technical ballistics question, not strictly firearms

[EXPRESS]

I have just built a large, what we call bluewater speargun which is to be used for hunting pelagic fish like tuna marlin and wahoo. For this kind of hunting you often shoot quite far (up to 25 feet+) and complete penetration of the fish is vital in order to deploy the special kind of tips we use to hold them to the line.
The shaft is powered by rubber bands, in this case 5 of them so the propulsion energy is constant. So is the Drag coefficient, and we can assume that a thicker shaft will have a slightly lower ballistic coefficient.

Most people use a 3/8 inch shaft for this kind of gun, where I have built mine to take a 5/16.
11/32 shaft are also available but from one company only, and in the US. (I live in Itlay)

The shaft weights:
5/16 (8mm) - 700grams
11/32 (8.7mm) - 840 grams
3/8 (9.5mm) - 1000grams

Here is the question: Given that the propulsion energy and drag coefficients remain the same, how much more kinetic energy will the heavier shaft take downrange?

I am asking this question because I do not have access to any of the 11/32 or 3/8 shafts, so I cannot test it before I go modifying the guns' barrel channel to take a thicker shaft.

I do however have a 9/32 (7mm shaft) that I could use to compare to the 8mm and hope that the differences might remain relatively constant between an 8mm and the 8.7mm. Should it hold true??

Anyone got an idea?

 

[britz]

I'm sure someone here can give you the formula to figure out the percent gain, but I can't. I can tell you that E = MV so it all depends on how fast you can shoot the heavior Arrow.

 

[EXPRESS]

Well, I have been thinking about this, and the number I really need is the ballistic coefficient of each shaft, in water.

See, the kinetic energy will be identical regardless of the weight since the propelling energy is the same.
Since water is so dense it has a very dramatic effect on flight of objects, here BC becomes the most important part of the ballistic equasion, whereas with rifle bullets, it is a relatively(comparatively) inneffectual factor for most circumstances.

This will be determined by it's hydrodynamics, which to a point will be also effected by the way you attatch the line and what kind of point you use.

I have a chronograph, but I doubt it will work underwater since it works on light being reflected back to it and would be thrown off by the water water effects light travelling through it. Also it would not be possible to waterproof it in any way that would allow it to still function.

There comes a point at which the rubbers are labouring to transfer their energy to the shaft and the launch becomes inneficient. Likewise, a too light a shaft will be initally propelled much faster than it's underwater BC should allow, therefore it would slow down very quickly.

Other problems involved are also recoil and shaft whip(rigidity), which both effect accuracy, but with this gun those factors should be minimal due to the enclosed track and the large mass and stability of the gun.

It is a given that the heavier shaft will carry more punch downrange, however I need to find out how thick a shaft I can shoot before it starts to loose effeciency, or how long the lighter shaft will continue to fly with enough speed.

Unless I can chrono the shafts underwater at the muzzle and at the target in order to extract their BC the best bet is going to have to be testing the 7mm and comparing that difference to the 8mm then drawing some conclusions from those results, judjing them simply by appearance of speed in the water.

The most effective way to do this would probably be to set up a high speed camera with a backdrop that allows to you visualize and time flight, as well as drop. But there is no way I am going to be able to get that kind of equipment...

 

[Buffalobob]

I can tell you that E = MV

That is the equation for momentum which we will need to make the final calculation. This is the equation for energy.

E = 1/2 x M x V*2


To answer your question do the following.

Calculate you present E and your present Momentum

Using your Present E as what the spear gun will deliver, substitute in the new weight and solve for the new V.

Use the new weight and the new V to calculate the new Momentum. Compare the new momentum to the old momentum and that is your improvement.

 

[EXPRESS]

I was thinking that maybe, just maybe, if I could chrono these shafts in the air both at the muzzle and the target then I could get a BC of sorts.
Then I could multiply this BC by the difference in density of seawater compared to air and get an answer.

Something tells me that this wouldn't work, since fluid dynamics are not that linear, nor is the BC of an object weighing a kilogram initally moving at say 100fps going to be effected enough by drag as much as simply running out of energy and gravity.

It would be so simple to test but I don't have the shafts I need and I live an hour away from the sea, so I am trying to nut it out in paper before I commit to anything concrete.

Thanks.

 

[jwp475]

Forget the KE and think Momentum and the heavier shaft will carry and transfer more momentum

 

[Buffalobob]

If you can get the speed of your spear as it leaves the gun in air we can calculate the answer. We do not need the speed in water to make a very good estimate.

 

[edge]

IMO, and it just a guess, but heavier seems better.
The line drag is probably a big factor and worse the lighter you go.

Why not add weight to the shaft that you have? First try it at the tip, but if it bend too much and hurts accuracy then add it to the tail where it won't hurt.

You could go under water and fire a shot. See how much line pulls out until it stops.
Change weight and compare again.
Which ever pulls out the most line wins.

Perhaps not a mathematical answer, but it should be conclusive

edge.