lb.ft force of a paintball

[PBpunk]

[Wat]

Force = Mass * Acceleration

Otherwise known as Newton's first law of motion

Once a projectile is in the air, the only forces acting on it are gravity and air resistance. All its got now is kinetic energy and momentum. But the ball its self has no force.

Energy = Force * Distance

A Foot pound is actually a unit of energy and is one pound of force exerted over one foot of distance.

This is where using english units really suck because the major problem isn't the conversion but that a lb is used as both a unit of force (the force exerted by 1 lb of stuff at 1 gravity) and a unit of mass. Then you got other odd units like the poundela and the slug. But i digress.

I believe a paintball is on the order of 60-80 grams. I however do not know what the speed of a paintball is at various distances. It would be interesting if anyone had good numbers on this to see how quickly a paintball slows down.

[bjjb99]

Originally posted by Wat
I believe a paintball is on the order of 60-80 grams. I however do not know what the speed of a paintball is at various distances. It would be interesting if anyone had good numbers on this to see how quickly a paintball slows down.

It's not too difficult to calculate the first-order effects of air resistance on a paintball from basic physics. Check the results section of the following website for some paintball velocity data:

http://home.attbi.com/~dyrgcmn/pball/pballphys1.html

Paintballs have a mass around 3 grams, not 60-80 grams.

BJJB

[sdsm_99]

Lets assume you want to calculate the maximum energy that could be transferred from a paint ball to a target. 3 gram ball traveling at 91 m/s (300ft/s).

Kinetic Energy = 1/2 (mass)(Velocity^2)

So in this case = 24.8Joules or 18.29ftlb.

This means assuming all energy is transferred to the target, (which it is not) and that you are right next to the barrel (which your not), the maximum energy is 18 ftlb. Making this problem any more realistic will only decrease this number.

To give an idea about how much of a decrease there is, years ago I ran an experiment with a ballistic pendulum and if my memory is correct the energy at point blank range is only a couple of ftlb or less.

sdsm

[bjjb99]

Yep, 24.8 joules is what you should get.

Next step, calculate the energy density (i.e. energy per unit area) for a paintball. To keep things simple at first, assume the kinetic energy at impact is distributed evenly across an area equal to the cross sectional area of the paintball. If you want to get fancy, you can assume other distribution profiles, such as one which concentrates more of the energy around the circumference of the paintball to simulate the ring-shaped welts one gets.

You should end up with joules/square meter.

It's also interesting to look at what velocities non-68-caliber paintballs can have and still deliver the same energy per unit area to the target. Play around with 50 and 62 caliber paintballs since they were once alternatives to 68. :)

BJJB

-edit- DOH! Forgot the 1/2 in the energy formula. Make that 24.8 into 12.4.

[sdsm_99]

Interesting Stuff.

I missed the 1/2 part of the energy equation so KE=12.42J. This leads to an energy density of 53076 J/square meter.

For a 50cal. paintball to achieve this it needs only travel at 219ft/s and for a 62cal. only 272ft/s. (Assuming 3 gram mass is constant)

Then next interesting thing is that the 50cal. paintball traveling at 300ft/s will have an energy density of 97807 J/square meter, Almost double that of the 68cal OUCH!!

:)

sdsm

[PBpunk]

[bjjb99]

Originally posted by sdsm_99
Interesting Stuff.

I missed the 1/2 part of the energy equation so KE=12.42J. This leads to an energy density of 53076 J/square meter.

You're not the only one who missed the 1/2 term *blush*. Your energy value is correct.

Originally posted by sdsm_99

For a 50cal. paintball to achieve this it needs only travel at 219ft/s and for a 62cal. only 272ft/s. (Assuming 3 gram mass is constant)

Then next interesting thing is that the 50cal. paintball traveling at 300ft/s will have an energy density of 97807 J/square meter, Almost double that of the 68cal OUCH!!

sdsm

A 50 caliber paintball is going to have a similar type of paintball fill inside. Less volume with constant density equals less mass. A 50 caliber paintball has a mass of around 1.1 grams, if my volume ratios are correct. So at 300 fps a 50 cal paintball moving at 300 fps will deliver around 39000 joules per square meter--less than a 68 caliber paintball at the same velocity. You can actually increase the velocity of the 50 caliber paintball to around 340-350 fps before it starts delivering the same energy per unit area to its target.

Since much of the energy is absorbed in the deformation and breaking of the paintball shell, and in the subsequent spreading of the paintball fill, one must also consider paintball rigidity. A 50 caliber paintball with the same shell thickness as a 68 caliber paintball will tend to bounce more often, simply because of the difference in shell curvature.

BJJB

[athomas]

Also mention that the force to break the 50 cal paintball would be spread over a smaller area. This may result in punture wounds.

A local indoor field used to use 50 cal crossman paintball markers. Even at reduced velocities, they hurt more than 68 cal paintballs.

[dfs]

equation used for bullets:

weight (in grains) x velocity^2(in feet per second)
---------------------------------------------------
436380 (constant to account for funky english units)

=

energy in foot-pounds

so....


assuming 3 grams per ball (3g x 15.432gr/g = approx 46.3 grains)

46.3 gr. x 300 fps x 300 fps
----------------------------
436380

= 9.54 ft/lbs muzzle energy

comparison of muzzle energy:

.22 long rifle = 131 ft-lbs
7.62 nato = 2690 ft-lbs
.50 bmg = 12575 ft-lbs

also paint balls have a low sectional density (ratio of mass to cross sectional area) which compounds their poor aerodynamic performance.