/sci/ - Science & Math

>>11562646
Typo, sorry. That whole line should be [math]
S-ba-ba^2=S\big[(b\tan\theta-ba\cos\theta)/(b\tan\theta)\big]=Sa^2 [/math]. There are no nested trig functions, so BE = b.tan t - b.sin t.cos t
>>11562619
Use trig to find CE. You should easily find it is b.sin t. Similarly, DE is b.(sin t)^2 and FE = b.(sin t)^3 and so on.
>>11562545
>>11562544
Pick [math] \epsilon=f'(a)/2 [/math]. Then by continuity of f' at a, we have some delta where [math] |x-a|<\delta\implies |f'(x)-f'(a)|<\epsilon [/math]. So there's [math] f'(x)-f'(a)<f'(a)/2 [/math] and [math] f'(a)-f'(x)<f'(a)/2 [/math]. Then [math] f'(x)>f'(a)/2 [/math] which is a positive number.
>>11562705
I just think the argument without explicitly writing the series is fun. Of course you can write down the inf sum and realize it is a geometric series.

>>11435056
I'm pretty sure fracture science is outside the scope of rigid bodies.

>>11335753
Basically, you are trying to minimize the drag coefficient of the bullet. The drag coefficient of a body at a specified angle of attack is defined as the ratio of the drag force the object experiences to the dynamic pressure exerted on the area normal to fluid flow. Or,
[eqn] C_d\equiv\frac{F_d}{\rho v^2A/2} [/eqn]
It turns out that this dimensionless coefficient is a complicated function of the geometry of the body (for a bullet it would be a function of the ratio of areas of the fronts to the sides), as well as a function of the speed of sound in the fluid, and something called the Reynolds's number, which in turn is a function of the velocity, density, and viscosity of flow. There's a bunch of different aerodynamic theories that try to explain it, but it's still very hard to find this coefficient from first principles only. Engineers usually end up doing simulations and wind tunnel tests with prototypes to determine it.
Empirically, you want the bullet to be ogival at the front front and tapered at the back, to be long, and to have no sudden changes in curvature or sharp angles elsewhere. I guess ballisticsfags also have something called the ballistic coefficient, but BC sucks to use because it is not a dimensionless quantity.
>it is the only company that uses the venturi effect in order to achieve higher velocity from their bullets, see the weatherby design on the right compared to traditional bullets
I'm not sure that makes any sense. The venturi effect doesn't do anything to dynamic pressure, which is what you are actually concerned with. This sounds like marketing. Also, you can't even see the shape of the bullets in that pic. The shape of the case itself it going to have fuckall to do with drag forces.
>How would /sci/entests design the shoulder of a bottle necked rifle or pistol bullet casing in order to maximize ballistic performance?
Run a bunch of simulations in ANSYS. That's probably what Weatherby does.
>>11335759
This is incredibly stupid

>>11303955
the eigenvalues of the stress tensor are the principle stresses in a material (the maximum stresses that occur at a location)

not a question but i wanted to share since i am so happy. i passed a really hard class!