Internal Ballistics: Determine Muzzle Velocity from Powder Mass

[Ardem]

Hi guys,

I am hoping some one can help me out here and after some forumlas and very basic ones at that on internal ballistics. There is a heap of information out there and they tend to jump straight to the hard stuff which tends to be tough on a novice like myself.

I have done a heap of googling and the formulas are either totally over my head or not what I am after.

The formulas are based around ww2 tank guns, so caibres of 20mm up to 120mm

I have some real world figures below, but cannot work out the relationship that can determine the muzzle velocity from the powder mass

diameter=37mm shellweight=.600kg cartridgesize=145mm velocity=670m/s barrellength=37.7 calibre

diameter=50mm shellweight=2.06kg cartridgesize=419mm velocity=835m/s barrellength=60 calibre

diameter=75mm shellweight=6.8kg cartridgesize=495mm velocity=740m/s barrellength=43 calibreThe formula I have come up with just does not cut it. I was using X as a pseudo factor to get the rough estimates so Force would equal Force. As you can see I am far from a physics genius and that why I need help.

P = Volume of Powder
X = Explosive force Factor
m = shell mass
v = velocity

PX = mv^2

sqr (PX / m) = v

Now I know there huge amount of factors that add and subtract but I am after even ballpark forumla based on powder being the same quality and power, shells the same aerodynamic velocity.

What I am trying to achieve is if I know the powder volume and the shell weight and the calibre, what is the muzzle velocity

Please remember to keep it simple and a example is always great, thanks for any help that can be given.

 

[0xDEADBEEF]

I am no ballistics expert but I am not sure if your formula works. When the explosion happens then the chemical energy gets converted into heat and into pressure, but this is only half the story. The explosion also produces an expansion speed, which the projectile cannot surpass.
I don't know how much the explosion shock wave matters when shooting large caliber, but if it does, then maybe the barrel length is adjusted such that we get some target high speed.

If the shock wave doesn't matter I would assume that the explosive reaches the same temperature in all cases and produces some amount of gas proportional to the mass of the explosive and try to calculate the work done (equaling the kinetic energy) by adiabatic expansion of the pipe volume.

 

[astrokreng]

Hi there,

I understand your frustration with trying to understand internal ballistics formulas. It can definitely be overwhelming for someone who is not well-versed in physics and ballistics. However, I will try my best to provide a simplified explanation for determining muzzle velocity from powder mass.

Firstly, it is important to understand that there are many factors that can affect muzzle velocity, such as barrel length, projectile weight, and even atmospheric conditions. Therefore, it is difficult to come up with a single formula that can accurately determine muzzle velocity based on just powder mass and shell weight.

However, one basic formula that you can use is the conservation of momentum equation: m1v1 = m2v2, where m1 and v1 are the mass and velocity of the powder charge, and m2 and v2 are the mass and velocity of the projectile.

In this case, we can assume that the powder charge and projectile are the only two objects involved in the equation. Therefore, we can rearrange the equation to solve for v2 (muzzle velocity):

v2 = m1v1 / m2

Now, let's apply this formula to your examples:

Example 1:
m1 = 0.600 kg (shell weight)
v1 = 670 m/s (velocity)
m2 = 0.145 kg (cartridge size)

v2 = (0.600 kg)(670 m/s) / 0.145 kg = 2770 m/s

Example 2:
m1 = 2.06 kg (shell weight)
v1 = 835 m/s (velocity)
m2 = 0.419 kg (cartridge size)

v2 = (2.06 kg)(835 m/s) / 0.419 kg = 4110 m/s

Example 3:
m1 = 6.8 kg (shell weight)
v1 = 740 m/s (velocity)
m2 = 0.495 kg (cartridge size)

v2 = (6.8 kg)(740 m/s) / 0.495 kg = 10,140 m/s

As you can see, the muzzle velocities calculated using this formula are much higher than the actual velocities listed in your examples. This is because there are many other factors that affect muzzle velocity, such as barrel length and projectile aerodynamics. Therefore, this formula can only provide a rough estimate and should not be used to determine actual muzzle velocities.

In conclusion