Range Report Something doesn’t compute

[kraigWY]

I know I’m trying to re-event the wheel but: I’m trying to help my granddaughter with her science project. They don’t want to hear she got the 300 yard velocity from a Ballistic calculator, the want to see the formula.
Back in my accident reconstruction days, we learned to compute velocity at a second point, if we knew
1: A= Gravity or 32.2 fps ps
2: Vi = initial Velocity
3: d = distance
4: Ve = the square root of Vi squared +2ad
So if I use Vi of 2826
And distance is 900 ft (300) yards
2816 squared is 7986276
The square root of 7986276 X 32.2 X 900 = 2815.727
I know that this isn’t anywhere close, Ballistic tables give in a velocity at 900 ft (300 yards) of 2240 fps

Where did I go wrong? And what is the correct formula to finds Ve

 

[Woodlanddude]

Re: Something doesn’t compute

The velocity equation is not taking into account the effects of the air resistance encountered at those velocities. That equation works great for concept purposes in a physics lab on round balls launched with known mass and acceleration in a physics lab at slow speeds. It is probably the basis for the more complex ballistics calculations, but not going to get you near on high velocity projectiles, as air resistance becomes huge at higher speeds, warranting the need for a aerodynamically shaped projectile. I would have her show that basic formula and explain that there are other forces acting on velocity(identifying and quantifying as many as you can). I think you will finde some very complex equations for this calculation. Maybe Brian Litz or Mitch Alsup will respond if you PM them. I am a Civil Engineer and can just barely hang on to understand some of thier writings on the subject, LOL. They are VERY knowledgeable and Mitch has helped me better understand several ballistic issues.

 

[kraigWY]

Re: Something doesn’t compute

OK lets try this a bit differant. Here's what I came up with from Hatcher's Notebook. The fomula sheet will be attached to her Chart. I'm hoping, being in the 8th grade, they wont have her explain it. If so, how can I make it simpler?
---------------------------------------------------------
Formula #1:
KE = velocity Squared X weight in grains / 450240
Energy in foot-pound =( 1/2m X v squared) =(1/2w X v Squared/g) = (w X v Squared/2g
w = bullet weight in pounds
v = velocity in feet per second
g = 32.16 f.s. per second
The weight is converted into grains = 1 lb = 7000 grains avoirdupois
The formula becomes (w x v squared)/(2g X 7000) = 2 X 32.2 X 7000 = 450240
Therefore, energy in foot pounds = (w x V squared) / 450240
Formula #2
Remaining velocity at a given range
NOTE: The data used in project comes from published Ballistic tables
V2 = V1 + X/C
V1 is initial Velocity
V2 = Velocity at X
X = Range in feet
C = Ballistic Coefficient of the bullet
Formula #3
Determining “C” Ballistic Coefficient of a Bullet
Note: The Data for C was taken from Remington Arms BC of the test bullet
C = w/(i X d squared)
C = Ballistic Coefficient
I = Form factor (shape of the bullet or ogive & caliber) taken from Chart
d = diameter of the bullet

 

[MitchAlsup]

Re: Something doesn’t compute

The decrease in velocity is not constant, what is (almost) constant is the decrease in deceleration with respect to velocity.

Some data extracted from JBM ballistics from bullets we use around here all the time (pre-Litz data):

 

[dreamlander]

Re: Something doesn’t compute

Mitch can you explain the chart. What are the numbers on the left? I am wondering because of the difference between the 155 bullets. Is the chart based on manufacturer bc or actual tested bc, which 155 was better?

 

[MitchAlsup]

Re: Something doesn’t compute

All I did was to compute the deceleration rate in fps/s and divide by 32 f/s*82 = 1G, and then plot the deceleration with respect to velocity. The numbers are straight from JBM.

So, take two consecutive* fps entries in the JBM data printout, subtract the fps numbers and subtract the time of flight numbers. Divide the delta-fps by the delta-time to get fps/s. Then divide by 32 fps/s = 1 Gs. This gives you a fps/s calculation. Then take this colum of numbers and plot it in a x-y plot in eXcel.

(*)It works better to take two numbers two rows apart and use the deltas to represent the values for the skipped row.

BTW if you do this, the starting fps does notmater on this chart (excepting for the noise of the computation).

Also note, you can see vestiments of the drag model if you look carefully.