remember the details, but an analysis would probably make a good blog post.

  4. #4 Uncle Al
    June 22, 2009

    Mythbusters used a train of really big Fe-Nd-B magnets,

    http://www.unitednuclear.com/magnets.htm
    half-way down

    Field divergence rather than magnitude is controlling for steering -but their magnets had broad flat faces. The violently spinning (~10^5 rpm) and translating bullet has Lenz’ law inductance issues, plus it is a copper jacket on a lead core. It would have been interesting to have a train of big magnets as such, as a Halback array, and with a gapped double layer sporting soft iron pyramidal pole pieces re Stern-Gerlach experiment geometry.

    http://en.wikipedia.org/wiki/Halbach_array
    http://kwelos.tripod.com/sternact.gif

  5. #5 Rhett
    June 22, 2009

    @Uncle Al,

    Good point. We should petition the mythbusters to redo this one with teh Stern-Gerlach setup.

  6. #6 Sapceman's Hairdo
    June 24, 2009

    I cannot believe I stumbled upon this blog. Cool stuff. I think I’m gonna have a lot of fun here–and everyone is so knowledgeable. It’s kind of intimidating, but in a good way.

  7. #7 eduard1
    July 15, 2009

    In Mythbusters s7 they put the curving bullet myth to the test and the result is that it is definitely impossible to curve a bullet.Just leave it at that and dont think that someone can actually curve a bullet,because no one can!

  8. #8 annoymer
    July 21, 2009

    if you fire a bullet at a blackhole, it will definitely curve :P

  9. #9 RC
    July 25, 2009

    i suppose this may not be a relative idea but am thinking outa the box here if a bullet is fired but a bullet mechaniced to be control kinda of like a plane is controlled by am not sure what there called but all call them flaps for now, it can be possible to control a bullet to move in difrent direction but a computer would have to take control since the human mind is not fast enoghe to move any thign the speed of a bullet i gess it can be curved.

    but i u think its stupid then its stupid

  10. #10 Pete
    August 27, 2009

    if the projectile is a tiny little bit off balence it might curve a bit in a spiral as it rotates. I’ve seen this while shooting arrows at kangaroos…

  11. #11 Jake
    November 11, 2009

    I’ve thought about this alot, and I’m watching wanted again right now. Here’s what I think.

    All bullets curve downward over long distances. And if you fire a BB from an air rifle, it can definitely do all sorts of weird things. The key is the velocity of the projectile and the vector forces that can be applied to it. A normal bullet from a normal gun is not capable of curving, because its velocity simply overpowers any vector forces that might be applied to it. This is, of course, the result of hundreds of years of technological advancements in guns, the goal of which was to make guns fire accurately over longer distances.

    If, and this is a big if, you could design a gun and bullet with a smaller powder load, and thereby a lower velocity, the vector forces you might apply to it could make an impact on the path of the bullet. Especially if you crafted special bullets (with seams like a baseball, or with a non-centered point).

    The question I have is whether a bullet that you slowed down enough to curve could still attain enough velocity to do damage when it hit a target. Considering the kind of damage that can be done with a very sharp knife blade, even at extremely slow velocities, I suspect it is possible, if you filed down the point of the bullet to a very sharp edge.

    However, creating a gun and bullet that will curve is one thing. Creating a gun and bullet that will curve in a predictable fashion, or one that will fly straight when you want it to and curve when you want it to, is another thing entirely. And I don’t know enough about the forces in question to say how much you could make a bullet curve, either. Again, it depends on what velocity the bullet has when it leaves the barrel of the gun.

  12. #12 Caps Dragon
    December 16, 2009

    Ok if you use a normal pistol its pretty much ruled that it will not be curved. But putting a spin on a musket ball could enable you to curve the bullet and in time you may be able to control it. This is what ive ruled as the only way to “curve” a bullet.

  13. #13 joseph
    May 16, 2010

    what about the myth of the curve

  14. #14 Rhett Allain
    May 16, 2010

    @joseph,

    Didn’t I talk about curves before? Try my posts on grades.

  15. #15 HaleySher
    May 16, 2010

    I am writing an essay for physics and it is due tomorrow. I need help with an intro for my paragraph on curving a bullet. Please help?

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