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My table of drag coefficients are matched up with mach number, not velocity. This gives a max height of about 1300 meters with a total time of about 34 seconds. I will use a mass of 14 grams and an initial velocity of 760 m/s.

Let me try the one with the lower muzzle velocity, but higher mass. What if I go with the smaller area value?īetter, but still does not agree? I could try a different bullet.

Well, that doesn't agree with the MythBusters' model. Here is a plot of the vertical position of the bullet as a function of time, shot straight up. Or rather, what would be the percent difference between the surface and 3000 meters up? It is 99.9% the value at the surface. What would the value of g be at 4000 meters? (the MythBusters said the bullet went 10,000 feet - about 3000 meters). Where G is the universal gravitational constant, m E is the mass of the Earth, R E is the radius of the Earth, and h is the height above the surface. Of course the gravitational field is not constant with height, but is it close enough? The real gravitational field (g) is: Using this expression (which I am not showing because it is boring), I can plot density as a function of altitude. Here is an explanation of the density with altitude calculation. If the MythBusters are correct and the bullet goes 10,000 feet high, then I will need to look at the change in the density of air. Good thing I am making a computer do all the work. Well, there is a way to test which is right - but I will start with the one from the terminal velocity. I guess these are kind of in the same ball park. Wikipedia lists the bullet as having a diameter of 7.823 mm - this would give an area of 1.9 x 10 -4 m 2. Using the known values for mass, g, C (from the table) and the density of air (at sea level), I get an area of A = 3.45 x 10 -4 m 2. At terminal velocity, the weight = air resistance so: So, that is C, I can find the effective area by looking at terminal velocity. I will just use the table above to make variable drag coefficient. In this case, there is this very useful table:Īpparently, there is lots of debate about the air drag of a bullet. It is not safe to assume that the drag coefficient (C) is constant with speed. The problem is that bullets go really fast. If I want to model the air resistance, I can use the following: Muzzle velocity = 880 m/s (actually, this is just the fastest - the slowest is 760 m/s and 14 g - not sure which the Mythbusters used).Here is what I found ( wikipedia, of course) If you want more details on numerical calculations, check out this basic post. Calculate change in position (assuming constant momentum).Calculate change in momentum (assuming constant force).With a small enough time, this is true enough. During these steps, I can pretend (assume) that the force is constant. Break the motion into tiny little time steps.I don't want to go into the details, but in case you forgot, the numerical calculation works this way: What about the change in gravitational field of the Earth as the bullet moves up?.What about the density of air? Do I need to take that into account?.What is the drag coefficient of a bullet?.Does the normal model of air resistance work (being proportional to v 2)?.But in this case, there are some other things to consider.

So, this problem seems simple enough - right? I have actually done this before ( here is an example of the air resistance on a football). This means that moving up bullet will look different than going down. I made two force diagrams because the air resistance force is going to be in opposite direction as the motion. After the bullet leaves the gun, it has forces acting on it like this: The basic plan is to use a numerical calculation to model the motion of a bullet. This is actually similar to Hancock throwing a boy. Oh - also, they measured how far a 9mm bullet penetrated into the dirt (but they couldn't find the. 30-06 have a terminal speed of about 100 mph. A 9 mm will go 4000 feet and take 37 seconds to come back down.Īdam was also able to experimentally determine that both the 9 mm and the.30-06 cartridge will go 10,000 feet high and take 58 seconds to come back down Here is what Adam said about the bullets: What I will do instead is make a numerical calculation of the motion of a bullet shot into the air. I am not going to shoot any guns, or even drop bullets - that is for the MythBusters. If you didn't catch that particular episode, the MythBusters wanted to see how dangerous it was to shoot a bullet straight up in the air. You know I like the Mythbusters, right? Well, I have been meaning to look at the shooting bullets in the air myth for quite some time.